LMFDB - Embedded newform 117.2.f.a.61.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

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

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

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

Embedding invariants

Embedding label			61.3
Character	$\chi$	$=$	117.61
Dual form			117.2.f.a.94.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.900808 - 1.56024i) q^{2} +(-1.30323 + 1.14087i) q^{3} +(-0.622909 + 1.07891i) q^{4} +(1.73153 + 2.99909i) q^{5} +(2.95400 + 1.00565i) q^{6} +3.24477 q^{7} -1.35875 q^{8} +(0.396816 - 2.97364i) q^{9} +(3.11954 - 5.40321i) q^{10} +(-0.304566 - 0.527523i) q^{11} +(-0.419106 - 2.11673i) q^{12} +(2.81952 + 2.24729i) q^{13} +(-2.92291 - 5.06264i) q^{14} +(-5.67816 - 1.93305i) q^{15} +(2.46979 + 4.27780i) q^{16} +(1.20773 + 2.09186i) q^{17} +(-4.99706 + 2.05955i) q^{18} +(-0.877705 - 1.52023i) q^{19} -4.31433 q^{20} +(-4.22868 + 3.70187i) q^{21} +(-0.548710 + 0.950393i) q^{22} +0.162448 q^{23} +(1.77076 - 1.55016i) 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} +(-1.45362 - 2.51774i) q^{29} +(2.09889 + 10.6006i) q^{30} +(-4.62084 - 8.00352i) q^{31} +(3.09086 - 5.35353i) q^{32} +(0.998756 + 0.340013i) q^{33} +(2.17587 - 3.76872i) q^{34} +(5.61840 + 9.73136i) q^{35} +(2.96111 + 2.28044i) q^{36} +(-0.826776 + 1.43202i) q^{37} +(-1.58129 + 2.73887i) q^{38} +(-6.23835 + 0.287986i) q^{39} +(-2.35270 - 4.07500i) q^{40} -8.22245 q^{41} +(9.58506 + 3.26310i) q^{42} -12.0056 q^{43} +0.758866 q^{44} +(9.60531 - 3.95885i) q^{45} +(-0.146335 - 0.253459i) q^{46} +(4.38799 - 7.60023i) q^{47} +(-8.09912 - 2.75724i) q^{48} +3.52854 q^{49} +12.5982 q^{50} +(-3.96050 - 1.34830i) q^{51} +(-4.18093 + 1.64216i) q^{52} +9.43717 q^{53} +(4.16264 - 8.38508i) q^{54} +(1.05473 - 1.82684i) q^{55} -4.40882 q^{56} +(2.87824 + 0.979859i) q^{57} +(-2.61886 + 4.53599i) q^{58} +(4.13217 - 7.15713i) q^{59} +(5.62256 - 4.92210i) q^{60} +9.92836 q^{61} +(-8.32497 + 14.4193i) q^{62} +(1.28758 - 9.64878i) q^{63} -1.25794 q^{64} +(-1.85774 + 12.3472i) q^{65} +(-0.369183 - 1.86459i) q^{66} +2.29525 q^{67} -3.00924 q^{68} +(-0.211707 + 0.185333i) q^{69} +(10.1222 - 17.5322i) q^{70} +(-4.87460 - 8.44305i) q^{71} +(-0.539172 + 4.04042i) q^{72} -2.59634 q^{73} +2.97906 q^{74} +(-2.35242 - 11.8811i) q^{75} +2.18692 q^{76} +(-0.988245 - 1.71169i) q^{77} +(6.06889 + 9.47394i) q^{78} +(-2.53739 + 4.39489i) q^{79} +(-8.55300 + 14.8142i) q^{80} +(-8.68507 - 2.35998i) q^{81} +(7.40685 + 12.8290i) q^{82} +(-4.14134 + 7.17301i) q^{83} +(-1.35990 - 6.86830i) q^{84} +(-4.18245 + 7.24421i) q^{85} +(10.8147 + 18.7316i) q^{86} +(4.76682 + 1.62280i) q^{87} +(0.413827 + 0.716770i) 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} +(15.1530 + 5.15864i) q^{93} -15.8109 q^{94} +(3.03954 - 5.26463i) q^{95} +(2.07960 + 10.5032i) q^{96} -7.47810 q^{97} +(-3.17853 - 5.50538i) q^{98} +(-1.68952 + 0.696339i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + q^{2} - q^{3} - 9 q^{4} - 2 q^{5} + 9 q^{6} - 6 q^{7} - 18 q^{8} - 3 q^{9} - 3 q^{11} - 3 q^{12} + 2 q^{14} + 8 q^{15} - 3 q^{16} + 6 q^{17} - 8 q^{18} - 3 q^{19} + 22 q^{20} - 25 q^{21} + 9 q^{22}+ \cdots + 18 q^{99}+O(q^{100}) $ 24 * q + q^2 - q^3 - 9 * q^4 - 2 * q^5 + 9 * q^6 - 6 * q^7 - 18 * q^8 - 3 * q^9 - 3 * q^11 - 3 * q^12 + 2 * q^14 + 8 * q^15 - 3 * q^16 + 6 * q^17 - 8 * q^18 - 3 * q^19 + 22 * q^20 - 25 * q^21 + 9 * q^22 - 34 * q^23 - 6 * q^24 - 6 * q^25 - 12 * q^26 + 2 * q^27 + 12 * q^29 + 25 * q^30 - 6 * q^31 + 19 * q^32 - 16 * q^33 + 18 * q^35 + 59 * q^36 - 3 * q^37 + 8 * q^38 - 9 * q^39 - 12 * q^40 - 10 * q^41 - 30 * q^42 + 6 * q^43 + 44 * q^44 - 5 * q^45 - 6 * q^46 + 21 * q^47 - 22 * q^48 - 6 * q^49 + 40 * q^50 + 7 * q^51 - 6 * q^52 - 20 * q^53 - 78 * q^54 + 3 * q^55 - 80 * q^56 + 9 * q^57 - 9 * q^58 - 19 * q^59 + 51 * q^60 + 12 * q^61 + 19 * q^62 - 2 * q^63 - 42 * q^64 + 19 * q^65 - 18 * q^66 + 12 * q^67 - 10 * q^69 + 27 * q^70 + 14 * q^71 + 45 * q^72 + 6 * q^73 - 58 * q^74 - 22 * q^75 + 30 * q^76 + 4 * q^77 + 65 * q^78 + 3 * q^79 - 16 * q^80 + 9 * q^81 - 9 * q^82 - 33 * q^83 + 86 * q^84 + 72 * q^86 + 37 * q^87 + 39 * q^88 - q^89 + 21 * q^90 - 6 * q^91 - 10 * q^92 + 63 * q^93 + 18 * q^94 + 50 * q^95 - 79 * q^96 - 48 * q^97 - 61 * q^98 + 18 * q^99

Character values

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

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

Coefficient data

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

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

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

$2$	−0.900808	−	1.56024i	−0.636967	−	1.10326i	−0.986095	−	0.166184i	$-0.946855\pi$
$2$	−0.900808	−	1.56024i	−0.636967	−	1.10326i	0.349127	−	0.937075i	$-0.386478\pi$
$3$	−1.30323	+	1.14087i	−0.752420	+	0.658684i
$3$	−1.30323	+	1.14087i	−0.752420	+	0.658684i
$4$	−0.622909	+	1.07891i	−0.311455	+	0.539455i
$5$	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	$0.551405\pi$
$6$	2.95400	+	1.00565i	1.20597	+	0.410555i
$7$	3.24477			1.22641			0.613204	−	0.789925i	$-0.289880\pi$
$7$	3.24477			1.22641			0.613204	+	0.789925i	$0.289880\pi$
$8$	−1.35875			−0.480389
$9$	0.396816	−	2.97364i	0.132272	−	0.991213i
$10$	3.11954	−	5.40321i	0.986486	−	1.70864i
$11$	−0.304566	−	0.527523i	−0.0918300	−	0.159054i	0.816451	−	0.577414i	$-0.195938\pi$
$11$	−0.304566	−	0.527523i	−0.0918300	−	0.159054i	−0.908281	+	0.418360i	$0.862605\pi$
$12$	−0.419106	−	2.11673i	−0.120986	−	0.611047i
$13$	2.81952	+	2.24729i	0.781995	+	0.623285i
$13$	2.81952	+	2.24729i	0.781995	+	0.623285i
$14$	−2.92291	−	5.06264i	−0.781182	−	1.35305i
$15$	−5.67816	−	1.93305i	−1.46609	−	0.499112i
$16$	2.46979	+	4.27780i	0.617447	+	1.06945i
$17$	1.20773	+	2.09186i	0.292919	+	0.507350i	0.974499	−	0.224394i	$-0.0720402\pi$
$17$	1.20773	+	2.09186i	0.292919	+	0.507350i	−0.681580	+	0.731744i	$0.738707\pi$
$18$	−4.99706	+	2.05955i	−1.17782	+	0.485440i
$19$	−0.877705	−	1.52023i	−0.201359	−	0.348765i	0.747607	−	0.664141i	$-0.231203\pi$
$19$	−0.877705	−	1.52023i	−0.201359	−	0.348765i	−0.948967	+	0.315376i	$0.897869\pi$
$20$	−4.31433			−0.964714
$21$	−4.22868	+	3.70187i	−0.922774	+	0.807815i
$22$	−0.548710	+	0.950393i	−0.116985	+	0.202625i
$23$	0.162448			0.0338728			0.0169364	−	0.999857i	$-0.494609\pi$
$23$	0.162448			0.0338728			0.0169364	+	0.999857i	$0.494609\pi$
$24$	1.77076	−	1.55016i	0.361454	−	0.316424i
$25$	−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
$29$	−1.45362	−	2.51774i	−0.269930	−	0.467532i	0.698914	−	0.715206i	$-0.253667\pi$
$29$	−1.45362	−	2.51774i	−0.269930	−	0.467532i	−0.968843	+	0.247674i	$0.920334\pi$
$30$	2.09889	+	10.6006i	0.383204	+	1.93540i
$31$	−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	$-0.478285\pi$
$32$	3.09086	−	5.35353i	0.546392	−	0.946379i
$33$	0.998756	+	0.340013i	0.173861	+	0.0591887i
$34$	2.17587	−	3.76872i	0.373159	−	0.646331i
$35$	5.61840	+	9.73136i	0.949683	+	1.64490i
$36$	2.96111	+	2.28044i	0.493518	+	0.380073i
$37$	−0.826776	+	1.43202i	−0.135921	+	0.235422i	−0.925949	−	0.377649i	$-0.876733\pi$
$37$	−0.826776	+	1.43202i	−0.135921	+	0.235422i	0.790028	+	0.613071i	$0.210066\pi$
$38$	−1.58129	+	2.73887i	−0.256519	+	0.444303i
$39$	−6.23835	+	0.287986i	−0.998936	+	0.0461147i
$40$	−2.35270	−	4.07500i	−0.371995	−	0.644314i
$41$	−8.22245			−1.28413			−0.642065	−	0.766650i	$-0.721922\pi$
$41$	−8.22245			−1.28413			−0.642065	+	0.766650i	$0.721922\pi$
$42$	9.58506	+	3.26310i	1.47901	+	0.503508i
$43$	−12.0056			−1.83083			−0.915415	−	0.402512i	$-0.868137\pi$
$43$	−12.0056			−1.83083			−0.915415	+	0.402512i	$0.868137\pi$
$44$	0.758866			0.114403
$45$	9.60531	−	3.95885i	1.43188	−	0.590150i
$46$	−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	$-0.0544215\pi$
$48$	−8.09912	−	2.75724i	−1.16901	−	0.397973i
$49$	3.52854			0.504077
$50$	12.5982			1.78165
$51$	−3.96050	−	1.34830i	−0.554581	−	0.188800i
$52$	−4.18093	+	1.64216i	−0.579790	+	0.227726i
$53$	9.43717			1.29630			0.648148	−	0.761515i	$-0.275544\pi$
$53$	9.43717			1.29630			0.648148	+	0.761515i	$0.275544\pi$
$54$	4.16264	−	8.38508i	0.566463	−	1.14106i
$55$	1.05473	−	1.82684i	0.142219	−	0.246331i
$56$	−4.40882			−0.589153
$57$	2.87824	+	0.979859i	0.381233	+	0.129785i
$58$	−2.61886	+	4.53599i	−0.343873	+	0.595605i
$59$	4.13217	−	7.15713i	0.537963	−	0.931779i	−0.461051	−	0.887374i	$-0.652527\pi$
$59$	4.13217	−	7.15713i	0.537963	−	0.931779i	0.999014	−	0.0444054i	$-0.0141393\pi$
$60$	5.62256	−	4.92210i	0.725870	−	0.635441i
$61$	9.92836			1.27120			0.635598	−	0.772020i	$-0.280753\pi$
$61$	9.92836			1.27120			0.635598	+	0.772020i	$0.280753\pi$
$62$	−8.32497	+	14.4193i	−1.05727	+	1.83125i
$63$	1.28758	−	9.64878i	0.162219	−	1.21563i
$64$	−1.25794			−0.157242
$65$	−1.85774	+	12.3472i	−0.230424	+	1.53149i
$66$	−0.369183	−	1.86459i	−0.0454433	−	0.229515i
$67$	2.29525			0.280410			0.140205	−	0.990123i	$-0.455224\pi$
$67$	2.29525			0.280410			0.140205	+	0.990123i	$0.455224\pi$
$68$	−3.00924			−0.364923
$69$	−0.211707	+	0.185333i	−0.0254866	+	0.0223115i
$70$	10.1222	−	17.5322i	1.20983	−	2.09549i
$71$	−4.87460	−	8.44305i	−0.578508	−	1.00201i	−0.995651	−	0.0931644i	$-0.970302\pi$
$71$	−4.87460	−	8.44305i	−0.578508	−	1.00201i	0.417143	−	0.908841i	$-0.363032\pi$
$72$	−0.539172	+	4.04042i	−0.0635420	+	0.476168i
$73$	−2.59634			−0.303878			−0.151939	−	0.988390i	$-0.548552\pi$
$73$	−2.59634			−0.303878			−0.151939	+	0.988390i	$0.548552\pi$
$74$	2.97906			0.346309
$75$	−2.35242	−	11.8811i	−0.271634	−	1.37191i
$76$	2.18692			0.250857
$77$	−0.988245	−	1.71169i	−0.112621	−	0.195065i
$78$	6.06889	+	9.47394i	0.687166	+	1.07271i
$79$	−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
$81$	−8.68507	−	2.35998i	−0.965008	−	0.262220i
$82$	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	$0.316874\pi$
$84$	−1.35990	−	6.86830i	−0.148378	−	0.749393i
$85$	−4.18245	+	7.24421i	−0.453650	+	0.785745i
$86$	10.8147	+	18.7316i	1.16618	+	2.01988i
$87$	4.76682	+	1.62280i	0.511056	+	0.173982i
$88$	0.413827	+	0.716770i	0.0441141	+	0.0764079i
$89$	4.93949	−	8.55544i	0.523584	−	0.906875i	−0.476039	−	0.879424i	$-0.657928\pi$
$89$	4.93949	−	8.55544i	0.523584	−	0.906875i	0.999623	−	0.0274506i	$-0.00873889\pi$
$90$	−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
$93$	15.1530	+	5.15864i	1.57129	+	0.534926i
$94$	−15.8109			−1.63077
$95$	3.03954	−	5.26463i	0.311850	−	0.540140i
$96$	2.07960	+	10.5032i	0.212248	+	1.07197i
$97$	−7.47810			−0.759286			−0.379643	−	0.925133i	$-0.623953\pi$
$97$	−7.47810			−0.759286			−0.379643	+	0.925133i	$0.623953\pi$
$98$	−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
$101$	3.94810	+	6.83830i	0.392850	+	0.680437i	0.992824	−	0.119583i	$-0.0381557\pi$
$101$	3.94810	+	6.83830i	0.392850	+	0.680437i	−0.599974	+	0.800020i	$0.704822\pi$
$102$	1.46397	+	7.39391i	0.144955	+	0.732106i
$103$	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	$0.827547\pi$
$104$	−3.83101	−	3.05349i	−0.375662	−	0.299419i
$105$	−18.4243	−	6.27231i	−1.79803	−	0.612115i
$106$	−8.50108	−	14.7243i	−0.825698	−	1.43015i
$107$	1.89748	−	3.28654i	0.183437	−	0.317721i	−0.759612	−	0.650376i	$-0.774611\pi$
$107$	1.89748	−	3.28654i	0.183437	−	0.317721i	0.943049	+	0.332655i	$0.107944\pi$
$108$	−6.46070	+	0.406320i	−0.621681	+	0.0390981i
$109$	−12.8213			−1.22806			−0.614028	−	0.789284i	$-0.710452\pi$
$109$	−12.8213			−1.22806			−0.614028	+	0.789284i	$0.710452\pi$
$110$	−3.80042			−0.362356
$111$	−0.556272	−	2.80949i	−0.0527990	−	0.266665i
$112$	8.01389	+	13.8805i	0.757242	+	1.31158i
$113$	−2.98803	+	5.17543i	−0.281091	+	0.486863i	−0.971654	−	0.236409i	$-0.924029\pi$
$113$	−2.98803	+	5.17543i	−0.281091	+	0.486863i	0.690563	+	0.723272i	$0.257363\pi$
$114$	−1.06392	−	5.37343i	−0.0996455	−	0.503268i
$115$	0.281283	+	0.487197i	0.0262298	+	0.0454314i
$116$	3.62188			0.336283
$117$	7.80145	−	7.49248i	0.721245	−	0.692680i
$118$	−14.8892			−1.37066
$119$	3.91882	+	6.78760i	0.359238	+	0.622218i
$120$	7.71517	+	2.62653i	0.704295	+	0.239768i
$121$	5.31448	−	9.20495i	0.483135	−	0.836814i
$122$	−8.94355	−	15.4907i	−0.809711	−	1.40246i
$123$	10.7157	−	9.38077i	0.966206	−	0.845836i
$124$	11.5134			1.03394
$125$	−6.90087			−0.617233
$126$	−16.2143	+	6.68276i	−1.44449	+	0.595348i
$127$	−0.321192	+	0.556321i	−0.0285012	+	0.0493655i	−0.879924	−	0.475114i	$-0.842407\pi$
$127$	−0.321192	+	0.556321i	−0.0285012	+	0.0493655i	0.851423	+	0.524480i	$0.175740\pi$
$128$	−5.04856	−	8.74437i	−0.446234	−	0.772900i
$129$	15.6460	−	13.6968i	1.37755	−	1.20594i
$130$	20.9382	−	8.22395i	1.83640	−	0.721288i
$131$	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	$0.604548\pi$
$132$	−0.988977	+	0.865771i	−0.0860794	+	0.0753557i
$133$	−2.84795	−	4.93280i	−0.246949	−	0.427728i
$134$	−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
$137$	−4.26192			−0.364120			−0.182060	−	0.983287i	$-0.558277\pi$
$137$	−4.26192			−0.364120			−0.182060	+	0.983287i	$0.558277\pi$
$138$	0.479873	+	0.163366i	0.0408495	+	0.0139066i
$139$	0.361151	−	0.625532i	0.0306324	−	0.0530569i	−0.850303	−	0.526294i	$-0.823581\pi$
$139$	0.361151	−	0.625532i	0.0306324	−	0.0530569i	0.880935	+	0.473237i	$0.156915\pi$
$140$	−13.9990			−1.18313
$141$	2.95233	+	14.9110i	0.248631	+	1.25573i
$142$	−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
$146$	2.33880	+	4.05092i	0.193560	+	0.335256i
$147$	−4.59849	+	4.02561i	−0.379277	+	0.332027i
$148$	−1.03001	−	1.78403i	−0.0846665	−	0.146647i
$149$	0.133320	−	0.230917i	0.0109220	−	0.0189174i	−0.860513	−	0.509429i	$-0.829857\pi$
$149$	0.133320	−	0.230917i	0.0109220	−	0.0189174i	0.871435	+	0.490511i	$0.163190\pi$
$150$	−16.4183	+	14.3729i	−1.34055	+	1.17355i
$151$	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
$153$	6.69968	−	2.76129i	0.541637	−	0.223237i
$154$	−1.78044	+	3.08381i	−0.143472	+	0.248500i
$155$	16.0022	−	27.7166i	1.28533	−	2.22625i
$156$	3.57522	−	6.91001i	0.286246	−	0.553244i
$157$	−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	$0.938249\pi$
$158$	9.14280			0.727362
$159$	−12.2988	+	10.7666i	−0.975358	+	0.853848i
$160$	21.4076			1.69242
$161$	0.527108			0.0415419
$162$	4.14144	+	15.6767i	0.325382	+	1.23168i
$163$	7.27273	+	12.5967i	0.569644	+	0.986653i	0.996601	+	0.0823808i	$0.0262524\pi$
$163$	7.27273	+	12.5967i	0.569644	+	0.986653i	−0.426957	+	0.904272i	$0.640414\pi$
$164$	5.12184	−	8.87128i	0.399948	−	0.692731i
$165$	0.709641	+	3.58410i	0.0552455	+	0.279022i
$166$	14.9222			1.15819
$167$	−12.8810			−0.996761			−0.498380	−	0.866959i	$-0.666072\pi$
$167$	−12.8810			−0.996761			−0.498380	+	0.866959i	$0.666072\pi$
$168$	5.74570	−	5.02990i	0.443291	−	0.388065i
$169$	2.89941	+	12.6725i	0.223031	+	0.974811i
$170$	15.0703			1.15584
$171$	−4.86891	+	2.00673i	−0.372335	+	0.153458i
$172$	7.47837	−	12.9529i	0.570220	−	0.987650i
$173$	−0.622550			−0.0473316			−0.0236658	−	0.999720i	$-0.507534\pi$
$173$	−0.622550			−0.0473316			−0.0236658	+	0.999720i	$0.507534\pi$
$174$	−1.76202	−	8.89923i	−0.133579	−	0.674649i
$175$	−11.3449	+	19.6499i	−0.857592	+	1.48539i
$176$	1.50442	−	2.60574i	0.113400	−	0.196415i
$177$	2.78021	+	14.0417i	0.208973	+	1.05544i
$178$	−17.7981			−1.33402
$179$	0.386554	−	0.669532i	0.0288924	−	0.0500431i	−0.851218	−	0.524813i	$-0.824135\pi$
$179$	0.386554	−	0.669532i	0.0288924	−	0.0500431i	0.880110	+	0.474770i	$0.157469\pi$
$180$	−1.71199	+	12.8293i	−0.127605	+	0.956237i
$181$	4.86050			0.361278			0.180639	−	0.983549i	$-0.442183\pi$
$181$	4.86050			0.361278			0.180639	+	0.983549i	$0.442183\pi$
$182$	3.13597	−	20.8428i	0.232454	−	1.54497i
$183$	−12.9389	+	11.3270i	−0.956474	+	0.837316i
$184$	−0.220726			−0.0162721
$185$	−5.72633			−0.421008
$186$	−5.60121	−	28.2894i	−0.410701	−	2.07428i
$187$	0.735669	−	1.27422i	0.0537974	−	0.0931799i
$188$	5.46664	+	9.46850i	0.398696	+	0.690561i
$189$	9.33003	+	14.0435i	0.678660	+	1.02152i
$190$	−10.9522			−0.794553
$191$	−4.54169			−0.328625			−0.164312	−	0.986408i	$-0.552541\pi$
$191$	−4.54169			−0.328625			−0.164312	+	0.986408i	$0.552541\pi$
$192$	1.63938	−	1.43515i	0.118312	−	0.103573i
$193$	20.8535			1.50107			0.750534	−	0.660832i	$-0.229796\pi$
$193$	20.8535			1.50107			0.750534	+	0.660832i	$0.229796\pi$
$194$	6.73633	+	11.6677i	0.483640	+	0.837689i
$195$	−11.6656	−	18.2107i	−0.835388	−	1.30410i
$196$	−2.19796	+	3.80697i	−0.156997	+	0.271927i
$197$	5.56079	−	9.63157i	0.396190	−	0.686221i	−0.597062	−	0.802195i	$-0.703666\pi$
$197$	5.56079	−	9.63157i	0.396190	−	0.686221i	0.993252	+	0.115974i	$0.0369989\pi$
$198$	2.60839	+	2.00880i	0.185370	+	0.142759i
$199$	5.04128	+	8.73176i	0.357367	+	0.618978i	0.987520	−	0.157493i	$-0.0503412\pi$
$199$	5.04128	+	8.73176i	0.357367	+	0.618978i	−0.630153	+	0.776471i	$0.717008\pi$
$200$	4.75066	−	8.22839i	0.335922	−	0.581835i
$201$	−2.99124	+	2.61859i	−0.210986	+	0.184701i
$202$	7.11295	−	12.3200i	0.500465	−	0.866832i
$203$	−4.71665	−	8.16948i	−0.331044	−	0.573385i
$204$	3.92172	−	3.43316i	0.274576	−	0.240369i
$205$	−14.2374	−	24.6599i	−0.994382	−	1.72232i
$206$	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
$210$	6.81043	+	34.3966i	0.469964	+	2.37359i
$211$	−20.4202			−1.40578			−0.702891	−	0.711298i	$-0.748108\pi$
$211$	−20.4202			−1.40578			−0.702891	+	0.711298i	$0.748108\pi$
$212$	−5.87850	+	10.1819i	−0.403737	+	0.699293i
$213$	15.9852	+	5.44194i	1.09529	+	0.372875i
$214$	−6.83707			−0.467372
$215$	−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
$218$	11.5495	+	20.0043i	0.782231	+	1.35486i
$219$	3.38362	−	2.96209i	0.228644	−	0.200159i
$220$	1.31400	+	2.27591i	0.0885896	+	0.153442i
$221$	−1.29577	+	8.61216i	−0.0871629	+	0.579317i
$222$	−3.88240	+	3.39873i	−0.260570	+	0.228108i
$223$	12.3480	+	21.3873i	0.826882	+	1.43220i	0.900473	+	0.434912i	$0.143221\pi$
$223$	12.3480	+	21.3873i	0.826882	+	1.43220i	−0.0735912	+	0.997288i	$0.523446\pi$
$224$	10.0291	−	17.3710i	0.670100	−	1.16065i
$225$	16.6206	+	12.8000i	1.10804	+	0.853332i
$226$	10.7666			0.716182
$227$	−13.2083			−0.876666			−0.438333	−	0.898813i	$-0.644431\pi$
$227$	−13.2083			−0.876666			−0.438333	+	0.898813i	$0.644431\pi$
$228$	−2.85006	+	2.49500i	−0.188750	+	0.165236i
$229$	−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	$-0.440632\pi$
$230$	0.506764	−	0.877742i	0.0334151	−	0.0578766i
$231$	3.24073	+	1.10326i	0.213225	+	0.0725894i
$232$	1.97510	+	3.42097i	0.129671	+	0.224597i
$233$	−6.61682			−0.433482			−0.216741	−	0.976229i	$-0.569543\pi$
$233$	−6.61682			−0.433482			−0.216741	+	0.976229i	$0.569543\pi$
$234$	−18.7177	−	5.42289i	−1.22362	−	0.354505i
$235$	30.3917			1.98253
$236$	5.14793	+	8.91648i	0.335102	+	0.580414i
$237$	−1.70721	−	8.62239i	−0.110895	−	0.560084i
$238$	7.06021	−	12.2286i	0.457645	−	0.792665i
$239$	−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	$0.929830\pi$
$240$	−5.75463	−	29.0642i	−0.371460	−	1.87609i
$241$	18.3680			1.18319			0.591593	−	0.806237i	$-0.298499\pi$
$241$	18.3680			1.18319			0.591593	+	0.806237i	$0.298499\pi$
$242$	−19.1493			−1.23096
$243$	14.0111	−	6.83298i	0.898811	−	0.438336i
$244$	−6.18447	+	10.7118i	−0.395920	+	0.685753i
$245$	6.10975	+	10.5824i	0.390338	+	0.676085i
$246$	−24.2891	−	8.26891i	−1.54862	−	0.527206i
$247$	0.941684	−	6.25878i	0.0599179	−	0.398237i
$248$	6.27854	+	10.8748i	0.398688	+	0.690548i
$249$	−2.78638	−	14.0728i	−0.176579	−	0.891828i
$250$	6.21636	+	10.7671i	0.393157	+	0.680968i
$251$	5.22170	+	9.04424i	0.329591	+	0.570868i	0.982431	−	0.186628i	$-0.0597560\pi$
$251$	5.22170	+	9.04424i	0.329591	+	0.570868i	−0.652840	+	0.757496i	$0.726423\pi$
$252$	9.60812	+	7.39949i	0.605255	+	0.466124i
$253$	−0.0494762	−	0.0856952i	−0.00311054	−	0.00538761i
$254$	1.15733			0.0726172
$255$	−2.81404	−	14.2125i	−0.176222	−	0.890022i
$256$	−10.3535	+	17.9328i	−0.647094	+	1.12080i
$257$	−27.6727			−1.72617			−0.863087	−	0.505055i	$-0.831472\pi$
$257$	−27.6727			−1.72617			−0.863087	+	0.505055i	$0.831472\pi$
$258$	−35.4644	−	12.0734i	−2.20792	−	0.751656i
$259$	−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
$263$	12.4727	+	21.6034i	0.769102	+	1.33212i	0.938051	+	0.346498i	$0.112629\pi$
$263$	12.4727	+	21.6034i	0.769102	+	1.33212i	−0.168949	+	0.985625i	$0.554037\pi$
$264$	−1.35706	−	0.461991i	−0.0835210	−	0.0284336i
$265$	16.3407	+	28.3029i	1.00380	+	1.73863i
$266$	−5.13092	+	8.88701i	−0.314597	+	0.544897i
$267$	3.32339	+	16.7850i	0.203388	+	1.02723i
$268$	−1.42973	+	2.47637i	−0.0873349	+	0.151269i
$269$	9.61561	+	16.6547i	0.586274	+	1.01546i	0.994715	+	0.102672i	$0.0327393\pi$
$269$	9.61561	+	16.6547i	0.586274	+	1.01546i	−0.408441	+	0.912785i	$0.633927\pi$
$270$	32.3553	−	2.03486i	1.96908	−	0.123837i
$271$	−1.80591	+	3.12793i	−0.109701	+	0.190008i	−0.915649	−	0.401978i	$-0.868323\pi$
$271$	−1.80591	+	3.12793i	−0.109701	+	0.190008i	0.805948	+	0.591986i	$0.201656\pi$
$272$	−5.96569	+	10.3329i	−0.361723	+	0.626523i
$273$	−20.2420	+	0.934449i	−1.22510	+	0.0565554i
$274$	3.83917	+	6.64963i	0.231933	+	0.401719i
$275$	4.25948			0.256856
$276$	−0.0680831	−	0.343859i	−0.00409812	−	0.0206979i
$277$	−22.8143			−1.37078			−0.685388	−	0.728178i	$-0.740367\pi$
$277$	−22.8143			−1.37078			−0.685388	+	0.728178i	$0.740367\pi$
$278$	−1.30131			−0.0780474
$279$	−25.6332	+	10.5648i	−1.53462	+	0.632497i
$280$	−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	$0.266646\pi$
$282$	20.6053	−	18.0383i	1.22703	−	1.07416i
$283$	−6.88491			−0.409265			−0.204633	−	0.978839i	$-0.565600\pi$
$283$	−6.88491			−0.409265			−0.204633	+	0.978839i	$0.565600\pi$
$284$	12.1457			0.720716
$285$	2.04506	+	10.3288i	0.121139	+	0.611823i
$286$	−3.68291	+	1.44655i	−0.217775	+	0.0855361i
$287$	−26.6800			−1.57487
$288$	−14.6930	−	11.3155i	−0.865791	−	0.666771i
$289$	5.58275	−	9.66961i	0.328397	−	0.568801i
$290$	−18.1385			−1.06513
$291$	9.74568	−	8.53156i	0.571302	−	0.500129i
$292$	1.61728	−	2.80121i	0.0946442	−	0.163929i
$293$	−2.62095	+	4.53962i	−0.153118	+	0.265208i	−0.932372	−	0.361500i	$-0.882265\pi$
$293$	−2.62095	+	4.53962i	−0.153118	+	0.265208i	0.779254	+	0.626708i	$0.215598\pi$
$294$	10.4233	+	3.54847i	0.607899	+	0.206951i
$295$	28.6198			1.66631
$296$	1.12338	−	1.94575i	0.0652950	−	0.113094i
$297$	1.40740	−	2.83502i	0.0816655	−	0.164504i
$298$	−0.480382			−0.0278278
$299$	0.458027	+	0.365068i	0.0264884	+	0.0211124i
$300$	14.2840	+	4.86279i	0.824686	+	0.280753i
$301$	−38.9553			−2.24534
$302$	−0.0747290			−0.00430017
$303$	−12.9469	−	4.40760i	−0.743781	−	0.253210i
$304$	4.33549	−	7.50929i	0.248657	−	0.430687i
$305$	17.1912	+	29.7760i	0.984366	+	1.70497i
$306$	−10.3434	−	7.96575i	−0.591293	−	0.455372i
$307$	6.73227			0.384231			0.192115	−	0.981372i	$-0.438465\pi$
$307$	6.73227			0.384231			0.192115	+	0.981372i	$0.438465\pi$
$308$	2.46235			0.140305
$309$	−0.605000	−	0.205964i	−0.0344173	−	0.0117169i
$310$	−57.6596			−3.27484
$311$	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	$0.489868\pi$
$312$	8.47634	−	0.391300i	0.479878	−	0.0221530i
$313$	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
$315$	31.1670	−	12.8455i	1.75606	−	0.723765i
$316$	−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	$0.202455\pi$
$318$	27.8774	+	9.49049i	1.56329	+	0.532200i
$319$	−0.885443	+	1.53363i	−0.0495753	+	0.0858669i
$320$	−2.17815	−	3.77266i	−0.121762	−	0.210898i
$321$	1.27667	+	6.44790i	0.0712565	+	0.359887i
$322$	−0.474823	−	0.822417i	−0.0264608	−	0.0458315i
$323$	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
$327$	16.7091	−	14.6275i	0.924014	−	0.808900i
$328$	11.1722			0.616883
$329$	14.2380	−	24.6610i	0.784968	−	1.35960i
$330$	4.95282	−	4.33580i	0.272644	−	0.238678i
$331$	3.87157			0.212801			0.106400	−	0.994323i	$-0.466067\pi$
$331$	3.87157			0.212801			0.106400	+	0.994323i	$0.466067\pi$
$332$	−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
$335$	3.97429	+	6.88367i	0.217139	+	0.376095i
$336$	−26.2798	−	8.94660i	−1.43368	−	0.488077i
$337$	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	$0.787314\pi$
$338$	17.1605	−	15.9393i	0.933406	−	0.866984i
$339$	−2.01041	−	10.1537i	−0.109191	−	0.551475i
$340$	−5.21057	−	9.02497i	−0.282583	−	0.489447i
$341$	−2.81470	+	4.87519i	−0.152424	+	0.264007i
$342$	7.51694	+	5.78901i	0.406469	+	0.313034i
$343$	−11.2641			−0.608204
$344$	16.3125			0.879511
$345$	−0.922407	−	0.314021i	−0.0496607	−	0.0169063i
$346$	0.560797	+	0.971330i	0.0301487	+	0.0522190i
$347$	9.50851	−	16.4692i	0.510444	−	0.884114i	−0.489483	−	0.872013i	$-0.662815\pi$
$347$	9.50851	−	16.4692i	0.510444	−	0.884114i	0.999927	−	0.0121015i	$-0.00385213\pi$
$348$	−4.72015	+	4.13211i	−0.253026	+	0.221504i
$349$	7.27021	+	12.5924i	0.389165	+	0.674054i	0.992337	−	0.123557i	$-0.0394301\pi$
$349$	7.27021	+	12.5924i	0.389165	+	0.674054i	−0.603172	+	0.797611i	$0.706097\pi$
$350$	40.8782			2.18503
$351$	−1.61911	+	18.6649i	−0.0864217	+	0.996259i
$352$	−3.76548			−0.200701
$353$	−7.92105	−	13.7197i	−0.421595	−	0.730223i	0.574501	−	0.818504i	$-0.305196\pi$
$353$	−7.92105	−	13.7197i	−0.421595	−	0.730223i	−0.996096	+	0.0882805i	$0.971863\pi$
$354$	19.4040	−	16.9867i	1.03131	−	0.902831i
$355$	16.8810	−	29.2387i	0.895949	−	1.55183i
$356$	6.15370	+	10.6585i	0.326146	+	0.564901i
$357$	−12.8509	−	4.37492i	−0.680143	−	0.231545i
$358$	−1.39284			−0.0736141
$359$	15.2227			0.803426			0.401713	−	0.915766i	$-0.368415\pi$
$359$	15.2227			0.803426			0.401713	+	0.915766i	$0.368415\pi$
$360$	−13.0512	+	5.37907i	−0.687857	+	0.283502i
$361$	7.95927	−	13.7859i	0.418909	−	0.725571i
$362$	−4.37838	−	7.58357i	−0.230122	−	0.398584i
$363$	3.57569	+	18.0593i	0.187675	+	0.947868i
$364$	−13.5661	+	5.32842i	−0.711059	+	0.279285i
$365$	−4.49562	−	7.78664i	−0.235312	−	0.407571i
$366$	29.3284	+	9.98446i	1.53302	+	0.521896i
$367$	−1.08716	−	1.88301i	−0.0567491	−	0.0982923i	0.836255	−	0.548340i	$-0.184740\pi$
$367$	−1.08716	−	1.88301i	−0.0567491	−	0.0982923i	−0.893004	+	0.450048i	$0.851407\pi$
$368$	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
$371$	30.6215			1.58979
$372$	−15.0047	+	13.1354i	−0.777956	+	0.681038i
$373$	−1.24333	+	2.15351i	−0.0643771	+	0.111504i	−0.896418	−	0.443211i	$-0.853839\pi$
$373$	−1.24333	+	2.15351i	−0.0643771	+	0.111504i	0.832040	+	0.554715i	$0.187173\pi$
$374$	−2.65078			−0.137069
$375$	8.99343	−	7.87302i	0.464419	−	0.406561i
$376$	−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	−0.999997	−	0.00234514i	$-0.999254\pi$
$379$	−9.69440	+	16.7912i	−0.497968	+	0.862505i	0.502030	+	0.864850i	$0.332587\pi$
$380$	3.78671	+	6.55878i	0.194254	+	0.336458i
$381$	−0.216105	−	1.09145i	−0.0110714	−	0.0559168i
$382$	4.09119	+	7.08614i	0.209323	+	0.362559i
$383$	7.02574	−	12.1689i	0.358998	−	0.621804i	−0.628795	−	0.777571i	$-0.716452\pi$
$383$	7.02574	−	12.1689i	0.358998	−	0.621804i	0.987794	+	0.155767i	$0.0497850\pi$
$384$	16.5557	+	5.63615i	0.844852	+	0.287619i
$385$	3.42234	−	5.92767i	0.174419	−	0.302102i
$386$	−18.7850	−	32.5366i	−0.956131	−	1.65607i
$387$	−4.76399	+	35.7002i	−0.242167	+	1.81474i
$388$	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	$0.288711\pi$
$390$	−17.9048	+	34.6055i	−0.906643	+	1.75232i
$391$	0.196194	+	0.339819i	0.00992198	+	0.0171854i
$392$	−4.79438			−0.242153
$393$	−24.7135	−	8.41337i	−1.24663	−	0.424398i
$394$	−20.0368			−1.00944
$395$	−17.5742			−0.884255
$396$	0.301130	−	2.25660i	0.0151324	−	0.113398i
$397$	−8.04573	−	13.9356i	−0.403804	−	0.699409i	0.590378	−	0.807127i	$-0.298979\pi$
$397$	−8.04573	−	13.9356i	−0.403804	−	0.699409i	−0.994181	+	0.107719i	$0.965645\pi$
$398$	9.08245	−	15.7313i	0.455262	−	0.788537i
$399$	9.33924	+	3.17942i	0.467547	+	0.159170i
$400$	−34.5410			−1.72705
$401$	−34.1863			−1.70718			−0.853590	−	0.520945i	$-0.825580\pi$
$401$	−34.1863			−1.70718			−0.853590	+	0.520945i	$0.825580\pi$
$402$	6.78018	+	2.30822i	0.338165	+	0.115124i
$403$	4.95766	−	32.9505i	0.246959	−	1.64138i
$404$	−9.83722			−0.489420
$405$	−7.96065	−	30.1337i	−0.395568	−	1.49735i
$406$	−8.49759	+	14.7183i	−0.421728	+	0.730455i
$407$	1.00723			0.0499265
$408$	5.38131	+	1.83200i	0.266415	+	0.0906973i
$409$	17.3826	−	30.1076i	0.859516	−	1.48873i	−0.0128745	−	0.999917i	$-0.504098\pi$
$409$	17.3826	−	30.1076i	0.859516	−	1.48873i	0.872391	−	0.488809i	$-0.162568\pi$
$410$	−25.6503	+	44.4276i	−1.26678	+	2.19412i
$411$	5.55426	−	4.86231i	0.273971	−	0.239840i
$412$	−0.459686			−0.0226471
$413$	13.4080	−	23.2233i	0.659762	−	1.14274i
$414$	−0.811764	+	0.334570i	−0.0398960	+	0.0164432i
$415$	−28.6833			−1.40801
$416$	20.7457	−	8.14834i	1.01714	−	0.399505i
$417$	0.242990	+	1.22724i	0.0118993	+	0.0600982i
$418$	1.92642			0.0942244
$419$	−2.83069			−0.138288			−0.0691442	−	0.997607i	$-0.522027\pi$
$419$	−2.83069			−0.138288			−0.0691442	+	0.997607i	$0.522027\pi$
$420$	18.2439	−	15.9711i	0.890213	−	0.779310i
$421$	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
$423$	−20.8591	−	16.0642i	−1.01420	−	0.781068i
$424$	−12.8227			−0.622726
$425$	−16.8907			−0.819319
$426$	−5.90881	−	29.8429i	−0.286283	−	1.44589i
$427$	32.2153			1.55901
$428$	2.36392	+	4.09443i	0.114264	+	0.197912i
$429$	2.05191	+	3.20316i	0.0990670	+	0.154650i
$430$	−37.4518	+	64.8685i	−1.80609	+	3.12823i
$431$	−14.2820	+	24.7371i	−0.687937	+	1.19154i	0.284567	+	0.958656i	$0.408150\pi$
$431$	−14.2820	+	24.7371i	−0.687937	+	1.19154i	−0.972504	+	0.232886i	$0.925183\pi$
$432$	−11.4129	+	22.9898i	−0.549103	+	1.10610i
$433$	5.26413	+	9.11774i	0.252978	+	0.438171i	0.964344	−	0.264651i	$-0.0852566\pi$
$433$	5.26413	+	9.11774i	0.252978	+	0.438171i	−0.711366	+	0.702821i	$0.751923\pi$
$434$	−27.0126	+	46.7872i	−1.29665	+	2.24586i
$435$	3.38694	+	17.1060i	0.162392	+	0.820171i
$436$	7.98649	−	13.8330i	0.382484	−	0.662481i
$437$	−0.142582	−	0.246959i	−0.00682061	−	0.0118136i
$438$	−7.66958	−	2.61100i	−0.366467	−	0.124759i
$439$	−11.9260	−	20.6565i	−0.569199	−	0.985881i	−0.996645	−	0.0818405i	$-0.973920\pi$
$439$	−11.9260	−	20.6565i	−0.569199	−	0.985881i	0.427447	−	0.904041i	$-0.359413\pi$
$440$	−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	$0.149032\pi$
$444$	3.37770	+	1.14989i	0.160298	+	0.0545715i
$445$	34.2114			1.62177
$446$	22.2463	−	38.5317i	1.05339	−	1.82453i
$447$	0.0897003	+	0.453038i	0.00424268	+	0.0214280i
$448$	−4.08171			−0.192843
$449$	11.4132	+	19.7682i	0.538622	+	0.932920i	0.998979	+	0.0451861i	$0.0143881\pi$
$449$	11.4132	+	19.7682i	0.538622	+	0.932920i	−0.460357	+	0.887734i	$0.652279\pi$
$450$	4.99916	−	37.4625i	0.235663	−	1.76600i
$451$	2.50427	+	4.33753i	0.117922	+	0.204246i
$452$	−3.72255	−	6.44764i	−0.175094	−	0.303271i
$453$	0.0139539	+	0.0704754i	0.000655613	+	0.00331122i
$454$	11.8981	+	20.6082i	0.558408	+	0.967191i
$455$	−6.02794	+	40.0639i	−0.282594	+	1.87823i
$456$	−3.91080	−	1.33138i	−0.183140	−	0.0623475i
$457$	−6.68817	−	11.5842i	−0.312859	−	0.541888i	0.666121	−	0.745844i	$-0.267954\pi$
$457$	−6.68817	−	11.5842i	−0.312859	−	0.541888i	−0.978980	+	0.203956i	$0.934620\pi$
$458$	−20.6736	+	35.8077i	−0.966013	+	1.67318i
$459$	−5.58095	+	11.2421i	−0.260496	+	0.524735i
$460$	−0.700856			−0.0326776
$461$	−4.05793			−0.188997			−0.0944983	−	0.995525i	$-0.530125\pi$
$461$	−4.05793			−0.188997			−0.0944983	+	0.995525i	$0.530125\pi$
$462$	−1.19792	−	6.05017i	−0.0557321	−	0.281479i
$463$	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	$0.621096\pi$
$464$	7.18024	−	12.4365i	0.333335	−	0.577352i
$465$	10.7666	+	54.3776i	0.499289	+	2.52170i
$466$	5.96048	+	10.3239i	0.276114	+	0.478243i
$467$	2.84428			0.131617			0.0658087	−	0.997832i	$-0.479037\pi$
$467$	2.84428			0.131617			0.0658087	+	0.997832i	$0.479037\pi$
$468$	3.22412	+	13.0842i	0.149035	+	0.604818i
$469$	7.44757			0.343897
$470$	−27.3771	−	47.4184i	−1.26281	−	2.18725i
$471$	13.2992	+	4.52754i	0.612796	+	0.208618i
$472$	−5.61457	+	9.72472i	−0.258432	+	0.447617i
$473$	3.65648	+	6.33320i	0.168125	+	0.291201i
$474$	−11.9152	+	10.4308i	−0.547282	+	0.479101i
$475$	12.2751			0.563220
$476$	−9.76428			−0.447545
$477$	3.74482	−	28.0628i	0.171464	−	1.28491i
$478$	−8.31481	+	14.4017i	−0.380311	+	0.658717i
$479$	1.20092	+	2.08006i	0.0548715	+	0.0950402i	0.892156	−	0.451727i	$-0.149192\pi$
$479$	1.20092	+	2.08006i	0.0548715	+	0.0950402i	−0.837285	+	0.546767i	$0.815858\pi$
$480$	−27.8990	+	24.4234i	−1.27341	+	1.11477i
$481$	−5.54927	+	2.17960i	−0.253025	+	0.0993813i
$482$	−16.5460	−	28.6585i	−0.753650	−	1.30536i
$483$	−0.686942	+	0.601363i	−0.0312570	+	0.0273630i
$484$	6.62087	+	11.4677i	0.300949	+	0.521259i
$485$	−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	0.904414	−	0.426655i	$-0.140308\pi$
$487$	1.82532	+	3.16155i	0.0827133	+	0.143264i	−0.821701	+	0.569918i	$0.806975\pi$
$488$	−13.4901			−0.610669
$489$	−23.8493	−	8.11918i	−1.07850	−	0.367162i
$490$	11.0074	−	19.0654i	0.497265	−	0.861287i
$491$	16.4593			0.742800			0.371400	−	0.928473i	$-0.378878\pi$
$491$	16.4593			0.742800			0.371400	+	0.928473i	$0.378878\pi$
$492$	3.44608	+	17.4047i	0.155361	+	0.784664i
$493$	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
$497$	−15.8169	−	27.3958i	−0.709487	−	1.22887i
$498$	−19.4470	+	17.0243i	−0.871443	+	0.762878i
$499$	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	$0.747652\pi$
$500$	4.29862	−	7.44542i	0.192240	−	0.332969i
$501$	16.7869	−	14.6956i	0.749983	−	0.656550i
$502$	9.40749	−	16.2942i	0.419877	−	0.727248i
$503$	−7.32319	−	12.6841i	−0.326525	−	0.565558i	0.655295	−	0.755373i	$-0.272544\pi$
$503$	−7.32319	−	12.6841i	−0.326525	−	0.565558i	−0.981820	+	0.189816i	$0.939211\pi$
$504$	−1.74949	+	13.1102i	−0.0779284	+	0.583977i
$505$	−13.6725	+	23.6814i	−0.608416	+	1.05381i
$506$	−0.0891370	+	0.154390i	−0.00396262	+	0.00686346i
$507$	−18.2364	−	13.2074i	−0.809905	−	0.586561i
$508$	−0.400147	−	0.693074i	−0.0177536	−	0.0307502i
$509$	43.0747			1.90925			0.954627	−	0.297804i	$-0.0962541\pi$
$509$	43.0747			1.90925			0.954627	+	0.297804i	$0.0962541\pi$
$510$	−19.6401	+	17.1933i	−0.869678	+	0.761333i
$511$	−8.42451			−0.372679
$512$	17.1118			0.756242
$513$	4.05588	−	8.17003i	0.179071	−	0.360716i
$514$	24.9278	+	43.1762i	1.09952	+	1.90442i
$515$	−0.638904	+	1.10661i	−0.0281535	+	0.0487633i
$516$	5.03160	+	25.4125i	0.221504	+	1.11872i
$517$	−5.34572			−0.235105
$518$	9.66638			0.424716
$519$	0.811325	−	0.710250i	0.0356132	−	0.0311765i
$520$	2.52420	−	16.7767i	0.110693	−	0.735709i
$521$	22.2643			0.975418			0.487709	−	0.873006i	$-0.337833\pi$
$521$	22.2643			0.975418			0.487709	+	0.873006i	$0.337833\pi$
$522$	12.4492	+	9.58750i	0.544887	+	0.419633i
$523$	−2.18706	+	3.78810i	−0.0956335	+	0.165642i	−0.909873	−	0.414887i	$-0.863821\pi$
$523$	−2.18706	+	3.78810i	−0.0956335	+	0.165642i	0.814239	+	0.580529i	$0.197154\pi$
$524$	−18.7776			−0.820303
$525$	−7.63307	−	38.5514i	−0.333135	−	1.68252i
$526$	22.4711	−	38.9210i	0.979785	−	1.69704i
$527$	11.1615	−	19.3323i	0.486202	−	0.842127i
$528$	1.01221	+	5.11223i	0.0440507	+	0.222481i
$529$	−22.9736			−0.998853
$530$	29.4397	−	50.9910i	1.27878	−	2.21491i
$531$	−19.6430	−	15.1277i	−0.852435	−	0.656484i
$532$	7.09606			0.307653
$533$	−23.1834	−	18.4782i	−1.00418	−	0.800380i
$534$	23.1950	−	20.3054i	1.00375	−	0.878700i
$535$	13.1422			0.568185
$536$	−3.11867			−0.134706
$537$	0.260082	+	1.31356i	0.0112234	+	0.0566844i
$538$	17.3236	−	30.0054i	0.746875	−	1.29363i
$539$	−1.07467	−	1.86138i	−0.0462893	−	0.0801755i
$540$	−12.4054	−	18.6727i	−0.533845	−	0.803543i
$541$	28.9397			1.24422			0.622108	−	0.782932i	$-0.286277\pi$
$541$	28.9397			1.24422			0.622108	+	0.782932i	$0.286277\pi$
$542$	6.50712			0.279505
$543$	−6.33435	+	5.54522i	−0.271833	+	0.237968i
$544$	14.9318			0.640194
$545$	−22.2004	−	38.4522i	−0.950959	−	1.64711i
$546$	19.6921	+	30.7408i	0.842746	+	1.31558i
$547$	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
$549$	3.93973	−	29.5234i	0.168144	−	1.26003i
$550$	−3.83697	−	6.64583i	−0.163609	−	0.283379i
$551$	−2.55169	+	4.41966i	−0.108706	+	0.188284i
$552$	0.287657	−	0.251820i	0.0122435	−	0.0107182i
$553$	−8.23325	+	14.2604i	−0.350113	+	0.606414i
$554$	20.5513	+	35.5958i	0.873139	+	1.51232i
$555$	7.46273	−	6.53302i	0.316775	−	0.277311i
$556$	0.449928	+	0.779299i	0.0190812	+	0.0330496i
$557$	−17.0404	+	29.5149i	−0.722026	+	1.25059i	0.238161	+	0.971226i	$0.423455\pi$
$557$	−17.0404	+	29.5149i	−0.722026	+	1.25059i	−0.960187	+	0.279359i	$0.909878\pi$
$558$	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
$561$	0.494973	+	2.49990i	0.0208978	+	0.105546i
$562$	18.6612			0.787175
$563$	−3.12563	+	5.41376i	−0.131730	+	0.228163i	−0.924343	−	0.381562i	$-0.875386\pi$
$563$	−3.12563	+	5.41376i	−0.131730	+	0.228163i	0.792614	+	0.609724i	$0.208720\pi$
$564$	−17.9266	−	6.10289i	−0.754848	−	0.256978i
$565$	−20.6954			−0.870663
$566$	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
$569$	−1.95049	−	3.37835i	−0.0817688	−	0.141628i	0.822241	−	0.569140i	$-0.192724\pi$
$569$	−1.95049	−	3.37835i	−0.0817688	−	0.141628i	−0.904010	+	0.427512i	$0.859390\pi$
$570$	14.2732	−	12.4950i	0.597838	−	0.523359i
$571$	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	$0.763245\pi$
$572$	2.13964	+	1.70539i	0.0894629	+	0.0713060i
$573$	5.91886	−	5.18149i	0.247264	−	0.216460i
$574$	24.0335	+	41.6273i	1.00314	+	1.73749i
$575$	−0.567977	+	0.983766i	−0.0236863	+	0.0410259i
$576$	−0.499169	+	3.74065i	−0.0207987	+	0.155860i
$577$	26.1767			1.08975			0.544874	−	0.838518i	$-0.316577\pi$
$577$	26.1767			1.08975			0.544874	+	0.838518i	$0.316577\pi$
$578$	−20.1160			−0.836713
$579$	−27.1769	+	23.7912i	−1.12943	+	0.988729i
$580$	6.27138	+	10.8624i	0.260405	+	0.451035i
$581$	−13.4377	+	23.2748i	−0.557489	+	0.965600i
$582$	−22.0903	−	7.52035i	−0.915673	−	0.311728i
$583$	−2.87424	−	4.97832i	−0.119039	−	0.206181i
$584$	3.52776			0.145980
$585$	35.9790	+	10.4238i	1.48755	+	0.430972i
$586$	9.44390			0.390124
$587$	4.48438	+	7.76717i	0.185090	+	0.320585i	0.943607	−	0.331068i	$-0.107409\pi$
$587$	4.48438	+	7.76717i	0.185090	+	0.320585i	−0.758517	+	0.651653i	$0.774076\pi$
$588$	−1.47883	−	7.46895i	−0.0609860	−	0.308014i
$589$	−8.11147	+	14.0495i	−0.334227	+	0.578898i
$590$	−25.7810	−	44.6540i	−1.06139	−	1.83837i
$591$	3.74142	+	18.8963i	0.153901	+	0.777290i
$592$	−8.16784			−0.335696
$593$	4.06097			0.166764			0.0833820	−	0.996518i	$-0.473428\pi$
$593$	4.06097			0.166764			0.0833820	+	0.996518i	$0.473428\pi$
$594$	−5.69112	+	0.357920i	−0.233509	+	0.0146856i
$595$	−13.5711	+	23.5058i	−0.556360	+	0.963644i
$596$	0.166092	+	0.287680i	0.00680340	+	0.0117838i
$597$	−16.5318	−	5.62802i	−0.676601	−	0.230340i
$598$	0.157001	−	1.04349i	0.00642027	−	0.0426715i
$599$	−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	$0.975140\pi$
$600$	3.19634	+	16.1434i	0.130490	+	0.659051i
$601$	11.8519	+	20.5281i	0.483448	+	0.837357i	0.999819	−	0.0190078i	$-0.00605073\pi$
$601$	11.8519	+	20.5281i	0.483448	+	0.837357i	−0.516371	+	0.856365i	$0.672717\pi$
$602$	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
$605$	36.8086			1.49648
$606$	4.78574	+	24.1708i	0.194407	+	0.981870i
$607$	−18.7183	+	32.4210i	−0.759752	+	1.31593i	0.183225	+	0.983071i	$0.441346\pi$
$607$	−18.7183	+	32.4210i	−0.759752	+	1.31593i	−0.942977	+	0.332858i	$0.891987\pi$
$608$	−10.8515			−0.440085
$609$	15.4672	+	5.26561i	0.626764	+	0.213373i
$610$	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	0.397442	+	0.917627i	$0.369898\pi$
$613$	−14.7555	+	25.5572i	−0.595967	+	1.03225i	−0.993410	+	0.114618i	$0.963435\pi$
$614$	−6.06448	−	10.5040i	−0.244742	−	0.423906i
$615$	46.6884	+	15.8944i	1.88266	+	0.640925i
$616$	1.34277	+	2.32575i	0.0541019	+	0.0937073i
$617$	−2.97499	+	5.15284i	−0.119769	+	0.207445i	−0.919676	−	0.392678i	$-0.871549\pi$
$617$	−2.97499	+	5.15284i	−0.119769	+	0.207445i	0.799907	+	0.600124i	$0.204882\pi$
$618$	0.223634	+	1.12948i	0.00899590	+	0.0454345i
$619$	−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
$621$	0.467105	+	0.703085i	0.0187443	+	0.0282138i
$622$	28.0068	−	48.5093i	1.12297	−	1.94504i
$623$	16.0275	−	27.7604i	0.642128	−	1.11220i
$624$	−16.6394	−	25.9751i	−0.666107	−	1.03984i
$625$	5.53275	+	9.58301i	0.221310	+	0.383320i
$626$	−27.5969			−1.10299
$627$	−0.359715	−	1.81677i	−0.0143656	−	0.0725548i
$628$	10.1049			0.403229
$629$	−3.99410			−0.159255
$630$	−48.1177	−	37.0568i	−1.91705	−	1.47638i
$631$	−21.6580	−	37.5128i	−0.862192	−	1.49336i	−0.869809	−	0.493389i	$-0.835758\pi$
$631$	−21.6580	−	37.5128i	−0.862192	−	1.49336i	0.00761652	−	0.999971i	$-0.497576\pi$
$632$	3.44767	−	5.97154i	0.137141	−	0.237535i
$633$	26.6122	−	23.2968i	1.05774	−	0.925966i
$634$	7.19769			0.285857
$635$	−2.22461			−0.0882808
$636$	−3.95518	−	19.9759i	−0.156833	−	0.792097i
$637$	9.94879	+	7.92963i	0.394185	+	0.314184i
$638$	3.19046			0.126311
$639$	−27.0409	+	11.1450i	−1.06972	+	0.440888i
$640$	17.4834	−	30.2822i	0.691093	−	1.19701i
$641$	−18.1878			−0.718373			−0.359187	−	0.933266i	$-0.616946\pi$
$641$	−18.1878			−0.718373			−0.359187	+	0.933266i	$0.616946\pi$
$642$	8.91027	−	7.80023i	0.351660	−	0.307850i
$643$	2.94585	−	5.10237i	0.116173	−	0.201218i	−0.802075	−	0.597223i	$-0.796271\pi$
$643$	2.94585	−	5.10237i	0.116173	−	0.201218i	0.918248	+	0.396006i	$0.129604\pi$
$644$	−0.328340	+	0.568702i	−0.0129384	+	0.0224100i
$645$	68.1694	+	23.2074i	2.68417	+	0.913789i
$646$	−7.63910			−0.300556
$647$	−1.22045	+	2.11389i	−0.0479810	+	0.0831055i	−0.889018	−	0.457871i	$-0.848612\pi$
$647$	−1.22045	+	2.11389i	−0.0479810	+	0.0831055i	0.841037	+	0.540977i	$0.181945\pi$
$648$	11.8008	+	3.20661i	0.463580	+	0.125967i
$649$	−5.03407			−0.197604
$650$	35.5209	+	28.3117i	1.39324	+	1.11048i
$651$	49.1681	+	16.7386i	1.92705	+	0.656038i
$652$	−18.1210			−0.709673
$653$	5.46072			0.213694			0.106847	−	0.994275i	$-0.465924\pi$
$653$	5.46072			0.213694			0.106847	+	0.994275i	$0.465924\pi$
$654$	−37.8741	−	12.8937i	−1.48099	−	0.504184i
$655$	−26.0984	+	45.2038i	−1.01975	+	1.76626i
$656$	−20.3077	−	35.1740i	−0.792882	−	1.37331i
$657$	−1.03027	+	7.72057i	−0.0401946	+	0.301208i
$658$	−51.3029			−2.00000
$659$	−7.96274			−0.310184			−0.155092	−	0.987900i	$-0.549567\pi$
$659$	−7.96274			−0.310184			−0.155092	+	0.987900i	$0.549567\pi$
$660$	−4.30896	−	1.46693i	−0.167726	−	0.0571001i
$661$	−35.7501			−1.39052			−0.695259	−	0.718760i	$-0.744710\pi$
$661$	−35.7501			−1.39052			−0.695259	+	0.718760i	$0.744710\pi$
$662$	−3.48754	−	6.04060i	−0.135547	−	0.234774i
$663$	−8.13670	−	12.7019i	−0.316003	−	0.493302i
$664$	5.62702	−	9.74629i	0.218371	−	0.378229i
$665$	9.86260	−	17.0825i	0.382455	−	0.662432i
$666$	1.18214	−	8.85866i	0.0458070	−	0.343266i
$667$	−0.236138	−	0.409002i	−0.00914328	−	0.0158366i
$668$	8.02368	−	13.8974i	0.310446	−	0.537707i
$669$	−40.4925	−	13.7851i	−1.56553	−	0.532963i
$670$	7.16014	−	12.4017i	0.276620	−	0.479121i
$671$	−3.02384	−	5.23744i	−0.116734	−	0.202189i
$672$	6.74781	+	34.0803i	0.260302	+	1.31468i
$673$	13.7231	+	23.7691i	0.528988	+	0.916233i	0.999429	+	0.0338018i	$0.0107615\pi$
$673$	13.7231	+	23.7691i	0.528988	+	0.916233i	−0.470441	+	0.882431i	$0.655905\pi$
$674$	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	$0.996428\pi$
$678$	−14.0313	+	12.2833i	−0.538870	+	0.471737i
$679$	−24.2647			−0.931194
$680$	5.68288	−	9.84304i	0.217928	−	0.377463i
$681$	17.2135	−	15.0690i	0.659621	−	0.577446i
$682$	10.1420			0.388357
$683$	−4.96358	−	8.59717i	−0.189926	−	0.328961i	0.755299	−	0.655380i	$-0.227491\pi$
$683$	−4.96358	−	8.59717i	−0.189926	−	0.328961i	−0.945225	+	0.326419i	$0.894158\pi$
$684$	0.867806	−	6.50312i	0.0331814	−	0.248653i
$685$	−7.37962	−	12.7819i	−0.281961	−	0.488370i
$686$	10.1468	+	17.5748i	0.387406	+	0.671007i
$687$	37.6298	+	12.8106i	1.43567	+	0.488754i
$688$	−29.6511	−	51.3573i	−1.13044	−	1.95798i
$689$	26.6083	+	21.2080i	1.01370	+	0.807962i
$690$	0.340962	+	1.72205i	0.0129802	+	0.0655574i
$691$	22.3733	+	38.7516i	0.851119	+	1.47418i	0.880199	+	0.474605i	$0.157409\pi$
$691$	22.3733	+	38.7516i	0.851119	+	1.47418i	−0.0290796	+	0.999577i	$0.509258\pi$
$692$	0.387792	−	0.671675i	0.0147416	−	0.0255333i
$693$	−5.48210	+	2.25946i	−0.208248	+	0.0858298i
$694$	−34.2614			−1.30054
$695$	2.50137			0.0948823
$696$	−6.47689	−	2.20497i	−0.245506	−	0.0835792i
$697$	−9.93054	−	17.2002i	−0.376146	−	0.651504i
$698$	13.0981	−	22.6866i	0.495771	−	0.858701i
$699$	8.62323	−	7.54895i	0.326161	−	0.285528i
$700$	−14.1337	−	24.4802i	−0.534202	−	0.925265i
$701$	−41.3040			−1.56003			−0.780015	−	0.625761i	$-0.784789\pi$
$701$	−41.3040			−1.56003			−0.780015	+	0.625761i	$0.784789\pi$
$702$	30.5803	−	14.2873i	1.15418	−	0.539238i
$703$	2.90266			0.109476
$704$	0.383124	+	0.663590i	0.0144395	+	0.0250100i
$705$	−39.6073	+	34.6731i	−1.49170	+	1.30586i
$706$	−14.2707	+	24.7175i	−0.537084	+	0.930257i
$707$	12.8107	+	22.1887i	0.481795	+	0.834493i
$708$	−16.8815	−	5.74709i	−0.634446	−	0.215989i
$709$	−17.2742			−0.648748			−0.324374	−	0.945929i	$-0.605154\pi$
$709$	−17.2742			−0.648748			−0.324374	+	0.945929i	$0.605154\pi$
$710$	−60.8260			−2.28276
$711$	12.0619	+	9.28925i	0.452358	+	0.348374i
$712$	−6.71151	+	11.6247i	−0.251524	+	0.435653i
$713$	−0.750647	−	1.30016i	−0.0281120	−	0.0486913i
$714$	4.75026	+	23.9915i	0.177774	+	0.897861i
$715$	7.07925	−	2.78054i	0.264749	−	0.103986i
$716$	0.481576	+	0.834115i	0.0179974	+	0.0311723i
$717$	15.1345	+	5.15235i	0.565209	+	0.192418i
$718$	−13.7128	−	23.7512i	−0.511756	−	0.886387i
$719$	13.9402	+	24.1452i	0.519883	+	0.900463i	0.999733	+	0.0231129i	$0.00735771\pi$
$719$	13.9402	+	24.1452i	0.519883	+	0.900463i	−0.479850	+	0.877350i	$0.659309\pi$
$720$	40.6582	+	31.3121i	1.51524	+	1.16693i
$721$	0.598634	+	1.03686i	0.0222943	+	0.0386148i
$722$	−28.6791			−1.06732
$723$	−23.9377	+	20.9555i	−0.890252	+	0.779345i
$724$	−3.02765	+	5.24405i	−0.112522	+	0.194893i
$725$	20.3295			0.755017
$726$	24.9559	−	21.8469i	0.926202	−	0.810815i
$727$	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
$731$	−14.4995	−	25.1139i	−0.536284	−	0.928871i
$732$	−4.16104	−	21.0156i	−0.153796	−	0.776761i
$733$	−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	$0.886142\pi$
$734$	−1.95864	+	3.39246i	−0.0722946	+	0.125218i
$735$	−20.0356	−	6.82084i	−0.739024	−	0.251591i
$736$	0.502105	−	0.869671i	0.0185078	−	0.0320565i
$737$	−0.699055	−	1.21080i	−0.0257500	−	0.0446004i
$738$	41.0881	−	16.9345i	1.51247	−	0.623369i
$739$	8.96934	−	15.5354i	0.329943	−	0.571477i	−0.652558	−	0.757739i	$-0.726304\pi$
$739$	8.96934	−	15.5354i	0.329943	−	0.571477i	0.982500	+	0.186262i	$0.0596373\pi$
$740$	3.56698	−	6.17820i	0.131125	−	0.227115i
$741$	5.91324	+	9.23097i	0.217228	+	0.339108i
$742$	−27.5840	−	47.7770i	−1.01264	−	1.75395i
$743$	16.2118			0.594754			0.297377	−	0.954760i	$-0.403888\pi$
$743$	16.2118			0.594754			0.297377	+	0.954760i	$0.403888\pi$
$744$	−20.5891	−	7.00928i	−0.754833	−	0.256973i
$745$	0.923386			0.0338302
$746$	4.48000			0.164025
$747$	19.6866	+	15.1612i	0.720295	+	0.554720i
$748$	0.916509	+	1.58744i	0.0335109	+	0.0580426i
$749$	6.15690	−	10.6641i	0.224968	−	0.389656i
$750$	−20.3852	−	6.93986i	−0.744362	−	0.253408i
$751$	−2.87747			−0.105000			−0.0525002	−	0.998621i	$-0.516719\pi$
$751$	−2.87747			−0.105000			−0.0525002	+	0.998621i	$0.516719\pi$
$752$	43.3496			1.58080
$753$	−17.1234	−	5.82943i	−0.624012	−	0.212436i
$754$	−17.5776	+	6.90401i	−0.640139	+	0.251429i
$755$	0.143643			0.00522772
$756$	−20.9635	+	1.31841i	−0.762434	+	0.0479503i
$757$	−15.4379	+	26.7392i	−0.561100	+	0.971854i	0.436301	+	0.899801i	$0.356288\pi$
$757$	−15.4379	+	26.7392i	−0.561100	+	0.971854i	−0.997401	+	0.0720530i	$0.977045\pi$
$758$	34.9311			1.26876
$759$	0.162246	+	0.0552345i	0.00588916	+	0.00200489i
$760$	−4.12996	+	7.15330i	−0.149809	+	0.259477i
$761$	27.2801	−	47.2506i	0.988904	−	1.71283i	0.365797	−	0.930695i	$-0.380796\pi$
$761$	27.2801	−	47.2506i	0.988904	−	1.71283i	0.623107	−	0.782137i	$-0.285870\pi$
$762$	−1.50826	+	1.32036i	−0.0546387	+	0.0478318i
$763$	−41.6021			−1.50610
$764$	2.82906	−	4.90007i	0.102352	−	0.177278i
$765$	19.8820	+	15.3117i	0.718836	+	0.553596i
$766$	−25.3154			−0.914681
$767$	27.7349	−	10.8935i	1.00145	−	0.393342i
$768$	−6.96605	−	35.1826i	−0.251366	−	1.26954i
$769$	−26.0530			−0.939495			−0.469747	−	0.882801i	$-0.655655\pi$
$769$	−26.0530			−0.939495			−0.469747	+	0.882801i	$0.655655\pi$
$770$	−12.3315			−0.444396
$771$	36.0639	−	31.5710i	1.29881	−	1.13700i
$772$	−12.9898	+	22.4991i	−0.467515	+	0.809759i
$773$	15.3837	+	26.6453i	0.553313	+	0.958366i	0.998033	+	0.0626965i	$0.0199700\pi$
$773$	15.3837	+	26.6453i	0.553313	+	0.958366i	−0.444720	+	0.895670i	$0.646697\pi$
$774$	59.9925	−	24.7260i	2.15638	−	0.888758i
$775$	64.6244			2.32138
$776$	10.1608			0.364753
$777$	−1.80497	−	9.11616i	−0.0647531	−	0.327041i
$778$	26.5854			0.953132
$779$	7.21689	+	12.5000i	0.258572	+	0.447860i
$780$	26.9143	−	1.24247i	0.963687	−	0.0444875i
$781$	−2.96927	+	5.14292i	−0.106249	+	0.184028i
$782$	0.353467	−	0.612223i	0.0126400	−	0.0218930i
$783$	6.71717	−	13.5308i	0.240052	−	0.483553i
$784$	8.71473	+	15.0944i	0.311240	+	0.539084i
$785$	14.0445	−	24.3258i	0.501270	−	0.868225i
$786$	9.13517	+	46.1379i	0.325841	+	1.64568i
$787$	−25.0267	+	43.3476i	−0.892106	+	1.54517i	−0.0547605	+	0.998500i	$0.517440\pi$
$787$	−25.0267	+	43.3476i	−0.892106	+	1.54517i	−0.837346	+	0.546674i	$0.815894\pi$
$788$	6.92773	+	11.9992i	0.246790	+	0.427453i
$789$	−40.9016	−	13.9244i	−1.45613	−	0.495722i
$790$	15.8310	+	27.4201i	0.563241	+	0.975563i
$791$	−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
$795$	−53.5857	−	18.2425i	−1.90049	−	0.646996i
$796$	−12.5610			−0.445214
$797$	−19.8067	+	34.3063i	−0.701590	+	1.21519i	0.266318	+	0.963885i	$0.414193\pi$
$797$	−19.8067	+	34.3063i	−0.701590	+	1.21519i	−0.967908	+	0.251305i	$0.919140\pi$
$798$	−3.45219	−	17.4355i	−0.122206	−	0.617211i
$799$	21.1981			0.749936
$800$	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
$803$	0.790754	+	1.36963i	0.0279051	+	0.0483331i
$804$	−0.961955	−	4.85843i	−0.0339255	−	0.171344i
$805$	0.912700	+	1.58084i	0.0321684	+	0.0557174i
$806$	−55.8767	+	21.9469i	−1.96817	+	0.773045i
$807$	−31.5323	−	10.7347i	−1.10999	−	0.377881i
$808$	−5.36446	−	9.29151i	−0.188721	−	0.326874i
$809$	13.5323	−	23.4386i	0.475770	−	0.824058i	−0.523845	−	0.851814i	$-0.675503\pi$
$809$	13.5323	−	23.4386i	0.475770	−	0.824058i	0.999615	+	0.0277559i	$0.00883610\pi$
$810$	−39.8449	+	39.5652i	−1.40001	+	1.39018i
$811$	−32.3039			−1.13434			−0.567171	−	0.823600i	$-0.691962\pi$
$811$	−32.3039			−1.13434			−0.567171	+	0.823600i	$0.691962\pi$
$812$	11.7522			0.412421
$813$	−1.21506	−	6.13673i	−0.0426138	−	0.215224i
$814$	−0.907320	−	1.57152i	−0.0318016	−	0.0550819i
$815$	−25.1858	+	43.6231i	−0.882221	+	1.52805i
$816$	−4.01384	−	20.2722i	−0.140513	−	0.709670i
$817$	10.5373	+	18.2512i	0.368655	+	0.638529i
$818$	−62.6337			−2.18994
$819$	25.3139	−	24.3114i	0.884540	−	0.849509i
$820$	35.4744			1.23882
$821$	11.9299	+	20.6633i	0.416358	+	0.721153i	0.995570	−	0.0940241i	$-0.0299731\pi$
$821$	11.9299	+	20.6633i	0.416358	+	0.721153i	−0.579212	+	0.815177i	$0.696640\pi$
$822$	−12.5897	−	4.28600i	−0.439117	−	0.149491i
$823$	3.74417	−	6.48509i	0.130514	−	0.226056i	−0.793361	−	0.608751i	$-0.791671\pi$
$823$	3.74417	−	6.48509i	0.130514	−	0.226056i	0.923875	+	0.382695i	$0.125004\pi$
$824$	−0.250677	−	0.434186i	−0.00873276	−	0.0151256i
$825$	−5.55108	+	4.85953i	−0.193264	+	0.169187i
$826$	−48.3119			−1.68099
$827$	−10.0589			−0.349783			−0.174891	−	0.984588i	$-0.555957\pi$
$827$	−10.0589			−0.349783			−0.174891	+	0.984588i	$0.555957\pi$
$828$	0.481027	+	0.370453i	0.0167169	+	0.0128741i
$829$	26.1786	−	45.3428i	0.909222	−	1.57482i	0.0940747	−	0.995565i	$-0.470011\pi$
$829$	26.1786	−	45.3428i	0.909222	−	1.57482i	0.815147	−	0.579254i	$-0.196656\pi$
$830$	25.8381	+	44.7530i	0.896855	+	1.55340i
$831$	29.7322	−	26.0282i	1.03140	−	0.902908i
$832$	−3.54678	−	2.82694i	−0.122962	−	0.0980066i
$833$	4.26154	+	7.38120i	0.147653	+	0.255743i
$834$	1.69591	−	1.48463i	0.0587244	−	0.0514085i
$835$	−22.3037	−	38.6312i	−0.771853	−	1.33689i
$836$	−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
$839$	−16.3747			−0.565319			−0.282659	−	0.959220i	$-0.591217\pi$
$839$	−16.3747			−0.565319			−0.282659	+	0.959220i	$0.591217\pi$
$840$	25.0340	+	8.52247i	0.863754	+	0.294053i
$841$	10.2740	−	17.7951i	0.354276	−	0.613624i
$842$	−25.8677			−0.891459
$843$	−3.48455	−	17.5990i	−0.120014	−	0.606142i
$844$	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
$848$	23.3078	+	40.3703i	0.800393	+	1.38632i
$849$	8.97261	−	7.85481i	0.307939	−	0.269576i
$850$	15.2153	+	26.3536i	0.521879	+	0.903921i
$851$	−0.134308	+	0.232629i	−0.00460403	+	0.00797441i
$852$	−15.8287	+	13.8567i	−0.542281	+	0.474724i
$853$	−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
$855$	−14.4490	−	11.1276i	−0.494145	−	0.380555i
$856$	−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	$0.916043\pi$
$858$	3.14935	−	6.08691i	0.107517	−	0.207804i
$859$	−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	$0.894565\pi$
$860$	51.7959			1.76623
$861$	34.7701	−	30.4385i	1.18496	−	1.03734i
$862$	51.4612			1.75277
$863$	27.4495			0.934391			0.467196	−	0.884154i	$-0.345264\pi$
$863$	27.4495			0.934391			0.467196	+	0.884154i	$0.345264\pi$
$864$	32.0578	−	2.01615i	1.09063	−	0.0685908i
$865$	−1.07796	−	1.86708i	−0.0366517	−	0.0634827i
$866$	9.48394	−	16.4267i	0.322277	−	0.558201i
$867$	3.75619	+	18.9709i	0.127567	+	0.644287i
$868$	37.3585			1.26803
$869$	3.09121			0.104862
$870$	23.6386	−	20.6937i	0.801423	−	0.701582i
$871$	6.47152	+	5.15809i	0.219279	+	0.174775i
$872$	17.4209			0.589945
$873$	−2.96743	+	22.2372i	−0.100432	+	0.752614i
$874$	−0.256878	+	0.444925i	−0.00868901	+	0.0150498i
$875$	−22.3918			−0.756980
$876$	1.08814	+	5.49574i	0.0367649	+	0.185684i
$877$	5.85683	−	10.1443i	0.197771	−	0.342550i	−0.750034	−	0.661399i	$-0.769963\pi$
$877$	5.85683	−	10.1443i	0.197771	−	0.342550i	0.947805	+	0.318849i	$0.103296\pi$
$878$	−21.4861	+	37.2151i	−0.725122	+	1.25595i
$879$	−1.76343	−	8.90635i	−0.0594791	−	0.300404i
$880$	10.4198			0.351251
$881$	25.7417	−	44.5860i	0.867261	−	1.50214i	0.00247662	−	0.999997i	$-0.499212\pi$
$881$	25.7417	−	44.5860i	0.867261	−	1.50214i	0.864784	−	0.502143i	$-0.167455\pi$
$882$	−17.6323	+	7.26719i	−0.593711	+	0.244699i
$883$	30.6074			1.03002			0.515011	−	0.857183i	$-0.327788\pi$
$883$	30.6074			1.03002			0.515011	+	0.857183i	$0.327788\pi$
$884$	−8.48460	−	6.76261i	−0.285368	−	0.227451i
$885$	−37.2982	+	32.6516i	−1.25377	+	1.09757i
$886$	−4.19932			−0.141079
$887$	8.42217			0.282789			0.141394	−	0.989953i	$-0.454841\pi$
$887$	8.42217			0.282789			0.141394	+	0.989953i	$0.454841\pi$
$888$	0.755832	+	3.81739i	0.0253641	+	0.128103i
$889$	−1.04219	+	1.80513i	−0.0349541	+	0.0605422i
$890$	−30.8179	−	53.3781i	−1.03302	−	1.78924i
$891$	1.40023	+	5.30034i	0.0469096	+	0.177568i
$892$	−30.7667			−1.03014
$893$	−15.4055			−0.515524
$894$	0.626048	−	0.548055i	0.0209382	−	0.0183297i
$895$	2.67731			0.0894927
$896$	−16.3814	−	28.3735i	−0.547265	−	0.947891i
$897$	−1.01341	+	0.0467829i	−0.0338368	+	0.00156203i
$898$	20.5622	−	35.6147i	0.686169	−	1.18848i
$899$	−13.4338	+	23.2681i	−0.448044	+	0.776035i
$900$	−24.1631	+	9.95888i	−0.805438	+	0.331963i
$901$	11.3976	+	19.7412i	0.379709	+	0.657675i
$902$	4.51174	−	7.81456i	0.150225	−	0.260196i
$903$	50.7677	−	44.4430i	1.68944	−	1.47897i
$904$	4.05998	−	7.03209i	0.135033	−	0.233884i
$905$	8.41608	+	14.5771i	0.279760	+	0.484559i
$906$	0.0973891	−	0.0852563i	0.00323554	−	0.00283245i
$907$	4.92791	+	8.53539i	0.163629	+	0.283413i	0.936167	−	0.351555i	$-0.114347\pi$
$907$	4.92791	+	8.53539i	0.163629	+	0.283413i	−0.772539	+	0.634967i	$0.781013\pi$
$908$	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	$0.129314\pi$
$912$	2.91701	+	14.7326i	0.0965918	+	0.487844i
$913$	5.04523			0.166973
$914$	−12.0495	+	20.8704i	−0.398562	+	0.690330i
$915$	−56.3748	−	19.1920i	−1.86369	−	0.634469i
$916$	28.5916			0.944693
$917$	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	0.524757	−	0.851252i	$-0.324156\pi$
$919$	−14.3944	−	24.9318i	−0.474828	−	0.822426i	−0.999584	+	0.0288266i	$0.990823\pi$
$920$	−0.382193	−	0.661977i	−0.0126005	−	0.0218247i
$921$	−8.77369	+	7.68066i	−0.289103	+	0.253087i
$922$	3.65542	+	6.33137i	0.120385	+	0.208512i
$923$	5.22992	−	34.7600i	0.172145	−	1.14414i
$924$	−3.20900	+	2.80923i	−0.105569	+	0.0924168i
$925$	−5.78141	−	10.0137i	−0.190091	−	0.329248i
$926$	23.9748	−	41.5255i	0.787860	−	1.36461i
$927$	1.02343	−	0.421810i	0.0336140	−	0.0138541i
$928$	−17.9717			−0.589950
$929$	−12.5542			−0.411888			−0.205944	−	0.978564i	$-0.566027\pi$
$929$	−12.5542			−0.411888			−0.205944	+	0.978564i	$0.566027\pi$
$930$	75.1437	−	65.7823i	2.46406	−	2.15709i
$931$	−3.09702	−	5.36419i	−0.101501	−	0.175804i
$932$	4.12168	−	7.13895i	0.135010	−	0.233844i
$933$	−50.9778	−	17.3547i	−1.66894	−	0.568167i
$934$	−2.56215	−	4.43777i	−0.0838360	−	0.145208i
$935$	5.09531			0.166635
$936$	−10.6002	+	10.1804i	−0.346478	+	0.332756i
$937$	−32.7254			−1.06909			−0.534547	−	0.845139i	$-0.679518\pi$
$937$	−32.7254			−1.06909			−0.534547	+	0.845139i	$0.679518\pi$
$938$	−6.70883	−	11.6200i	−0.219051	−	0.379408i
$939$	5.15308	+	26.0260i	0.168164	+	0.849328i
$940$	−18.9312	+	32.7899i	−0.617469	+	1.06949i
$941$	−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	$-0.481257\pi$
$942$	−4.91597	−	24.8285i	−0.160171	−	0.808955i
$943$	−1.33572			−0.0434971
$944$	40.8223			1.32865
$945$	−25.9627	+	52.2983i	−0.844565	+	1.70126i
$946$	6.58756	−	11.4100i	0.214180	−	0.370971i
$947$	−18.3880	−	31.8490i	−0.597531	−	1.03495i	−0.993184	−	0.116554i	$-0.962815\pi$
$947$	−18.3880	−	31.8490i	−0.597531	−	1.03495i	0.395653	−	0.918400i	$-0.370518\pi$
$948$	10.3662	+	3.52904i	0.336679	+	0.114618i
$949$	−7.32042	−	5.83471i	−0.237631	−	0.189403i
$950$	−11.0575	−	19.1521i	−0.358753	−	0.621378i
$951$	−1.34400	−	6.78799i	−0.0435823	−	0.220116i
$952$	−5.32468	−	9.22262i	−0.172574	−	0.298907i
$953$	9.04123	+	15.6599i	0.292874	+	0.507273i	0.974488	−	0.224439i	$-0.0720550\pi$
$953$	9.04123	+	15.6599i	0.292874	+	0.507273i	−0.681614	+	0.731712i	$0.738722\pi$
$954$	−47.1581	+	19.4363i	−1.52680	+	0.629274i
$955$	−7.86405	−	13.6209i	−0.254475	−	0.440763i
$956$	11.4994			0.371917
$957$	−0.595744	−	3.00885i	−0.0192577	−	0.0972624i
$958$	2.16360	−	3.74746i	0.0699027	−	0.121075i
$959$	−13.8289			−0.446560
$960$	7.14275	+	2.43165i	0.230531	+	0.0784813i
$961$	−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
$965$	36.1084	+	62.5415i	1.16237	+	2.01328i
$966$	1.55708	+	0.530086i	0.0500981	+	0.0170552i
$967$	−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	$-0.411356\pi$
$968$	−7.22103	+	12.5072i	−0.232093	+	0.401996i
$969$	1.42643	+	7.20428i	0.0458235	+	0.231435i
$970$	−23.3282	+	40.4057i	−0.749024	+	1.29735i
$971$	−10.3259	−	17.8850i	−0.331374	−	0.573956i	0.651408	−	0.758728i	$-0.274179\pi$
$971$	−10.3259	−	17.8850i	−0.331374	−	0.573956i	−0.982781	+	0.184772i	$0.940845\pi$
$972$	−1.35546	+	19.3730i	−0.0434764	+	0.621390i
$973$	1.17185	−	2.02971i	0.0375678	−	0.0650694i
$974$	3.28853	−	5.69590i	0.105371	−	0.182508i
$975$	20.0675	−	38.7856i	0.642675	−	1.24213i
$976$	24.5209	+	42.4715i	0.784896	+	1.35948i
$977$	23.9802			0.767196			0.383598	−	0.923500i	$-0.374685\pi$
$977$	23.9802			0.767196			0.383598	+	0.923500i	$0.374685\pi$
$978$	8.81575	+	44.5246i	0.281896	+	1.42374i
$979$	−6.01759			−0.192323
$980$	−15.2233			−0.486290
$981$	−5.08769	+	38.1259i	−0.162437	+	1.21727i
$982$	−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	$-0.111480\pi$
$984$	−14.5600	+	12.7461i	−0.464155	+	0.406330i
$985$	38.5146			1.22718
$986$	−12.6515			−0.402907
$987$	9.57964	+	48.3827i	0.304923	+	1.54004i
$988$	6.16608	+	4.91464i	0.196169	+	0.156356i
$989$	−1.95028			−0.0620153
$990$	−1.50807	+	11.3011i	−0.0479295	+	0.359172i
$991$	−29.2993	+	50.7479i	−0.930723	+	1.61206i	−0.148634	+	0.988892i	$0.547488\pi$
$991$	−29.2993	+	50.7479i	−0.930723	+	1.61206i	−0.782089	+	0.623167i	$0.785846\pi$
$992$	−57.1294			−1.81386
$993$	−5.04555	+	4.41697i	−0.160116	+	0.140168i
$994$	−28.4961	+	49.3566i	−0.903840	+	1.56550i
$995$	−17.4582	+	30.2385i	−0.553463	+	0.958625i
$996$	16.9190	+	5.75983i	0.536098	+	0.182507i
$997$	61.6685			1.95306			0.976530	−	0.215379i	$-0.0690988\pi$
$997$	61.6685			1.95306			0.976530	+	0.215379i	$0.0690988\pi$
$998$	10.7027	−	18.5375i	0.338786	−	0.586795i
$999$	−8.57516	+	0.539301i	−0.271306	+	0.0170627i

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.f.a.61.3	✓	24	1.1	even	1	trivial
117.2.f.a.94.3	yes	24	117.94	even	3	inner
117.2.h.a.16.10	yes	24	13.3	even	3
117.2.h.a.22.10	yes	24	9.4	even	3
351.2.f.a.100.10		24	3.2	odd	2
351.2.f.a.172.10		24	117.68	odd	6
351.2.h.a.289.3		24	39.29	odd	6
351.2.h.a.334.3		24	9.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.900808 - 1.56024i) q^{2} +(-1.30323 + 1.14087i) q^{3} +(-0.622909 + 1.07891i) q^{4} +(1.73153 + 2.99909i) q^{5} +(2.95400 + 1.00565i) q^{6} +3.24477 q^{7} -1.35875 q^{8} +(0.396816 - 2.97364i) q^{9} +(3.11954 - 5.40321i) q^{10} +(-0.304566 - 0.527523i) q^{11} +(-0.419106 - 2.11673i) q^{12} +(2.81952 + 2.24729i) q^{13} +(-2.92291 - 5.06264i) q^{14} +(-5.67816 - 1.93305i) q^{15} +(2.46979 + 4.27780i) q^{16} +(1.20773 + 2.09186i) q^{17} +(-4.99706 + 2.05955i) q^{18} +(-0.877705 - 1.52023i) q^{19} -4.31433 q^{20} +(-4.22868 + 3.70187i) q^{21} +(-0.548710 + 0.950393i) q^{22} +0.162448 q^{23} +(1.77076 - 1.55016i) 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} +(-1.45362 - 2.51774i) q^{29} +(2.09889 + 10.6006i) q^{30} +(-4.62084 - 8.00352i) q^{31} +(3.09086 - 5.35353i) q^{32} +(0.998756 + 0.340013i) q^{33} +(2.17587 - 3.76872i) q^{34} +(5.61840 + 9.73136i) q^{35} +(2.96111 + 2.28044i) q^{36} +(-0.826776 + 1.43202i) q^{37} +(-1.58129 + 2.73887i) q^{38} +(-6.23835 + 0.287986i) q^{39} +(-2.35270 - 4.07500i) q^{40} -8.22245 q^{41} +(9.58506 + 3.26310i) q^{42} -12.0056 q^{43} +0.758866 q^{44} +(9.60531 - 3.95885i) q^{45} +(-0.146335 - 0.253459i) q^{46} +(4.38799 - 7.60023i) q^{47} +(-8.09912 - 2.75724i) q^{48} +3.52854 q^{49} +12.5982 q^{50} +(-3.96050 - 1.34830i) q^{51} +(-4.18093 + 1.64216i) q^{52} +9.43717 q^{53} +(4.16264 - 8.38508i) q^{54} +(1.05473 - 1.82684i) q^{55} -4.40882 q^{56} +(2.87824 + 0.979859i) q^{57} +(-2.61886 + 4.53599i) q^{58} +(4.13217 - 7.15713i) q^{59} +(5.62256 - 4.92210i) q^{60} +9.92836 q^{61} +(-8.32497 + 14.4193i) q^{62} +(1.28758 - 9.64878i) q^{63} -1.25794 q^{64} +(-1.85774 + 12.3472i) q^{65} +(-0.369183 - 1.86459i) q^{66} +2.29525 q^{67} -3.00924 q^{68} +(-0.211707 + 0.185333i) q^{69} +(10.1222 - 17.5322i) q^{70} +(-4.87460 - 8.44305i) q^{71} +(-0.539172 + 4.04042i) q^{72} -2.59634 q^{73} +2.97906 q^{74} +(-2.35242 - 11.8811i) q^{75} +2.18692 q^{76} +(-0.988245 - 1.71169i) q^{77} +(6.06889 + 9.47394i) q^{78} +(-2.53739 + 4.39489i) q^{79} +(-8.55300 + 14.8142i) q^{80} +(-8.68507 - 2.35998i) q^{81} +(7.40685 + 12.8290i) q^{82} +(-4.14134 + 7.17301i) q^{83} +(-1.35990 - 6.86830i) q^{84} +(-4.18245 + 7.24421i) q^{85} +(10.8147 + 18.7316i) q^{86} +(4.76682 + 1.62280i) q^{87} +(0.413827 + 0.716770i) 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} +(15.1530 + 5.15864i) q^{93} -15.8109 q^{94} +(3.03954 - 5.26463i) q^{95} +(2.07960 + 10.5032i) q^{96} -7.47810 q^{97} +(-3.17853 - 5.50538i) q^{98} +(-1.68952 + 0.696339i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + q^{2} - q^{3} - 9 q^{4} - 2 q^{5} + 9 q^{6} - 6 q^{7} - 18 q^{8} - 3 q^{9} - 3 q^{11} - 3 q^{12} + 2 q^{14} + 8 q^{15} - 3 q^{16} + 6 q^{17} - 8 q^{18} - 3 q^{19} + 22 q^{20} - 25 q^{21} + 9 q^{22}+ \cdots + 18 q^{99}+O(q^{100}) \) 24 * q + q^2 - q^3 - 9 * q^4 - 2 * q^5 + 9 * q^6 - 6 * q^7 - 18 * q^8 - 3 * q^9 - 3 * q^11 - 3 * q^12 + 2 * q^14 + 8 * q^15 - 3 * q^16 + 6 * q^17 - 8 * q^18 - 3 * q^19 + 22 * q^20 - 25 * q^21 + 9 * q^22 - 34 * q^23 - 6 * q^24 - 6 * q^25 - 12 * q^26 + 2 * q^27 + 12 * q^29 + 25 * q^30 - 6 * q^31 + 19 * q^32 - 16 * q^33 + 18 * q^35 + 59 * q^36 - 3 * q^37 + 8 * q^38 - 9 * q^39 - 12 * q^40 - 10 * q^41 - 30 * q^42 + 6 * q^43 + 44 * q^44 - 5 * q^45 - 6 * q^46 + 21 * q^47 - 22 * q^48 - 6 * q^49 + 40 * q^50 + 7 * q^51 - 6 * q^52 - 20 * q^53 - 78 * q^54 + 3 * q^55 - 80 * q^56 + 9 * q^57 - 9 * q^58 - 19 * q^59 + 51 * q^60 + 12 * q^61 + 19 * q^62 - 2 * q^63 - 42 * q^64 + 19 * q^65 - 18 * q^66 + 12 * q^67 - 10 * q^69 + 27 * q^70 + 14 * q^71 + 45 * q^72 + 6 * q^73 - 58 * q^74 - 22 * q^75 + 30 * q^76 + 4 * q^77 + 65 * q^78 + 3 * q^79 - 16 * q^80 + 9 * q^81 - 9 * q^82 - 33 * q^83 + 86 * q^84 + 72 * q^86 + 37 * q^87 + 39 * q^88 - q^89 + 21 * q^90 - 6 * q^91 - 10 * q^92 + 63 * q^93 + 18 * q^94 + 50 * q^95 - 79 * q^96 - 48 * q^97 - 61 * q^98 + 18 * q^99

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