LMFDB - Embedded newform 117.2.h.a.16.10

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)

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);

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")

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			16.10
Character	$\chi$	$=$	117.16
Dual form			117.2.h.a.22.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.80162 q^{2} +(-0.336410 - 1.69907i) q^{3} +1.24582 q^{4} +(1.73153 + 2.99909i) q^{5} +(-0.606082 - 3.06106i) q^{6} +(-1.62239 - 2.81005i) q^{7} -1.35875 q^{8} +(-2.77366 + 1.14317i) q^{9} +(3.11954 + 5.40321i) q^{10} +0.609131 q^{11} +(-0.419106 - 2.11673i) q^{12} +(0.536447 + 3.56542i) q^{13} +(-2.92291 - 5.06264i) q^{14} +(4.51315 - 3.95090i) q^{15} -4.93957 q^{16} +(1.20773 - 2.09186i) q^{17} +(-4.99706 + 2.05955i) q^{18} +(-0.877705 + 1.52023i) q^{19} +(2.15717 + 3.73632i) q^{20} +(-4.22868 + 3.70187i) q^{21} +1.09742 q^{22} +(-0.0812242 + 0.140684i) q^{23} +(0.457096 + 2.30860i) q^{24} +(-3.49636 + 6.05587i) q^{25} +(0.966470 + 6.42352i) q^{26} +(2.87540 + 4.32805i) q^{27} +(-2.02120 - 3.50082i) q^{28} +2.90723 q^{29} +(8.13096 - 7.11801i) q^{30} +(-4.62084 - 8.00352i) q^{31} -6.18172 q^{32} +(-0.204918 - 1.03495i) q^{33} +(2.17587 - 3.76872i) q^{34} +(5.61840 - 9.73136i) q^{35} +(-3.45547 + 1.42418i) q^{36} +(-0.826776 - 1.43202i) q^{37} +(-1.58129 + 2.73887i) q^{38} +(5.87742 - 2.11090i) q^{39} +(-2.35270 - 4.07500i) q^{40} +(4.11123 - 7.12085i) q^{41} +(-7.61846 + 6.66935i) q^{42} +(6.00278 + 10.3971i) q^{43} +0.758866 q^{44} +(-8.23112 - 6.33902i) q^{45} +(-0.146335 + 0.253459i) q^{46} +(4.38799 - 7.60023i) q^{47} +(1.66172 + 8.39267i) q^{48} +(-1.76427 + 3.05580i) q^{49} +(-6.29909 + 10.9103i) q^{50} +(-3.96050 - 1.34830i) q^{51} +(0.668315 + 4.44187i) q^{52} +9.43717 q^{53} +(5.18037 + 7.79749i) q^{54} +(1.05473 + 1.82684i) q^{55} +(2.20441 + 3.81815i) q^{56} +(2.87824 + 0.979859i) q^{57} +5.23772 q^{58} -8.26434 q^{59} +(5.62256 - 4.92210i) q^{60} +(-4.96418 - 8.59821i) q^{61} +(-8.32497 - 14.4193i) q^{62} +(7.71230 + 5.93946i) q^{63} -1.25794 q^{64} +(-9.76414 + 7.78247i) q^{65} +(-0.369183 - 1.86459i) q^{66} +(-1.14763 + 1.98775i) q^{67} +(1.50462 - 2.60607i) q^{68} +(0.266357 + 0.0906776i) q^{69} +(10.1222 - 17.5322i) q^{70} +(-4.87460 + 8.44305i) q^{71} +(3.76869 - 1.55327i) q^{72} -2.59634 q^{73} +(-1.48953 - 2.57994i) q^{74} +(11.4655 + 3.90329i) q^{75} +(-1.09346 + 1.89393i) q^{76} +(-0.988245 - 1.71169i) q^{77} +(10.5889 - 3.80304i) q^{78} +(-2.53739 + 4.39489i) q^{79} +(-8.55300 - 14.8142i) q^{80} +(6.38634 - 6.34151i) q^{81} +(7.40685 - 12.8290i) q^{82} +(-4.14134 + 7.17301i) q^{83} +(-5.26817 + 4.61186i) q^{84} +8.36489 q^{85} +(10.8147 + 18.7316i) q^{86} +(-0.978023 - 4.93958i) q^{87} -0.827654 q^{88} +(4.93949 + 8.55544i) q^{89} +(-14.8293 - 11.4205i) q^{90} +(9.14870 - 7.29193i) q^{91} +(-0.101191 + 0.175267i) q^{92} +(-12.0440 + 10.5436i) q^{93} +(7.90547 - 13.6927i) q^{94} -6.07908 q^{95} +(2.07960 + 10.5032i) q^{96} +(3.73905 + 6.47622i) q^{97} +(-3.17853 + 5.50538i) q^{98} +(-1.68952 + 0.696339i) 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 $

$2$	1.80162			1.27393			0.636967	−	0.770891i	$-0.280189\pi$
$2$	1.80162			1.27393			0.636967	+	0.770891i	$0.280189\pi$
$3$	−0.336410	−	1.69907i	−0.194227	−	0.980957i
$3$	−0.336410	−	1.69907i	−0.194227	−	0.980957i
$4$	1.24582			0.622909
$5$	1.73153	+	2.99909i	0.774362	+	1.34123i	0.935153	+	0.354245i	$0.115262\pi$
$5$	1.73153	+	2.99909i	0.774362	+	1.34123i	−0.160791	+	0.986988i	$0.551405\pi$
$6$	−0.606082	−	3.06106i	−0.247432	−	1.24967i
$7$	−1.62239	−	2.81005i	−0.613204	−	1.06210i	−0.990697	−	0.136088i	$-0.956547\pi$
$7$	−1.62239	−	2.81005i	−0.613204	−	1.06210i	0.377493	−	0.926013i	$-0.376786\pi$
$8$	−1.35875			−0.480389
$9$	−2.77366	+	1.14317i	−0.924552	+	0.381056i
$10$	3.11954	+	5.40321i	0.986486	+	1.70864i
$11$	0.609131			0.183660			0.0918300	−	0.995775i	$-0.470728\pi$
$11$	0.609131			0.183660			0.0918300	+	0.995775i	$0.470728\pi$
$12$	−0.419106	−	2.11673i	−0.120986	−	0.611047i
$13$	0.536447	+	3.56542i	0.148783	+	0.988870i
$13$	0.536447	+	3.56542i	0.148783	+	0.988870i
$14$	−2.92291	−	5.06264i	−0.781182	−	1.35305i
$15$	4.51315	−	3.95090i	1.16529	−	1.02012i
$16$	−4.93957			−1.23489
$17$	1.20773	−	2.09186i	0.292919	−	0.507350i	−0.681580	−	0.731744i	$-0.738707\pi$
$17$	1.20773	−	2.09186i	0.292919	−	0.507350i	0.974499	+	0.224394i	$0.0720402\pi$
$18$	−4.99706	+	2.05955i	−1.17782	+	0.485440i
$19$	−0.877705	+	1.52023i	−0.201359	+	0.348765i	−0.948967	−	0.315376i	$-0.897869\pi$
$19$	−0.877705	+	1.52023i	−0.201359	+	0.348765i	0.747607	+	0.664141i	$0.231203\pi$
$20$	2.15717	+	3.73632i	0.482357	+	0.835466i
$21$	−4.22868	+	3.70187i	−0.922774	+	0.807815i
$22$	1.09742			0.233971
$23$	−0.0812242	+	0.140684i	−0.0169364	+	0.0293347i	−0.874369	−	0.485261i	$-0.838725\pi$
$23$	−0.0812242	+	0.140684i	−0.0169364	+	0.0293347i	0.857433	+	0.514596i	$0.172058\pi$
$24$	0.457096	+	2.30860i	0.0933044	+	0.471241i
$25$	−3.49636	+	6.05587i	−0.699272	+	1.21117i
$26$	0.966470	+	6.42352i	0.189540	+	1.25976i
$27$	2.87540	+	4.32805i	0.553372	+	0.832934i
$28$	−2.02120	−	3.50082i	−0.381970	−	0.661592i
$29$	2.90723			0.539860			0.269930	−	0.962880i	$-0.413000\pi$
$29$	2.90723			0.539860			0.269930	+	0.962880i	$0.413000\pi$
$30$	8.13096	−	7.11801i	1.48450	−	1.29956i
$31$	−4.62084	−	8.00352i	−0.829927	−	1.43748i	−0.898095	−	0.439802i	$-0.855049\pi$
$31$	−4.62084	−	8.00352i	−0.829927	−	1.43748i	0.0681682	−	0.997674i	$-0.478285\pi$
$32$	−6.18172			−1.09278
$33$	−0.204918	−	1.03495i	−0.0356716	−	0.180162i
$34$	2.17587	−	3.76872i	0.373159	−	0.646331i
$35$	5.61840	−	9.73136i	0.949683	−	1.64490i
$36$	−3.45547	+	1.42418i	−0.575912	+	0.237363i
$37$	−0.826776	−	1.43202i	−0.135921	−	0.235422i	0.790028	−	0.613071i	$-0.210066\pi$
$37$	−0.826776	−	1.43202i	−0.135921	−	0.235422i	−0.925949	+	0.377649i	$0.876733\pi$
$38$	−1.58129	+	2.73887i	−0.256519	+	0.444303i
$39$	5.87742	−	2.11090i	0.941141	−	0.338015i
$40$	−2.35270	−	4.07500i	−0.371995	−	0.644314i
$41$	4.11123	−	7.12085i	0.642065	−	1.11209i	−0.342905	−	0.939370i	$-0.611411\pi$
$41$	4.11123	−	7.12085i	0.642065	−	1.11209i	0.984971	−	0.172720i	$-0.0552556\pi$
$42$	−7.61846	+	6.66935i	−1.17555	+	1.02910i
$43$	6.00278	+	10.3971i	0.915415	+	1.58554i	0.806293	+	0.591516i	$0.201470\pi$
$43$	6.00278	+	10.3971i	0.915415	+	1.58554i	0.109122	+	0.994028i	$0.465196\pi$
$44$	0.758866			0.114403
$45$	−8.23112	−	6.33902i	−1.22702	−	0.944965i
$46$	−0.146335	+	0.253459i	−0.0215759	+	0.0373705i
$47$	4.38799	−	7.60023i	0.640054	−	1.10861i	−0.345366	−	0.938468i	$-0.612245\pi$
$47$	4.38799	−	7.60023i	0.640054	−	1.10861i	0.985420	−	0.170139i	$-0.0544215\pi$
$48$	1.66172	+	8.39267i	0.239849	+	1.21138i
$49$	−1.76427	+	3.05580i	−0.252038	+	0.436543i
$50$	−6.29909	+	10.9103i	−0.890826	+	1.54296i
$51$	−3.96050	−	1.34830i	−0.554581	−	0.188800i
$52$	0.668315	+	4.44187i	0.0926786	+	0.615976i
$53$	9.43717			1.29630			0.648148	−	0.761515i	$-0.275544\pi$
$53$	9.43717			1.29630			0.648148	+	0.761515i	$0.275544\pi$
$54$	5.18037	+	7.79749i	0.704960	+	1.06110i
$55$	1.05473	+	1.82684i	0.142219	+	0.246331i
$56$	2.20441	+	3.81815i	0.294577	+	0.510222i
$57$	2.87824	+	0.979859i	0.381233	+	0.129785i
$58$	5.23772			0.687746
$59$	−8.26434			−1.07593			−0.537963	−	0.842968i	$-0.680806\pi$
$59$	−8.26434			−1.07593			−0.537963	+	0.842968i	$0.680806\pi$
$60$	5.62256	−	4.92210i	0.725870	−	0.635441i
$61$	−4.96418	−	8.59821i	−0.635598	−	1.10089i	−0.986388	−	0.164434i	$-0.947420\pi$
$61$	−4.96418	−	8.59821i	−0.635598	−	1.10089i	0.350790	−	0.936454i	$-0.385913\pi$
$62$	−8.32497	−	14.4193i	−1.05727	−	1.83125i
$63$	7.71230	+	5.93946i	0.971659	+	0.748302i
$64$	−1.25794			−0.157242
$65$	−9.76414	+	7.78247i	−1.21109	+	0.965296i
$66$	−0.369183	−	1.86459i	−0.0454433	−	0.229515i
$67$	−1.14763	+	1.98775i	−0.140205	+	0.242842i	−0.927574	−	0.373640i	$-0.878109\pi$
$67$	−1.14763	+	1.98775i	−0.140205	+	0.242842i	0.787369	+	0.616482i	$0.211443\pi$
$68$	1.50462	−	2.60607i	0.182462	−	0.316033i
$69$	0.266357	+	0.0906776i	0.0320656	+	0.0109163i
$70$	10.1222	−	17.5322i	1.20983	−	2.09549i
$71$	−4.87460	+	8.44305i	−0.578508	+	1.00201i	0.417143	+	0.908841i	$0.363032\pi$
$71$	−4.87460	+	8.44305i	−0.578508	+	1.00201i	−0.995651	+	0.0931644i	$0.970302\pi$
$72$	3.76869	−	1.55327i	0.444145	−	0.183055i
$73$	−2.59634			−0.303878			−0.151939	−	0.988390i	$-0.548552\pi$
$73$	−2.59634			−0.303878			−0.151939	+	0.988390i	$0.548552\pi$
$74$	−1.48953	−	2.57994i	−0.173155	−	0.299912i
$75$	11.4655	+	3.90329i	1.32393	+	0.450713i
$76$	−1.09346	+	1.89393i	−0.125429	+	0.217249i
$77$	−0.988245	−	1.71169i	−0.112621	−	0.195065i
$78$	10.5889	−	3.80304i	1.19895	−	0.430609i
$79$	−2.53739	+	4.39489i	−0.285479	+	0.494464i	−0.972725	−	0.231961i	$-0.925486\pi$
$79$	−2.53739	+	4.39489i	−0.285479	+	0.494464i	0.687246	+	0.726424i	$0.258819\pi$
$80$	−8.55300	−	14.8142i	−0.956254	−	1.65628i
$81$	6.38634	−	6.34151i	0.709593	−	0.704612i
$82$	7.40685	−	12.8290i	0.817949	−	1.41673i
$83$	−4.14134	+	7.17301i	−0.454571	+	0.787340i	−0.998663	−	0.0516855i	$-0.983541\pi$
$83$	−4.14134	+	7.17301i	−0.454571	+	0.787340i	0.544093	+	0.839025i	$0.316874\pi$
$84$	−5.26817	+	4.61186i	−0.574804	+	0.503195i
$85$	8.36489			0.907300
$86$	10.8147	+	18.7316i	1.16618	+	2.01988i
$87$	−0.978023	−	4.93958i	−0.104855	−	0.529579i
$88$	−0.827654			−0.0882282
$89$	4.93949	+	8.55544i	0.523584	+	0.906875i	0.999623	+	0.0274506i	$0.00873889\pi$
$89$	4.93949	+	8.55544i	0.523584	+	0.906875i	−0.476039	+	0.879424i	$0.657928\pi$
$90$	−14.8293	−	11.4205i	−1.56315	−	1.20382i
$91$	9.14870	−	7.29193i	0.959044	−	0.764402i
$92$	−0.101191	+	0.175267i	−0.0105498	+	0.0182729i
$93$	−12.0440	+	10.5436i	−1.24891	+	1.09332i
$94$	7.90547	−	13.6927i	0.815387	−	1.41229i
$95$	−6.07908			−0.623700
$96$	2.07960	+	10.5032i	0.212248	+	1.07197i
$97$	3.73905	+	6.47622i	0.379643	+	0.657561i	0.991010	−	0.133786i	$-0.0427136\pi$
$97$	3.73905	+	6.47622i	0.379643	+	0.657561i	−0.611367	+	0.791347i	$0.709380\pi$
$98$	−3.17853	+	5.50538i	−0.321080	+	0.556127i
$99$	−1.68952	+	0.696339i	−0.169803	+	0.0699847i
$100$	−4.35583	+	7.54451i	−0.435583	+	0.754451i
$101$	−7.89619			−0.785700			−0.392850	−	0.919602i	$-0.628511\pi$
$101$	−7.89619			−0.785700			−0.392850	+	0.919602i	$0.628511\pi$
$102$	−7.13530	−	2.42912i	−0.706500	−	0.240518i
$103$	0.184492	+	0.319549i	0.0181785	+	0.0314861i	0.874972	−	0.484174i	$-0.160880\pi$
$103$	0.184492	+	0.319549i	0.0181785	+	0.0314861i	−0.856793	+	0.515660i	$0.827547\pi$
$104$	−0.728894	−	4.84450i	−0.0714740	−	0.475042i
$105$	−18.4243	−	6.27231i	−1.79803	−	0.612115i
$106$	17.0022			1.65140
$107$	1.89748	+	3.28654i	0.183437	+	0.317721i	0.943049	−	0.332655i	$-0.107944\pi$
$107$	1.89748	+	3.28654i	0.183437	+	0.317721i	−0.759612	+	0.650376i	$0.774611\pi$
$108$	3.58223	+	5.39197i	0.344700	+	0.518842i
$109$	−12.8213			−1.22806			−0.614028	−	0.789284i	$-0.710452\pi$
$109$	−12.8213			−1.22806			−0.614028	+	0.789284i	$0.710452\pi$
$110$	1.90021	+	3.29126i	0.181178	+	0.313809i
$111$	−2.15496	+	1.88649i	−0.204540	+	0.179058i
$112$	8.01389	+	13.8805i	0.757242	+	1.31158i
$113$	5.97607			0.562181			0.281091	−	0.959681i	$-0.409304\pi$
$113$	5.97607			0.562181			0.281091	+	0.959681i	$0.409304\pi$
$114$	5.18549	+	1.76533i	0.485665	+	0.165338i
$115$	−0.562567			−0.0524596
$116$	3.62188			0.336283
$117$	−5.56379	−	9.27600i	−0.514373	−	0.857567i
$118$	−14.8892			−1.37066
$119$	−7.83764			−0.718476
$120$	−6.13222	+	5.36827i	−0.559793	+	0.490054i
$121$	−10.6290			−0.966269
$122$	−8.94355	−	15.4907i	−0.809711	−	1.40246i
$123$	−13.4819	−	4.58972i	−1.21562	−	0.413841i
$124$	−5.75672	−	9.97093i	−0.516969	−	0.895416i
$125$	−6.90087			−0.617233
$126$	13.8946	+	10.7006i	1.23783	+	0.953288i
$127$	−0.321192	−	0.556321i	−0.0285012	−	0.0493655i	0.851423	−	0.524480i	$-0.175740\pi$
$127$	−0.321192	−	0.556321i	−0.0285012	−	0.0493655i	−0.879924	+	0.475114i	$0.842407\pi$
$128$	10.0971			0.892468
$129$	15.6460	−	13.6968i	1.37755	−	1.20594i
$130$	−17.5912	+	14.0210i	−1.54285	+	1.22972i
$131$	7.53625	+	13.0532i	0.658445	+	1.14046i	0.981018	+	0.193916i	$0.0621189\pi$
$131$	7.53625	+	13.0532i	0.658445	+	1.14046i	−0.322573	+	0.946545i	$0.604548\pi$
$132$	−0.255291	−	1.28936i	−0.0222202	−	0.112225i
$133$	5.69591			0.493898
$134$	−2.06758	+	3.58116i	−0.178612	+	0.309365i
$135$	−8.00138	+	16.1177i	−0.688649	+	1.38719i
$136$	−1.64100	+	2.84230i	−0.140715	+	0.243725i
$137$	2.13096	+	3.69093i	0.182060	+	0.315337i	0.942582	−	0.333975i	$-0.108390\pi$
$137$	2.13096	+	3.69093i	0.182060	+	0.315337i	−0.760522	+	0.649312i	$0.775057\pi$
$138$	0.479873	+	0.163366i	0.0408495	+	0.0139066i
$139$	−0.722302			−0.0612648			−0.0306324	−	0.999531i	$-0.509752\pi$
$139$	−0.722302			−0.0612648			−0.0306324	+	0.999531i	$0.509752\pi$
$140$	6.99951	−	12.1235i	0.591566	−	1.02462i
$141$	−14.3895	−	4.89870i	−1.21181	−	0.412545i
$142$	−8.78215	+	15.2111i	−0.736981	+	1.27649i
$143$	0.326766	+	2.17181i	0.0273256	+	0.181616i
$144$	13.7007	−	5.64676i	1.14172	−	0.470563i
$145$	5.03395	+	8.71905i	0.418046	+	0.724078i
$146$	−4.67760			−0.387121
$147$	5.78553	+	1.96961i	0.477183	+	0.162450i
$148$	−1.03001	−	1.78403i	−0.0846665	−	0.146647i
$149$	−0.266639			−0.0218440			−0.0109220	−	0.999940i	$-0.503477\pi$
$149$	−0.266639			−0.0218440			−0.0109220	+	0.999940i	$0.503477\pi$
$150$	20.6565	+	7.03222i	1.68660	+	0.574179i
$151$	0.0207394	−	0.0359218i	0.00168775	−	0.00292327i	−0.865180	−	0.501461i	$-0.832796\pi$
$151$	0.0207394	−	0.0359218i	0.00168775	−	0.00292327i	0.866868	+	0.498538i	$0.166129\pi$
$152$	1.19258	−	2.06561i	0.0967309	−	0.167543i
$153$	−0.958497	+	7.18274i	−0.0774899	+	0.580690i
$154$	−1.78044	−	3.08381i	−0.143472	−	0.248500i
$155$	16.0022	−	27.7166i	1.28533	−	2.22625i
$156$	7.32220	−	2.62980i	0.586245	−	0.210553i
$157$	−4.05553	−	7.02438i	−0.323666	−	0.560607i	0.657575	−	0.753389i	$-0.271582\pi$
$157$	−4.05553	−	7.02438i	−0.323666	−	0.560607i	−0.981242	+	0.192782i	$0.938249\pi$
$158$	−4.57140	+	7.91790i	−0.363681	+	0.629914i
$159$	−3.17476	−	16.0344i	−0.251775	−	1.27161i
$160$	−10.7038	−	18.5395i	−0.846210	−	1.46568i
$161$	0.527108			0.0415419
$162$	11.5057	−	11.4250i	0.903975	−	0.897629i
$163$	7.27273	−	12.5967i	0.569644	−	0.986653i	−0.426957	−	0.904272i	$-0.640414\pi$
$163$	7.27273	−	12.5967i	0.569644	−	0.986653i	0.996601	−	0.0823808i	$-0.0262524\pi$
$164$	5.12184	−	8.87128i	0.399948	−	0.692731i
$165$	2.74910	−	2.40662i	0.214017	−	0.187355i
$166$	−7.46110	+	12.9230i	−0.579093	+	1.00302i
$167$	6.44049	−	11.1553i	0.498380	−	0.863220i	−0.501618	−	0.865089i	$-0.667262\pi$
$167$	6.44049	−	11.1553i	0.498380	−	0.863220i	0.999998	+	0.00186931i	$0.000595021\pi$
$168$	5.74570	−	5.02990i	0.443291	−	0.388065i
$169$	−12.4245	+	3.82532i	−0.955727	+	0.294255i
$170$	15.0703			1.15584
$171$	0.696575	−	5.21996i	0.0532684	−	0.399180i
$172$	7.47837	+	12.9529i	0.570220	+	0.987650i
$173$	0.311275	+	0.539144i	0.0236658	+	0.0409903i	0.877616	−	0.479365i	$-0.159133\pi$
$173$	0.311275	+	0.539144i	0.0236658	+	0.0409903i	−0.853950	+	0.520355i	$0.825800\pi$
$174$	−1.76202	−	8.89923i	−0.133579	−	0.674649i
$175$	22.6898			1.71518
$176$	−3.00885			−0.226800
$177$	2.78021	+	14.0417i	0.208973	+	1.05544i
$178$	8.89905	+	15.4136i	0.667012	+	1.15530i
$179$	0.386554	+	0.669532i	0.0288924	+	0.0500431i	0.880110	−	0.474770i	$-0.157469\pi$
$179$	0.386554	+	0.669532i	0.0288924	+	0.0500431i	−0.851218	+	0.524813i	$0.824135\pi$
$180$	−10.2545	−	7.89726i	−0.764323	−	0.588627i
$181$	4.86050			0.361278			0.180639	−	0.983549i	$-0.442183\pi$
$181$	4.86050			0.361278			0.180639	+	0.983549i	$0.442183\pi$
$182$	16.4824	−	13.1373i	1.22176	−	0.973798i
$183$	−12.9389	+	11.3270i	−0.956474	+	0.837316i
$184$	0.110363	−	0.191154i	0.00813607	−	0.0140921i
$185$	2.86317	−	4.95915i	0.210504	−	0.364604i
$186$	−21.6987	+	18.9955i	−1.59103	+	1.39282i
$187$	0.735669	−	1.27422i	0.0537974	−	0.0931799i
$188$	5.46664	−	9.46850i	0.398696	−	0.690561i
$189$	7.49705	−	15.1018i	0.545330	−	1.09850i
$190$	−10.9522			−0.794553
$191$	2.27084	+	3.93322i	0.164312	+	0.284598i	0.936411	−	0.350905i	$-0.114126\pi$
$191$	2.27084	+	3.93322i	0.164312	+	0.284598i	−0.772098	+	0.635503i	$0.780793\pi$
$192$	0.423183	+	2.13732i	0.0305406	+	0.154248i
$193$	−10.4268	+	18.0597i	−0.750534	+	1.29996i	0.197030	+	0.980397i	$0.436870\pi$
$193$	−10.4268	+	18.0597i	−0.750534	+	1.29996i	−0.947564	+	0.319566i	$0.896463\pi$
$194$	6.73633	+	11.6677i	0.483640	+	0.837689i
$195$	16.5077	+	13.9718i	1.18214	+	1.00054i
$196$	−2.19796	+	3.80697i	−0.156997	+	0.271927i
$197$	5.56079	+	9.63157i	0.396190	+	0.686221i	0.993252	−	0.115974i	$-0.0369989\pi$
$197$	5.56079	+	9.63157i	0.396190	+	0.686221i	−0.597062	+	0.802195i	$0.703666\pi$
$198$	−3.04387	+	1.25453i	−0.216318	+	0.0891559i
$199$	5.04128	−	8.73176i	0.357367	−	0.618978i	−0.630153	−	0.776471i	$-0.717008\pi$
$199$	5.04128	−	8.73176i	0.357367	−	0.618978i	0.987520	+	0.157493i	$0.0503412\pi$
$200$	4.75066	−	8.22839i	0.335922	−	0.581835i
$201$	3.76339	+	1.28120i	0.265449	+	0.0903686i
$202$	−14.2259			−1.00093
$203$	−4.71665	−	8.16948i	−0.331044	−	0.573385i
$204$	−4.93406	−	1.67974i	−0.345454	−	0.117605i
$205$	28.4748			1.98876
$206$	0.332383	+	0.575705i	0.0231582	+	0.0401113i
$207$	0.0644621	−	0.483063i	0.00448042	−	0.0335752i
$208$	−2.64982	−	17.6117i	−0.183732	−	1.22115i
$209$	−0.534638	+	0.926020i	−0.0369817	+	0.0640541i
$210$	−33.1935	−	11.3003i	−2.29057	−	0.779794i
$211$	10.2101	−	17.6844i	0.702891	−	1.21744i	−0.264556	−	0.964370i	$-0.585225\pi$
$211$	10.2101	−	17.6844i	0.702891	−	1.21744i	0.967447	−	0.253073i	$-0.0814412\pi$
$212$	11.7570			0.807474
$213$	15.9852	+	5.44194i	1.09529	+	0.372875i
$214$	3.41853	+	5.92107i	0.233686	+	0.404756i
$215$	−20.7879	+	36.0057i	−1.41772	+	2.45557i
$216$	−3.90694	−	5.88072i	−0.265834	−	0.400133i
$217$	−14.9936	+	25.9696i	−1.01783	+	1.76293i
$218$	−23.0990			−1.56446
$219$	0.873434	+	4.41135i	0.0590212	+	0.298091i
$220$	1.31400	+	2.27591i	0.0885896	+	0.153442i
$221$	8.10624	+	3.18391i	0.545285	+	0.214173i
$222$	−3.88240	+	3.39873i	−0.260570	+	0.228108i
$223$	−24.6959			−1.65376			−0.826882	−	0.562376i	$-0.809887\pi$
$223$	−24.6959			−1.65376			−0.826882	+	0.562376i	$0.809887\pi$
$224$	10.0291	+	17.3710i	0.670100	+	1.16065i
$225$	2.77482	−	20.7938i	0.184988	−	1.38625i
$226$	10.7666			0.716182
$227$	6.60416	+	11.4387i	0.438333	+	0.759215i	0.997561	−	0.0697986i	$-0.0222356\pi$
$227$	6.60416	+	11.4387i	0.438333	+	0.759215i	−0.559228	+	0.829014i	$0.688902\pi$
$228$	3.58577	+	1.22073i	0.237473	+	0.0808445i
$229$	−11.4750	−	19.8753i	−0.758291	−	1.31340i	−0.943722	−	0.330741i	$-0.892701\pi$
$229$	−11.4750	−	19.8753i	−0.758291	−	1.31340i	0.185431	−	0.982657i	$-0.440632\pi$
$230$	−1.01353			−0.0668301
$231$	−2.57582	+	2.25493i	−0.169477	+	0.148363i
$232$	−3.95019			−0.259343
$233$	−6.61682			−0.433482			−0.216741	−	0.976229i	$-0.569543\pi$
$233$	−6.61682			−0.433482			−0.216741	+	0.976229i	$0.569543\pi$
$234$	−10.0238	−	16.7118i	−0.655277	−	1.09248i
$235$	30.3917			1.98253
$236$	−10.2959			−0.670204
$237$	8.32081	+	2.83271i	0.540495	+	0.184004i
$238$	−14.1204			−0.915291
$239$	−4.61520	−	7.99376i	−0.298532	−	0.517073i	0.677268	−	0.735736i	$-0.263164\pi$
$239$	−4.61520	−	7.99376i	−0.298532	−	0.517073i	−0.975800	+	0.218663i	$0.929830\pi$
$240$	−22.2930	+	19.5158i	−1.43901	+	1.25974i
$241$	−9.18399	−	15.9071i	−0.591593	−	1.02467i	−0.994018	−	0.109216i	$-0.965166\pi$
$241$	−9.18399	−	15.9071i	−0.591593	−	1.02467i	0.402425	−	0.915453i	$-0.368167\pi$
$242$	−19.1493			−1.23096
$243$	−12.9231	−	8.71746i	−0.829016	−	0.559225i
$244$	−6.18447	−	10.7118i	−0.395920	−	0.685753i
$245$	−12.2195			−0.780675
$246$	−24.2891	−	8.26891i	−1.54862	−	0.527206i
$247$	−5.89110	−	2.31387i	−0.374842	−	0.147228i
$248$	6.27854	+	10.8748i	0.398688	+	0.690548i
$249$	13.5806	+	4.62333i	0.860636	+	0.292992i
$250$	−12.4327			−0.786314
$251$	5.22170	−	9.04424i	0.329591	−	0.570868i	−0.652840	−	0.757496i	$-0.726423\pi$
$251$	5.22170	−	9.04424i	0.329591	−	0.570868i	0.982431	+	0.186628i	$0.0597560\pi$
$252$	9.60812	+	7.39949i	0.605255	+	0.466124i
$253$	−0.0494762	+	0.0856952i	−0.00311054	+	0.00538761i
$254$	−0.578664	−	1.00228i	−0.0363086	−	0.0628884i
$255$	−2.81404	−	14.2125i	−0.176222	−	0.890022i
$256$	20.7070			1.29419
$257$	13.8363	−	23.9652i	0.863087	−	1.49491i	−0.00584674	−	0.999983i	$-0.501861\pi$
$257$	13.8363	−	23.9652i	0.863087	−	1.49491i	0.868934	−	0.494928i	$-0.164806\pi$
$258$	28.1881	−	24.6764i	1.75491	−	1.53628i
$259$	−2.68270	+	4.64657i	−0.166695	+	0.288724i
$260$	−12.1643	+	9.69554i	−0.754401	+	0.601292i
$261$	−8.06366	+	3.32345i	−0.499128	+	0.205717i
$262$	13.5774	+	23.5168i	0.838816	+	1.45287i
$263$	−24.9455			−1.53820			−0.769102	−	0.639127i	$-0.779296\pi$
$263$	−24.9455			−1.53820			−0.769102	+	0.639127i	$0.779296\pi$
$264$	0.278431	+	1.40624i	0.0171363	+	0.0865481i
$265$	16.3407	+	28.3029i	1.00380	+	1.73863i
$266$	10.2618			0.629193
$267$	12.8746	−	11.2707i	0.787911	−	0.689753i
$268$	−1.42973	+	2.47637i	−0.0873349	+	0.151269i
$269$	9.61561	−	16.6547i	0.586274	−	1.01546i	−0.408441	−	0.912785i	$-0.633927\pi$
$269$	9.61561	−	16.6547i	0.586274	−	1.01546i	0.994715	−	0.102672i	$-0.0327393\pi$
$270$	−14.4154	+	29.0379i	−0.877294	+	1.76719i
$271$	−1.80591	−	3.12793i	−0.109701	−	0.190008i	0.805948	−	0.591986i	$-0.201656\pi$
$271$	−1.80591	−	3.12793i	−0.109701	−	0.190008i	−0.915649	+	0.401978i	$0.868323\pi$
$272$	−5.96569	+	10.3329i	−0.361723	+	0.626523i
$273$	−15.4672	−	13.0912i	−0.936117	−	0.792314i
$274$	3.83917	+	6.64963i	0.231933	+	0.401719i
$275$	−2.12974	+	3.68882i	−0.128428	+	0.222444i
$276$	0.331832	+	0.112968i	0.0199739	+	0.00679986i
$277$	11.4071	+	19.7577i	0.685388	+	1.18713i	0.973315	+	0.229474i	$0.0737007\pi$
$277$	11.4071	+	19.7577i	0.685388	+	1.18713i	−0.287927	+	0.957652i	$0.592966\pi$
$278$	−1.30131			−0.0780474
$279$	21.9660	+	16.9166i	1.31507	+	1.01277i
$280$	−7.63398	+	13.2224i	−0.456218	+	0.790192i
$281$	−5.17902	+	8.97032i	−0.308954	+	0.535125i	−0.978134	−	0.207976i	$-0.933312\pi$
$281$	−5.17902	+	8.97032i	−0.308954	+	0.535125i	0.669180	+	0.743101i	$0.266646\pi$
$282$	−25.9243	−	8.82557i	−1.54377	−	0.525555i
$283$	3.44245	−	5.96250i	0.204633	−	0.354434i	−0.745383	−	0.666636i	$-0.767733\pi$
$283$	3.44245	−	5.96250i	0.204633	−	0.354434i	0.950016	+	0.312202i	$0.101067\pi$
$284$	−6.07286	+	10.5185i	−0.360358	+	0.624158i
$285$	2.04506	+	10.3288i	0.121139	+	0.611823i
$286$	0.588707	+	3.91276i	0.0348110	+	0.231367i
$287$	−26.6800			−1.57487
$288$	17.1460	−	7.06674i	1.01034	−	0.416412i
$289$	5.58275	+	9.66961i	0.328397	+	0.568801i
$290$	9.06924	+	15.7084i	0.532564	+	0.922428i
$291$	9.74568	−	8.53156i	0.571302	−	0.500129i
$292$	−3.23456			−0.189288
$293$	5.24190			0.306235			0.153118	−	0.988208i	$-0.451069\pi$
$293$	5.24190			0.306235			0.153118	+	0.988208i	$0.451069\pi$
$294$	10.4233	+	3.54847i	0.607899	+	0.206951i
$295$	−14.3099	−	24.7855i	−0.833156	−	1.44307i
$296$	1.12338	+	1.94575i	0.0652950	+	0.113094i
$297$	1.75150	+	2.63635i	0.101632	+	0.152977i
$298$	−0.480382			−0.0278278
$299$	−0.545171	−	0.214129i	−0.0315281	−	0.0123834i
$300$	14.2840	+	4.86279i	0.824686	+	0.280753i
$301$	19.4776	−	33.7362i	1.12267	−	1.94452i
$302$	0.0373645	−	0.0647172i	0.00215009	−	0.00372406i
$303$	2.65636	+	13.4162i	0.152604	+	0.770738i
$304$	4.33549	−	7.50929i	0.248657	−	0.430687i
$305$	17.1912	−	29.7760i	0.984366	−	1.70497i
$306$	−1.72684	+	12.9405i	−0.0987170	+	0.739761i
$307$	6.73227			0.384231			0.192115	−	0.981372i	$-0.438465\pi$
$307$	6.73227			0.384231			0.192115	+	0.981372i	$0.438465\pi$
$308$	−1.23117	−	2.13246i	−0.0701526	−	0.121508i
$309$	0.480870	−	0.420964i	0.0273558	−	0.0239478i
$310$	28.8298	−	49.9347i	1.63742	−	2.83610i
$311$	15.5454	+	26.9254i	0.881499	+	1.52680i	0.849674	+	0.527308i	$0.176799\pi$
$311$	15.5454	+	26.9254i	0.881499	+	1.52680i	0.0318249	+	0.999493i	$0.489868\pi$
$312$	−7.98592	+	2.86818i	−0.452114	+	0.162379i
$313$	7.65892	−	13.2656i	0.432908	−	0.749818i	−0.564214	−	0.825628i	$-0.690821\pi$
$313$	7.65892	−	13.2656i	0.432908	−	0.749818i	0.997122	+	0.0758098i	$0.0241542\pi$
$314$	−7.30650	−	12.6552i	−0.412330	−	0.714176i
$315$	−4.45894	+	33.4142i	−0.251233	+	1.88268i
$316$	−3.16113	+	5.47523i	−0.177827	+	0.308006i
$317$	−1.99756	+	3.45988i	−0.112194	+	0.194326i	−0.916655	−	0.399680i	$-0.869121\pi$
$317$	−1.99756	+	3.45988i	−0.112194	+	0.194326i	0.804460	+	0.594006i	$0.202455\pi$
$318$	−5.71970	−	28.8878i	−0.320745	−	1.61995i
$319$	1.77089			0.0991506
$320$	−2.17815	−	3.77266i	−0.121762	−	0.210898i
$321$	4.94571	−	4.32957i	0.276043	−	0.241653i
$322$	0.949645			0.0529217
$323$	2.12007	+	3.67207i	0.117964	+	0.204319i
$324$	7.95621	−	7.90036i	0.442012	−	0.438909i
$325$	−23.4673	−	9.21734i	−1.30173	−	0.511286i
$326$	13.1027	−	22.6945i	0.725690	−	1.25693i
$327$	4.31321	+	21.7842i	0.238521	+	1.20467i
$328$	−5.58611	+	9.67543i	−0.308441	+	0.534236i
$329$	−28.4761			−1.56994
$330$	4.95282	−	4.33580i	0.272644	−	0.238678i
$331$	−1.93579	−	3.35288i	−0.106400	−	0.184291i	0.807909	−	0.589307i	$-0.200599\pi$
$331$	−1.93579	−	3.35288i	−0.106400	−	0.184291i	−0.914309	+	0.405016i	$0.867266\pi$
$332$	−5.15935	+	8.93626i	−0.283156	+	0.490441i
$333$	3.93023	+	3.02678i	0.215375	+	0.165867i
$334$	11.6033	−	20.0975i	0.634904	−	1.09969i
$335$	−7.94858			−0.434277
$336$	20.8879	−	18.2857i	1.13953	−	0.997565i
$337$	2.64476	+	4.58086i	0.144069	+	0.249536i	0.929025	−	0.370016i	$-0.120648\pi$
$337$	2.64476	+	4.58086i	0.144069	+	0.249536i	−0.784956	+	0.619552i	$0.787314\pi$
$338$	−22.3841	+	6.89175i	−1.21753	+	0.374862i
$339$	−2.01041	−	10.1537i	−0.109191	−	0.551475i
$340$	10.4211			0.565165
$341$	−2.81470	−	4.87519i	−0.152424	−	0.264007i
$342$	1.25496	−	9.40436i	0.0678605	−	0.508530i
$343$	−11.2641			−0.608204
$344$	−8.15625	−	14.1270i	−0.439755	−	0.761678i
$345$	0.189253	+	0.955838i	0.0101891	+	0.0514606i
$346$	0.560797	+	0.971330i	0.0301487	+	0.0522190i
$347$	−19.0170			−1.02089			−0.510444	−	0.859911i	$-0.670519\pi$
$347$	−19.0170			−1.02089			−0.510444	+	0.859911i	$0.670519\pi$
$348$	−1.21844	−	6.15382i	−0.0653152	−	0.329879i
$349$	−14.5404			−0.778331			−0.389165	−	0.921168i	$-0.627237\pi$
$349$	−14.5404			−0.778331			−0.389165	+	0.921168i	$0.627237\pi$
$350$	40.8782			2.18503
$351$	−13.8888	+	12.5738i	−0.741331	+	0.671140i
$352$	−3.76548			−0.200701
$353$	15.8421			0.843189			0.421595	−	0.906784i	$-0.361471\pi$
$353$	15.8421			0.843189			0.421595	+	0.906784i	$0.361471\pi$
$354$	5.00887	+	25.2977i	0.266219	+	1.34456i
$355$	−33.7619			−1.79190
$356$	6.15370	+	10.6585i	0.326146	+	0.564901i
$357$	2.63666	+	13.3167i	0.139547	+	0.704793i
$358$	0.696422	+	1.20624i	0.0368071	+	0.0637517i
$359$	15.2227			0.803426			0.401713	−	0.915766i	$-0.368415\pi$
$359$	15.2227			0.803426			0.401713	+	0.915766i	$0.368415\pi$
$360$	11.1840	+	8.61312i	0.589448	+	0.453951i
$361$	7.95927	+	13.7859i	0.418909	+	0.725571i
$362$	8.75676			0.460245
$363$	3.57569	+	18.0593i	0.187675	+	0.947868i
$364$	11.3976	−	9.08442i	0.597397	−	0.476153i
$365$	−4.49562	−	7.78664i	−0.235312	−	0.407571i
$366$	−23.3110	+	20.4069i	−1.21849	+	1.06669i
$367$	2.17431			0.113498			0.0567491	−	0.998388i	$-0.481926\pi$
$367$	2.17431			0.113498			0.0567491	+	0.998388i	$0.481926\pi$
$368$	0.401213	−	0.694921i	0.0209147	−	0.0362253i
$369$	−3.26280	+	24.4506i	−0.169855	+	1.27285i
$370$	5.15832	−	8.93448i	0.268168	−	0.464481i
$371$	−15.3107	−	26.5190i	−0.794893	−	1.37680i
$372$	−15.0047	+	13.1354i	−0.777956	+	0.681038i
$373$	2.48666			0.128754			0.0643771	−	0.997926i	$-0.479494\pi$
$373$	2.48666			0.128754			0.0643771	+	0.997926i	$0.479494\pi$
$374$	1.32539	−	2.29565i	0.0685344	−	0.118705i
$375$	2.32153	+	11.7250i	0.119883	+	0.605479i
$376$	−5.96217	+	10.3268i	−0.307475	+	0.532563i
$377$	1.55957	+	10.3655i	0.0803222	+	0.533851i
$378$	13.5068	−	27.2077i	0.694715	−	1.39941i
$379$	−9.69440	−	16.7912i	−0.497968	−	0.862505i	0.502030	−	0.864850i	$-0.332587\pi$
$379$	−9.69440	−	16.7912i	−0.497968	−	0.862505i	−0.999997	+	0.00234514i	$0.999254\pi$
$380$	−7.57342			−0.388508
$381$	−0.837173	+	0.732878i	−0.0428897	+	0.0375465i
$382$	4.09119	+	7.08614i	0.209323	+	0.362559i
$383$	−14.0515			−0.717997			−0.358998	−	0.933338i	$-0.616882\pi$
$383$	−14.0515			−0.717997			−0.358998	+	0.933338i	$0.616882\pi$
$384$	−3.39678	−	17.1557i	−0.173341	−	0.875473i
$385$	3.42234	−	5.92767i	0.174419	−	0.302102i
$386$	−18.7850	+	32.5366i	−0.956131	+	1.65607i
$387$	−28.5353	−	21.9758i	−1.45053	−	1.11709i
$388$	4.65817	+	8.06819i	0.236483	+	0.409600i
$389$	−7.37820	+	12.7794i	−0.374090	+	0.647943i	−0.990190	−	0.139725i	$-0.955378\pi$
$389$	−7.37820	+	12.7794i	−0.374090	+	0.647943i	0.616101	+	0.787668i	$0.288711\pi$
$390$	29.7405	+	25.1719i	1.50597	+	1.27463i
$391$	0.196194	+	0.339819i	0.00992198	+	0.0171854i
$392$	2.39719	−	4.15206i	0.121076	−	0.209711i
$393$	19.6429	−	17.1958i	0.990855	−	0.867414i
$394$	10.0184	+	17.3524i	0.504720	+	0.874201i
$395$	−17.5742			−0.884255
$396$	−2.10483	+	0.867512i	−0.105772	+	0.0435941i
$397$	−8.04573	+	13.9356i	−0.403804	+	0.699409i	−0.994181	−	0.107719i	$-0.965645\pi$
$397$	−8.04573	+	13.9356i	−0.403804	+	0.699409i	0.590378	+	0.807127i	$0.298979\pi$
$398$	9.08245	−	15.7313i	0.455262	−	0.788537i
$399$	−1.91616	−	9.67772i	−0.0959281	−	0.484492i
$400$	17.2705	−	29.9134i	0.863526	−	1.49567i
$401$	17.0931	−	29.6062i	0.853590	−	1.47846i	−0.0243566	−	0.999703i	$-0.507754\pi$
$401$	17.0931	−	29.6062i	0.853590	−	1.47846i	0.877947	−	0.478758i	$-0.158913\pi$
$402$	6.78018	+	2.30822i	0.338165	+	0.115124i
$403$	26.0571	−	20.7687i	1.29800	−	1.03456i
$404$	−9.83722			−0.489420
$405$	30.0768	+	8.17271i	1.49453	+	0.406105i
$406$	−8.49759	−	14.7183i	−0.421728	−	0.730455i
$407$	−0.503615	−	0.872286i	−0.0249633	−	0.0432376i
$408$	5.38131	+	1.83200i	0.266415	+	0.0906973i
$409$	−34.7653			−1.71903			−0.859516	−	0.511108i	$-0.829235\pi$
$409$	−34.7653			−1.71903			−0.859516	+	0.511108i	$0.829235\pi$
$410$	51.3006			2.53355
$411$	5.55426	−	4.86231i	0.273971	−	0.239840i
$412$	0.229843	+	0.398100i	0.0113236	+	0.0196130i
$413$	13.4080	+	23.2233i	0.659762	+	1.14274i
$414$	0.116136	−	0.870294i	0.00570777	−	0.0427726i
$415$	−28.6833			−1.40801
$416$	−3.31616	−	22.0404i	−0.162588	−	1.08062i
$417$	0.242990	+	1.22724i	0.0118993	+	0.0600982i
$418$	−0.963211	+	1.66833i	−0.0471122	+	0.0816007i
$419$	1.41535	−	2.45145i	0.0691442	−	0.119761i	−0.829381	−	0.558684i	$-0.811306\pi$
$419$	1.41535	−	2.45145i	0.0691442	−	0.119761i	0.898525	+	0.438923i	$0.144640\pi$
$420$	−22.9533	−	7.81416i	−1.12001	−	0.381292i
$421$	7.17902	−	12.4344i	0.349884	−	0.606017i	−0.636344	−	0.771405i	$-0.719554\pi$
$421$	7.17902	−	12.4344i	0.349884	−	0.606017i	0.986229	+	0.165388i	$0.0528876\pi$
$422$	18.3946	−	31.8605i	0.895437	−	1.55094i
$423$	−3.48245	+	26.0966i	−0.169323	+	1.26886i
$424$	−12.8227			−0.622726
$425$	8.44534	+	14.6278i	0.409659	+	0.709551i
$426$	28.7991	+	9.80427i	1.39532	+	0.475019i
$427$	−16.1076	+	27.8992i	−0.779503	+	1.35014i
$428$	2.36392	+	4.09443i	0.114264	+	0.197912i
$429$	3.58012	−	1.28582i	0.172850	−	0.0620798i
$430$	−37.4518	+	64.8685i	−1.80609	+	3.12823i
$431$	−14.2820	−	24.7371i	−0.687937	−	1.19154i	−0.972504	−	0.232886i	$-0.925183\pi$
$431$	−14.2820	−	24.7371i	−0.687937	−	1.19154i	0.284567	−	0.958656i	$-0.408150\pi$
$432$	−14.2033	−	21.3787i	−0.683355	−	1.02859i
$433$	5.26413	−	9.11774i	0.252978	−	0.438171i	−0.711366	−	0.702821i	$-0.751923\pi$
$433$	5.26413	−	9.11774i	0.252978	−	0.438171i	0.964344	+	0.264651i	$0.0852566\pi$
$434$	−27.0126	+	46.7872i	−1.29665	+	2.24586i
$435$	13.1208	−	11.4862i	0.629093	−	0.550721i
$436$	−15.9730			−0.764967
$437$	−0.142582	−	0.246959i	−0.00682061	−	0.0118136i
$438$	1.57359	+	7.94755i	0.0751892	+	0.379749i
$439$	23.8521			1.13840			0.569199	−	0.822200i	$-0.307254\pi$
$439$	23.8521			1.13840			0.569199	+	0.822200i	$0.307254\pi$
$440$	−1.43310	−	2.48221i	−0.0683206	−	0.118335i
$441$	1.40018	−	10.4926i	0.0666752	−	0.499648i
$442$	14.6043	+	5.73619i	0.694657	+	0.272843i
$443$	1.16543	−	2.01859i	0.0553714	−	0.0959061i	−0.837011	−	0.547186i	$-0.815699\pi$
$443$	1.16543	−	2.01859i	0.0553714	−	0.0959061i	0.892382	+	0.451280i	$0.149032\pi$
$444$	−2.68468	+	2.35023i	−0.127410	+	0.111537i
$445$	−17.1057	+	29.6279i	−0.810887	+	1.40450i
$446$	−44.4926			−2.10679
$447$	0.0897003	+	0.453038i	0.00424268	+	0.0214280i
$448$	2.04086	+	3.53487i	0.0964214	+	0.167007i
$449$	11.4132	−	19.7682i	0.538622	−	0.932920i	−0.460357	−	0.887734i	$-0.652279\pi$
$449$	11.4132	−	19.7682i	0.538622	−	0.932920i	0.998979	−	0.0451861i	$-0.0143881\pi$
$450$	4.99916	−	37.4625i	0.235663	−	1.76600i
$451$	2.50427	−	4.33753i	0.117922	−	0.204246i
$452$	7.44509			0.350188
$453$	−0.0680105	−	0.0231532i	−0.00319541	−	0.00108783i
$454$	11.8981	+	20.6082i	0.558408	+	0.967191i
$455$	37.7104	+	14.8116i	1.76789	+	0.694379i
$456$	−3.91080	−	1.33138i	−0.183140	−	0.0623475i
$457$	13.3763			0.625719			0.312859	−	0.949799i	$-0.398713\pi$
$457$	13.3763			0.625719			0.312859	+	0.949799i	$0.398713\pi$
$458$	−20.6736	−	35.8077i	−0.966013	−	1.67318i
$459$	12.5264	−	0.787798i	0.584682	−	0.0367712i
$460$	−0.700856			−0.0326776
$461$	2.02897	+	3.51427i	0.0944983	+	0.163676i	0.909399	−	0.415925i	$-0.136542\pi$
$461$	2.02897	+	3.51427i	0.0944983	+	0.163676i	−0.814901	+	0.579600i	$0.803209\pi$
$462$	−4.64064	+	4.06251i	−0.215902	+	0.189005i
$463$	13.3074	+	23.0491i	0.618447	+	1.07118i	0.989769	+	0.142677i	$0.0455710\pi$
$463$	13.3074	+	23.0491i	0.618447	+	1.07118i	−0.371323	+	0.928504i	$0.621096\pi$
$464$	−14.3605			−0.666669
$465$	−52.4757	−	17.8646i	−2.43350	−	0.828453i
$466$	−11.9210			−0.552228
$467$	2.84428			0.131617			0.0658087	−	0.997832i	$-0.479037\pi$
$467$	2.84428			0.131617			0.0658087	+	0.997832i	$0.479037\pi$
$468$	−6.93147	−	11.5562i	−0.320407	−	0.534186i
$469$	7.44757			0.343897
$470$	54.7541			2.52562
$471$	−10.5706	+	9.25369i	−0.487066	+	0.426388i
$472$	11.2291			0.516863
$473$	3.65648	+	6.33320i	0.168125	+	0.291201i
$474$	14.9909	+	5.10345i	0.688555	+	0.234409i
$475$	−6.13754	−	10.6305i	−0.281610	−	0.487763i
$476$	−9.76428			−0.447545
$477$	−26.1755	+	10.7883i	−1.19849	+	0.493961i
$478$	−8.31481	−	14.4017i	−0.380311	−	0.658717i
$479$	−2.40184			−0.109743			−0.0548715	−	0.998493i	$-0.517475\pi$
$479$	−2.40184			−0.109743			−0.0548715	+	0.998493i	$0.517475\pi$
$480$	−27.8990	+	24.4234i	−1.27341	+	1.11477i
$481$	4.66222	−	3.71600i	0.212579	−	0.169435i
$482$	−16.5460	−	28.6585i	−0.753650	−	1.30536i
$483$	−0.177324	−	0.895591i	−0.00806854	−	0.0407508i
$484$	−13.2417			−0.601898
$485$	−12.9485	+	22.4275i	−0.587962	+	1.01838i
$486$	−23.2824	−	15.7055i	−1.05611	−	0.712417i
$487$	1.82532	−	3.16155i	0.0827133	−	0.143264i	−0.821701	−	0.569918i	$-0.806975\pi$
$487$	1.82532	−	3.16155i	0.0827133	−	0.143264i	0.904414	+	0.426655i	$0.140308\pi$
$488$	6.74506	+	11.6828i	0.305335	+	0.528855i
$489$	−23.8493	−	8.11918i	−1.07850	−	0.367162i
$490$	−22.0148			−0.994529
$491$	−8.22967	+	14.2542i	−0.371400	+	0.643284i	−0.989781	−	0.142595i	$-0.954455\pi$
$491$	−8.22967	+	14.2542i	−0.371400	+	0.643284i	0.618381	+	0.785878i	$0.287789\pi$
$492$	−16.7959	−	5.71795i	−0.757220	−	0.257785i
$493$	3.51117	−	6.08152i	0.158135	−	0.273898i
$494$	−10.6135	−	4.16870i	−0.477524	−	0.187559i
$495$	−5.01383	−	3.86129i	−0.225355	−	0.173552i
$496$	22.8250	+	39.5340i	1.02487	+	1.77513i
$497$	31.6339			1.41897
$498$	24.4670	+	8.32947i	1.09639	+	0.373252i
$499$	5.94059	+	10.2894i	0.265937	+	0.460617i	0.967809	−	0.251687i	$-0.0809853\pi$
$499$	5.94059	+	10.2894i	0.265937	+	0.460617i	−0.701872	+	0.712303i	$0.747652\pi$
$500$	−8.59723			−0.384480
$501$	−21.1202	−	7.19008i	−0.943580	−	0.321229i
$502$	9.40749	−	16.2942i	0.419877	−	0.727248i
$503$	−7.32319	+	12.6841i	−0.326525	+	0.565558i	−0.981820	−	0.189816i	$-0.939211\pi$
$503$	−7.32319	+	12.6841i	−0.326525	+	0.565558i	0.655295	+	0.755373i	$0.272544\pi$
$504$	−10.4791	−	8.07022i	−0.466774	−	0.359476i
$505$	−13.6725	−	23.6814i	−0.608416	−	1.05381i
$506$	−0.0891370	+	0.154390i	−0.00396262	+	0.00686346i
$507$	10.6792	+	19.8231i	0.474279	+	0.880375i
$508$	−0.400147	−	0.693074i	−0.0177536	−	0.0307502i
$509$	−21.5374	+	37.3038i	−0.954627	+	1.65346i	−0.219408	+	0.975633i	$0.570413\pi$
$509$	−21.5374	+	37.3038i	−0.954627	+	1.65346i	−0.735219	+	0.677830i	$0.762921\pi$
$510$	−5.06981	−	25.6055i	−0.224495	−	1.13383i
$511$	4.21226	+	7.29584i	0.186339	+	0.322749i
$512$	17.1118			0.756242
$513$	−9.10340	+	0.572522i	−0.401925	+	0.0252775i
$514$	24.9278	−	43.1762i	1.09952	−	1.90442i
$515$	−0.638904	+	1.10661i	−0.0281535	+	0.0487633i
$516$	19.4921	−	17.0637i	0.858090	−	0.751189i
$517$	2.67286	−	4.62953i	0.117552	−	0.203607i
$518$	−4.83319	+	8.37133i	−0.212358	+	0.367815i
$519$	0.811325	−	0.710250i	0.0356132	−	0.0311765i
$520$	13.2670	−	10.5744i	0.581796	−	0.463718i
$521$	22.2643			0.975418			0.487709	−	0.873006i	$-0.337833\pi$
$521$	22.2643			0.975418			0.487709	+	0.873006i	$0.337833\pi$
$522$	−14.5276	+	5.98759i	−0.635857	+	0.262070i
$523$	−2.18706	−	3.78810i	−0.0956335	−	0.165642i	0.814239	−	0.580529i	$-0.197154\pi$
$523$	−2.18706	−	3.78810i	−0.0956335	−	0.165642i	−0.909873	+	0.414887i	$0.863821\pi$
$524$	9.38880	+	16.2619i	0.410151	+	0.710403i
$525$	−7.63307	−	38.5514i	−0.333135	−	1.68252i
$526$	−44.9421			−1.95957
$527$	−22.3230			−0.972404
$528$	1.01221	+	5.11223i	0.0440507	+	0.222481i
$529$	11.4868	+	19.8957i	0.499426	+	0.865032i
$530$	29.4397	+	50.9910i	1.27878	+	2.21491i
$531$	22.9224	−	9.44753i	0.994750	−	0.409988i
$532$	7.09606			0.307653
$533$	27.5943	+	10.8383i	1.19524	+	0.469459i
$534$	23.1950	−	20.3054i	1.00375	−	0.878700i
$535$	−6.57108	+	11.3814i	−0.284092	+	0.492062i
$536$	1.55933	−	2.70084i	0.0673529	−	0.116659i
$537$	1.00754	−	0.882019i	0.0434785	−	0.0380619i
$538$	17.3236	−	30.0054i	0.746875	−	1.29363i
$539$	−1.07467	+	1.86138i	−0.0462893	+	0.0801755i
$540$	−9.96827	+	20.0798i	−0.428966	+	0.864095i
$541$	28.9397			1.24422			0.622108	−	0.782932i	$-0.286277\pi$
$541$	28.9397			1.24422			0.622108	+	0.782932i	$0.286277\pi$
$542$	−3.25356	−	5.63533i	−0.139752	−	0.242058i
$543$	−1.63512	−	8.25832i	−0.0701699	−	0.354398i
$544$	−7.46588	+	12.9313i	−0.320097	+	0.554424i
$545$	−22.2004	−	38.4522i	−0.950959	−	1.64711i
$546$	−27.8659	−	23.5853i	−1.19255	−	1.00936i
$547$	7.33819	−	12.7101i	0.313758	−	0.543445i	−0.665414	−	0.746474i	$-0.731745\pi$
$547$	7.33819	−	12.7101i	0.313758	−	0.543445i	0.979173	+	0.203029i	$0.0650785\pi$
$548$	2.65479	+	4.59823i	0.113407	+	0.196426i
$549$	23.5981	+	18.1736i	1.00714	+	0.775630i
$550$	−3.83697	+	6.64583i	−0.163609	+	0.283379i
$551$	−2.55169	+	4.41966i	−0.108706	+	0.188284i
$552$	−0.361911	−	0.123208i	−0.0154040	−	0.00524407i
$553$	16.4665			0.700227
$554$	20.5513	+	35.5958i	0.873139	+	1.51232i
$555$	−9.38912	−	3.19640i	−0.398546	−	0.135680i
$556$	−0.899857			−0.0381624
$557$	−17.0404	−	29.5149i	−0.722026	−	1.25059i	−0.960187	−	0.279359i	$-0.909878\pi$
$557$	−17.0404	−	29.5149i	−0.722026	−	1.25059i	0.238161	−	0.971226i	$-0.423455\pi$
$558$	39.5742	+	30.4773i	1.67531	+	1.29021i
$559$	−33.8499	+	26.9799i	−1.43170	+	1.14113i
$560$	−27.7525	+	48.0688i	−1.17276	+	2.03128i
$561$	−2.41246	−	0.821291i	−0.101854	−	0.0346749i
$562$	−9.33060	+	16.1611i	−0.393588	+	0.681714i
$563$	6.25127			0.263460			0.131730	−	0.991286i	$-0.457947\pi$
$563$	6.25127			0.263460			0.131730	+	0.991286i	$0.457947\pi$
$564$	−17.9266	−	6.10289i	−0.754848	−	0.256978i
$565$	10.3477	+	17.9228i	0.435331	+	0.754016i
$566$	6.20198	−	10.7421i	0.260688	−	0.451526i
$567$	−28.1811	−	7.65758i	−1.18349	−	0.321588i
$568$	6.62334	−	11.4720i	0.277909	−	0.481353i
$569$	3.90098			0.163538			0.0817688	−	0.996651i	$-0.473943\pi$
$569$	3.90098			0.163538			0.0817688	+	0.996651i	$0.473943\pi$
$570$	3.68442	+	18.6084i	0.154323	+	0.779422i
$571$	5.21913	+	9.03980i	0.218414	+	0.378304i	0.954323	−	0.298776i	$-0.0965784\pi$
$571$	5.21913	+	9.03980i	0.218414	+	0.378304i	−0.735909	+	0.677080i	$0.763245\pi$
$572$	0.407091	+	2.70568i	0.0170213	+	0.113130i
$573$	5.91886	−	5.18149i	0.247264	−	0.216460i
$574$	−48.0670			−2.00628
$575$	−0.567977	−	0.983766i	−0.0236863	−	0.0410259i
$576$	3.48908	−	1.43803i	0.145378	−	0.0599180i
$577$	26.1767			1.08975			0.544874	−	0.838518i	$-0.316577\pi$
$577$	26.1767			1.08975			0.544874	+	0.838518i	$0.316577\pi$
$578$	10.0580	+	17.4209i	0.418357	+	0.724615i
$579$	34.1923	+	11.6403i	1.42098	+	0.483754i
$580$	6.27138	+	10.8624i	0.260405	+	0.451035i
$581$	26.8754			1.11498
$582$	17.5580	−	15.3706i	0.727801	−	0.637131i
$583$	5.74847			0.238077
$584$	3.52776			0.145980
$585$	18.1857	−	32.7479i	0.751887	−	1.35396i
$586$	9.44390			0.390124
$587$	−8.96875			−0.370180			−0.185090	−	0.982722i	$-0.559258\pi$
$587$	−8.96875			−0.370180			−0.185090	+	0.982722i	$0.559258\pi$
$588$	7.20772	+	2.45377i	0.297241	+	0.101192i
$589$	16.2229			0.668454
$590$	−25.7810	−	44.6540i	−1.06139	−	1.83837i
$591$	14.4940	−	12.6883i	0.596202	−	0.521928i
$592$	4.08392	+	7.07356i	0.167848	+	0.290721i
$593$	4.06097			0.166764			0.0833820	−	0.996518i	$-0.473428\pi$
$593$	4.06097			0.166764			0.0833820	+	0.996518i	$0.473428\pi$
$594$	3.15553	+	4.74969i	0.129473	+	0.194882i
$595$	−13.5711	−	23.5058i	−0.556360	−	0.963644i
$596$	−0.332184			−0.0136068
$597$	−16.5318	−	5.62802i	−0.676601	−	0.230340i
$598$	−0.982189	−	0.385778i	−0.0401647	−	0.0157756i
$599$	−10.5462	−	18.2666i	−0.430907	−	0.746352i	0.566045	−	0.824374i	$-0.308473\pi$
$599$	−10.5462	−	18.2666i	−0.430907	−	0.746352i	−0.996952	+	0.0780222i	$0.975140\pi$
$600$	−15.5788	−	5.30358i	−0.636000	−	0.216518i
$601$	−23.7038			−0.966897			−0.483448	−	0.875373i	$-0.660616\pi$
$601$	−23.7038			−0.966897			−0.483448	+	0.875373i	$0.660616\pi$
$602$	35.0912	−	60.7797i	1.43021	−	2.47720i
$603$	0.910793	−	6.82526i	0.0370904	−	0.277946i
$604$	0.0258376	−	0.0447520i	0.00105132	−	0.00182093i
$605$	−18.4043	−	31.8772i	−0.748242	−	1.29599i
$606$	4.78574	+	24.1708i	0.194407	+	0.981870i
$607$	37.4366			1.51950			0.759752	−	0.650213i	$-0.225321\pi$
$607$	37.4366			1.51950			0.759752	+	0.650213i	$0.225321\pi$
$608$	5.42573	−	9.39764i	0.220042	−	0.381125i
$609$	−12.2938	+	10.7622i	−0.498168	+	0.436107i
$610$	30.9719	−	53.6450i	1.25402	−	2.17202i
$611$	29.4519	+	11.5679i	1.19150	+	0.467988i
$612$	−1.19411	+	8.94838i	−0.0482691	+	0.361717i
$613$	−14.7555	−	25.5572i	−0.595967	−	1.03225i	−0.993410	−	0.114618i	$-0.963435\pi$
$613$	−14.7555	−	25.5572i	−0.595967	−	1.03225i	0.397442	−	0.917627i	$-0.369898\pi$
$614$	12.1290			0.489485
$615$	−9.57920	−	48.3805i	−0.386271	−	1.95089i
$616$	1.34277	+	2.32575i	0.0541019	+	0.0937073i
$617$	5.94999			0.239537			0.119769	−	0.992802i	$-0.461785\pi$
$617$	5.94999			0.239537			0.119769	+	0.992802i	$0.461785\pi$
$618$	0.866344	−	0.758415i	0.0348495	−	0.0305079i
$619$	−9.09862	+	15.7593i	−0.365705	+	0.633419i	−0.988889	−	0.148656i	$-0.952505\pi$
$619$	−9.09862	+	15.7593i	−0.365705	+	0.633419i	0.623184	+	0.782075i	$0.285839\pi$
$620$	19.9358	−	34.5298i	0.800642	−	1.38675i
$621$	−0.842442	+	0.0529820i	−0.0338060	+	0.00212609i
$622$	28.0068	+	48.5093i	1.12297	+	1.94504i
$623$	16.0275	−	27.7604i	0.642128	−	1.11220i
$624$	−29.0320	+	10.4270i	−1.16221	+	0.417413i
$625$	5.53275	+	9.58301i	0.221310	+	0.383320i
$626$	13.7984	−	23.8996i	0.551496	−	0.955220i
$627$	1.75323	+	0.596862i	0.0700171	+	0.0238364i
$628$	−5.05245	−	8.75110i	−0.201615	−	0.349207i
$629$	−3.99410			−0.159255
$630$	−8.03330	+	60.1996i	−0.320054	+	2.39841i
$631$	−21.6580	+	37.5128i	−0.862192	+	1.49336i	0.00761652	+	0.999971i	$0.497576\pi$
$631$	−21.6580	+	37.5128i	−0.862192	+	1.49336i	−0.869809	+	0.493389i	$0.835758\pi$
$632$	3.44767	−	5.97154i	0.137141	−	0.237535i
$633$	−33.4817	−	11.3984i	−1.33078	−	0.453046i
$634$	−3.59884	+	6.23338i	−0.142928	+	0.247559i
$635$	1.11230	−	1.92657i	0.0441404	−	0.0764534i
$636$	−3.95518	−	19.9759i	−0.156833	−	0.792097i
$637$	−11.8417	−	4.65108i	−0.469184	−	0.184283i
$638$	3.19046			0.126311
$639$	3.86863	−	28.9906i	0.153041	−	1.14685i
$640$	17.4834	+	30.2822i	0.691093	+	1.19701i
$641$	9.09388	+	15.7511i	0.359187	+	0.622129i	0.987825	−	0.155568i	$-0.0497208\pi$
$641$	9.09388	+	15.7511i	0.359187	+	0.622129i	−0.628639	+	0.777698i	$0.716388\pi$
$642$	8.91027	−	7.80023i	0.351660	−	0.307850i
$643$	−5.89171			−0.232346			−0.116173	−	0.993229i	$-0.537063\pi$
$643$	−5.89171			−0.232346			−0.116173	+	0.993229i	$0.537063\pi$
$644$	0.656680			0.0258768
$645$	68.1694	+	23.2074i	2.68417	+	0.913789i
$646$	3.81955	+	6.61566i	0.150278	+	0.260290i
$647$	−1.22045	−	2.11389i	−0.0479810	−	0.0831055i	0.841037	−	0.540977i	$-0.181945\pi$
$647$	−1.22045	−	2.11389i	−0.0479810	−	0.0831055i	−0.889018	+	0.457871i	$0.848612\pi$
$648$	−8.67741	+	8.61650i	−0.340881	+	0.338488i
$649$	−5.03407			−0.197604
$650$	−42.2791	−	16.6061i	−1.65832	−	0.651345i
$651$	49.1681	+	16.7386i	1.92705	+	0.656038i
$652$	9.06050	−	15.6932i	0.354837	−	0.614595i
$653$	−2.73036	+	4.72912i	−0.106847	+	0.185065i	−0.914491	−	0.404605i	$-0.867409\pi$
$653$	−2.73036	+	4.72912i	−0.106847	+	0.185065i	0.807644	+	0.589670i	$0.200742\pi$
$654$	7.77075	+	39.2468i	0.303860	+	1.53467i
$655$	−26.0984	+	45.2038i	−1.01975	+	1.76626i
$656$	−20.3077	+	35.1740i	−0.792882	+	1.37331i
$657$	7.20134	−	2.96805i	0.280951	−	0.115795i
$658$	−51.3029			−2.00000
$659$	3.98137	+	6.89593i	0.155092	+	0.268627i	0.933093	−	0.359636i	$-0.117099\pi$
$659$	3.98137	+	6.89593i	0.155092	+	0.268627i	−0.778000	+	0.628264i	$0.783766\pi$
$660$	3.42488	−	2.99821i	0.133313	−	0.116705i
$661$	17.8750	−	30.9605i	0.695259	−	1.20422i	−0.274835	−	0.961491i	$-0.588623\pi$
$661$	17.8750	−	30.9605i	0.695259	−	1.20422i	0.970093	−	0.242732i	$-0.0780435\pi$
$662$	−3.48754	−	6.04060i	−0.135547	−	0.234774i
$663$	2.68266	−	14.8441i	0.104186	−	0.576499i
$664$	5.62702	−	9.74629i	0.218371	−	0.378229i
$665$	9.86260	+	17.0825i	0.382455	+	0.662432i
$666$	7.08076	+	5.45309i	0.274374	+	0.211303i
$667$	−0.236138	+	0.409002i	−0.00914328	+	0.0158366i
$668$	8.02368	−	13.8974i	0.310446	−	0.537707i
$669$	8.30797	+	41.9601i	0.321205	+	1.62227i
$670$	−14.3203			−0.553241
$671$	−3.02384	−	5.23744i	−0.116734	−	0.202189i
$672$	26.1405	−	22.8839i	1.00839	−	0.882767i
$673$	−27.4462			−1.05798			−0.528988	−	0.848630i	$-0.677428\pi$
$673$	−27.4462			−1.05798			−0.528988	+	0.848630i	$0.677428\pi$
$674$	4.76485	+	8.25296i	0.183535	+	0.317892i
$675$	−36.2636	+	2.28065i	−1.39579	+	0.0877823i
$676$	−15.4786	+	4.76565i	−0.595331	+	0.183294i
$677$	−13.2616	+	22.9699i	−0.509687	+	0.882803i	0.490250	+	0.871582i	$0.336905\pi$
$677$	−13.2616	+	22.9699i	−0.509687	+	0.882803i	−0.999937	+	0.0112215i	$0.996428\pi$
$678$	−3.62199	−	18.2931i	−0.139102	−	0.702543i
$679$	12.1324	−	21.0139i	0.465597	−	0.806438i
$680$	−11.3658			−0.435857
$681$	17.2135	−	15.0690i	0.659621	−	0.577446i
$682$	−5.07100	−	8.78323i	−0.194179	−	0.336327i
$683$	−4.96358	+	8.59717i	−0.189926	+	0.328961i	−0.945225	−	0.326419i	$-0.894158\pi$
$683$	−4.96358	+	8.59717i	−0.189926	+	0.328961i	0.755299	+	0.655380i	$0.227491\pi$
$684$	0.867806	−	6.50312i	0.0331814	−	0.248653i
$685$	−7.37962	+	12.7819i	−0.281961	+	0.488370i
$686$	−20.2936			−0.774812
$687$	−29.9092	+	26.1831i	−1.14111	+	0.998948i
$688$	−29.6511	−	51.3573i	−1.13044	−	1.95798i
$689$	5.06254	+	33.6475i	0.192867	+	1.28187i
$690$	0.340962	+	1.72205i	0.0129802	+	0.0655574i
$691$	−44.7465			−1.70224			−0.851119	−	0.524972i	$-0.824076\pi$
$691$	−44.7465			−1.70224			−0.851119	+	0.524972i	$0.824076\pi$
$692$	0.387792	+	0.671675i	0.0147416	+	0.0255333i
$693$	4.69780	+	3.61791i	0.178455	+	0.137433i
$694$	−34.2614			−1.30054
$695$	−1.25068	−	2.16625i	−0.0474411	−	0.0821705i
$696$	1.32889	+	6.71164i	0.0503713	+	0.254404i
$697$	−9.93054	−	17.2002i	−0.376146	−	0.651504i
$698$	−26.1962			−0.991542
$699$	2.22597	+	11.2424i	0.0841938	+	0.425227i
$700$	28.2673			1.06840
$701$	−41.3040			−1.56003			−0.780015	−	0.625761i	$-0.784789\pi$
$701$	−41.3040			−1.56003			−0.780015	+	0.625761i	$0.784789\pi$
$702$	−25.0223	+	22.6531i	−0.944407	+	0.854988i
$703$	2.90266			0.109476
$704$	−0.766248			−0.0288790
$705$	−10.2241	−	51.6375i	−0.385061	−	1.94478i
$706$	28.5414			1.07417
$707$	12.8107	+	22.1887i	0.481795	+	0.834493i
$708$	3.46364	+	17.4934i	0.130171	+	0.657441i
$709$	8.63712	+	14.9599i	0.324374	+	0.561832i	0.981385	−	0.192049i	$-0.0615131\pi$
$709$	8.63712	+	14.9599i	0.324374	+	0.561832i	−0.657012	+	0.753880i	$0.728180\pi$
$710$	−60.8260			−2.28276
$711$	2.01375	−	15.0906i	0.0755216	−	0.565941i
$712$	−6.71151	−	11.6247i	−0.251524	−	0.435653i
$713$	1.50129			0.0562239
$714$	4.75026	+	23.9915i	0.177774	+	0.897861i
$715$	−5.94764	+	4.74054i	−0.222429	+	0.177286i
$716$	0.481576	+	0.834115i	0.0179974	+	0.0311723i
$717$	−12.0293	+	10.5307i	−0.449244	+	0.393277i
$718$	27.4255			1.02351
$719$	13.9402	−	24.1452i	0.519883	−	0.900463i	−0.479850	−	0.877350i	$-0.659309\pi$
$719$	13.9402	−	24.1452i	0.519883	−	0.900463i	0.999733	−	0.0231129i	$-0.00735771\pi$
$720$	40.6582	+	31.3121i	1.51524	+	1.16693i
$721$	0.598634	−	1.03686i	0.0222943	−	0.0386148i
$722$	14.3395	+	24.8368i	0.533662	+	0.924330i
$723$	−23.9377	+	20.9555i	−0.890252	+	0.779345i
$724$	6.05530			0.225044
$725$	−10.1647	+	17.6058i	−0.377508	+	0.653864i
$726$	6.44202	+	32.5359i	0.239086	+	1.20752i
$727$	18.3106	−	31.7148i	0.679102	−	1.17624i	−0.296150	−	0.955141i	$-0.595703\pi$
$727$	18.3106	−	31.7148i	0.679102	−	1.17624i	0.975252	−	0.221097i	$-0.0709638\pi$
$728$	−12.4308	+	9.90788i	−0.460715	+	0.367210i
$729$	−10.4641	+	24.8898i	−0.387559	+	0.921845i
$730$	−8.09938	−	14.0285i	−0.299771	−	0.519219i
$731$	28.9990			1.07257
$732$	−16.1196	+	14.1114i	−0.595796	+	0.521572i
$733$	−4.47106	−	7.74411i	−0.165143	−	0.286035i	0.771563	−	0.636152i	$-0.219475\pi$
$733$	−4.47106	−	7.74411i	−0.165143	−	0.286035i	−0.936706	+	0.350117i	$0.886142\pi$
$734$	3.91727			0.144589
$735$	4.11077	+	20.7617i	0.151628	+	0.765809i
$736$	0.502105	−	0.869671i	0.0185078	−	0.0320565i
$737$	−0.699055	+	1.21080i	−0.0257500	+	0.0446004i
$738$	−5.87831	+	44.0506i	−0.216384	+	1.62152i
$739$	8.96934	+	15.5354i	0.329943	+	0.571477i	0.982500	−	0.186262i	$-0.0596373\pi$
$739$	8.96934	+	15.5354i	0.329943	+	0.571477i	−0.652558	+	0.757739i	$0.726304\pi$
$740$	3.56698	−	6.17820i	0.131125	−	0.227115i
$741$	−1.94959	+	10.7878i	−0.0716198	+	0.396299i
$742$	−27.5840	−	47.7770i	−1.01264	−	1.75395i
$743$	−8.10591	+	14.0399i	−0.297377	+	0.515072i	−0.975535	−	0.219844i	$-0.929445\pi$
$743$	−8.10591	+	14.0399i	−0.297377	+	0.515072i	0.678158	+	0.734916i	$0.262779\pi$
$744$	16.3648	−	14.3260i	0.599961	−	0.525218i
$745$	−0.461693	−	0.799676i	−0.0169151	−	0.0292978i
$746$	4.48000			0.164025
$747$	3.28670	−	24.6297i	0.120254	−	0.901153i
$748$	0.916509	−	1.58744i	0.0335109	−	0.0580426i
$749$	6.15690	−	10.6641i	0.224968	−	0.389656i
$750$	4.18250	+	21.1240i	0.152723	+	0.771340i
$751$	1.43874	−	2.49196i	0.0525002	−	0.0909331i	−0.838581	−	0.544777i	$-0.816614\pi$
$751$	1.43874	−	2.49196i	0.0525002	−	0.0909331i	0.891081	+	0.453844i	$0.149948\pi$
$752$	−21.6748	+	37.5419i	−0.790399	+	1.36901i
$753$	−17.1234	−	5.82943i	−0.624012	−	0.212436i
$754$	2.80975	+	18.6747i	0.102325	+	0.680091i
$755$	0.143643			0.00522772
$756$	9.33996	−	18.8141i	0.339691	−	0.684263i
$757$	−15.4379	−	26.7392i	−0.561100	−	0.971854i	−0.997401	−	0.0720530i	$-0.977045\pi$
$757$	−15.4379	−	26.7392i	−0.561100	−	0.971854i	0.436301	−	0.899801i	$-0.356288\pi$
$758$	−17.4656	−	30.2513i	−0.634378	−	1.09878i
$759$	0.162246	+	0.0552345i	0.00588916	+	0.00200489i
$760$	8.25992			0.299619
$761$	−54.5602			−1.97781			−0.988904	−	0.148558i	$-0.952537\pi$
$761$	−54.5602			−1.97781			−0.988904	+	0.148558i	$0.952537\pi$
$762$	−1.50826	+	1.32036i	−0.0546387	+	0.0478318i
$763$	20.8011	+	36.0285i	0.753049	+	1.30432i
$764$	2.82906	+	4.90007i	0.102352	+	0.177278i
$765$	−23.2013	+	9.56247i	−0.838846	+	0.345732i
$766$	−25.3154			−0.914681
$767$	−4.43338	−	29.4659i	−0.160080	−	1.06395i
$768$	−6.96605	−	35.1826i	−0.251366	−	1.26954i
$769$	13.0265	−	22.5626i	0.469747	−	0.813626i	−0.529654	−	0.848214i	$-0.677678\pi$
$769$	13.0265	−	22.5626i	0.469747	−	0.813626i	0.999402	+	0.0345872i	$0.0110117\pi$
$770$	6.16575	−	10.6794i	0.222198	−	0.384858i
$771$	−45.3732	−	15.4467i	−1.63408	−	0.556300i
$772$	−12.9898	+	22.4991i	−0.467515	+	0.809759i
$773$	15.3837	−	26.6453i	0.553313	−	0.958366i	−0.444720	−	0.895670i	$-0.646697\pi$
$773$	15.3837	−	26.6453i	0.553313	−	0.958366i	0.998033	−	0.0626965i	$-0.0199700\pi$
$774$	−51.4096	−	39.5920i	−1.84788	−	1.42311i
$775$	64.6244			2.32138
$776$	−5.08042	−	8.79954i	−0.182376	−	0.315885i
$777$	8.79732	+	2.99493i	0.315602	+	0.107442i
$778$	−13.2927	+	23.0236i	−0.476566	+	0.825436i
$779$	7.21689	+	12.5000i	0.258572	+	0.447860i
$780$	20.5656	+	17.4064i	0.736366	+	0.623248i
$781$	−2.96927	+	5.14292i	−0.106249	+	0.184028i
$782$	0.353467	+	0.612223i	0.0126400	+	0.0218930i
$783$	8.35947	+	12.5827i	0.298743	+	0.449668i
$784$	8.71473	−	15.0944i	0.311240	−	0.539084i
$785$	14.0445	−	24.3258i	0.501270	−	0.868225i
$786$	35.3890	−	30.9802i	1.26228	−	1.10503i
$787$	50.0534			1.78421			0.892106	−	0.451826i	$-0.149227\pi$
$787$	50.0534			1.78421			0.892106	+	0.451826i	$0.149227\pi$
$788$	6.92773	+	11.9992i	0.246790	+	0.427453i
$789$	8.39191	+	42.3840i	0.298760	+	1.50891i
$790$	−31.6620			−1.12648
$791$	−9.69548	−	16.7931i	−0.344732	−	0.597093i
$792$	2.29563	−	0.946147i	0.0815716	−	0.0336199i
$793$	27.9932	−	22.3119i	0.994069	−	0.792318i
$794$	−14.4953	+	25.1066i	−0.514420	+	0.891001i
$795$	42.5914	−	37.2853i	1.51056	−	1.32237i
$796$	6.28052	−	10.8782i	0.222607	−	0.385567i
$797$	39.6135			1.40318			0.701590	−	0.712581i	$-0.252474\pi$
$797$	39.6135			1.40318			0.701590	+	0.712581i	$0.252474\pi$
$798$	−3.45219	−	17.4355i	−0.122206	−	0.617211i
$799$	−10.5991	−	18.3581i	−0.374968	−	0.649463i
$800$	21.6135	−	37.4357i	0.764153	−	1.32355i
$801$	−23.4807	−	18.0832i	−0.829651	−	0.638938i
$802$	30.7952	−	53.3389i	1.08742	−	1.88346i
$803$	−1.58151			−0.0558102
$804$	4.68850	+	1.59614i	0.165351	+	0.0562914i
$805$	0.912700	+	1.58084i	0.0321684	+	0.0557174i
$806$	46.9449	−	37.4172i	1.65356	−	1.31796i
$807$	−31.5323	−	10.7347i	−1.10999	−	0.377881i
$808$	10.7289			0.377442
$809$	13.5323	+	23.4386i	0.475770	+	0.824058i	0.999615	−	0.0277559i	$-0.00883610\pi$
$809$	13.5323	+	23.4386i	0.475770	+	0.824058i	−0.523845	+	0.851814i	$0.675503\pi$
$810$	54.1869	+	14.7241i	1.90393	+	0.517352i
$811$	−32.3039			−1.13434			−0.567171	−	0.823600i	$-0.691962\pi$
$811$	−32.3039			−1.13434			−0.567171	+	0.823600i	$0.691962\pi$
$812$	−5.87609	−	10.1777i	−0.206210	−	0.357167i
$813$	−4.70704	+	4.12063i	−0.165083	+	0.144517i
$814$	−0.907320	−	1.57152i	−0.0318016	−	0.0550819i
$815$	50.3717			1.76444
$816$	19.5632	+	6.66002i	0.684848	+	0.233147i
$817$	−21.0747			−0.737310
$818$	−62.6337			−2.18994
$819$	−17.0395	+	30.6838i	−0.595407	+	1.07218i
$820$	35.4744			1.23882
$821$	−23.8599			−0.832715			−0.416358	−	0.909201i	$-0.636694\pi$
$821$	−23.8599			−0.832715			−0.416358	+	0.909201i	$0.636694\pi$
$822$	10.0066	−	8.76001i	0.349022	−	0.305540i
$823$	−7.48834			−0.261027			−0.130514	−	0.991447i	$-0.541663\pi$
$823$	−7.48834			−0.261027			−0.130514	+	0.991447i	$0.541663\pi$
$824$	−0.250677	−	0.434186i	−0.00873276	−	0.0151256i
$825$	6.98402	+	2.37761i	0.243152	+	0.0827779i
$826$	24.1560	+	41.8394i	0.840494	+	1.45578i
$827$	−10.0589			−0.349783			−0.174891	−	0.984588i	$-0.555957\pi$
$827$	−10.0589			−0.349783			−0.174891	+	0.984588i	$0.555957\pi$
$828$	0.0803080	−	0.601808i	0.00279090	−	0.0209143i
$829$	26.1786	+	45.3428i	0.909222	+	1.57482i	0.815147	+	0.579254i	$0.196656\pi$
$829$	26.1786	+	45.3428i	0.909222	+	1.57482i	0.0940747	+	0.995565i	$0.470011\pi$
$830$	−51.6763			−1.79371
$831$	29.7322	−	26.0282i	1.03140	−	0.902908i
$832$	−0.674815	−	4.48507i	−0.0233950	−	0.155492i
$833$	4.26154	+	7.38120i	0.147653	+	0.255743i
$834$	0.437774	+	2.21101i	0.0151589	+	0.0765611i
$835$	44.6075			1.54371
$836$	−0.666061	+	1.15365i	−0.0230362	+	0.0398999i
$837$	21.3529	−	43.0126i	0.738064	−	1.48673i
$838$	2.54991	−	4.41657i	0.0880851	−	0.152568i
$839$	8.18737	+	14.1809i	0.282659	+	0.489580i	0.972039	−	0.234820i	$-0.0754500\pi$
$839$	8.18737	+	14.1809i	0.282659	+	0.489580i	−0.689379	+	0.724400i	$0.742117\pi$
$840$	25.0340	+	8.52247i	0.863754	+	0.294053i
$841$	−20.5480			−0.708552
$842$	12.9338	−	22.4021i	0.445730	−	0.772026i
$843$	16.9835	+	5.78179i	0.584941	+	0.199135i
$844$	12.7199	−	22.0315i	0.437837	−	0.758356i
$845$	−32.9857	−	30.6384i	−1.13474	−	1.05399i
$846$	−6.27404	+	47.0161i	−0.215706	+	1.61645i
$847$	17.2443	+	29.8679i	0.592520	+	1.02627i
$848$	−46.6156			−1.60079
$849$	−11.2888	−	3.84311i	−0.387430	−	0.131895i
$850$	15.2153	+	26.3536i	0.521879	+	0.903921i
$851$	0.268617			0.00920806
$852$	19.9146	+	6.77966i	0.682263	+	0.232267i
$853$	−4.65970	+	8.07084i	−0.159545	+	0.276340i	−0.934705	−	0.355425i	$-0.884336\pi$
$853$	−4.65970	+	8.07084i	−0.159545	+	0.276340i	0.775160	+	0.631765i	$0.217669\pi$
$854$	−29.0198	+	50.2637i	−0.993036	+	1.71999i
$855$	16.8613	−	6.94940i	0.576643	−	0.237665i
$856$	−2.57820	−	4.46557i	−0.0881209	−	0.152630i
$857$	−20.7408	+	35.9241i	−0.708491	+	1.22714i	0.256925	+	0.966431i	$0.417291\pi$
$857$	−20.7408	+	35.9241i	−0.708491	+	1.22714i	−0.965417	+	0.260712i	$0.916043\pi$
$858$	6.45000	−	2.31655i	0.220199	−	0.0790856i
$859$	−5.60325	−	9.70511i	−0.191180	−	0.331134i	0.754461	−	0.656344i	$-0.227898\pi$
$859$	−5.60325	−	9.70511i	−0.191180	−	0.331134i	−0.945642	+	0.325210i	$0.894565\pi$
$860$	−25.8980	+	44.8566i	−0.883113	+	1.52960i
$861$	8.97542	+	45.3310i	0.305881	+	1.54488i
$862$	−25.7306	−	44.5667i	−0.876387	−	1.51795i
$863$	27.4495			0.934391			0.467196	−	0.884154i	$-0.345264\pi$
$863$	27.4495			0.934391			0.467196	+	0.884154i	$0.345264\pi$
$864$	−17.7749	−	26.7548i	−0.604716	−	0.910217i
$865$	−1.07796	+	1.86708i	−0.0366517	+	0.0634827i
$866$	9.48394	−	16.4267i	0.322277	−	0.558201i
$867$	14.5512	−	12.7384i	0.494185	−	0.432620i
$868$	−18.6792	+	32.3534i	−0.634015	+	1.09815i
$869$	−1.54560	+	2.67706i	−0.0524310	+	0.0908131i
$870$	23.6386	−	20.6937i	0.801423	−	0.701582i
$871$	−7.70280	−	3.02545i	−0.260999	−	0.102514i
$872$	17.4209			0.589945
$873$	−17.7742	−	13.6885i	−0.601567	−	0.463284i
$874$	−0.256878	−	0.444925i	−0.00868901	−	0.0150498i
$875$	11.1959	+	19.3918i	0.378490	+	0.655563i
$876$	1.08814	+	5.49574i	0.0367649	+	0.185684i
$877$	−11.7137			−0.395542			−0.197771	−	0.980248i	$-0.563370\pi$
$877$	−11.7137			−0.395542			−0.197771	+	0.980248i	$0.563370\pi$
$878$	42.9723			1.45024
$879$	−1.76343	−	8.90635i	−0.0594791	−	0.300404i
$880$	−5.20989	−	9.02380i	−0.175626	−	0.304192i
$881$	25.7417	+	44.5860i	0.867261	+	1.50214i	0.864784	+	0.502143i	$0.167455\pi$
$881$	25.7417	+	44.5860i	0.867261	+	1.50214i	0.00247662	+	0.999997i	$0.499212\pi$
$882$	2.52259	−	18.9036i	0.0849399	−	0.636518i
$883$	30.6074			1.03002			0.515011	−	0.857183i	$-0.327788\pi$
$883$	30.6074			1.03002			0.515011	+	0.857183i	$0.327788\pi$
$884$	10.0989	+	3.96658i	0.339663	+	0.133410i
$885$	−37.2982	+	32.6516i	−1.25377	+	1.09757i
$886$	2.09966	−	3.63672i	0.0705395	−	0.122178i
$887$	−4.21108	+	7.29381i	−0.141394	+	0.244902i	−0.928022	−	0.372526i	$-0.878492\pi$
$887$	−4.21108	+	7.29381i	−0.141394	+	0.244902i	0.786628	+	0.617428i	$0.211825\pi$
$888$	2.92804	−	2.56326i	0.0982586	−	0.0860175i
$889$	−1.04219	+	1.80513i	−0.0349541	+	0.0605422i
$890$	−30.8179	+	53.3781i	−1.03302	+	1.78924i
$891$	3.89012	−	3.86281i	0.130324	−	0.129409i
$892$	−30.7667			−1.03014
$893$	7.70273	+	13.3415i	0.257762	+	0.446457i
$894$	0.161605	+	0.816201i	0.00540489	+	0.0272978i
$895$	−1.33866	+	2.31862i	−0.0447464	+	0.0775030i
$896$	−16.3814	−	28.3735i	−0.547265	−	0.947891i
$897$	−0.180418	+	0.998318i	−0.00602397	+	0.0333329i
$898$	20.5622	−	35.6147i	0.686169	−	1.18848i
$899$	−13.4338	−	23.2681i	−0.448044	−	0.776035i
$900$	3.45692	−	25.9053i	0.115231	−	0.863511i
$901$	11.3976	−	19.7412i	0.379709	−	0.657675i
$902$	4.51174	−	7.81456i	0.150225	−	0.260196i
$903$	−63.8726	−	21.7446i	−2.12555	−	0.723614i
$904$	−8.11996			−0.270066
$905$	8.41608	+	14.5771i	0.279760	+	0.484559i
$906$	−0.122529	−	0.0417132i	−0.00407074	−	0.00138583i
$907$	−9.85582			−0.327257			−0.163629	−	0.986522i	$-0.552320\pi$
$907$	−9.85582			−0.327257			−0.163629	+	0.986522i	$0.552320\pi$
$908$	8.22758	+	14.2506i	0.273042	+	0.472922i
$909$	21.9013	−	9.02667i	0.726421	−	0.299396i
$910$	67.9396	+	26.6848i	2.25217	+	0.884594i
$911$	3.53377	−	6.12067i	0.117079	−	0.202787i	−0.801530	−	0.597955i	$-0.795980\pi$
$911$	3.53377	−	6.12067i	0.117079	−	0.202787i	0.918609	+	0.395168i	$0.129314\pi$
$912$	−14.2173	−	4.84008i	−0.470781	−	0.160271i
$913$	−2.52262	+	4.36930i	−0.0834864	+	0.144603i
$914$	24.0990			0.797125
$915$	−56.3748	−	19.1920i	−1.86369	−	0.634469i
$916$	−14.2958	−	24.7610i	−0.472346	−	0.818128i
$917$	24.4534	−	42.3545i	0.807522	−	1.39867i
$918$	22.5678	−	1.41931i	0.744847	−	0.0468442i
$919$	−14.3944	+	24.9318i	−0.474828	+	0.822426i	−0.999584	−	0.0288266i	$-0.990823\pi$
$919$	−14.3944	+	24.9318i	−0.474828	+	0.822426i	0.524757	+	0.851252i	$0.324156\pi$
$920$	0.764385			0.0252010
$921$	−2.26480	−	11.4386i	−0.0746279	−	0.376914i
$922$	3.65542	+	6.33137i	0.120385	+	0.208512i
$923$	−32.7180	−	12.8507i	−1.07693	−	0.422987i
$924$	−3.20900	+	2.80923i	−0.105569	+	0.0924168i
$925$	11.5628			0.380183
$926$	23.9748	+	41.5255i	0.787860	+	1.36461i
$927$	−0.877015	−	0.675415i	−0.0288050	−	0.0221835i
$928$	−17.9717			−0.589950
$929$	6.27708	+	10.8722i	0.205944	+	0.356706i	0.950433	−	0.310929i	$-0.100640\pi$
$929$	6.27708	+	10.8722i	0.205944	+	0.356706i	−0.744489	+	0.667635i	$0.767307\pi$
$930$	−94.5410	−	32.1852i	−3.10012	−	1.05539i
$931$	−3.09702	−	5.36419i	−0.101501	−	0.175804i
$932$	−8.24335			−0.270020
$933$	40.5185	−	35.4707i	1.32652	−	1.16126i
$934$	5.12429			0.167672
$935$	5.09531			0.166635
$936$	7.55978	+	12.6037i	0.247099	+	0.411966i
$937$	−32.7254			−1.06909			−0.534547	−	0.845139i	$-0.679518\pi$
$937$	−32.7254			−1.06909			−0.534547	+	0.845139i	$0.679518\pi$
$938$	13.4177			0.438102
$939$	−25.1158	−	8.55032i	−0.819622	−	0.279029i
$940$	37.8625			1.23494
$941$	−25.6173	−	44.3705i	−0.835100	−	1.44644i	−0.893949	−	0.448169i	$-0.852076\pi$
$941$	−25.6173	−	44.3705i	−0.835100	−	1.44644i	0.0588484	−	0.998267i	$-0.481257\pi$
$942$	−19.0441	+	16.6716i	−0.620490	+	0.543190i
$943$	0.667862	+	1.15677i	0.0217486	+	0.0376696i
$944$	40.8223			1.32865
$945$	58.2730	−	3.66485i	1.89562	−	0.119218i
$946$	6.58756	+	11.4100i	0.214180	+	0.370971i
$947$	36.7761			1.19506			0.597531	−	0.801846i	$-0.296148\pi$
$947$	36.7761			1.19506			0.597531	+	0.801846i	$0.296148\pi$
$948$	10.3662	+	3.52904i	0.336679	+	0.114618i
$949$	−1.39280	−	9.25703i	−0.0452120	−	0.300496i
$950$	−11.0575	−	19.1521i	−0.358753	−	0.621378i
$951$	6.55057	+	2.23005i	0.212417	+	0.0723145i
$952$	10.6494			0.345148
$953$	9.04123	−	15.6599i	0.292874	−	0.507273i	−0.681614	−	0.731712i	$-0.738722\pi$
$953$	9.04123	−	15.6599i	0.292874	−	0.507273i	0.974488	+	0.224439i	$0.0720550\pi$
$954$	−47.1581	+	19.4363i	−1.52680	+	0.629274i
$955$	−7.86405	+	13.6209i	−0.254475	+	0.440763i
$956$	−5.74970	−	9.95877i	−0.185959	−	0.322090i
$957$	−0.595744	−	3.00885i	−0.0192577	−	0.0972624i
$958$	−4.32720			−0.139805
$959$	6.91447	−	11.9762i	0.223280	−	0.386732i
$960$	−5.67725	+	4.96998i	−0.183233	+	0.160405i
$961$	−27.2043	+	47.1192i	−0.877557	+	1.51997i
$962$	8.39953	−	6.69481i	0.270812	−	0.215849i
$963$	−9.02002	−	6.94658i	−0.290666	−	0.223850i
$964$	−11.4416	−	19.8174i	−0.368508	−	0.638275i
$965$	−72.2167			−2.32474
$966$	−0.319470	−	1.61351i	−0.0102788	−	0.0519138i
$967$	−21.6188	−	37.4448i	−0.695213	−	1.20414i	−0.970109	−	0.242670i	$-0.921977\pi$
$967$	−21.6188	−	37.4448i	−0.695213	−	1.20414i	0.274896	−	0.961474i	$-0.411356\pi$
$968$	14.4421			0.464185
$969$	5.52588	−	4.83746i	0.177517	−	0.155402i
$970$	−23.3282	+	40.4057i	−0.749024	+	1.29735i
$971$	−10.3259	+	17.8850i	−0.331374	+	0.573956i	−0.982781	−	0.184772i	$-0.940845\pi$
$971$	−10.3259	+	17.8850i	−0.331374	+	0.573956i	0.651408	+	0.758728i	$0.274179\pi$
$972$	−16.0998	−	10.8604i	−0.516401	−	0.348347i
$973$	1.17185	+	2.02971i	0.0375678	+	0.0650694i
$974$	3.28853	−	5.69590i	0.105371	−	0.182508i
$975$	−7.76622	+	42.9734i	−0.248718	+	1.37625i
$976$	24.5209	+	42.4715i	0.784896	+	1.35948i
$977$	−11.9901	+	20.7675i	−0.383598	+	0.664411i	−0.991574	−	0.129545i	$-0.958648\pi$
$977$	−11.9901	+	20.7675i	−0.383598	+	0.664411i	0.607976	+	0.793956i	$0.291982\pi$
$978$	−42.9673	−	14.6276i	−1.37394	−	0.467741i
$979$	3.00879	+	5.21138i	0.0961615	+	0.166557i
$980$	−15.2233			−0.486290
$981$	35.5618	−	14.6569i	1.13540	−	0.467958i
$982$	−14.8267	+	25.6806i	−0.473139	+	0.819501i
$983$	24.0410	−	41.6403i	0.766790	−	1.32812i	−0.172506	−	0.985009i	$-0.555186\pi$
$983$	24.0410	−	41.6403i	0.766790	−	1.32812i	0.939295	−	0.343110i	$-0.111480\pi$
$984$	18.3184	+	6.23626i	0.583970	+	0.198805i
$985$	−19.2573	+	33.3546i	−0.613588	+	1.06277i
$986$	6.32577	−	10.9566i	0.201454	−	0.348928i
$987$	9.57964	+	48.3827i	0.304923	+	1.54004i
$988$	−7.33924	−	2.88266i	−0.233492	−	0.0917095i
$989$	−1.95028			−0.0620153
$990$	−9.03299	−	6.95657i	−0.287087	−	0.221094i
$991$	−29.2993	−	50.7479i	−0.930723	−	1.61206i	−0.782089	−	0.623167i	$-0.785846\pi$
$991$	−29.2993	−	50.7479i	−0.930723	−	1.61206i	−0.148634	−	0.988892i	$-0.547488\pi$
$992$	28.5647	+	49.4755i	0.906931	+	1.57085i
$993$	−5.04555	+	4.41697i	−0.160116	+	0.140168i
$994$	56.9921			1.80768
$995$	34.9164			1.10693
$996$	16.9190	+	5.75983i	0.536098	+	0.182507i
$997$	−30.8342	−	53.4065i	−0.976530	−	1.69140i	−0.674789	−	0.738010i	$-0.735765\pi$
$997$	−30.8342	−	53.4065i	−0.976530	−	1.69140i	−0.301741	−	0.953390i	$-0.597568\pi$
$998$	10.7027	+	18.5375i	0.338786	+	0.586795i
$999$	3.82053	−	7.69596i	0.120876	−	0.243489i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.h.a.16.10	yes	24
3.2	odd	2		351.2.h.a.289.3		24
9.4	even	3		117.2.f.a.94.3	yes	24
9.5	odd	6		351.2.f.a.172.10		24
13.9	even	3		117.2.f.a.61.3	✓	24
39.35	odd	6		351.2.f.a.100.10		24
117.22	even	3	inner	117.2.h.a.22.10	yes	24
117.113	odd	6		351.2.h.a.334.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.f.a.61.3	✓	24	13.9	even	3
117.2.f.a.94.3	yes	24	9.4	even	3
117.2.h.a.16.10	yes	24	1.1	even	1	trivial
117.2.h.a.22.10	yes	24	117.22	even	3	inner
351.2.f.a.100.10		24	39.35	odd	6
351.2.f.a.172.10		24	9.5	odd	6
351.2.h.a.289.3		24	3.2	odd	2
351.2.h.a.334.3		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+1.80162 q^{2} +(-0.336410 - 1.69907i) q^{3} +1.24582 q^{4} +(1.73153 + 2.99909i) q^{5} +(-0.606082 - 3.06106i) q^{6} +(-1.62239 - 2.81005i) q^{7} -1.35875 q^{8} +(-2.77366 + 1.14317i) q^{9} +(3.11954 + 5.40321i) q^{10} +0.609131 q^{11} +(-0.419106 - 2.11673i) q^{12} +(0.536447 + 3.56542i) q^{13} +(-2.92291 - 5.06264i) q^{14} +(4.51315 - 3.95090i) q^{15} -4.93957 q^{16} +(1.20773 - 2.09186i) q^{17} +(-4.99706 + 2.05955i) q^{18} +(-0.877705 + 1.52023i) q^{19} +(2.15717 + 3.73632i) q^{20} +(-4.22868 + 3.70187i) q^{21} +1.09742 q^{22} +(-0.0812242 + 0.140684i) q^{23} +(0.457096 + 2.30860i) q^{24} +(-3.49636 + 6.05587i) q^{25} +(0.966470 + 6.42352i) q^{26} +(2.87540 + 4.32805i) q^{27} +(-2.02120 - 3.50082i) q^{28} +2.90723 q^{29} +(8.13096 - 7.11801i) q^{30} +(-4.62084 - 8.00352i) q^{31} -6.18172 q^{32} +(-0.204918 - 1.03495i) q^{33} +(2.17587 - 3.76872i) q^{34} +(5.61840 - 9.73136i) q^{35} +(-3.45547 + 1.42418i) q^{36} +(-0.826776 - 1.43202i) q^{37} +(-1.58129 + 2.73887i) q^{38} +(5.87742 - 2.11090i) q^{39} +(-2.35270 - 4.07500i) q^{40} +(4.11123 - 7.12085i) q^{41} +(-7.61846 + 6.66935i) q^{42} +(6.00278 + 10.3971i) q^{43} +0.758866 q^{44} +(-8.23112 - 6.33902i) q^{45} +(-0.146335 + 0.253459i) q^{46} +(4.38799 - 7.60023i) q^{47} +(1.66172 + 8.39267i) q^{48} +(-1.76427 + 3.05580i) q^{49} +(-6.29909 + 10.9103i) q^{50} +(-3.96050 - 1.34830i) q^{51} +(0.668315 + 4.44187i) q^{52} +9.43717 q^{53} +(5.18037 + 7.79749i) q^{54} +(1.05473 + 1.82684i) q^{55} +(2.20441 + 3.81815i) q^{56} +(2.87824 + 0.979859i) q^{57} +5.23772 q^{58} -8.26434 q^{59} +(5.62256 - 4.92210i) q^{60} +(-4.96418 - 8.59821i) q^{61} +(-8.32497 - 14.4193i) q^{62} +(7.71230 + 5.93946i) q^{63} -1.25794 q^{64} +(-9.76414 + 7.78247i) q^{65} +(-0.369183 - 1.86459i) q^{66} +(-1.14763 + 1.98775i) q^{67} +(1.50462 - 2.60607i) q^{68} +(0.266357 + 0.0906776i) q^{69} +(10.1222 - 17.5322i) q^{70} +(-4.87460 + 8.44305i) q^{71} +(3.76869 - 1.55327i) q^{72} -2.59634 q^{73} +(-1.48953 - 2.57994i) q^{74} +(11.4655 + 3.90329i) q^{75} +(-1.09346 + 1.89393i) q^{76} +(-0.988245 - 1.71169i) q^{77} +(10.5889 - 3.80304i) q^{78} +(-2.53739 + 4.39489i) q^{79} +(-8.55300 - 14.8142i) q^{80} +(6.38634 - 6.34151i) q^{81} +(7.40685 - 12.8290i) q^{82} +(-4.14134 + 7.17301i) q^{83} +(-5.26817 + 4.61186i) q^{84} +8.36489 q^{85} +(10.8147 + 18.7316i) q^{86} +(-0.978023 - 4.93958i) q^{87} -0.827654 q^{88} +(4.93949 + 8.55544i) q^{89} +(-14.8293 - 11.4205i) q^{90} +(9.14870 - 7.29193i) q^{91} +(-0.101191 + 0.175267i) q^{92} +(-12.0440 + 10.5436i) q^{93} +(7.90547 - 13.6927i) q^{94} -6.07908 q^{95} +(2.07960 + 10.5032i) q^{96} +(3.73905 + 6.47622i) q^{97} +(-3.17853 + 5.50538i) q^{98} +(-1.68952 + 0.696339i) 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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