LMFDB - Embedded newform 117.2.h.a.16.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [117,2,Mod(16,117)] 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, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("117.16"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.h (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			16.1
Character	$\chi$	$=$	117.16
Dual form			117.2.h.a.22.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.65628 q^{2} +(1.38934 + 1.03428i) q^{3} +5.05585 q^{4} +(0.324360 + 0.561808i) q^{5} +(-3.69049 - 2.74733i) q^{6} +(-0.773958 - 1.34053i) q^{7} -8.11720 q^{8} +(0.860545 + 2.87393i) q^{9} +(-0.861592 - 1.49232i) q^{10} +5.07008 q^{11} +(7.02430 + 5.22914i) q^{12} +(-0.445184 + 3.57796i) q^{13} +(2.05585 + 3.56084i) q^{14} +(-0.130417 + 1.11602i) q^{15} +11.4499 q^{16} +(-0.103828 + 0.179835i) q^{17} +(-2.28585 - 7.63397i) q^{18} +(-1.79488 + 3.10883i) q^{19} +(1.63991 + 2.84041i) q^{20} +(0.311190 - 2.66295i) q^{21} -13.4676 q^{22} +(1.60137 - 2.77365i) q^{23} +(-11.2776 - 8.39543i) 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} -6.83026 q^{29} +(0.346426 - 2.96447i) q^{30} +(1.58024 + 2.73705i) q^{31} -14.1798 q^{32} +(7.04407 + 5.24386i) q^{33} +(0.275796 - 0.477692i) q^{34} +(0.502082 - 0.869631i) q^{35} +(4.35079 + 14.5301i) q^{36} +(-4.71300 - 8.16316i) q^{37} +(4.76772 - 8.25793i) q^{38} +(-4.31911 + 4.51057i) q^{39} +(-2.63289 - 4.56031i) q^{40} +(4.30114 - 7.44979i) q^{41} +(-0.826610 + 7.07355i) q^{42} +(-2.99929 - 5.19492i) q^{43} +25.6335 q^{44} +(-1.33547 + 1.41565i) q^{45} +(-4.25368 + 7.36759i) q^{46} +(-1.42859 + 2.47438i) q^{47} +(15.9078 + 11.8424i) q^{48} +(2.30198 - 3.98714i) q^{49} +(-6.08178 + 10.5340i) q^{50} +(-0.330251 + 0.142466i) q^{51} +(-2.25078 + 18.0896i) q^{52} -2.48667 q^{53} +(4.71980 - 12.9704i) q^{54} +(1.64453 + 2.84841i) q^{55} +(6.28237 + 10.8814i) q^{56} +(-5.70909 + 2.46282i) q^{57} +18.1431 q^{58} -2.98403 q^{59} +(-0.659371 + 5.64243i) q^{60} +(-4.02238 - 6.96697i) q^{61} +(-4.19756 - 7.27038i) q^{62} +(3.18657 - 3.37789i) q^{63} +14.7657 q^{64} +(-2.15453 + 0.910439i) q^{65} +(-18.7111 - 13.9292i) q^{66} +(-2.47432 + 4.28565i) q^{67} +(-0.524937 + 0.909217i) q^{68} +(5.09356 - 2.19729i) q^{69} +(-1.33367 + 2.30999i) q^{70} +(-0.787066 + 1.36324i) q^{71} +(-6.98522 - 23.3282i) q^{72} +3.03817 q^{73} +(12.5191 + 21.6837i) q^{74} +(7.28261 - 3.14162i) q^{75} +(-9.07465 + 15.7178i) q^{76} +(-3.92403 - 6.79661i) q^{77} +(11.4728 - 11.9814i) q^{78} +(3.23418 - 5.60177i) q^{79} +(3.71389 + 6.43264i) q^{80} +(-7.51892 + 4.94629i) q^{81} +(-11.4251 + 19.7888i) q^{82} +(1.24623 - 2.15854i) q^{83} +(1.57333 - 13.4635i) q^{84} -0.134710 q^{85} +(7.96696 + 13.7992i) q^{86} +(-9.48957 - 7.06437i) q^{87} -41.1548 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} +(-0.635376 + 5.43710i) q^{93} +(3.79473 - 6.57267i) q^{94} -2.32875 q^{95} +(-19.7006 - 14.6658i) q^{96} +(4.69325 + 8.12894i) q^{97} +(-6.11471 + 10.5910i) q^{98} +(4.36303 + 14.5710i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 2 q^{2} - q^{3} + 18 q^{4} - 2 q^{5} - 12 q^{6} + 3 q^{7} - 18 q^{8} - 3 q^{9} + 6 q^{11} - 3 q^{12} + 2 q^{14} + 11 q^{15} + 6 q^{16} + 6 q^{17} - 8 q^{18} - 3 q^{19} - 11 q^{20} - 25 q^{21} - 18 q^{22}+ \cdots + 18 q^{99}+O(q^{100}) $ 24 * q - 2 * q^2 - q^3 + 18 * q^4 - 2 * q^5 - 12 * q^6 + 3 * q^7 - 18 * q^8 - 3 * q^9 + 6 * q^11 - 3 * q^12 + 2 * q^14 + 11 * q^15 + 6 * q^16 + 6 * q^17 - 8 * q^18 - 3 * q^19 - 11 * q^20 - 25 * q^21 - 18 * q^22 + 17 * q^23 - 12 * q^24 - 6 * q^25 - 12 * q^26 + 2 * q^27 - 24 * q^29 - 8 * q^30 - 6 * q^31 - 38 * q^32 + 11 * q^33 + 18 * q^35 - 28 * q^36 - 3 * q^37 + 8 * q^38 + 3 * q^39 - 12 * q^40 + 5 * q^41 + 15 * q^42 - 3 * q^43 + 44 * q^44 + 19 * q^45 - 6 * q^46 + 21 * q^47 + 23 * q^48 + 3 * q^49 - 20 * q^50 + 7 * q^51 - 24 * q^52 - 20 * q^53 + 39 * q^54 + 3 * q^55 + 40 * q^56 + 9 * q^57 + 18 * q^58 + 38 * q^59 + 51 * q^60 - 6 * q^61 + 19 * q^62 + 13 * q^63 - 42 * q^64 - 2 * q^65 - 18 * q^66 - 6 * q^67 - 31 * q^69 + 27 * q^70 + 14 * q^71 - 18 * q^72 + 6 * q^73 + 29 * q^74 + 74 * q^75 - 15 * q^76 + 4 * q^77 + 80 * q^78 + 3 * q^79 - 16 * q^80 - 27 * q^81 - 9 * q^82 - 33 * q^83 + 5 * q^84 + 72 * q^86 - 32 * q^87 - 78 * q^88 - q^89 + 21 * q^90 - 6 * q^91 - 10 * q^92 - 84 * q^93 - 9 * q^94 - 100 * q^95 - 79 * q^96 + 24 * q^97 - 61 * q^98 + 18 * q^99

Character values

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

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.65628			−1.87828			−0.939138	−	0.343539i	$-0.888374\pi$
$2$	−2.65628			−1.87828			−0.939138	+	0.343539i	$0.888374\pi$
$3$	1.38934	+	1.03428i	0.802137	+	0.597140i
$3$	1.38934	+	1.03428i	0.802137	+	0.597140i
$4$	5.05585			2.52792
$5$	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	$0.786996\pi$
$6$	−3.69049	−	2.74733i	−1.50664	−	1.12159i
$7$	−0.773958	−	1.34053i	−0.292529	−	0.506674i	0.681878	−	0.731466i	$-0.261163\pi$
$7$	−0.773958	−	1.34053i	−0.292529	−	0.506674i	−0.974407	+	0.224791i	$0.927830\pi$
$8$	−8.11720			−2.86986
$9$	0.860545	+	2.87393i	0.286848	+	0.957976i
$10$	−0.861592	−	1.49232i	−0.272459	−	0.471913i
$11$	5.07008			1.52869			0.764343	−	0.644810i	$-0.223063\pi$
$11$	5.07008			1.52869			0.764343	+	0.644810i	$0.223063\pi$
$12$	7.02430	+	5.22914i	2.02774	+	1.50952i
$13$	−0.445184	+	3.57796i	−0.123472	+	0.992348i
$13$	−0.445184	+	3.57796i	−0.123472	+	0.992348i
$14$	2.05585	+	3.56084i	0.549450	+	0.951675i
$15$	−0.130417	+	1.11602i	−0.0336736	+	0.288155i
$16$	11.4499			2.86247
$17$	−0.103828	+	0.179835i	−0.0251819	+	0.0436163i	−0.878342	−	0.478033i	$-0.841350\pi$
$17$	−0.103828	+	0.179835i	−0.0251819	+	0.0436163i	0.853160	+	0.521650i	$0.174683\pi$
$18$	−2.28585	−	7.63397i	−0.538781	−	1.79934i
$19$	−1.79488	+	3.10883i	−0.411774	+	0.713214i	−0.995084	−	0.0990360i	$-0.968424\pi$
$19$	−1.79488	+	3.10883i	−0.411774	+	0.713214i	0.583310	+	0.812250i	$0.301757\pi$
$20$	1.63991	+	2.84041i	0.366696	+	0.635136i
$21$	0.311190	−	2.66295i	0.0679073	−	0.581103i
$22$	−13.4676			−2.87130
$23$	1.60137	−	2.77365i	0.333908	−	0.578345i	−0.649367	−	0.760475i	$-0.724966\pi$
$23$	1.60137	−	2.77365i	0.333908	−	0.578345i	0.983274	+	0.182130i	$0.0582993\pi$
$24$	−11.2776	−	8.39543i	−2.30202	−	1.71371i
$25$	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
$29$	−6.83026			−1.26835			−0.634173	−	0.773191i	$-0.718659\pi$
$29$	−6.83026			−1.26835			−0.634173	+	0.773191i	$0.718659\pi$
$30$	0.346426	−	2.96447i	0.0632484	−	0.541236i
$31$	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	$0.741732\pi$
$32$	−14.1798			−2.50665
$33$	7.04407	+	5.24386i	1.22622	+	0.912839i
$34$	0.275796	−	0.477692i	0.0472986	−	0.0819235i
$35$	0.502082	−	0.869631i	0.0848673	−	0.146995i
$36$	4.35079	+	14.5301i	0.725131	+	2.42169i
$37$	−4.71300	−	8.16316i	−0.774813	−	1.34202i	−0.934900	−	0.354912i	$-0.884511\pi$
$37$	−4.71300	−	8.16316i	−0.774813	−	1.34202i	0.160087	−	0.987103i	$-0.448823\pi$
$38$	4.76772	−	8.25793i	0.773426	−	1.33961i
$39$	−4.31911	+	4.51057i	−0.691612	+	0.722269i
$40$	−2.63289	−	4.56031i	−0.416297	−	0.721048i
$41$	4.30114	−	7.44979i	0.671725	−	1.16346i	−0.305689	−	0.952131i	$-0.598887\pi$
$41$	4.30114	−	7.44979i	0.671725	−	1.16346i	0.977415	−	0.211331i	$-0.0677798\pi$
$42$	−0.826610	+	7.07355i	−0.127549	+	1.09147i
$43$	−2.99929	−	5.19492i	−0.457387	−	0.792217i	0.541435	−	0.840743i	$-0.317881\pi$
$43$	−2.99929	−	5.19492i	−0.457387	−	0.792217i	−0.998822	+	0.0485254i	$0.984548\pi$
$44$	25.6335			3.86440
$45$	−1.33547	+	1.41565i	−0.199080	+	0.211032i
$46$	−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	$0.233486\pi$
$48$	15.9078	+	11.8424i	2.29610	+	1.70930i
$49$	2.30198	−	3.98714i	0.328854	−	0.569592i
$50$	−6.08178	+	10.5340i	−0.860093	+	1.48973i
$51$	−0.330251	+	0.142466i	−0.0462444	+	0.0199492i
$52$	−2.25078	+	18.0896i	−0.312128	+	2.50858i
$53$	−2.48667			−0.341571			−0.170786	−	0.985308i	$-0.554631\pi$
$53$	−2.48667			−0.341571			−0.170786	+	0.985308i	$0.554631\pi$
$54$	4.71980	−	12.9704i	0.642283	−	1.76505i
$55$	1.64453	+	2.84841i	0.221748	+	0.384079i
$56$	6.28237	+	10.8814i	0.839517	+	1.45409i
$57$	−5.70909	+	2.46282i	−0.756188	+	0.326209i
$58$	18.1431			2.38231
$59$	−2.98403			−0.388487			−0.194244	−	0.980953i	$-0.562225\pi$
$59$	−2.98403			−0.388487			−0.194244	+	0.980953i	$0.562225\pi$
$60$	−0.659371	+	5.64243i	−0.0851244	+	0.728435i
$61$	−4.02238	−	6.96697i	−0.515013	−	0.892029i	−0.999848	−	0.0174233i	$-0.994454\pi$
$61$	−4.02238	−	6.96697i	−0.515013	−	0.892029i	0.484835	−	0.874606i	$-0.338880\pi$
$62$	−4.19756	−	7.27038i	−0.533090	−	0.923339i
$63$	3.18657	−	3.37789i	0.401471	−	0.425574i
$64$	14.7657			1.84572
$65$	−2.15453	+	0.910439i	−0.267236	+	0.112926i
$66$	−18.7111	−	13.9292i	−2.30317	−	1.71456i
$67$	−2.47432	+	4.28565i	−0.302286	+	0.523575i	−0.976653	−	0.214821i	$-0.931083\pi$
$67$	−2.47432	+	4.28565i	−0.302286	+	0.523575i	0.674367	+	0.738396i	$0.264417\pi$
$68$	−0.524937	+	0.909217i	−0.0636579	+	0.110259i
$69$	5.09356	−	2.19729i	0.613193	−	0.264523i
$70$	−1.33367	+	2.30999i	−0.159404	+	0.276096i
$71$	−0.787066	+	1.36324i	−0.0934076	+	0.161787i	−0.908943	−	0.416921i	$-0.863109\pi$
$71$	−0.787066	+	1.36324i	−0.0934076	+	0.161787i	0.815535	+	0.578707i	$0.196443\pi$
$72$	−6.98522	−	23.3282i	−0.823216	−	2.74926i
$73$	3.03817			0.355591			0.177796	−	0.984067i	$-0.443103\pi$
$73$	3.03817			0.355591			0.177796	+	0.984067i	$0.443103\pi$
$74$	12.5191	+	21.6837i	1.45531	+	2.52068i
$75$	7.28261	−	3.14162i	0.840924	−	0.362763i
$76$	−9.07465	+	15.7178i	−1.04093	+	1.80295i
$77$	−3.92403	−	6.79661i	−0.447184	−	0.774546i
$78$	11.4728	−	11.9814i	1.29904	−	1.35662i
$79$	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
$81$	−7.51892	+	4.94629i	−0.835436	+	0.549588i
$82$	−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	$0.122987\pi$
$84$	1.57333	−	13.4635i	0.171664	−	1.46898i
$85$	−0.134710			−0.0146114
$86$	7.96696	+	13.7992i	0.859099	+	1.48800i
$87$	−9.48957	−	7.06437i	−1.01739	−	0.757380i
$88$	−41.1548			−4.38712
$89$	−1.76275	−	3.05317i	−0.186851	−	0.323635i	0.757348	−	0.653012i	$-0.226495\pi$
$89$	−1.76275	−	3.05317i	−0.186851	−	0.323635i	−0.944199	+	0.329376i	$0.893161\pi$
$90$	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
$93$	−0.635376	+	5.43710i	−0.0658854	+	0.563801i
$94$	3.79473	−	6.57267i	0.391397	−	0.677919i
$95$	−2.32875			−0.238925
$96$	−19.7006	−	14.6658i	−2.01068	−	1.49682i
$97$	4.69325	+	8.12894i	0.476527	+	0.825369i	0.999638	−	0.0268952i	$-0.00856206\pi$
$97$	4.69325	+	8.12894i	0.476527	+	0.825369i	−0.523111	+	0.852265i	$0.675229\pi$
$98$	−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
$101$	−4.18722			−0.416644			−0.208322	−	0.978060i	$-0.566800\pi$
$101$	−4.18722			−0.416644			−0.208322	+	0.978060i	$0.566800\pi$
$102$	0.877240	−	0.378429i	0.0868597	−	0.0374701i
$103$	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	$0.769166\pi$
$104$	3.61365	−	29.0430i	0.354348	−	2.84790i
$105$	1.59700	−	0.688924i	0.155852	−	0.0672321i
$106$	6.60532			0.641565
$107$	5.05806	+	8.76081i	0.488981	+	0.846940i	0.999920	−	0.0126775i	$-0.00403549\pi$
$107$	5.05806	+	8.76081i	0.488981	+	0.846940i	−0.510939	+	0.859617i	$0.670702\pi$
$108$	−8.98345	+	24.6873i	−0.864432	+	2.37553i
$109$	−4.37589			−0.419134			−0.209567	−	0.977794i	$-0.567205\pi$
$109$	−4.37589			−0.419134			−0.209567	+	0.977794i	$0.567205\pi$
$110$	−4.36834	−	7.56619i	−0.416505	−	0.721407i
$111$	1.89499	−	16.2160i	0.179864	−	1.53915i
$112$	−8.86174	−	15.3490i	−0.837355	−	1.45034i
$113$	−13.4142			−1.26190			−0.630951	−	0.775823i	$-0.717335\pi$
$113$	−13.4142			−1.26190			−0.630951	+	0.775823i	$0.717335\pi$
$114$	15.1650	−	6.54196i	1.42033	−	0.612710i
$115$	2.07767			0.193744
$116$	−34.5327			−3.20628
$117$	−10.6659	+	1.79957i	−0.986063	+	0.166370i
$118$	7.92642			0.729686
$119$	0.321433			0.0294657
$120$	1.05862	−	9.05897i	0.0966388	−	0.826967i
$121$	14.7057			1.33688
$122$	10.6846	+	18.5062i	0.967337	+	1.67548i
$123$	13.6809	−	5.90175i	1.23357	−	0.532143i
$124$	7.98943	+	13.8381i	0.717472	+	1.24270i
$125$	6.21419			0.555814
$126$	−8.46445	+	8.97264i	−0.754073	+	0.799346i
$127$	6.23233	+	10.7947i	0.553029	+	0.957875i	0.998054	+	0.0623567i	$0.0198617\pi$
$127$	6.23233	+	10.7947i	0.553029	+	0.957875i	−0.445024	+	0.895518i	$0.646805\pi$
$128$	−10.8624			−0.960113
$129$	1.20594	−	10.3196i	0.106177	−	0.908591i
$130$	5.72304	−	2.41839i	0.501943	−	0.212106i
$131$	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	$0.503504\pi$
$132$	35.6138	+	26.5122i	3.09978	+	2.30759i
$133$	5.55665			0.481823
$134$	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
$137$	−7.09825	−	12.2945i	−0.606444	−	1.05039i	−0.991821	−	0.127633i	$-0.959262\pi$
$137$	−7.09825	−	12.2945i	−0.606444	−	1.05039i	0.385377	−	0.922759i	$-0.374071\pi$
$138$	−13.5299	+	5.83663i	−1.15175	+	0.496847i
$139$	3.49371			0.296333			0.148166	−	0.988962i	$-0.452663\pi$
$139$	3.49371			0.296333			0.148166	+	0.988962i	$0.452663\pi$
$140$	2.53845	−	4.39672i	0.214538	−	0.371591i
$141$	−4.54399	+	1.96021i	−0.382673	+	0.165080i
$142$	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
$146$	−8.07025			−0.667899
$147$	7.32204	−	3.15863i	0.603912	−	0.260519i
$148$	−23.8282	−	41.2717i	−1.95867	−	3.39251i
$149$	−12.3716			−1.01352			−0.506761	−	0.862087i	$-0.669157\pi$
$149$	−12.3716			−1.01352			−0.506761	+	0.862087i	$0.669157\pi$
$150$	−19.3447	+	8.34503i	−1.57949	+	0.681369i
$151$	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
$153$	−0.606180	−	0.143637i	−0.0490068	−	0.0116124i
$154$	10.4233	+	18.0537i	0.839936	+	1.45481i
$155$	−1.02513	+	1.77558i	−0.0823405	+	0.142618i
$156$	−21.8368	+	22.8048i	−1.74834	+	1.82584i
$157$	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	$0.820514\pi$
$158$	−8.59091	+	14.8799i	−0.683456	+	1.18378i
$159$	−3.45484	−	2.57191i	−0.273987	−	0.203966i
$160$	−4.59935	−	7.96631i	−0.363611	−	0.629792i
$161$	−4.95756			−0.390710
$162$	19.9724	−	13.1388i	1.56918	−	1.03228i
$163$	−3.52876	+	6.11200i	−0.276394	+	0.478728i	−0.970486	−	0.241158i	$-0.922473\pi$
$163$	−3.52876	+	6.11200i	−0.276394	+	0.478728i	0.694092	+	0.719886i	$0.255806\pi$
$164$	21.7459	−	37.6650i	1.69807	−	2.94114i
$165$	−0.661227	+	5.65831i	−0.0514764	+	0.440499i
$166$	−3.31035	+	5.73370i	−0.256933	+	0.445021i
$167$	9.22813	−	15.9836i	0.714094	−	1.23685i	−0.249214	−	0.968448i	$-0.580172\pi$
$167$	9.22813	−	15.9836i	0.714094	−	1.23685i	0.963308	−	0.268398i	$-0.0864944\pi$
$168$	−2.52599	+	21.6157i	−0.194885	+	1.66769i
$169$	−12.6036	−	3.18571i	−0.969509	−	0.245054i
$170$	0.357828			0.0274442
$171$	−10.4791	−	2.48308i	−0.801359	−	0.189885i
$172$	−15.1639	−	26.2647i	−1.15624	−	2.00266i
$173$	−0.879831	−	1.52391i	−0.0668923	−	0.115861i	0.830640	−	0.556811i	$-0.187975\pi$
$173$	−0.879831	−	1.52391i	−0.0668923	−	0.115861i	−0.897532	+	0.440950i	$0.854642\pi$
$174$	25.2070	+	18.7650i	1.91094	+	1.42257i
$175$	−7.08816			−0.535814
$176$	58.0519			4.37582
$177$	−4.14583	−	3.08631i	−0.311620	−	0.231981i
$178$	4.68236	+	8.11009i	0.350958	+	0.607877i
$179$	−4.63867	−	8.03441i	−0.346711	−	0.600520i	0.638952	−	0.769246i	$-0.279368\pi$
$179$	−4.63867	−	8.03441i	−0.346711	−	0.600520i	−0.985663	+	0.168726i	$0.946035\pi$
$180$	−6.75193	+	7.15730i	−0.503259	+	0.533474i
$181$	−17.7014			−1.31574			−0.657868	−	0.753133i	$-0.728541\pi$
$181$	−17.7014			−1.31574			−0.657868	+	0.753133i	$0.728541\pi$
$182$	−13.6558	+	5.77053i	−1.01223	+	0.427740i
$183$	1.61730	−	13.8398i	0.119555	−	1.02306i
$184$	−12.9986	+	22.5142i	−0.958269	+	1.65977i
$185$	3.05742	−	5.29560i	0.224786	−	0.389341i
$186$	1.68774	−	14.4425i	0.123751	−	1.05897i
$187$	−0.526414	+	0.911776i	−0.0384952	+	0.0666757i
$188$	−7.22271	+	12.5101i	−0.526771	+	0.912393i
$189$	7.92091	−	1.39725i	0.576162	−	0.101635i
$190$	6.18583			0.448767
$191$	−0.271844	−	0.470847i	−0.0196699	−	0.0340693i	0.856023	−	0.516938i	$-0.172928\pi$
$191$	−0.271844	−	0.470847i	−0.0196699	−	0.0340693i	−0.875693	+	0.482869i	$0.839595\pi$
$192$	20.5147	+	15.2718i	1.48052	+	1.10215i
$193$	12.3513	−	21.3931i	0.889065	−	1.53991i	0.0480832	−	0.998843i	$-0.484689\pi$
$193$	12.3513	−	21.3931i	0.889065	−	1.53991i	0.840982	−	0.541063i	$-0.181978\pi$
$194$	−12.4666	−	21.5928i	−0.895050	−	1.55027i
$195$	−3.93502	−	0.963464i	−0.281793	−	0.0689951i
$196$	11.6384	−	20.1584i	0.831318	−	1.43988i
$197$	9.01337	+	15.6116i	0.642176	+	1.11228i	0.984946	+	0.172863i	$0.0553016\pi$
$197$	9.01337	+	15.6116i	0.642176	+	1.11228i	−0.342770	+	0.939419i	$0.611365\pi$
$198$	−11.5895	−	38.7048i	−0.823627	−	2.75063i
$199$	−8.59093	+	14.8799i	−0.608995	+	1.05481i	0.382412	+	0.923992i	$0.375094\pi$
$199$	−8.59093	+	14.8799i	−0.608995	+	1.05481i	−0.991406	+	0.130818i	$0.958240\pi$
$200$	−18.5850	+	32.1901i	−1.31416	+	2.27619i
$201$	−7.87022	+	3.39510i	−0.555123	+	0.239472i
$202$	11.1225			0.782573
$203$	5.28633	+	9.15620i	0.371028	+	0.642639i
$204$	−1.66970	+	0.720284i	−0.116902	+	0.0504300i
$205$	5.58047			0.389757
$206$	−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
$210$	−4.24209	+	1.82998i	−0.292732	+	0.126281i
$211$	−1.35161	+	2.34105i	−0.0930483	+	0.161164i	−0.908792	−	0.417249i	$-0.862994\pi$
$211$	−1.35161	+	2.34105i	−0.0930483	+	0.161164i	0.815744	+	0.578413i	$0.196328\pi$
$212$	−12.5722			−0.863465
$213$	−2.50347	+	1.07996i	−0.171535	+	0.0739978i
$214$	−13.4356	−	23.2712i	−0.918441	−	1.59079i
$215$	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
$218$	11.6236			0.787250
$219$	4.22106	+	3.14231i	0.285233	+	0.212338i
$220$	8.31449	+	14.4011i	0.560563	+	0.970923i
$221$	−0.597219	−	0.451551i	−0.0401733	−	0.0303746i
$222$	−5.03363	+	43.0742i	−0.337835	+	2.89095i
$223$	5.22419			0.349838			0.174919	−	0.984583i	$-0.444034\pi$
$223$	5.22419			0.349838			0.174919	+	0.984583i	$0.444034\pi$
$224$	10.9746	+	19.0085i	0.733268	+	1.27006i
$225$	13.3673	+	3.16745i	0.891156	+	0.211163i
$226$	35.6319			2.37020
$227$	2.78555	+	4.82471i	0.184883	+	0.320227i	0.943537	−	0.331267i	$-0.107476\pi$
$227$	2.78555	+	4.82471i	0.184883	+	0.320227i	−0.758654	+	0.651494i	$0.774143\pi$
$228$	−28.8643	+	12.4516i	−1.91158	+	0.824631i
$229$	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	$0.560350\pi$
$230$	−5.51889			−0.363905
$231$	1.57776	−	13.5014i	0.103809	−	0.888324i
$232$	55.4425			3.63998
$233$	15.4122			1.00969			0.504844	−	0.863211i	$-0.331550\pi$
$233$	15.4122			1.00969			0.504844	+	0.863211i	$0.331550\pi$
$234$	28.3317	−	4.78017i	1.85210	−	0.312490i
$235$	−1.85350			−0.120909
$236$	−15.0868			−0.982066
$237$	10.2872	−	4.43774i	0.668223	−	0.288262i
$238$	−0.853817			−0.0553447
$239$	−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	$0.959560\pi$
$240$	−1.49327	+	12.7783i	−0.0963899	+	0.824837i
$241$	8.91315	+	15.4380i	0.574146	+	0.994450i	0.996134	+	0.0878488i	$0.0279992\pi$
$241$	8.91315	+	15.4380i	0.574146	+	0.994450i	−0.421988	+	0.906602i	$0.638667\pi$
$242$	−39.0625			−2.51103
$243$	−15.5622	−	0.904551i	−0.998315	−	0.0580270i
$244$	−20.3365	−	35.2239i	−1.30191	−	2.25498i
$245$	2.98668			0.190812
$246$	−36.3404	+	15.6767i	−2.31698	+	0.999511i
$247$	−10.3242	−	7.80602i	−0.656914	−	0.496685i
$248$	−12.8271	−	22.2172i	−0.814521	−	1.41079i
$249$	3.96398	−	1.71000i	0.251207	−	0.108367i
$250$	−16.5067			−1.04397
$251$	0.779623	−	1.35035i	0.0492094	−	0.0852331i	−0.840372	−	0.542011i	$-0.817663\pi$
$251$	0.779623	−	1.35035i	0.0492094	−	0.0852331i	0.889581	+	0.456778i	$0.150997\pi$
$252$	16.1108	−	17.0781i	1.01489	−	1.07582i
$253$	8.11905	−	14.0626i	0.510440	−	0.884108i
$254$	−16.5548	−	28.6738i	−1.03874	−	1.79915i
$255$	−0.187158	−	0.139327i	−0.0117203	−	0.00872502i
$256$	−0.677748			−0.0423593
$257$	−9.90154	+	17.1500i	−0.617641	+	1.06979i	0.372274	+	0.928123i	$0.378578\pi$
$257$	−9.90154	+	17.1500i	−0.617641	+	1.06979i	−0.989915	+	0.141663i	$0.954755\pi$
$258$	−3.20333	+	27.4118i	−0.199430	+	1.70658i
$259$	−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
$263$	16.3224			1.00648			0.503241	−	0.864146i	$-0.332141\pi$
$263$	16.3224			1.00648			0.503241	+	0.864146i	$0.332141\pi$
$264$	−57.1782	−	42.5655i	−3.51907	−	2.61972i
$265$	−0.806578	−	1.39703i	−0.0495477	−	0.0858191i
$266$	−14.7601			−0.904997
$267$	0.708759	−	6.06507i	0.0433754	−	0.371176i
$268$	−12.5098	+	21.6676i	−0.764157	+	1.32356i
$269$	15.1854	−	26.3019i	0.925870	−	1.60365i	0.135714	−	0.990748i	$-0.456667\pi$
$269$	15.1854	−	26.3019i	0.925870	−	1.60365i	0.790156	−	0.612906i	$-0.210000\pi$
$270$	8.81779	−	1.55546i	0.536633	−	0.0946622i
$271$	−11.5518	−	20.0082i	−0.701719	−	1.21541i	−0.967863	−	0.251480i	$-0.919083\pi$
$271$	−11.5518	−	20.0082i	−0.701719	−	1.21541i	0.266143	−	0.963933i	$-0.414251\pi$
$272$	−1.18882	+	2.05909i	−0.0720825	+	0.124851i
$273$	9.38939	+	2.29893i	0.568272	+	0.139138i
$274$	18.8550	+	32.6578i	1.13907	+	1.97293i
$275$	11.6084	−	20.1063i	0.700010	−	1.21245i
$276$	25.7523	−	11.1092i	1.55010	−	0.668693i
$277$	6.84420	+	11.8545i	0.411228	+	0.712268i	0.995024	−	0.0996320i	$-0.0317665\pi$
$277$	6.84420	+	11.8545i	0.411228	+	0.712268i	−0.583796	+	0.811900i	$0.698433\pi$
$278$	−9.28030			−0.556595
$279$	−6.50622	+	6.89684i	−0.389517	+	0.412903i
$280$	−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	$0.877240\pi$
$282$	12.0701	−	5.20689i	0.718766	−	0.310066i
$283$	−3.30018	+	5.71608i	−0.196175	+	0.339786i	−0.947285	−	0.320392i	$-0.896185\pi$
$283$	−3.30018	+	5.71608i	−0.196175	+	0.339786i	0.751110	+	0.660177i	$0.229519\pi$
$284$	−3.97929	+	6.89233i	−0.236127	+	0.408984i
$285$	−3.23543	−	2.40857i	−0.191651	−	0.142671i
$286$	5.99555	−	48.1864i	0.354524	−	2.84932i
$287$	−13.3156			−0.785996
$288$	−12.2023	−	40.7517i	−0.719030	−	2.40131i
$289$	8.47844	+	14.6851i	0.498732	+	0.863829i
$290$	5.88490	+	10.1929i	0.345573	+	0.598550i
$291$	−1.88704	+	16.1480i	−0.110621	+	0.946613i
$292$	15.3605			0.898907
$293$	−0.494901			−0.0289124			−0.0144562	−	0.999896i	$-0.504602\pi$
$293$	−0.494901			−0.0289124			−0.0144562	+	0.999896i	$0.504602\pi$
$294$	−19.4494	+	8.39021i	−1.13431	+	0.489327i
$295$	−0.967898	−	1.67645i	−0.0563532	−	0.0976066i
$296$	38.2564	+	66.2620i	2.22361	+	3.85140i
$297$	−9.00873	+	24.7567i	−0.522740	+	1.43653i
$298$	32.8625			1.90367
$299$	9.21110	+	6.96441i	0.532691	+	0.402762i
$300$	36.8198	−	15.8835i	2.12579	−	0.917036i
$301$	−4.64264	+	8.04129i	−0.267597	+	0.463492i
$302$	−1.37457	+	2.38083i	−0.0790977	+	0.137001i
$303$	−5.81749	−	4.33075i	−0.334206	−	0.248795i
$304$	−20.5512	+	35.5957i	−1.17869	+	2.04156i
$305$	2.60940	−	4.51961i	0.149414	−	0.258792i
$306$	1.61019	+	0.381541i	0.0920483	+	0.0218113i
$307$	3.08744			0.176210			0.0881048	−	0.996111i	$-0.471919\pi$
$307$	3.08744			0.176210			0.0881048	+	0.996111i	$0.471919\pi$
$308$	−19.8393	−	34.3626i	−1.13045	−	1.95799i
$309$	−0.817047	+	6.99171i	−0.0464802	+	0.397745i
$310$	2.72304	−	4.71644i	0.154658	−	0.267876i
$311$	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	$0.757939\pi$
$312$	35.0591	−	36.6132i	1.98483	−	2.07281i
$313$	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
$315$	2.93132	+	0.694590i	0.165161	+	0.0391357i
$316$	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	$0.191923\pi$
$318$	9.17705	+	6.83172i	0.514623	+	0.383104i
$319$	−34.6299			−1.93890
$320$	4.78941	+	8.29551i	0.267736	+	0.463733i
$321$	−2.03373	+	17.4032i	−0.113511	+	0.971352i
$322$	13.1687			0.733862
$323$	−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
$327$	−6.07961	−	4.52588i	−0.336203	−	0.250282i
$328$	−34.9132	+	60.4715i	−1.92776	+	3.33898i
$329$	4.42266			0.243829
$330$	1.75641	−	15.0301i	0.0966870	−	0.827379i
$331$	6.07904	+	10.5292i	0.334134	+	0.578737i	0.983318	−	0.181894i	$-0.0582228\pi$
$331$	6.07904	+	10.5292i	0.334134	+	0.578737i	−0.649184	+	0.760631i	$0.724889\pi$
$332$	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
$335$	−3.21028			−0.175396
$336$	3.56310	−	30.4905i	0.194383	−	1.66339i
$337$	−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	$-0.355464\pi$
$338$	33.4788	+	8.46214i	1.82101	+	0.460280i
$339$	−18.6369	−	13.8740i	−1.01222	−	0.753532i
$340$	−0.681073			−0.0369364
$341$	8.01192	+	13.8771i	0.433870	+	0.751484i
$342$	27.8355	+	6.59575i	1.50517	+	0.356658i
$343$	−17.9619			−0.969854
$344$	24.3458	+	42.1682i	1.31264	+	2.27355i
$345$	2.88660	+	2.14889i	0.155409	+	0.115692i
$346$	2.33708	+	4.04794i	0.125642	+	0.217619i
$347$	21.6959			1.16470			0.582348	−	0.812940i	$-0.302134\pi$
$347$	21.6959			1.16470			0.582348	+	0.812940i	$0.302134\pi$
$348$	−47.9778	−	35.7164i	−2.57188	−	1.91460i
$349$	−34.4486			−1.84399			−0.921995	−	0.387201i	$-0.873442\pi$
$349$	−34.4486			−1.84399			−0.921995	+	0.387201i	$0.873442\pi$
$350$	18.8282			1.00641
$351$	−16.6798	−	8.53127i	−0.890305	−	0.455366i
$352$	−71.8926			−3.83189
$353$	−1.42723			−0.0759639			−0.0379819	−	0.999278i	$-0.512093\pi$
$353$	−1.42723			−0.0759639			−0.0379819	+	0.999278i	$0.512093\pi$
$354$	11.0125	+	8.19811i	0.585309	+	0.435725i
$355$	−1.02117			−0.0541981
$356$	−8.91218	−	15.4364i	−0.472345	−	0.818125i
$357$	0.446580	+	0.332450i	0.0236355	+	0.0175951i
$358$	12.3216	+	21.3417i	0.651218	+	1.12794i
$359$	8.30365			0.438250			0.219125	−	0.975697i	$-0.429680\pi$
$359$	8.30365			0.438250			0.219125	+	0.975697i	$0.429680\pi$
$360$	10.8403	−	11.4911i	0.571332	−	0.605634i
$361$	3.05680	+	5.29453i	0.160884	+	0.278659i
$362$	47.0200			2.47132
$363$	20.4312	+	15.2097i	1.07236	+	0.798304i
$364$	25.9918	−	10.9834i	1.36234	−	0.575684i
$365$	0.985461	+	1.70687i	0.0515814	+	0.0893416i
$366$	−4.29602	+	36.7623i	−0.224557	+	1.92160i
$367$	−30.9192			−1.61397			−0.806984	−	0.590573i	$-0.798902\pi$
$367$	−30.9192			−1.61397			−0.806984	+	0.590573i	$0.798902\pi$
$368$	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
$371$	1.92458	+	3.33347i	0.0999193	+	0.173065i
$372$	−3.21236	+	27.4891i	−0.166553	+	1.42525i
$373$	14.2576			0.738230			0.369115	−	0.929384i	$-0.379661\pi$
$373$	14.2576			0.738230			0.369115	+	0.929384i	$0.379661\pi$
$374$	1.39831	−	2.42194i	0.0723047	−	0.125235i
$375$	8.63364	+	6.42719i	0.445839	+	0.331899i
$376$	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	0.935999	−	0.352003i	$-0.114499\pi$
$379$	3.17631	+	5.50154i	0.163156	+	0.282595i	−0.772843	+	0.634598i	$0.781166\pi$
$380$	−11.7738			−0.603984
$381$	−2.50587	+	21.4435i	−0.128380	+	1.09858i
$382$	0.722094	+	1.25070i	0.0369455	+	0.0639915i
$383$	29.1159			1.48775			0.743877	−	0.668316i	$-0.232985\pi$
$383$	29.1159			1.48775			0.743877	+	0.668316i	$0.232985\pi$
$384$	−15.0916	−	11.2348i	−0.770142	−	0.573321i
$385$	2.54559	−	4.40910i	0.129735	−	0.224708i
$386$	−32.8085	+	56.8261i	−1.66991	+	2.89237i
$387$	12.3488	−	13.0902i	0.627724	−	0.665412i
$388$	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	$-0.130037\pi$
$390$	10.4525	+	2.55923i	0.529285	+	0.129592i
$391$	0.332532	+	0.575962i	0.0168169	+	0.0291277i
$392$	−18.6856	+	32.3644i	−0.943766	+	1.63465i
$393$	−3.95985	+	33.8856i	−0.199748	+	1.70930i
$394$	−23.9421	−	41.4689i	−1.20618	−	2.08917i
$395$	4.19616			0.211132
$396$	22.0588	+	73.6689i	1.10850	+	3.70200i
$397$	7.89246	−	13.6701i	0.396111	−	0.686085i	−0.597131	−	0.802144i	$-0.703693\pi$
$397$	7.89246	−	13.6701i	0.396111	−	0.686085i	0.993242	+	0.116059i	$0.0370261\pi$
$398$	22.8199	−	39.5253i	1.14386	−	1.98122i
$399$	7.72010	+	5.74711i	0.386488	+	0.287716i
$400$	26.2155	−	45.4065i	1.31077	−	2.27033i
$401$	0.379497	−	0.657309i	0.0189512	−	0.0328244i	−0.856394	−	0.516322i	$-0.827301\pi$
$401$	0.379497	−	0.657309i	0.0189512	−	0.0328244i	0.875345	+	0.483498i	$0.160634\pi$
$402$	20.9055	−	9.01836i	1.04267	−	0.449795i
$403$	−10.4966	+	4.43553i	−0.522871	+	0.220950i
$404$	−21.1700			−1.05324
$405$	−5.21770	−	2.61981i	−0.259270	−	0.130179i
$406$	−14.0420	−	24.3215i	−0.696893	−	1.20705i
$407$	−23.8953	−	41.3879i	−1.18445	−	2.05152i
$408$	2.68071	−	1.15642i	0.132715	−	0.0572514i
$409$	−26.9714			−1.33365			−0.666824	−	0.745215i	$-0.732347\pi$
$409$	−26.9714			−1.33365			−0.666824	+	0.745215i	$0.732347\pi$
$410$	−14.8233			−0.732071
$411$	2.85404	−	24.4229i	0.140779	−	1.20469i
$412$	10.2738	+	17.7948i	0.506155	+	0.876686i
$413$	2.30951	+	4.00019i	0.113644	+	0.196836i
$414$	−24.8344	−	5.88463i	−1.22054	−	0.289214i
$415$	1.61691			0.0793712
$416$	6.31262	−	50.7347i	0.309501	−	2.48747i
$417$	4.85396	+	3.61346i	0.237700	+	0.176952i
$418$	24.1727	−	41.8683i	1.18233	−	2.04785i
$419$	−5.30079	+	9.18123i	−0.258960	+	0.448533i	−0.965964	−	0.258678i	$-0.916713\pi$
$419$	−5.30079	+	9.18123i	−0.258960	+	0.448533i	0.707003	+	0.707210i	$0.250047\pi$
$420$	8.07420	−	3.48310i	0.393981	−	0.169958i
$421$	−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
$423$	−8.34057	−	1.97633i	−0.405532	−	0.0960927i
$424$	20.1848			0.980262
$425$	0.475444	+	0.823492i	0.0230624	+	0.0399452i
$426$	6.64993	−	2.86869i	0.322190	−	0.138988i
$427$	−6.22631	+	10.7843i	−0.301312	+	0.521888i
$428$	25.5728	+	44.2933i	1.23611	+	2.14100i
$429$	−21.8982	+	22.8689i	−1.05726	+	1.10412i
$430$	−5.16832	+	8.95180i	−0.249239	+	0.431694i
$431$	−4.15171	−	7.19098i	−0.199981	−	0.346377i	0.748541	−	0.663089i	$-0.230755\pi$
$431$	−4.15171	−	7.19098i	−0.199981	−	0.346377i	−0.948522	+	0.316711i	$0.897421\pi$
$432$	−20.3447	+	55.9088i	−0.978833	+	2.68991i
$433$	0.0394092	−	0.0682587i	0.00189388	−	0.00328030i	−0.865077	−	0.501639i	$-0.832730\pi$
$433$	0.0394092	−	0.0682587i	0.00189388	−	0.00328030i	0.866971	+	0.498359i	$0.166064\pi$
$434$	−6.49746	+	11.2539i	−0.311888	+	0.540206i
$435$	0.890785	−	7.62271i	0.0427099	−	0.365481i
$436$	−22.1238			−1.05954
$437$	5.74852	+	9.95673i	0.274989	+	0.476295i
$438$	−11.2123	−	8.34687i	−0.535746	−	0.398829i
$439$	25.7420			1.22860			0.614298	−	0.789074i	$-0.289439\pi$
$439$	25.7420			1.22860			0.614298	+	0.789074i	$0.289439\pi$
$440$	−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	$0.931539\pi$
$444$	9.58077	−	81.9855i	0.454683	−	3.89086i
$445$	1.14353	−	1.98065i	0.0542085	−	0.0938919i
$446$	−13.8769			−0.657092
$447$	−17.1884	−	12.7957i	−0.812983	−	0.605214i
$448$	−11.4281	−	19.7940i	−0.539925	−	0.935178i
$449$	2.18709	−	3.78815i	0.103215	−	0.178774i	−0.809792	−	0.586716i	$-0.800420\pi$
$449$	2.18709	−	3.78815i	0.103215	−	0.178774i	0.913008	+	0.407943i	$0.133754\pi$
$450$	−35.5075	−	8.41365i	−1.67384	−	0.396623i
$451$	21.8071	−	37.7710i	1.02686	−	1.77857i
$452$	−67.8201			−3.18999
$453$	1.64598	−	0.710051i	0.0773347	−	0.0333611i
$454$	−7.39920	−	12.8158i	−0.347262	−	0.601475i
$455$	2.88799	+	2.18358i	0.135391	+	0.102368i
$456$	46.3418	−	19.9912i	2.17016	−	0.936174i
$457$	−13.5568			−0.634161			−0.317080	−	0.948399i	$-0.602703\pi$
$457$	−13.5568			−0.634161			−0.317080	+	0.948399i	$0.602703\pi$
$458$	−30.3999	−	52.6542i	−1.42050	−	2.46037i
$459$	−0.693632	−	0.826519i	−0.0323760	−	0.0385786i
$460$	10.5044			0.489770
$461$	−1.00295	−	1.73716i	−0.0467120	−	0.0809076i	0.841724	−	0.539908i	$-0.181541\pi$
$461$	−1.00295	−	1.73716i	−0.0467120	−	0.0809076i	−0.888436	+	0.459000i	$0.848208\pi$
$462$	−4.19098	+	35.8634i	−0.194982	+	1.66852i
$463$	−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	$-0.581122\pi$
$464$	−78.2057			−3.63061
$465$	−3.26070	+	1.40662i	−0.151211	+	0.0652303i
$466$	−40.9392			−1.89647
$467$	−25.0664			−1.15993			−0.579967	−	0.814640i	$-0.696935\pi$
$467$	−25.0664			−1.15993			−0.579967	+	0.814640i	$0.696935\pi$
$468$	−53.9252	+	9.09835i	−2.49269	+	0.420572i
$469$	7.66008			0.353710
$470$	4.92344			0.227101
$471$	−0.202844	+	1.73580i	−0.00934656	+	0.0799813i
$472$	24.2219			1.11490
$473$	−15.2066	−	26.3386i	−0.699201	−	1.21105i
$474$	−27.3256	+	11.7879i	−1.25511	+	0.541436i
$475$	8.21906	+	14.2358i	0.377116	+	0.653184i
$476$	1.62512			0.0744870
$477$	−2.13990	−	7.14652i	−0.0979791	−	0.327217i
$478$	15.8610	+	27.4720i	0.725465	+	1.25654i
$479$	−6.11222			−0.279274			−0.139637	−	0.990203i	$-0.544594\pi$
$479$	−6.11222			−0.279274			−0.139637	+	0.990203i	$0.544594\pi$
$480$	1.84929	−	15.8249i	0.0844082	−	0.722306i
$481$	31.3056	−	13.2288i	1.42741	−	0.603183i
$482$	−23.6759	−	41.0078i	−1.07841	−	1.86785i
$483$	−6.88775	−	5.12748i	−0.313403	−	0.233309i
$484$	74.3497			3.37953
$485$	−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	−0.963948	−	0.266092i	$-0.914268\pi$
$487$	−5.55082	+	9.61430i	−0.251532	+	0.435666i	0.712416	+	0.701757i	$0.247601\pi$
$488$	32.6505	+	56.5523i	1.47802	+	2.56000i
$489$	−11.2242	+	4.84194i	−0.507574	+	0.218960i
$490$	−7.93346			−0.358397
$491$	−1.13858	+	1.97207i	−0.0513832	+	0.0889984i	−0.890573	−	0.454840i	$-0.849696\pi$
$491$	−1.13858	+	1.97207i	−0.0513832	+	0.0889984i	0.839190	+	0.543839i	$0.183030\pi$
$492$	69.1685	−	29.8383i	3.11836	−	1.34522i
$493$	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
$497$	2.43662			0.109298
$498$	−10.5294	+	4.54225i	−0.471836	+	0.203543i
$499$	−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	$0.915120\pi$
$500$	31.4180			1.40506
$501$	29.3525	−	12.6622i	1.31137	−	0.565707i
$502$	−2.07090	+	3.58690i	−0.0924288	+	0.160091i
$503$	−17.2266	+	29.8374i	−0.768097	+	1.33038i	0.170497	+	0.985358i	$0.445463\pi$
$503$	−17.2266	+	29.8374i	−0.768097	+	1.33038i	−0.938594	+	0.345025i	$0.887871\pi$
$504$	−25.8661	+	27.4190i	−1.15217	+	1.22134i
$505$	−1.35817	−	2.35241i	−0.0604377	−	0.104681i
$506$	−21.5665	+	37.3543i	−0.958748	+	1.66060i
$507$	−14.2158	−	17.4617i	−0.631348	−	0.775500i
$508$	31.5097	+	54.5764i	1.39802	+	2.42144i
$509$	−0.684664	+	1.18587i	−0.0303472	+	0.0525629i	−0.880800	−	0.473488i	$-0.842995\pi$
$509$	−0.684664	+	1.18587i	−0.0303472	+	0.0525629i	0.850453	+	0.526051i	$0.176328\pi$
$510$	0.497146	+	0.370093i	0.0220140	+	0.0163880i
$511$	−2.35142	−	4.07278i	−0.104021	−	0.180169i
$512$	23.5252			1.03968
$513$	−11.9909	−	14.2881i	−0.529411	−	0.630837i
$514$	26.3013	−	45.5552i	1.16010	−	2.00935i
$515$	−1.31824	+	2.28326i	−0.0580887	+	0.100613i
$516$	6.09706	−	52.1744i	0.268408	−	2.29685i
$517$	−7.24304	+	12.5453i	−0.318549	+	0.551743i
$518$	19.3785	−	33.5645i	0.851441	−	1.47474i
$519$	0.353759	−	3.02722i	0.0155283	−	0.132880i
$520$	17.4887	−	7.39022i	0.766931	−	0.324082i
$521$	−4.08021			−0.178757			−0.0893785	−	0.995998i	$-0.528488\pi$
$521$	−4.08021			−0.178757			−0.0893785	+	0.995998i	$0.528488\pi$
$522$	15.6130	+	52.1420i	0.683361	+	2.28219i
$523$	3.04053	+	5.26635i	0.132953	+	0.230281i	0.924814	−	0.380420i	$-0.124221\pi$
$523$	3.04053	+	5.26635i	0.132953	+	0.230281i	−0.791861	+	0.610702i	$0.790887\pi$
$524$	49.7926	+	86.2432i	2.17520	+	3.76755i
$525$	−9.84788	−	7.33111i	−0.429797	−	0.319956i
$526$	−43.3570			−1.89045
$527$	−0.656289			−0.0285884
$528$	80.6539	+	60.0416i	3.51001	+	2.61298i
$529$	6.37126	+	11.0353i	0.277011	+	0.479798i
$530$	2.14250	+	3.71092i	0.0930642	+	0.161192i
$531$	−2.56789	−	8.57588i	−0.111437	−	0.372161i
$532$	28.0936			1.21801
$533$	24.7403	+	18.7058i	1.07162	+	0.810240i
$534$	−1.88267	+	16.1105i	−0.0814710	+	0.697171i
$535$	−3.28126	+	5.68331i	−0.141861	+	0.245711i
$536$	20.0845	−	34.7875i	0.867520	−	1.50259i
$537$	1.86510	−	15.9602i	0.0804850	−	0.688734i
$538$	−40.3367	+	69.8653i	−1.73904	+	3.01211i
$539$	11.6712	−	20.2151i	0.502714	−	0.870727i
$540$	−16.7834	+	2.96059i	−0.722241	+	0.127403i
$541$	−25.5909			−1.10024			−0.550120	−	0.835086i	$-0.685418\pi$
$541$	−25.5909			−1.10024			−0.550120	+	0.835086i	$0.685418\pi$
$542$	30.6847	+	53.1475i	1.31802	+	2.28288i
$543$	−24.5933	−	18.3082i	−1.05540	−	0.785678i
$544$	1.47225	−	2.55002i	0.0631223	−	0.109331i
$545$	−1.41936	−	2.45841i	−0.0607988	−	0.105307i
$546$	−24.9409	−	6.10661i	−1.06737	−	0.261339i
$547$	−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
$549$	16.5611	−	17.5554i	0.706812	−	0.749247i
$550$	−30.8351	+	53.4079i	−1.31481	+	2.27732i
$551$	12.2595	−	21.2341i	0.522272	−	0.904602i
$552$	−41.3454	+	17.8358i	−1.75978	+	0.759144i
$553$	−10.0125			−0.425774
$554$	−18.1802	−	31.4889i	−0.772401	−	1.33784i
$555$	9.72492	−	4.19519i	0.412800	−	0.178076i
$556$	17.6637			0.749107
$557$	11.0730	+	19.1790i	0.469178	+	0.812639i	0.999379	−	0.0352323i	$-0.0112171\pi$
$557$	11.0730	+	19.1790i	0.469178	+	0.812639i	−0.530202	+	0.847872i	$0.677884\pi$
$558$	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
$561$	−1.67440	+	0.722312i	−0.0706931	+	0.0304960i
$562$	35.1343	−	60.8544i	1.48205	−	2.56699i
$563$	−20.7225			−0.873347			−0.436674	−	0.899620i	$-0.643844\pi$
$563$	−20.7225			−0.873347			−0.436674	+	0.899620i	$0.643844\pi$
$564$	−22.9737	+	9.91054i	−0.967369	+	0.417309i
$565$	−4.35103	−	7.53620i	−0.183049	−	0.317050i
$566$	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
$569$	−44.5426			−1.86732			−0.933661	−	0.358159i	$-0.883405\pi$
$569$	−44.5426			−1.86732			−0.933661	+	0.358159i	$0.883405\pi$
$570$	8.59423	+	6.39785i	0.359973	+	0.267977i
$571$	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	$0.584798\pi$
$572$	−11.4117	+	91.7158i	−0.477145	+	3.83483i
$573$	0.109302	−	0.935329i	0.00456615	−	0.0390739i
$574$	35.3700			1.47632
$575$	−7.33291	−	12.7010i	−0.305804	−	0.529667i
$576$	12.7066	+	42.4357i	0.529441	+	1.76815i
$577$	30.4547			1.26784			0.633922	−	0.773397i	$-0.281444\pi$
$577$	30.4547			1.26784			0.633922	+	0.773397i	$0.281444\pi$
$578$	−22.5211	−	39.0078i	−0.936756	−	1.62251i
$579$	39.2865	−	16.9476i	1.63269	−	0.704320i
$580$	−11.2010	−	19.4008i	−0.465098	−	0.805573i
$581$	−3.85813			−0.160062
$582$	5.01253	−	42.8937i	0.207776	−	1.77800i
$583$	−12.6076			−0.522155
$584$	−24.6615			−1.02050
$585$	−4.47061	−	5.40848i	−0.184837	−	0.223613i
$586$	1.31460			0.0543055
$587$	42.0287			1.73471			0.867354	−	0.497691i	$-0.165819\pi$
$587$	42.0287			1.73471			0.867354	+	0.497691i	$0.165819\pi$
$588$	37.0191	−	15.9695i	1.52664	−	0.658572i
$589$	−11.3453			−0.467477
$590$	2.57101	+	4.45313i	0.105847	+	0.183332i
$591$	−3.62407	+	31.0122i	−0.149074	+	1.27567i
$592$	−53.9634	−	93.4673i	−2.21788	−	3.84148i
$593$	−6.55587			−0.269217			−0.134609	−	0.990899i	$-0.542978\pi$
$593$	−6.55587			−0.269217			−0.134609	+	0.990899i	$0.542978\pi$
$594$	23.9298	−	65.7609i	0.981850	−	2.69820i
$595$	0.104260	+	0.180583i	0.00427424	+	0.00740320i
$596$	−62.5489			−2.56210
$597$	−27.3257	+	11.7879i	−1.11837	+	0.482447i
$598$	−24.4673	−	18.4994i	−1.00054	−	0.756499i
$599$	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	$0.677308\pi$
$600$	−59.1144	+	25.5011i	−2.41334	+	1.04108i
$601$	5.81390			0.237154			0.118577	−	0.992945i	$-0.462167\pi$
$601$	5.81390			0.237154			0.118577	+	0.992945i	$0.462167\pi$
$602$	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
$605$	4.76994	+	8.26177i	0.193925	+	0.335889i
$606$	15.4529	+	11.5037i	0.627731	+	0.467306i
$607$	32.8020			1.33139			0.665696	−	0.746223i	$-0.268135\pi$
$607$	32.8020			1.33139			0.665696	+	0.746223i	$0.268135\pi$
$608$	25.4510	−	44.0825i	1.03218	−	1.78778i
$609$	−2.12551	+	18.1886i	−0.0861300	+	0.737040i
$610$	−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	0.894367	−	0.447334i	$-0.147627\pi$
$613$	1.48010	+	2.56360i	0.0597805	+	0.103543i	−0.834586	+	0.550877i	$0.814293\pi$
$614$	−8.20112			−0.330970
$615$	7.75318	+	5.77175i	0.312639	+	0.232739i
$616$	31.8521	+	55.1695i	1.28336	+	2.22284i
$617$	−45.4995			−1.83174			−0.915871	−	0.401472i	$-0.868499\pi$
$617$	−45.4995			−1.83174			−0.915871	+	0.401472i	$0.868499\pi$
$618$	2.17031	−	18.5720i	0.0873026	−	0.747075i
$619$	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
$621$	10.6981	+	12.7477i	0.429300	+	0.511546i
$622$	−10.9919	−	19.0385i	−0.440735	−	0.763376i
$623$	−2.72859	+	4.72605i	−0.109318	+	0.189345i
$624$	−49.4534	+	51.6456i	−1.97972	+	2.06748i
$625$	−9.43227	−	16.3372i	−0.377291	−	0.653487i
$626$	−38.4060	+	66.5212i	−1.53501	+	2.65872i
$627$	−28.9455	+	12.4867i	−1.15597	+	0.498671i
$628$	2.55063	+	4.41782i	0.101781	+	0.176290i
$629$	1.95736			0.0780450
$630$	−7.78643	−	1.84503i	−0.310219	−	0.0735077i
$631$	−10.2771	+	17.8004i	−0.409123	+	0.708622i	−0.994792	−	0.101929i	$-0.967499\pi$
$631$	−10.2771	+	17.8004i	−0.409123	+	0.708622i	0.585669	+	0.810551i	$0.300832\pi$
$632$	−26.2525	+	45.4707i	−1.04427	+	1.80873i
$633$	−4.29913	+	1.85459i	−0.170875	+	0.0737132i
$634$	3.74858	−	6.49273i	0.148875	−	0.257859i
$635$	−4.04303	+	7.00274i	−0.160443	+	0.277895i
$636$	−17.4672	−	13.0032i	−0.692618	−	0.515609i
$637$	13.2410	+	10.0114i	0.524629	+	0.396666i
$638$	91.9869			3.64180
$639$	−4.59516	−	1.08884i	−0.181782	−	0.0430740i
$640$	−3.52334	−	6.10260i	−0.139272	−	0.241227i
$641$	−2.91485	−	5.04866i	−0.115129	−	0.199410i	0.802702	−	0.596380i	$-0.203395\pi$
$641$	−2.91485	−	5.04866i	−0.115129	−	0.199410i	−0.917832	+	0.396970i	$0.870062\pi$
$642$	5.40215	−	46.2278i	0.213206	−	1.82447i
$643$	44.2628			1.74555			0.872777	−	0.488119i	$-0.162317\pi$
$643$	44.2628			1.74555			0.872777	+	0.488119i	$0.162317\pi$
$644$	−25.0647			−0.987686
$645$	6.18879	−	2.66976i	0.243684	−	0.105122i
$646$	0.990041	+	1.71480i	0.0389527	+	0.0674680i
$647$	8.63857	+	14.9624i	0.339617	+	0.588234i	0.984361	−	0.176165i	$-0.0563692\pi$
$647$	8.63857	+	14.9624i	0.339617	+	0.588234i	−0.644744	+	0.764399i	$0.723036\pi$
$648$	61.0326	−	40.1500i	2.39759	−	1.57724i
$649$	−15.1292			−0.593875
$650$	−34.9826	−	26.4499i	−1.37213	−	1.03745i
$651$	7.78037	−	3.35634i	0.304937	−	0.131545i
$652$	−17.8409	+	30.9013i	−0.698703	+	1.21019i
$653$	3.47689	−	6.02216i	0.136061	−	0.235665i	−0.789941	−	0.613183i	$-0.789889\pi$
$653$	3.47689	−	6.02216i	0.136061	−	0.235665i	0.926002	+	0.377518i	$0.123222\pi$
$654$	16.1492	+	12.0220i	0.631482	+	0.470098i
$655$	−6.38892	+	11.0659i	−0.249636	+	0.432382i
$656$	49.2476	−	85.2994i	1.92280	−	3.33038i
$657$	2.61449	+	8.73149i	0.102001	+	0.340648i
$658$	−11.7479			−0.457979
$659$	−8.92277	−	15.4547i	−0.347582	−	0.602030i	0.638237	−	0.769840i	$-0.279664\pi$
$659$	−8.92277	−	15.4547i	−0.347582	−	0.602030i	−0.985819	+	0.167810i	$0.946330\pi$
$660$	−3.34306	+	28.6076i	−0.130128	+	1.11355i
$661$	2.20696	−	3.82256i	0.0858407	−	0.148680i	−0.819908	−	0.572495i	$-0.805976\pi$
$661$	2.20696	−	3.82256i	0.0858407	−	0.148680i	0.905749	+	0.423814i	$0.139309\pi$
$662$	−16.1477	−	27.9686i	−0.627596	−	1.08703i
$663$	−0.362714	−	1.24505i	−0.0140866	−	0.0483537i
$664$	−10.1159	+	17.5213i	−0.392574	+	0.679959i
$665$	1.80236	+	3.12177i	0.0698924	+	0.121057i
$666$	−51.5441	+	54.6387i	−1.99729	+	2.11721i
$667$	−10.9377	+	18.9447i	−0.423511	+	0.733542i
$668$	46.6560	−	80.8105i	1.80517	−	3.12665i
$669$	7.25819	+	5.40326i	0.280618	+	0.208902i
$670$	8.52742			0.329443
$671$	−20.3938	−	35.3231i	−0.787293	−	1.36363i
$672$	−4.41261	+	37.7600i	−0.170220	+	1.45662i
$673$	28.2309			1.08822			0.544110	−	0.839014i	$-0.316867\pi$
$673$	28.2309			1.08822			0.544110	+	0.839014i	$0.316867\pi$
$674$	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	$0.244555\pi$
$678$	49.5050	+	36.8533i	1.90123	+	1.41534i
$679$	7.26475	−	12.5829i	0.278796	−	0.482888i
$680$	1.09347			0.0419326
$681$	−1.12000	+	9.58419i	−0.0429186	+	0.367267i
$682$	−21.2819	−	36.8614i	−0.814927	−	1.41150i
$683$	−12.3897	+	21.4597i	−0.474081	+	0.821132i	−0.999560	−	0.0296749i	$-0.990553\pi$
$683$	−12.3897	+	21.4597i	−0.474081	+	0.821132i	0.525479	+	0.850807i	$0.323886\pi$
$684$	−52.9808	−	12.5540i	−2.02577	−	0.480016i
$685$	4.60477	−	7.97570i	0.175939	−	0.304736i
$686$	47.7120			1.82165
$687$	−4.60158	+	39.3771i	−0.175561	+	1.50233i
$688$	−34.3415	−	59.4812i	−1.30926	−	2.26770i
$689$	1.10703	−	8.89723i	0.0421744	−	0.338957i
$690$	−7.66764	−	5.70806i	−0.291902	−	0.217302i
$691$	16.8086			0.639430			0.319715	−	0.947514i	$-0.396413\pi$
$691$	16.8086			0.639430			0.319715	+	0.947514i	$0.396413\pi$
$692$	−4.44829	−	7.70466i	−0.169099	−	0.292887i
$693$	16.1562	−	17.1262i	0.613722	−	0.650569i
$694$	−57.6304			−2.18762
$695$	1.13322	+	1.96280i	0.0429855	+	0.0744531i
$696$	77.0287	+	57.3429i	2.91976	+	2.17358i
$697$	0.893154	+	1.54699i	0.0338306	+	0.0585964i
$698$	91.5052			3.46352
$699$	21.4128	+	15.9405i	0.809908	+	0.602925i
$700$	−35.8366			−1.35450
$701$	11.1825			0.422358			0.211179	−	0.977447i	$-0.432270\pi$
$701$	11.1825			0.422358			0.211179	+	0.977447i	$0.432270\pi$
$702$	44.3064	+	22.6615i	1.67224	+	0.855303i
$703$	33.8371			1.27619
$704$	74.8634			2.82152
$705$	−2.57515	−	1.91704i	−0.0969859	−	0.0721997i
$706$	3.79113			0.142681
$707$	3.24073	+	5.61312i	0.121880	+	0.211103i
$708$	−20.9607	−	15.6039i	−0.787751	−	0.586430i
$709$	13.1682	+	22.8079i	0.494541	+	0.856570i	0.999980	−	0.00629240i	$-0.00200295\pi$
$709$	13.1682	+	22.8079i	0.494541	+	0.856570i	−0.505439	+	0.862862i	$0.668670\pi$
$710$	2.71252			0.101799
$711$	18.8822	+	4.47423i	0.708139	+	0.167797i
$712$	14.3086	+	24.7832i	0.536237	+	0.928789i
$713$	10.1221			0.379077
$714$	−1.18624	−	0.883083i	−0.0443941	−	0.0330485i
$715$	−10.9236	+	4.61600i	−0.408520	+	0.172629i
$716$	−23.4524	−	40.6208i	−0.876458	−	1.51807i
$717$	2.40085	−	20.5448i	0.0896613	−	0.767258i
$718$	−22.0569			−0.823154
$719$	−7.74314	+	13.4115i	−0.288770	+	0.500165i	−0.973516	−	0.228617i	$-0.926580\pi$
$719$	−7.74314	+	13.4115i	−0.288770	+	0.500165i	0.684746	+	0.728782i	$0.259913\pi$
$720$	−15.2910	+	16.2090i	−0.569861	+	0.604075i
$721$	3.14547	−	5.44812i	0.117143	−	0.202898i
$722$	−8.11972	−	14.0638i	−0.302185	−	0.523399i
$723$	−3.58377	+	30.6674i	−0.133282	+	1.14053i
$724$	−89.4956			−3.32608
$725$	−15.6384	+	27.0866i	−0.580797	+	1.00597i
$726$	−54.2712	−	40.4014i	−2.01419	−	1.49944i
$727$	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
$731$	1.24563			0.0460715
$732$	8.17684	−	69.9717i	0.302225	−	2.58623i
$733$	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	$0.808307\pi$
$734$	82.1302			3.03148
$735$	4.14952	+	3.08905i	0.153057	+	0.113941i
$736$	−22.7070	+	39.3297i	−0.836991	+	1.44971i
$737$	−12.5450	+	21.7286i	−0.462101	+	0.800382i
$738$	−66.7033	−	15.8056i	−2.45538	−	0.581814i
$739$	−2.29397	−	3.97326i	−0.0843849	−	0.146159i	0.820744	−	0.571296i	$-0.193559\pi$
$739$	−2.29397	−	3.97326i	−0.0843849	−	0.146159i	−0.905129	+	0.425137i	$0.860226\pi$
$740$	15.4578	−	26.7738i	0.568241	−	0.984223i
$741$	−6.27028	−	21.5233i	−0.230345	−	0.790679i
$742$	−5.11224	−	8.85465i	−0.187676	−	0.325065i
$743$	−11.1086	+	19.2406i	−0.407533	+	0.705868i	−0.994613	−	0.103661i	$-0.966944\pi$
$743$	−11.1086	+	19.2406i	−0.407533	+	0.705868i	0.587079	+	0.809529i	$0.300278\pi$
$744$	5.15747	−	44.1340i	0.189082	−	1.61803i
$745$	−4.01285	−	6.95046i	−0.147020	−	0.254645i
$746$	−37.8722			−1.38660
$747$	7.27593	+	1.72407i	0.266213	+	0.0630803i
$748$	−2.66147	+	4.60980i	−0.0973129	+	0.168551i
$749$	7.82945	−	13.5610i	0.286082	−	0.495508i
$750$	−22.9334	−	17.0724i	−0.837410	−	0.623398i
$751$	4.83340	−	8.37170i	0.176373	−	0.305488i	−0.764262	−	0.644905i	$-0.776897\pi$
$751$	4.83340	−	8.37170i	0.176373	−	0.305488i	0.940636	+	0.339418i	$0.110230\pi$
$752$	−16.3572	+	28.3314i	−0.596484	+	1.03314i
$753$	2.47979	−	1.06975i	0.0903688	−	0.0389838i
$754$	−8.07703	+	64.9153i	−0.294148	+	2.36408i
$755$	0.671398			0.0244347
$756$	40.0469	−	7.06428i	1.45649	−	0.256925i
$757$	9.26864	+	16.0538i	0.336875	+	0.583484i	0.983843	−	0.179033i	$-0.0572968\pi$
$757$	9.26864	+	16.0538i	0.336875	+	0.583484i	−0.646969	+	0.762517i	$0.723964\pi$
$758$	−8.43719	−	14.6136i	−0.306453	−	0.530791i
$759$	25.8247	−	11.1404i	0.937379	−	0.404372i
$760$	18.9029			0.685682
$761$	23.1466			0.839065			0.419533	−	0.907740i	$-0.362194\pi$
$761$	23.1466			0.839065			0.419533	+	0.907740i	$0.362194\pi$
$762$	6.65631	−	56.9600i	0.241133	−	2.06344i
$763$	3.38675	+	5.86603i	0.122609	+	0.212365i
$764$	−1.37440	−	2.38053i	−0.0497240	−	0.0861245i
$765$	−0.115924	−	0.387147i	−0.00419125	−	0.0139973i
$766$	−77.3402			−2.79442
$767$	1.32844	−	10.6767i	0.0479673	−	0.385514i
$768$	−0.941624	−	0.700979i	−0.0339779	−	0.0252944i
$769$	−20.9179	+	36.2309i	−0.754318	+	1.30652i	0.191394	+	0.981513i	$0.438699\pi$
$769$	−20.9179	+	36.2309i	−0.754318	+	1.30652i	−0.945712	+	0.325005i	$0.894634\pi$
$770$	−6.76182	+	11.7118i	−0.243679	+	0.422065i
$771$	−31.4945	+	13.5863i	−1.13425	+	0.489297i
$772$	62.4462	−	108.160i	2.24749	−	3.89277i
$773$	−8.76453	+	15.1806i	−0.315238	+	0.546009i	−0.979488	−	0.201502i	$-0.935418\pi$
$773$	−8.76453	+	15.1806i	−0.315238	+	0.546009i	0.664250	+	0.747511i	$0.268751\pi$
$774$	−32.8019	+	34.7713i	−1.17904	+	1.24983i
$775$	14.4723			0.519861
$776$	−38.0960	−	65.9843i	−1.36757	−	2.36870i
$777$	−23.2047	+	10.0102i	−0.832464	+	0.359113i
$778$	−42.0634	+	72.8559i	−1.50804	+	2.61201i
$779$	15.4401	+	26.7430i	0.553198	+	0.958168i
$780$	−19.8949	−	4.87113i	−0.712351	−	0.174414i
$781$	−3.99049	+	6.91173i	−0.142791	+	0.247321i
$782$	−0.883299	−	1.52992i	−0.0315867	−	0.0547098i
$783$	12.1363	−	33.3515i	0.433716	−	1.19189i
$784$	26.3574	−	45.6524i	0.941336	−	1.63044i
$785$	−0.327273	+	0.566854i	−0.0116809	+	0.0202319i
$786$	10.5185	−	90.0099i	0.375182	−	3.21055i
$787$	−19.5951			−0.698489			−0.349245	−	0.937032i	$-0.613562\pi$
$787$	−19.5951			−0.698489			−0.349245	+	0.937032i	$0.613562\pi$
$788$	45.5702	+	78.9300i	1.62337	+	2.81176i
$789$	22.6774	+	16.8819i	0.807337	+	0.601011i
$790$	−11.1462			−0.396564
$791$	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
$795$	0.324306	−	2.77518i	0.0115019	−	0.0984256i
$796$	−43.4344	+	75.2306i	−1.53949	+	2.66648i
$797$	−10.7281			−0.380010			−0.190005	−	0.981783i	$-0.560850\pi$
$797$	−10.7281			−0.380010			−0.190005	+	0.981783i	$0.560850\pi$
$798$	−20.5068	−	15.2660i	−0.725932	−	0.540410i
$799$	−0.296653	−	0.513819i	−0.0104948	−	0.0181776i
$800$	−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
$803$	15.4038			0.543587
$804$	−39.7906	+	17.1651i	−1.40331	+	0.605367i
$805$	−1.60803	−	2.78519i	−0.0566757	−	0.0981652i
$806$	27.8818	−	11.7820i	0.982096	−	0.415005i
$807$	48.3011	−	20.8364i	1.70028	−	0.733477i
$808$	33.9885			1.19571
$809$	−21.3013	−	36.8949i	−0.748914	−	1.29716i	−0.948344	−	0.317245i	$-0.897242\pi$
$809$	−21.3013	−	36.8949i	−0.748914	−	1.29716i	0.199430	−	0.979912i	$-0.436091\pi$
$810$	13.8597	+	6.95896i	0.486980	+	0.244513i
$811$	−12.5260			−0.439847			−0.219923	−	0.975517i	$-0.570581\pi$
$811$	−12.5260			−0.439847			−0.219923	+	0.975517i	$0.570581\pi$
$812$	26.7269	+	46.2923i	0.937930	+	1.62454i
$813$	4.64469	−	39.7460i	0.162896	−	1.39395i
$814$	63.4727	+	109.938i	2.22472	+	3.85332i
$815$	−4.57836			−0.160373
$816$	−3.78134	+	1.63122i	−0.132373	+	0.0571040i
$817$	21.5335			0.753360
$818$	71.6436			2.50496
$819$	10.6674	+	12.9052i	0.372747	+	0.450945i
$820$	28.2140			0.985276
$821$	38.9488			1.35932			0.679661	−	0.733527i	$-0.262127\pi$
$821$	38.9488			1.35932			0.679661	+	0.733527i	$0.262127\pi$
$822$	−7.58114	+	64.8740i	−0.264422	+	2.26274i
$823$	39.5846			1.37983			0.689916	−	0.723890i	$-0.257648\pi$
$823$	39.5846			1.37983			0.689916	+	0.723890i	$0.257648\pi$
$824$	−16.4947	−	28.5697i	−0.574620	−	0.995271i
$825$	36.9234	−	15.9282i	1.28551	−	0.554550i
$826$	−6.13472	−	10.6256i	−0.213454	−	0.369713i
$827$	−19.0344			−0.661890			−0.330945	−	0.943650i	$-0.607367\pi$
$827$	−19.0344			−0.661890			−0.330945	+	0.943650i	$0.607367\pi$
$828$	47.2687	+	11.2005i	1.64270	+	0.389245i
$829$	−5.06015	−	8.76445i	−0.175746	−	0.304402i	0.764673	−	0.644419i	$-0.222901\pi$
$829$	−5.06015	−	8.76445i	−0.175746	−	0.304402i	−0.940419	+	0.340017i	$0.889567\pi$
$830$	−4.29498			−0.149081
$831$	−2.75189	+	23.5488i	−0.0954621	+	0.816898i
$832$	−6.57348	+	52.8312i	−0.227894	+	1.83159i
$833$	0.478018	+	0.827951i	0.0165623	+	0.0286868i
$834$	−12.8935	−	9.59839i	−0.446466	−	0.332365i
$835$	11.9729			0.414341
$836$	−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
$839$	−13.6152	−	23.5823i	−0.470050	−	0.814151i	0.529363	−	0.848395i	$-0.322431\pi$
$839$	−13.6152	−	23.5823i	−0.470050	−	0.814151i	−0.999413	+	0.0342445i	$0.989098\pi$
$840$	−12.9632	+	5.59214i	−0.447272	+	0.192947i
$841$	17.6524			0.608703
$842$	22.1952	−	38.4432i	0.764897	−	1.32484i
$843$	−42.0715	+	18.1491i	−1.44902	+	0.625087i
$844$	−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
$848$	−28.4722			−0.977738
$849$	−10.4971	+	4.52829i	−0.360259	+	0.155411i
$850$	−1.26291	−	2.18743i	−0.0433176	−	0.0750282i
$851$	−30.1890			−1.03486
$852$	−12.6572	+	5.46012i	−0.433627	+	0.187061i
$853$	−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
$855$	−2.00400	−	6.69266i	−0.0685352	−	0.228884i
$856$	−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	$0.948671\pi$
$858$	58.1680	−	60.7464i	1.98582	−	2.07385i
$859$	−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	$-0.459150\pi$
$860$	9.83714	−	17.0384i	0.335444	−	0.581006i
$861$	−18.4999	−	13.7720i	−0.630476	−	0.469349i
$862$	11.0281	+	19.1013i	0.375620	+	0.650593i
$863$	−38.8584			−1.32275			−0.661377	−	0.750053i	$-0.730028\pi$
$863$	−38.8584			−1.32275			−0.661377	+	0.750053i	$0.730028\pi$
$864$	25.1952	−	69.2386i	0.857159	−	2.35555i
$865$	0.570764	−	0.988591i	0.0194065	−	0.0336131i
$866$	−0.104682	+	0.181315i	−0.00355724	+	0.00616132i
$867$	−3.40898	+	29.1717i	−0.115775	+	0.990722i
$868$	12.3670	−	21.4202i	0.419762	−	0.727050i
$869$	16.3976	−	28.4014i	0.556249	−	0.963452i
$870$	−2.36618	+	20.2481i	−0.0802209	+	0.686475i
$871$	−14.2324	−	10.7609i	−0.482245	−	0.364620i
$872$	35.5199			1.20286
$873$	−19.3232	+	20.4834i	−0.653993	+	0.693257i
$874$	−15.2697	−	26.4479i	−0.516506	−	0.894614i
$875$	−4.80952	−	8.33034i	−0.162592	−	0.281617i
$876$	21.3410	+	15.8870i	0.721047	+	0.536773i
$877$	−16.2126			−0.547460			−0.273730	−	0.961807i	$-0.588258\pi$
$877$	−16.2126			−0.547460			−0.273730	+	0.961807i	$0.588258\pi$
$878$	−68.3780			−2.30764
$879$	−0.687586	−	0.511864i	−0.0231917	−	0.0172647i
$880$	18.8297	+	32.6140i	0.634749	+	1.09942i
$881$	−17.4979	−	30.3072i	−0.589518	−	1.02107i	−0.994296	−	0.106660i	$-0.965984\pi$
$881$	−17.4979	−	30.3072i	−0.589518	−	1.02107i	0.404778	−	0.914415i	$-0.367349\pi$
$882$	−35.6997	−	8.45921i	−1.20207	−	0.284836i
$883$	−22.3562			−0.752346			−0.376173	−	0.926549i	$-0.622760\pi$
$883$	−22.3562			−0.752346			−0.376173	+	0.926549i	$0.622760\pi$
$884$	−3.01945	−	2.28297i	−0.101555	−	0.0767847i
$885$	0.389169	−	3.33024i	0.0130818	−	0.111945i
$886$	37.6436	−	65.2006i	1.26466	−	2.19046i
$887$	6.93763	−	12.0163i	0.232943	−	0.403469i	−0.725730	−	0.687980i	$-0.758498\pi$
$887$	6.93763	−	12.0163i	0.232943	−	0.403469i	0.958673	+	0.284511i	$0.0918311\pi$
$888$	−15.3820	+	131.628i	−0.516186	+	4.41716i
$889$	9.64712	−	16.7093i	0.323554	−	0.560412i
$890$	−3.03754	+	5.26117i	−0.101819	+	0.176355i
$891$	−38.1215	+	25.0781i	−1.27712	+	0.840147i
$892$	26.4127			0.884363
$893$	−5.12829	−	8.88246i	−0.171612	−	0.297240i
$894$	45.6573	+	33.9889i	1.52701	+	1.13676i
$895$	3.00920	−	5.21208i	0.100586	−	0.174221i
$896$	8.40707	+	14.5615i	0.280861	+	0.486465i
$897$	5.59425	+	19.2028i	0.186786	+	0.641162i
$898$	−5.80953	+	10.0624i	−0.193866	+	0.335787i
$899$	−10.7934	−	18.6947i	−0.359981	−	0.623505i
$900$	67.5832	+	16.0142i	2.25277	+	0.533805i
$901$	0.258185	−	0.447190i	0.00860141	−	0.0148981i
$902$	−57.9259	+	100.331i	−1.92872	+	3.34064i
$903$	−14.7671	+	6.37034i	−0.491420	+	0.211991i
$904$	108.886			3.62149
$905$	−5.74163	−	9.94479i	−0.190858	−	0.330576i
$906$	−4.37218	+	1.88610i	−0.145256	+	0.0626614i
$907$	−47.0793			−1.56324			−0.781621	−	0.623754i	$-0.785607\pi$
$907$	−47.0793			−1.56324			−0.781621	+	0.623754i	$0.785607\pi$
$908$	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	$-0.0413559\pi$
$912$	−65.3685	+	28.1990i	−2.16457	+	0.933764i
$913$	6.31851	−	10.9440i	0.209112	−	0.362193i
$914$	36.0107			1.19113
$915$	8.29987	−	3.58045i	0.274385	−	0.118366i
$916$	57.8618	+	100.220i	1.91181	+	3.31135i
$917$	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	−0.922830	−	0.385206i	$-0.874130\pi$
$919$	−3.87476	+	6.71128i	−0.127817	+	0.221385i	0.795014	+	0.606591i	$0.207464\pi$
$920$	−16.8649			−0.556019
$921$	4.28951	+	3.19327i	0.141344	+	0.105222i
$922$	2.66412	+	4.61439i	0.0877381	+	0.151967i
$923$	−4.52723	−	3.42299i	−0.149015	−	0.112669i
$924$	7.97691	−	68.2608i	0.262421	−	2.24561i
$925$	−43.1632			−1.41920
$926$	55.1048	+	95.4443i	1.81085	+	3.13649i
$927$	−8.36652	+	8.86883i	−0.274793	+	0.291291i
$928$	96.8515			3.17931
$929$	9.51347	+	16.4778i	0.312127	+	0.540619i	0.978823	−	0.204711i	$-0.0656253\pi$
$929$	9.51347	+	16.4778i	0.312127	+	0.540619i	−0.666696	+	0.745330i	$0.732292\pi$
$930$	8.66133	−	3.73638i	0.284016	−	0.122521i
$931$	8.26356	+	14.3129i	0.270827	+	0.469086i
$932$	77.9218			2.55241
$933$	−1.66382	+	14.2378i	−0.0544711	+	0.466126i
$934$	66.5835			2.17868
$935$	−0.682990			−0.0223362
$936$	86.5773	−	14.6075i	2.82987	−	0.477460i
$937$	−19.2901			−0.630179			−0.315090	−	0.949062i	$-0.602035\pi$
$937$	−19.2901			−0.630179			−0.315090	+	0.949062i	$0.602035\pi$
$938$	−20.3473			−0.664364
$939$	45.9892	−	19.8391i	1.50080	−	0.647424i
$940$	−9.37103			−0.305649
$941$	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	$0.608392\pi$
$942$	0.538811	−	4.61077i	0.0175554	−	0.150227i
$943$	−13.7754	−	23.8597i	−0.448589	−	0.776978i
$944$	−34.1668			−1.11203
$945$	3.35421	+	3.99682i	0.109113	+	0.130017i
$946$	40.3931	+	69.9629i	1.31329	+	2.27469i
$947$	−16.2284			−0.527351			−0.263675	−	0.964611i	$-0.584935\pi$
$947$	−16.2284			−0.527351			−0.263675	+	0.964611i	$0.584935\pi$
$948$	52.0103	−	22.4365i	1.68922	−	0.728704i
$949$	−1.35255	+	10.8705i	−0.0439055	+	0.352870i
$950$	−21.8322	−	37.8144i	−0.708329	−	1.22686i
$951$	−4.48873	+	1.93637i	−0.145557	+	0.0627912i
$952$	−2.60913			−0.0845625
$953$	4.95942	−	8.58997i	0.160651	−	0.278256i	−0.774451	−	0.632634i	$-0.781974\pi$
$953$	4.95942	−	8.58997i	0.160651	−	0.278256i	0.935102	+	0.354377i	$0.115307\pi$
$954$	5.68417	+	18.9832i	0.184032	+	0.614604i
$955$	0.176350	−	0.305448i	0.00570656	−	0.00988405i
$956$	−30.1891	−	52.2890i	−0.976384	−	1.69115i
$957$	−48.1128	−	35.8169i	−1.55527	−	1.15780i
$958$	16.2358			0.524555
$959$	−10.9875	+	19.0309i	−0.354805	+	0.614540i
$960$	−1.92571	+	16.4789i	−0.0621520	+	0.531853i
$961$	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
$965$	16.0251			0.515865
$966$	18.2958	+	13.6201i	0.588658	+	0.438218i
$967$	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	$0.647024\pi$
$968$	−119.369			−3.83666
$969$	0.149861	−	1.28240i	0.00481422	−	0.0411967i
$970$	8.08733	−	14.0077i	0.259669	−	0.449759i
$971$	28.7211	−	49.7464i	0.921705	−	1.59644i	0.124928	−	0.992166i	$-0.460130\pi$
$971$	28.7211	−	49.7464i	0.921705	−	1.59644i	0.796777	−	0.604273i	$-0.206537\pi$
$972$	−78.6801	−	4.57327i	−2.52366	−	0.146688i
$973$	−2.70399	−	4.68344i	−0.0866859	−	0.150144i
$974$	14.7446	−	25.5383i	0.472446	−	0.818300i
$975$	7.99848	+	27.4555i	0.256156	+	0.879280i
$976$	−46.0558	−	79.7711i	−1.47421	−	2.55341i
$977$	8.57672	−	14.8553i	0.274394	−	0.475264i	−0.695588	−	0.718441i	$-0.744856\pi$
$977$	8.57672	−	14.8553i	0.274394	−	0.475264i	0.969982	+	0.243177i	$0.0781896\pi$
$978$	29.8145	−	12.8616i	0.953364	−	0.411268i
$979$	−8.93727	−	15.4798i	−0.285636	−	0.494737i
$980$	15.1002			0.482358
$981$	−3.76565	−	12.5760i	−0.120228	−	0.401520i
$982$	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	$0.737495\pi$
$984$	−111.051	+	47.9057i	−3.54016	+	1.52718i
$985$	−5.84715	+	10.1276i	−0.186306	+	0.322691i
$986$	−1.88376	+	3.26276i	−0.0599910	+	0.103907i
$987$	6.14459	+	4.57426i	0.195585	+	0.145600i
$988$	−52.1976	−	39.4660i	−1.66063	−	1.25558i
$989$	−19.2118			−0.610900
$990$	17.9855	−	19.0653i	0.571617	−	0.605936i
$991$	11.0154	+	19.0792i	0.349915	+	0.606071i	0.986234	−	0.165355i	$-0.0528770\pi$
$991$	11.0154	+	19.0792i	0.349915	+	0.606071i	−0.636319	+	0.771426i	$0.719544\pi$
$992$	−22.4074	−	38.8107i	−0.711436	−	1.23224i
$993$	−2.44424	+	20.9161i	−0.0775656	+	0.663752i
$994$	−6.47237			−0.205291
$995$	−11.1462			−0.353359
$996$	20.0413	−	8.64551i	0.635031	−	0.273944i
$997$	−16.4450	−	28.4835i	−0.520818	−	0.902083i	−0.999707	−	0.0242074i	$-0.992294\pi$
$997$	−16.4450	−	28.4835i	−0.520818	−	0.902083i	0.478889	−	0.877875i	$-0.341040\pi$
$998$	15.0788	+	26.1173i	0.477311	+	0.826727i
$999$	48.2343	−	8.50852i	1.52606	−	0.269198i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.f.a.61.12	✓	24	13.9	even	3
117.2.f.a.94.12	yes	24	9.4	even	3
117.2.h.a.16.1	yes	24	1.1	even	1	trivial
117.2.h.a.22.1	yes	24	117.22	even	3	inner
351.2.f.a.100.1		24	39.35	odd	6
351.2.f.a.172.1		24	9.5	odd	6
351.2.h.a.289.12		24	3.2	odd	2
351.2.h.a.334.12		24	117.113	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.h (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.65628 q^{2} +(1.38934 + 1.03428i) q^{3} +5.05585 q^{4} +(0.324360 + 0.561808i) q^{5} +(-3.69049 - 2.74733i) q^{6} +(-0.773958 - 1.34053i) q^{7} -8.11720 q^{8} +(0.860545 + 2.87393i) q^{9} +(-0.861592 - 1.49232i) q^{10} +5.07008 q^{11} +(7.02430 + 5.22914i) q^{12} +(-0.445184 + 3.57796i) q^{13} +(2.05585 + 3.56084i) q^{14} +(-0.130417 + 1.11602i) q^{15} +11.4499 q^{16} +(-0.103828 + 0.179835i) q^{17} +(-2.28585 - 7.63397i) q^{18} +(-1.79488 + 3.10883i) q^{19} +(1.63991 + 2.84041i) q^{20} +(0.311190 - 2.66295i) q^{21} -13.4676 q^{22} +(1.60137 - 2.77365i) q^{23} +(-11.2776 - 8.39543i) 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} -6.83026 q^{29} +(0.346426 - 2.96447i) q^{30} +(1.58024 + 2.73705i) q^{31} -14.1798 q^{32} +(7.04407 + 5.24386i) q^{33} +(0.275796 - 0.477692i) q^{34} +(0.502082 - 0.869631i) q^{35} +(4.35079 + 14.5301i) q^{36} +(-4.71300 - 8.16316i) q^{37} +(4.76772 - 8.25793i) q^{38} +(-4.31911 + 4.51057i) q^{39} +(-2.63289 - 4.56031i) q^{40} +(4.30114 - 7.44979i) q^{41} +(-0.826610 + 7.07355i) q^{42} +(-2.99929 - 5.19492i) q^{43} +25.6335 q^{44} +(-1.33547 + 1.41565i) q^{45} +(-4.25368 + 7.36759i) q^{46} +(-1.42859 + 2.47438i) q^{47} +(15.9078 + 11.8424i) q^{48} +(2.30198 - 3.98714i) q^{49} +(-6.08178 + 10.5340i) q^{50} +(-0.330251 + 0.142466i) q^{51} +(-2.25078 + 18.0896i) q^{52} -2.48667 q^{53} +(4.71980 - 12.9704i) q^{54} +(1.64453 + 2.84841i) q^{55} +(6.28237 + 10.8814i) q^{56} +(-5.70909 + 2.46282i) q^{57} +18.1431 q^{58} -2.98403 q^{59} +(-0.659371 + 5.64243i) q^{60} +(-4.02238 - 6.96697i) q^{61} +(-4.19756 - 7.27038i) q^{62} +(3.18657 - 3.37789i) q^{63} +14.7657 q^{64} +(-2.15453 + 0.910439i) q^{65} +(-18.7111 - 13.9292i) q^{66} +(-2.47432 + 4.28565i) q^{67} +(-0.524937 + 0.909217i) q^{68} +(5.09356 - 2.19729i) q^{69} +(-1.33367 + 2.30999i) q^{70} +(-0.787066 + 1.36324i) q^{71} +(-6.98522 - 23.3282i) q^{72} +3.03817 q^{73} +(12.5191 + 21.6837i) q^{74} +(7.28261 - 3.14162i) q^{75} +(-9.07465 + 15.7178i) q^{76} +(-3.92403 - 6.79661i) q^{77} +(11.4728 - 11.9814i) q^{78} +(3.23418 - 5.60177i) q^{79} +(3.71389 + 6.43264i) q^{80} +(-7.51892 + 4.94629i) q^{81} +(-11.4251 + 19.7888i) q^{82} +(1.24623 - 2.15854i) q^{83} +(1.57333 - 13.4635i) q^{84} -0.134710 q^{85} +(7.96696 + 13.7992i) q^{86} +(-9.48957 - 7.06437i) q^{87} -41.1548 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} +(-0.635376 + 5.43710i) q^{93} +(3.79473 - 6.57267i) q^{94} -2.32875 q^{95} +(-19.7006 - 14.6658i) q^{96} +(4.69325 + 8.12894i) q^{97} +(-6.11471 + 10.5910i) q^{98} +(4.36303 + 14.5710i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 2 q^{2} - q^{3} + 18 q^{4} - 2 q^{5} - 12 q^{6} + 3 q^{7} - 18 q^{8} - 3 q^{9} + 6 q^{11} - 3 q^{12} + 2 q^{14} + 11 q^{15} + 6 q^{16} + 6 q^{17} - 8 q^{18} - 3 q^{19} - 11 q^{20} - 25 q^{21} - 18 q^{22}+ \cdots + 18 q^{99}+O(q^{100}) \) 24 * q - 2 * q^2 - q^3 + 18 * q^4 - 2 * q^5 - 12 * q^6 + 3 * q^7 - 18 * q^8 - 3 * q^9 + 6 * q^11 - 3 * q^12 + 2 * q^14 + 11 * q^15 + 6 * q^16 + 6 * q^17 - 8 * q^18 - 3 * q^19 - 11 * q^20 - 25 * q^21 - 18 * q^22 + 17 * q^23 - 12 * q^24 - 6 * q^25 - 12 * q^26 + 2 * q^27 - 24 * q^29 - 8 * q^30 - 6 * q^31 - 38 * q^32 + 11 * q^33 + 18 * q^35 - 28 * q^36 - 3 * q^37 + 8 * q^38 + 3 * q^39 - 12 * q^40 + 5 * q^41 + 15 * q^42 - 3 * q^43 + 44 * q^44 + 19 * q^45 - 6 * q^46 + 21 * q^47 + 23 * q^48 + 3 * q^49 - 20 * q^50 + 7 * q^51 - 24 * q^52 - 20 * q^53 + 39 * q^54 + 3 * q^55 + 40 * q^56 + 9 * q^57 + 18 * q^58 + 38 * q^59 + 51 * q^60 - 6 * q^61 + 19 * q^62 + 13 * q^63 - 42 * q^64 - 2 * q^65 - 18 * q^66 - 6 * q^67 - 31 * q^69 + 27 * q^70 + 14 * q^71 - 18 * q^72 + 6 * q^73 + 29 * q^74 + 74 * q^75 - 15 * q^76 + 4 * q^77 + 80 * q^78 + 3 * q^79 - 16 * q^80 - 27 * q^81 - 9 * q^82 - 33 * q^83 + 5 * q^84 + 72 * q^86 - 32 * q^87 - 78 * q^88 - q^89 + 21 * q^90 - 6 * q^91 - 10 * q^92 - 84 * q^93 - 9 * q^94 - 100 * q^95 - 79 * q^96 + 24 * q^97 - 61 * q^98 + 18 * q^99

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