LMFDB - Embedded newform 180.2.n.d.59.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [180,2,Mod(59,180)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(180, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([3, 5, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("180.59"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 180 = 2^{2} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	180.n (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$1.43730723638$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			59.3
Character	$\chi$	$=$	180.59
Dual form			180.2.n.d.119.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.38444 - 0.288666i) q^{2} +(0.112475 + 1.72840i) q^{3} +(1.83334 + 0.799280i) q^{4} +(2.23134 - 0.145382i) q^{5} +(0.343213 - 2.42533i) q^{6} +(0.573658 + 0.993605i) q^{7} +(-2.30743 - 1.63578i) q^{8} +(-2.97470 + 0.388803i) q^{9} +(-3.13112 - 0.442837i) q^{10} +(-0.629615 - 1.09053i) q^{11} +(-1.17527 + 3.25864i) q^{12} +(4.39750 + 2.53890i) q^{13} +(-0.507375 - 1.54118i) q^{14} +(0.502248 + 3.84028i) q^{15} +(2.72230 + 2.93071i) q^{16} -3.29816 q^{17} +(4.23052 + 0.320420i) q^{18} +3.62414i q^{19} +(4.20701 + 1.51693i) q^{20} +(-1.65282 + 1.10326i) q^{21} +(0.556867 + 1.69152i) q^{22} +(3.09936 + 1.78942i) q^{23} +(2.56774 - 4.17213i) q^{24} +(4.95773 - 0.648794i) q^{25} +(-5.35518 - 4.78436i) q^{26} +(-1.00658 - 5.09772i) q^{27} +(0.257544 + 2.28013i) q^{28} +(-0.184856 + 0.106727i) q^{29} +(0.413225 - 5.46162i) q^{30} +(-9.12339 - 5.26739i) q^{31} +(-2.92287 - 4.84323i) q^{32} +(1.81404 - 1.21088i) q^{33} +(4.56610 + 0.952066i) q^{34} +(1.42448 + 2.13367i) q^{35} +(-5.76441 - 1.66481i) q^{36} -4.72925i q^{37} +(1.04616 - 5.01740i) q^{38} +(-3.89361 + 7.88619i) q^{39} +(-5.38647 - 3.31451i) q^{40} +(5.81019 + 3.35452i) q^{41} +(2.60670 - 1.05029i) q^{42} +(-1.41598 - 2.45255i) q^{43} +(-0.282666 - 2.50255i) q^{44} +(-6.58103 + 1.30002i) q^{45} +(-3.77433 - 3.37202i) q^{46} +(0.925776 - 0.534497i) q^{47} +(-4.75924 + 5.03485i) q^{48} +(2.84183 - 4.92220i) q^{49} +(-7.05096 - 0.532910i) q^{50} +(-0.370961 - 5.70053i) q^{51} +(6.03285 + 8.16951i) q^{52} -9.12493 q^{53} +(-0.0779834 + 7.34806i) q^{54} +(-1.56343 - 2.34180i) q^{55} +(0.301642 - 3.23105i) q^{56} +(-6.26394 + 0.407625i) q^{57} +(0.286731 - 0.0943952i) q^{58} +(4.87018 - 8.43539i) q^{59} +(-2.14867 + 7.44199i) q^{60} +(-5.24521 - 9.08497i) q^{61} +(11.1103 + 9.92600i) q^{62} +(-2.09278 - 2.73264i) q^{63} +(2.64846 + 7.54889i) q^{64} +(10.1814 + 5.02582i) q^{65} +(-2.86097 + 1.15274i) q^{66} +(7.42407 - 12.8589i) q^{67} +(-6.04666 - 2.63615i) q^{68} +(-2.74422 + 5.55818i) q^{69} +(-1.35619 - 3.36513i) q^{70} +9.68598 q^{71} +(7.49990 + 3.96881i) q^{72} +9.08215i q^{73} +(-1.36517 + 6.54736i) q^{74} +(1.67899 + 8.49594i) q^{75} +(-2.89670 + 6.64429i) q^{76} +(0.722368 - 1.25118i) q^{77} +(7.66694 - 9.79399i) q^{78} +(5.78563 - 3.34033i) q^{79} +(6.50045 + 6.14363i) q^{80} +(8.69767 - 2.31314i) q^{81} +(-7.07552 - 6.32133i) q^{82} +(-4.93496 + 2.84920i) q^{83} +(-3.91200 + 0.701596i) q^{84} +(-7.35931 + 0.479494i) q^{85} +(1.25237 + 3.80415i) q^{86} +(-0.205258 - 0.307501i) q^{87} +(-0.331066 + 3.54622i) q^{88} -2.26303i q^{89} +(9.48631 + 0.0999207i) q^{90} +5.82584i q^{91} +(4.25195 + 5.75787i) q^{92} +(8.07798 - 16.3613i) q^{93} +(-1.43597 + 0.472739i) q^{94} +(0.526885 + 8.08667i) q^{95} +(8.04226 - 5.59661i) q^{96} +(-6.69770 + 3.86692i) q^{97} +(-5.35521 + 5.99415i) q^{98} +(2.29692 + 2.99919i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 2 q^{4} - 18 q^{5} - 12 q^{9} - 16 q^{10} - 42 q^{14} + 30 q^{16} - 12 q^{21} - 6 q^{24} - 26 q^{25} - 12 q^{30} - 4 q^{34} + 96 q^{36} + 10 q^{40} + 96 q^{41} - 66 q^{45} + 4 q^{46} + 32 q^{49}+ \cdots + 54 q^{96}+O(q^{100}) $ 48 * q - 2 * q^4 - 18 * q^5 - 12 * q^9 - 16 * q^10 - 42 * q^14 + 30 * q^16 - 12 * q^21 - 6 * q^24 - 26 * q^25 - 12 * q^30 - 4 * q^34 + 96 * q^36 + 10 * q^40 + 96 * q^41 - 66 * q^45 + 4 * q^46 + 32 * q^49 - 90 * q^50 - 30 * q^54 + 6 * q^56 - 42 * q^60 + 8 * q^61 - 20 * q^64 - 6 * q^65 + 36 * q^66 - 96 * q^69 + 4 * q^70 + 72 * q^74 + 36 * q^81 - 6 * q^84 - 4 * q^85 + 108 * q^86 - 6 * q^90 - 62 * q^94 + 54 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

$n$	$37$	$91$	$101$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.38444	−	0.288666i	−0.978946	−	0.204117i
$2$	−1.38444	−	0.288666i	−0.978946	−	0.204117i
$3$	0.112475	+	1.72840i	0.0649375	+	0.997889i
$3$	0.112475	+	1.72840i	0.0649375	+	0.997889i
$4$	1.83334	+	0.799280i	0.916672	+	0.399640i
$5$	2.23134	−	0.145382i	0.997884	−	0.0650170i
$5$	2.23134	−	0.145382i	0.997884	−	0.0650170i
$6$	0.343213	−	2.42533i	0.140116	−	0.990135i
$7$	0.573658	+	0.993605i	0.216822	+	0.375547i	0.953835	−	0.300332i	$-0.0970974\pi$
$7$	0.573658	+	0.993605i	0.216822	+	0.375547i	−0.737012	+	0.675879i	$0.763764\pi$
$8$	−2.30743	−	1.63578i	−0.815799	−	0.578335i
$9$	−2.97470	+	0.388803i	−0.991566	+	0.129601i
$10$	−3.13112	−	0.442837i	−0.990146	−	0.140037i
$11$	−0.629615	−	1.09053i	−0.189836	−	0.328806i	0.755359	−	0.655311i	$-0.227462\pi$
$11$	−0.629615	−	1.09053i	−0.189836	−	0.328806i	−0.945196	+	0.326505i	$0.894129\pi$
$12$	−1.17527	+	3.25864i	−0.339270	+	0.940689i
$13$	4.39750	+	2.53890i	1.21965	+	0.704164i	0.964843	−	0.262828i	$-0.0846553\pi$
$13$	4.39750	+	2.53890i	1.21965	+	0.704164i	0.254805	+	0.966992i	$0.417989\pi$
$14$	−0.507375	−	1.54118i	−0.135602	−	0.411898i
$15$	0.502248	+	3.84028i	0.129680	+	0.991556i
$16$	2.72230	+	2.93071i	0.680576	+	0.732678i
$17$	−3.29816			−0.799922			−0.399961	−	0.916532i	$-0.630976\pi$
$17$	−3.29816			−0.799922			−0.399961	+	0.916532i	$0.630976\pi$
$18$	4.23052	+	0.320420i	0.997144	+	0.0755236i
$19$			3.62414i			0.831434i	0.909494	+	0.415717i	$0.136469\pi$
$19$			3.62414i			0.831434i	−0.909494	+	0.415717i	$0.863531\pi$
$20$	4.20701	+	1.51693i	0.940716	+	0.339195i
$21$	−1.65282	+	1.10326i	−0.360675	+	0.240752i
$22$	0.556867	+	1.69152i	0.118724	+	0.360632i
$23$	3.09936	+	1.78942i	0.646261	+	0.373119i	0.787022	−	0.616924i	$-0.211622\pi$
$23$	3.09936	+	1.78942i	0.646261	+	0.373119i	−0.140761	+	0.990044i	$0.544955\pi$
$24$	2.56774	−	4.17213i	0.524138	−	0.851633i
$25$	4.95773	−	0.648794i	0.991546	−	0.129759i
$26$	−5.35518	−	4.78436i	−1.05024	−	0.938290i
$27$	−1.00658	−	5.09772i	−0.193717	−	0.981057i
$28$	0.257544	+	2.28013i	0.0486713	+	0.430905i
$29$	−0.184856	+	0.106727i	−0.0343270	+	0.0198187i	−0.517065	−	0.855946i	$-0.672976\pi$
$29$	−0.184856	+	0.106727i	−0.0343270	+	0.0198187i	0.482738	+	0.875765i	$0.339642\pi$
$30$	0.413225	−	5.46162i	0.0754442	−	0.997150i
$31$	−9.12339	−	5.26739i	−1.63861	−	0.946052i	−0.981313	−	0.192420i	$-0.938366\pi$
$31$	−9.12339	−	5.26739i	−1.63861	−	0.946052i	−0.657297	−	0.753632i	$-0.728300\pi$
$32$	−2.92287	−	4.84323i	−0.516695	−	0.856170i
$33$	1.81404	−	1.21088i	0.315784	−	0.210787i
$34$	4.56610	+	0.952066i	0.783080	+	0.163278i
$35$	1.42448	+	2.13367i	0.240781	+	0.360656i
$36$	−5.76441	−	1.66481i	−0.960735	−	0.277468i
$37$		−	4.72925i		−	0.777484i	−0.921347	−	0.388742i	$-0.872910\pi$
$37$		−	4.72925i		−	0.777484i	0.921347	−	0.388742i	$-0.127090\pi$
$38$	1.04616	−	5.01740i	0.169710	−	0.813929i
$39$	−3.89361	+	7.88619i	−0.623477	+	1.26280i
$40$	−5.38647	−	3.31451i	−0.851675	−	0.524070i
$41$	5.81019	+	3.35452i	0.907399	+	0.523887i	0.879594	−	0.475726i	$-0.157815\pi$
$41$	5.81019	+	3.35452i	0.907399	+	0.523887i	0.0278059	+	0.999613i	$0.491148\pi$
$42$	2.60670	−	1.05029i	0.402223	−	0.162063i
$43$	−1.41598	−	2.45255i	−0.215935	−	0.374010i	0.737626	−	0.675209i	$-0.235947\pi$
$43$	−1.41598	−	2.45255i	−0.215935	−	0.374010i	−0.953561	+	0.301199i	$0.902613\pi$
$44$	−0.282666	−	2.50255i	−0.0426135	−	0.377273i
$45$	−6.58103	+	1.30002i	−0.981042	+	0.193795i
$46$	−3.77433	−	3.37202i	−0.556495	−	0.497177i
$47$	0.925776	−	0.534497i	0.135038	−	0.0779644i	−0.430959	−	0.902372i	$-0.641825\pi$
$47$	0.925776	−	0.534497i	0.135038	−	0.0779644i	0.565997	+	0.824407i	$0.308491\pi$
$48$	−4.75924	+	5.03485i	−0.686936	+	0.726717i
$49$	2.84183	−	4.92220i	0.405976	−	0.703171i
$50$	−7.05096	−	0.532910i	−0.997156	−	0.0753648i
$51$	−0.370961	−	5.70053i	−0.0519449	−	0.798233i
$52$	6.03285	+	8.16951i	0.836605	+	1.13291i
$53$	−9.12493			−1.25341			−0.626703	−	0.779258i	$-0.715596\pi$
$53$	−9.12493			−1.25341			−0.626703	+	0.779258i	$0.715596\pi$
$54$	−0.0779834	+	7.34806i	−0.0106122	+	0.999944i
$55$	−1.56343	−	2.34180i	−0.210813	−	0.315768i
$56$	0.301642	−	3.23105i	0.0403086	−	0.431767i
$57$	−6.26394	+	0.407625i	−0.829679	+	0.0539912i
$58$	0.286731	−	0.0943952i	0.0376496	−	0.0123947i
$59$	4.87018	−	8.43539i	0.634043	−	1.09819i	−0.352674	−	0.935746i	$-0.614728\pi$
$59$	4.87018	−	8.43539i	0.634043	−	1.09819i	0.986717	−	0.162449i	$-0.0519391\pi$
$60$	−2.14867	+	7.44199i	−0.277392	+	0.960757i
$61$	−5.24521	−	9.08497i	−0.671580	−	1.16321i	−0.977456	−	0.211140i	$-0.932282\pi$
$61$	−5.24521	−	9.08497i	−0.671580	−	1.16321i	0.305876	−	0.952072i	$-0.401051\pi$
$62$	11.1103	+	9.92600i	1.41101	+	1.26060i
$63$	−2.09278	−	2.73264i	−0.263665	−	0.344280i
$64$	2.64846	+	7.54889i	0.331057	+	0.943611i
$65$	10.1814	+	5.02582i	1.26285	+	0.623376i
$66$	−2.86097	+	1.15274i	−0.352161	+	0.141892i
$67$	7.42407	−	12.8589i	0.906994	−	1.57096i	0.0887767	−	0.996052i	$-0.471704\pi$
$67$	7.42407	−	12.8589i	0.906994	−	1.57096i	0.818218	−	0.574909i	$-0.194962\pi$
$68$	−6.04666	−	2.63615i	−0.733266	−	0.319681i
$69$	−2.74422	+	5.55818i	−0.330365	+	0.669127i
$70$	−1.35619	−	3.36513i	−0.162095	−	0.402210i
$71$	9.68598			1.14951			0.574757	−	0.818324i	$-0.305097\pi$
$71$	9.68598			1.14951			0.574757	+	0.818324i	$0.305097\pi$
$72$	7.49990	+	3.96881i	0.883872	+	0.467729i
$73$			9.08215i			1.06299i	0.847063	+	0.531493i	$0.178369\pi$
$73$			9.08215i			1.06299i	−0.847063	+	0.531493i	$0.821631\pi$
$74$	−1.36517	+	6.54736i	−0.158698	+	0.761116i
$75$	1.67899	+	8.49594i	0.193873	+	0.981027i
$76$	−2.89670	+	6.64429i	−0.332274	+	0.762152i
$77$	0.722368	−	1.25118i	0.0823215	−	0.142585i
$78$	7.66694	−	9.79399i	0.868110	−	1.10895i
$79$	5.78563	−	3.34033i	0.650934	−	0.375817i	−0.137880	−	0.990449i	$-0.544029\pi$
$79$	5.78563	−	3.34033i	0.650934	−	0.375817i	0.788814	+	0.614632i	$0.210695\pi$
$80$	6.50045	+	6.14363i	0.726772	+	0.686879i
$81$	8.69767	−	2.31314i	0.966407	−	0.257016i
$82$	−7.07552	−	6.32133i	−0.781361	−	0.698074i
$83$	−4.93496	+	2.84920i	−0.541682	+	0.312740i	−0.745760	−	0.666214i	$-0.767914\pi$
$83$	−4.93496	+	2.84920i	−0.541682	+	0.312740i	0.204078	+	0.978955i	$0.434580\pi$
$84$	−3.91200	+	0.701596i	−0.426835	+	0.0765504i
$85$	−7.35931	+	0.479494i	−0.798229	+	0.0520085i
$86$	1.25237	+	3.80415i	0.135047	+	0.410212i
$87$	−0.205258	−	0.307501i	−0.0220060	−	0.0329675i
$88$	−0.331066	+	3.54622i	−0.0352917	+	0.378029i
$89$		−	2.26303i		−	0.239881i	−0.992781	−	0.119940i	$-0.961730\pi$
$89$		−	2.26303i		−	0.239881i	0.992781	−	0.119940i	$-0.0382703\pi$
$90$	9.48631	+	0.0999207i	0.999945	+	0.0105326i
$91$			5.82584i			0.610714i
$92$	4.25195	+	5.75787i	0.443296	+	0.600300i
$93$	8.07798	−	16.3613i	0.837648	−	1.69659i
$94$	−1.43597	+	0.472739i	−0.148109	+	0.0487593i
$95$	0.526885	+	8.08667i	0.0540573	+	0.829675i
$96$	8.04226	−	5.59661i	0.820810	−	0.571202i
$97$	−6.69770	+	3.86692i	−0.680048	+	0.392626i	−0.799873	−	0.600169i	$-0.795100\pi$
$97$	−6.69770	+	3.86692i	−0.680048	+	0.392626i	0.119825	+	0.992795i	$0.461767\pi$
$98$	−5.35521	+	5.99415i	−0.540958	+	0.605500i
$99$	2.29692	+	2.99919i	0.230849	+	0.301430i
$100$	9.60779	+	2.77315i	0.960779	+	0.277315i
$101$	−16.4845	+	9.51736i	−1.64027	+	0.947012i	−0.659538	+	0.751671i	$0.729248\pi$
$101$	−16.4845	+	9.51736i	−1.64027	+	0.947012i	−0.980735	+	0.195341i	$0.937419\pi$
$102$	−1.13197	+	7.99911i	−0.112082	+	0.792030i
$103$	−3.83891	+	6.64918i	−0.378259	+	0.655164i	−0.990809	−	0.135268i	$-0.956810\pi$
$103$	−3.83891	+	6.64918i	−0.378259	+	0.655164i	0.612550	+	0.790432i	$0.290144\pi$
$104$	−5.99385	−	13.0517i	−0.587745	−	1.27982i
$105$	−3.52760	+	2.70204i	−0.344259	+	0.263692i
$106$	12.6329	+	2.63405i	1.22702	+	0.255842i
$107$		−	11.8511i		−	1.14569i	−0.819665	−	0.572843i	$-0.805840\pi$
$107$		−	11.8511i		−	1.14569i	0.819665	−	0.572843i	$-0.194160\pi$
$108$	2.22909	−	10.1504i	0.214495	−	0.976725i
$109$	1.38567			0.132723			0.0663615	−	0.997796i	$-0.478861\pi$
$109$	1.38567			0.132723			0.0663615	+	0.997796i	$0.478861\pi$
$110$	1.48847	+	3.69338i	0.141920	+	0.352150i
$111$	8.17402	−	0.531923i	0.775843	−	0.0504879i
$112$	−1.35030	+	4.38612i	−0.127591	+	0.414449i
$113$	−0.291530	+	0.504944i	−0.0274248	+	0.0475012i	−0.879412	−	0.476061i	$-0.842064\pi$
$113$	−0.291530	+	0.504944i	−0.0274248	+	0.0475012i	0.851987	+	0.523563i	$0.175397\pi$
$114$	8.78971	+	1.24385i	0.823232	+	0.116497i
$115$	7.17587	+	3.54220i	0.669153	+	0.330312i
$116$	−0.424210	+	0.0479151i	−0.0393869	+	0.00444880i
$117$	−14.0684	−	5.84270i	−1.30062	−	0.540158i
$118$	−9.17747	+	10.2724i	−0.844855	+	0.945655i
$119$	−1.89202	−	3.27707i	−0.173441	−	0.300408i
$120$	5.12294	−	9.68274i	0.467659	−	0.883909i
$121$	4.70717	−	8.15306i	0.427924	−	0.741187i
$122$	4.63916	+	14.0917i	0.420009	+	1.27580i
$123$	−5.14443	+	10.4196i	−0.463857	+	0.939504i
$124$	−12.5162	−	16.9491i	−1.12399	−	1.52207i
$125$	10.9680	−	2.16844i	0.981011	−	0.193952i
$126$	2.10850	+	4.38728i	0.187840	+	0.390850i
$127$	−10.3137			−0.915191			−0.457595	−	0.889161i	$-0.651289\pi$
$127$	−10.3137			−0.915191			−0.457595	+	0.889161i	$0.651289\pi$
$128$	−1.48753	−	11.2155i	−0.131480	−	0.991319i
$129$	4.07971	−	2.72322i	0.359199	−	0.239766i
$130$	−12.6448	−	9.89697i	−1.10902	−	0.868022i
$131$	−7.18947	+	12.4525i	−0.628147	+	1.08798i	0.359776	+	0.933039i	$0.382853\pi$
$131$	−7.18947	+	12.4525i	−0.628147	+	1.08798i	−0.987923	+	0.154944i	$0.950480\pi$
$132$	4.29360	−	0.770033i	0.373710	−	0.0670228i
$133$	−3.60096	+	2.07902i	−0.312243	+	0.180274i
$134$	−13.9901	+	15.6592i	−1.20856	+	1.35275i
$135$	−2.98715	−	11.2284i	−0.257093	−	0.966387i
$136$	7.61027	+	5.39506i	0.652576	+	0.462623i
$137$	3.69847	+	6.40593i	0.315981	+	0.547296i	0.979646	−	0.200735i	$-0.0643330\pi$
$137$	3.69847	+	6.40593i	0.315981	+	0.547296i	−0.663664	+	0.748031i	$0.731000\pi$
$138$	5.40366	−	6.90281i	0.459990	−	0.587606i
$139$	1.44892	+	0.836533i	0.122896	+	0.0709538i	0.560188	−	0.828366i	$-0.310729\pi$
$139$	1.44892	+	0.836533i	0.122896	+	0.0709538i	−0.437292	+	0.899320i	$0.644062\pi$
$140$	0.906159	+	5.05030i	0.0765844	+	0.426829i
$141$	1.02795	+	1.53999i	0.0865689	+	0.129690i
$142$	−13.4096	−	2.79601i	−1.12531	−	0.234636i
$143$		−	6.39412i		−	0.534703i
$144$	−9.23750	−	7.65954i	−0.769792	−	0.638295i
$145$	−0.396960	+	0.265018i	−0.0329658	+	0.0220086i
$146$	2.62170	−	12.5737i	0.216974	−	1.04061i
$147$	8.82714	+	4.35818i	0.728050	+	0.359457i
$148$	3.78000	−	8.67035i	0.310714	−	0.712698i
$149$	3.87075	+	2.23478i	0.317104	+	0.183080i	0.650101	−	0.759848i	$-0.274727\pi$
$149$	3.87075	+	2.23478i	0.317104	+	0.183080i	−0.332997	+	0.942928i	$0.608060\pi$
$150$	0.128022	−	12.2468i	0.0104529	−	0.999945i
$151$	−11.2428	+	6.49105i	−0.914928	+	0.528234i	−0.882014	−	0.471224i	$-0.843812\pi$
$151$	−11.2428	+	6.49105i	−0.914928	+	0.528234i	−0.0329149	+	0.999458i	$0.510479\pi$
$152$	5.92828	−	8.36244i	0.480847	−	0.678283i
$153$	9.81104	−	1.28233i	0.793175	−	0.103671i
$154$	−1.36125	+	1.52366i	−0.109692	+	0.122780i
$155$	−21.1231	−	10.4269i	−1.69665	−	0.837513i
$156$	−13.4416	+	11.3460i	−1.07619	+	0.908408i
$157$	−6.37177	−	3.67874i	−0.508522	−	0.293595i	0.223704	−	0.974657i	$-0.428185\pi$
$157$	−6.37177	−	3.67874i	−0.508522	−	0.293595i	−0.732226	+	0.681062i	$0.761519\pi$
$158$	−8.97409	+	2.95438i	−0.713940	+	0.235038i
$159$	−1.02633	−	15.7715i	−0.0813930	−	1.25076i
$160$	−7.22602	−	10.3819i	−0.571267	−	0.820764i
$161$			4.10605i			0.323602i
$162$	−12.7091	+	0.691687i	−0.998522	+	0.0543440i
$163$	6.48159			0.507678			0.253839	−	0.967247i	$-0.418307\pi$
$163$	6.48159			0.507678			0.253839	+	0.967247i	$0.418307\pi$
$164$	7.97088	+	10.7940i	0.622421	+	0.842866i
$165$	3.87170	−	2.96561i	0.301412	−	0.230873i
$166$	7.65461	−	2.51999i	0.594113	−	0.195589i
$167$	11.3151	+	6.53280i	0.875592	+	0.505523i	0.869203	−	0.494456i	$-0.164633\pi$
$167$	11.3151	+	6.53280i	0.875592	+	0.505523i	0.00638974	+	0.999980i	$0.497966\pi$
$168$	5.61846	+	0.157944i	0.433474	+	0.0121856i
$169$	6.39203	+	11.0713i	0.491694	+	0.851639i
$170$	10.3269	+	1.46055i	0.792039	+	0.112019i
$171$	−1.40907	−	10.7807i	−0.107755	−	0.824422i
$172$	−0.635705	−	5.62813i	−0.0484720	−	0.429141i
$173$	−2.81588	−	4.87725i	−0.214087	−	0.370810i	0.738902	−	0.673812i	$-0.235344\pi$
$173$	−2.81588	−	4.87725i	−0.214087	−	0.370810i	−0.952990	+	0.303002i	$0.902011\pi$
$174$	0.195402	+	0.484967i	0.0148134	+	0.0367652i
$175$	3.48869	+	4.55384i	0.263720	+	0.344238i
$176$	1.48201	−	4.81396i	0.111711	−	0.362866i
$177$	15.1275	+	7.46882i	1.13705	+	0.561391i
$178$	−0.653259	+	3.13303i	−0.0489638	+	0.234830i
$179$	−14.3831			−1.07504			−0.537520	−	0.843251i	$-0.680639\pi$
$179$	−14.3831			−1.07504			−0.537520	+	0.843251i	$0.680639\pi$
$180$	−13.1044	−	2.87670i	−0.976742	−	0.214417i
$181$	−11.3978			−0.847194			−0.423597	−	0.905851i	$-0.639233\pi$
$181$	−11.3978			−0.847194			−0.423597	+	0.905851i	$0.639233\pi$
$182$	1.68172	−	8.06553i	0.124657	−	0.597857i
$183$	15.1125	−	10.0876i	1.11715	−	0.745699i
$184$	−4.22447	−	9.19882i	−0.311432	−	0.678146i
$185$	−0.687550	−	10.5526i	−0.0505497	−	0.775839i
$186$	−15.9064	+	20.3194i	−1.16631	+	1.48989i
$187$	2.07657	+	3.59673i	0.151854	+	0.263019i
$188$	2.12448	−	0.239963i	0.154944	−	0.0175011i
$189$	4.48769	−	3.92450i	0.326431	−	0.285465i
$190$	1.60490	−	11.3476i	0.116432	−	0.823241i
$191$	8.04586	+	13.9358i	0.582178	+	1.00836i	0.995221	+	0.0976507i	$0.0311328\pi$
$191$	8.04586	+	13.9358i	0.582178	+	1.00836i	−0.413042	+	0.910712i	$0.635534\pi$
$192$	−12.7496	+	5.42664i	−0.920121	+	0.391634i
$193$	10.5007	+	6.06256i	0.755854	+	0.436393i	0.827805	−	0.561016i	$-0.189589\pi$
$193$	10.5007	+	6.06256i	0.755854	+	0.436393i	−0.0719511	+	0.997408i	$0.522923\pi$
$194$	10.3888	−	3.42012i	0.745873	−	0.245550i
$195$	−7.54145	+	18.1628i	−0.540054	+	1.30067i
$196$	9.14427	−	6.75266i	0.653162	−	0.482333i
$197$	3.58143			0.255166			0.127583	−	0.991828i	$-0.459278\pi$
$197$	3.58143			0.255166			0.127583	+	0.991828i	$0.459278\pi$
$198$	−2.31418	−	4.81524i	−0.164461	−	0.342204i
$199$		−	6.39345i		−	0.453219i	−0.973986	−	0.226610i	$-0.927236\pi$
$199$		−	6.39345i		−	0.453219i	0.973986	−	0.226610i	$-0.0727642\pi$
$200$	−12.5009	−	6.61270i	−0.883946	−	0.467588i
$201$	23.0602	+	11.3854i	1.62654	+	0.803066i
$202$	25.5692	−	8.41768i	1.79904	−	0.592266i
$203$	−0.212089	−	0.122449i	−0.0148857	−	0.00859427i
$204$	3.87622	−	10.7475i	0.271389	−	0.752477i
$205$	13.4522	+	6.64035i	0.939541	+	0.463783i
$206$	7.23413	−	8.09723i	0.504025	−	0.564161i
$207$	−9.91539	−	4.11794i	−0.689168	−	0.286216i
$208$	4.53055	+	19.7995i	0.314137	+	1.37285i
$209$	3.95221	−	2.28181i	0.273380	−	0.157836i
$210$	5.66374	−	2.72252i	0.390835	−	0.187872i
$211$	12.6167	+	7.28424i	0.868568	+	0.501468i	0.866872	−	0.498531i	$-0.166127\pi$
$211$	12.6167	+	7.28424i	0.868568	+	0.501468i	0.00169595	+	0.999999i	$0.499460\pi$
$212$	−16.7291	−	7.29338i	−1.14896	−	0.500911i
$213$	1.08943	+	16.7412i	0.0746466	+	1.14709i
$214$	−3.42100	+	16.4071i	−0.233855	+	1.12157i
$215$	−3.51609	−	5.26660i	−0.239795	−	0.359179i
$216$	−6.01612	+	13.4092i	−0.409345	+	0.912379i
$217$		−	12.0867i		−	0.820501i
$218$	−1.91837	−	0.399995i	−0.129929	−	0.0270911i
$219$	−15.6975	+	1.02152i	−1.06074	+	0.0690276i
$220$	−0.994550	−	5.54293i	−0.0670525	−	0.373705i
$221$	−14.5037	−	8.37370i	−0.975623	−	0.563276i
$222$	−11.4700	−	1.62314i	−0.769815	−	0.108938i
$223$	0.623219	+	1.07945i	0.0417338	+	0.0722851i	0.886138	−	0.463422i	$-0.153379\pi$
$223$	0.623219	+	1.07945i	0.0417338	+	0.0722851i	−0.844404	+	0.535707i	$0.820045\pi$
$224$	3.13553	−	5.68253i	0.209501	−	0.379680i
$225$	−14.4955	+	3.85754i	−0.966366	+	0.257170i
$226$	0.549365	−	0.614910i	0.0365432	−	0.0409032i
$227$	−9.39358	+	5.42338i	−0.623474	+	0.359963i	−0.778220	−	0.627992i	$-0.783877\pi$
$227$	−9.39358	+	5.42338i	−0.623474	+	0.359963i	0.154747	+	0.987954i	$0.450544\pi$
$228$	−11.8098	−	4.25932i	−0.782121	−	0.282081i
$229$	−12.0859	+	20.9333i	−0.798656	+	1.38331i	0.121836	+	0.992550i	$0.461122\pi$
$229$	−12.0859	+	20.9333i	−0.798656	+	1.38331i	−0.920492	+	0.390762i	$0.872212\pi$
$230$	−8.91204	−	6.97539i	−0.587643	−	0.459943i
$231$	2.24378	+	1.10781i	0.147630	+	0.0728886i
$232$	0.601124	+	0.0561193i	0.0394657	+	0.00368441i
$233$	−8.94645			−0.586102			−0.293051	−	0.956097i	$-0.594671\pi$
$233$	−8.94645			−0.586102			−0.293051	+	0.956097i	$0.594671\pi$
$234$	17.7902	+	12.1499i	1.16298	+	0.794265i
$235$	1.98801	−	1.32723i	0.129684	−	0.0865792i
$236$	15.6710	−	11.5723i	1.02009	−	0.753296i
$237$	6.42416	+	9.62415i	0.417294	+	0.625156i
$238$	1.67341	+	5.08306i	0.108471	+	0.329486i
$239$	−7.59415	+	13.1535i	−0.491225	+	0.850826i	−0.999949	−	0.0101033i	$-0.996784\pi$
$239$	−7.59415	+	13.1535i	−0.491225	+	0.850826i	0.508724	+	0.860930i	$0.330117\pi$
$240$	−9.88748	+	11.9263i	−0.638234	+	0.769842i
$241$	−0.235922	−	0.408630i	−0.0151971	−	0.0263222i	0.858327	−	0.513103i	$-0.171504\pi$
$241$	−0.235922	−	0.408630i	−0.0151971	−	0.0263222i	−0.873524	+	0.486781i	$0.838171\pi$
$242$	−8.87030	+	9.92861i	−0.570204	+	0.638235i
$243$	4.97629	+	14.7728i	0.319229	+	0.947678i
$244$	−2.35484	−	20.8483i	−0.150753	−	1.33467i
$245$	5.62548	−	11.3962i	0.359399	−	0.728079i
$246$	10.1299	−	12.9403i	0.645861	−	0.825043i
$247$	−9.20132	+	15.9372i	−0.585466	+	1.01406i
$248$	12.4353	+	27.0780i	0.789642	+	1.71945i
$249$	−5.47960	−	8.20909i	−0.347256	−	0.520230i
$250$	−15.8105	−	0.164016i	−0.999946	−	0.0103733i
$251$	24.1551			1.52465			0.762327	−	0.647192i	$-0.224057\pi$
$251$	24.1551			1.52465			0.762327	+	0.647192i	$0.224057\pi$
$252$	−1.65264	−	6.68258i	−0.104106	−	0.420963i
$253$		−	4.50658i		−	0.283326i
$254$	14.2787	+	2.97720i	0.895923	+	0.186806i
$255$	−1.65649	−	12.6659i	−0.103734	−	0.793167i
$256$	−1.17814	+	15.9566i	−0.0736335	+	0.997285i
$257$	7.37360	−	12.7715i	0.459953	−	0.796661i	−0.539005	−	0.842302i	$-0.681200\pi$
$257$	7.37360	−	12.7715i	0.459953	−	0.796661i	0.998958	+	0.0456410i	$0.0145330\pi$
$258$	−6.43421	+	2.59246i	−0.400577	+	0.161400i
$259$	4.69901	−	2.71297i	0.291982	−	0.168576i
$260$	14.6490	+	17.3519i	0.908493	+	1.07612i
$261$	0.508396	−	0.389353i	0.0314689	−	0.0241003i
$262$	13.5480	−	15.1644i	0.836998	−	0.936861i
$263$	−1.13421	+	0.654834i	−0.0699381	+	0.0403788i	−0.534561	−	0.845130i	$-0.679523\pi$
$263$	−1.13421	+	0.654834i	−0.0699381	+	0.0403788i	0.464623	+	0.885509i	$0.346190\pi$
$264$	−6.16651	−	0.173351i	−0.379522	−	0.0106690i
$265$	−20.3608	+	1.32660i	−1.25075	+	0.0814927i
$266$	5.58545	−	1.83880i	0.342466	−	0.112744i
$267$	3.91141	−	0.254534i	0.239374	−	0.0155773i
$268$	23.8887	−	17.6408i	1.45924	−	1.07758i
$269$		−	21.5574i		−	1.31438i	−0.753725	−	0.657190i	$-0.771745\pi$
$269$		−	21.5574i		−	1.31438i	0.753725	−	0.657190i	$-0.228255\pi$
$270$	0.894270	+	16.4073i	0.0544236	+	0.998518i
$271$		−	1.58111i		−	0.0960453i	−0.998846	−	0.0480227i	$-0.984708\pi$
$271$		−	1.58111i		−	0.0960453i	0.998846	−	0.0480227i	$-0.0152920\pi$
$272$	−8.97859	−	9.66596i	−0.544407	−	0.586085i
$273$	−10.0694	+	0.655262i	−0.609425	+	0.0396583i
$274$	−3.27113	−	9.93624i	−0.197616	−	0.600270i
$275$	−3.82899	−	4.99804i	−0.230897	−	0.301393i
$276$	−9.47364	+	7.99667i	−0.570246	+	0.481343i
$277$	6.87650	−	3.97015i	0.413169	−	0.238543i	−0.278981	−	0.960297i	$-0.589997\pi$
$277$	6.87650	−	3.97015i	0.413169	−	0.238543i	0.692150	+	0.721753i	$0.256663\pi$
$278$	−1.76446	−	1.57638i	−0.105825	−	0.0945451i
$279$	29.1873	+	12.1217i	1.74740	+	0.725708i
$280$	0.203327	−	7.25342i	0.0121511	−	0.433475i
$281$	−5.88352	+	3.39685i	−0.350982	+	0.202639i	−0.665118	−	0.746739i	$-0.731619\pi$
$281$	−5.88352	+	3.39685i	−0.350982	+	0.202639i	0.314136	+	0.949378i	$0.398285\pi$
$282$	−0.978590	−	2.42875i	−0.0582742	−	0.144630i
$283$	−3.80426	+	6.58918i	−0.226140	+	0.391686i	−0.956661	−	0.291204i	$-0.905944\pi$
$283$	−3.80426	+	6.58918i	−0.226140	+	0.391686i	0.730521	+	0.682890i	$0.239277\pi$
$284$	17.7577	+	7.74181i	1.05373	+	0.459392i
$285$	−13.9177	+	1.82021i	−0.824413	+	0.107820i
$286$	−1.84576	+	8.85227i	−0.109142	+	0.523446i
$287$			7.69738i			0.454362i
$288$	10.5777	+	13.2707i	0.623297	+	0.781985i
$289$	−6.12213			−0.360126
$290$	0.626069	−	0.252313i	0.0367641	−	0.0148163i
$291$	−7.43689	−	11.1413i	−0.435958	−	0.653117i
$292$	−7.25918	+	16.6507i	−0.424811	+	0.974409i
$293$	4.95491	−	8.58215i	0.289469	−	0.501375i	−0.684214	−	0.729281i	$-0.739855\pi$
$293$	4.95491	−	8.58215i	0.289469	−	0.501375i	0.973683	+	0.227906i	$0.0731880\pi$
$294$	−10.9626	−	8.58173i	−0.639351	−	0.500497i
$295$	9.64065	−	19.5302i	0.561300	−	1.13709i
$296$	−7.73601	+	10.9124i	−0.449646	+	0.634271i
$297$	−4.92544	+	4.30731i	−0.285803	+	0.249936i
$298$	−4.71372	−	4.21127i	−0.273058	−	0.243952i
$299$	9.08630	+	15.7379i	0.525474	+	0.910148i
$300$	−3.71246	+	16.9180i	−0.214339	+	0.976759i
$301$	1.62458	−	2.81385i	0.0936391	−	0.162188i
$302$	17.4388	−	5.74105i	1.00349	−	0.330360i
$303$	−18.3039	−	27.4213i	−1.05153	−	1.57531i
$304$	−10.6213	+	9.86600i	−0.609173	+	0.565854i
$305$	−13.0246	−	19.5091i	−0.745788	−	1.11709i
$306$	−13.9529	−	1.05680i	−0.797637	−	0.0604130i
$307$	7.97501			0.455158			0.227579	−	0.973760i	$-0.426919\pi$
$307$	7.97501			0.455158			0.227579	+	0.973760i	$0.426919\pi$
$308$	2.32439	−	1.71647i	0.132444	−	0.0978047i
$309$	−11.9242	−	5.88728i	−0.678344	−	0.334916i
$310$	26.2338	+	20.5330i	1.48998	+	1.16620i
$311$	−3.50301	+	6.06739i	−0.198637	+	0.344050i	−0.948087	−	0.318011i	$-0.896985\pi$
$311$	−3.50301	+	6.06739i	−0.198637	+	0.344050i	0.749449	+	0.662062i	$0.230318\pi$
$312$	21.8843	−	11.8277i	1.23895	−	0.669613i
$313$	−12.7311	+	7.35028i	−0.719602	+	0.415462i	−0.814606	−	0.580014i	$-0.803047\pi$
$313$	−12.7311	+	7.35028i	−0.719602	+	0.415462i	0.0950041	+	0.995477i	$0.469714\pi$
$314$	7.75940	+	6.93230i	0.437888	+	0.391212i
$315$	−5.06697	−	5.79318i	−0.285491	−	0.326409i
$316$	13.2769	−	1.49965i	0.746885	−	0.0843616i
$317$	−1.16205	−	2.01274i	−0.0652675	−	0.113047i	0.831545	−	0.555457i	$-0.187457\pi$
$317$	−1.16205	−	2.01274i	−0.0652675	−	0.113047i	−0.896813	+	0.442411i	$0.854123\pi$
$318$	−3.13180	+	22.1309i	−0.175623	+	1.24104i
$319$	0.232777	+	0.134394i	0.0130330	+	0.00752460i
$320$	7.00708	+	16.4591i	0.391708	+	0.920090i
$321$	20.4833	−	1.33295i	1.14327	−	0.0743980i
$322$	1.18528	−	5.68458i	0.0660529	−	0.316789i
$323$		−	11.9530i		−	0.665082i
$324$	17.7947	+	2.71109i	0.988592	+	0.150616i
$325$	23.4488	+	9.73410i	1.30071	+	0.539951i
$326$	−8.97337	−	1.87101i	−0.496989	−	0.103626i
$327$	0.155853	+	2.39498i	0.00861870	+	0.132443i
$328$	−7.91936	−	17.2445i	−0.437274	−	0.952168i
$329$	1.06216	+	0.613237i	0.0585587	+	0.0338089i
$330$	−6.21621	+	2.98808i	−0.342191	+	0.164489i
$331$	−13.0699	+	7.54592i	−0.718388	+	0.414762i	−0.814159	−	0.580642i	$-0.802802\pi$
$331$	−13.0699	+	7.54592i	−0.718388	+	0.414762i	0.0957711	+	0.995403i	$0.469468\pi$
$332$	−11.3248	+	1.27915i	−0.621528	+	0.0702025i
$333$	1.83875	+	14.0681i	0.100763	+	0.770927i
$334$	−13.7793	−	12.3106i	−0.753972	−	0.673604i
$335$	14.6961	−	29.7718i	0.802936	−	1.62661i
$336$	−7.73282	−	1.84052i	−0.421860	−	0.100409i
$337$	18.8375	+	10.8759i	1.02615	+	0.592445i	0.915878	−	0.401456i	$-0.131496\pi$
$337$	18.8375	+	10.8759i	1.02615	+	0.592445i	0.110268	+	0.993902i	$0.464829\pi$
$338$	−5.65346	−	17.1727i	−0.307508	−	0.934073i
$339$	−0.905533	−	0.447085i	−0.0491818	−	0.0242823i
$340$	−13.8754	−	5.00307i	−0.752499	−	0.271330i
$341$			13.2657i			0.718380i
$342$	−1.16124	+	15.3320i	−0.0627929	+	0.829059i
$343$	14.5522			0.785744
$344$	−0.744553	+	7.97531i	−0.0401436	+	0.430000i
$345$	−5.31521	+	12.8011i	−0.286161	+	0.689190i
$346$	2.49052	+	7.56510i	0.133891	+	0.406702i
$347$	−23.6580	−	13.6590i	−1.27003	−	0.733251i	−0.295035	−	0.955487i	$-0.595331\pi$
$347$	−23.6580	−	13.6590i	−1.27003	−	0.733251i	−0.974993	+	0.222236i	$0.928665\pi$
$348$	−0.130529	−	0.727813i	−0.00699710	−	0.0390149i
$349$	−1.77750	−	3.07872i	−0.0951472	−	0.164800i	0.814523	−	0.580132i	$-0.196999\pi$
$349$	−1.77750	−	3.07872i	−0.0951472	−	0.164800i	−0.909670	+	0.415332i	$0.863666\pi$
$350$	−3.51534	−	7.31158i	−0.187903	−	0.390820i
$351$	8.51615	−	24.9729i	0.454559	−	1.33295i
$352$	−3.44138	+	6.23683i	−0.183426	+	0.332424i
$353$	1.30903	+	2.26731i	0.0696727	+	0.120677i	0.898757	−	0.438447i	$-0.144471\pi$
$353$	1.30903	+	2.26731i	0.0696727	+	0.120677i	−0.829085	+	0.559123i	$0.811138\pi$
$354$	−18.7871	−	14.7069i	−0.998521	−	0.781663i
$355$	21.6127	−	1.40817i	1.14708	−	0.0747379i
$356$	1.80880	−	4.14891i	0.0958659	−	0.219892i
$357$	5.45127	−	3.63874i	0.288512	−	0.192583i
$358$	19.9125	+	4.15190i	1.05241	+	0.219435i
$359$	−21.9608			−1.15904			−0.579522	−	0.814956i	$-0.696761\pi$
$359$	−21.9608			−1.15904			−0.579522	+	0.814956i	$0.696761\pi$
$360$	17.3118	+	7.76541i	0.912412	+	0.409273i
$361$	5.86564			0.308718
$362$	15.7796	+	3.29016i	0.829358	+	0.172927i
$363$	14.6211	+	7.21883i	0.767411	+	0.378890i
$364$	−4.65648	+	10.6808i	−0.244066	+	0.559825i
$365$	1.32038	+	20.2653i	0.0691121	+	1.06074i
$366$	−23.8342	+	9.60326i	−1.24584	+	0.501970i
$367$	10.1344	+	17.5533i	0.529012	+	0.916276i	0.999428	+	0.0338310i	$0.0107708\pi$
$367$	10.1344	+	17.5533i	0.529012	+	0.916276i	−0.470415	+	0.882445i	$0.655896\pi$
$368$	3.19313	+	13.9547i	0.166454	+	0.727437i
$369$	−18.5878	−	7.71966i	−0.967643	−	0.401869i
$370$	−2.09429	+	14.8078i	−0.108877	+	0.769823i
$371$	−5.23459	−	9.06658i	−0.271767	−	0.470713i
$372$	27.8870	−	23.5393i	1.44587	−	1.22046i
$373$	−10.7060	−	6.18110i	−0.554334	−	0.320045i	0.196534	−	0.980497i	$-0.437031\pi$
$373$	−10.7060	−	6.18110i	−0.554334	−	0.320045i	−0.750868	+	0.660452i	$0.770365\pi$
$374$	−1.83664	−	5.57889i	−0.0949702	−	0.288478i
$375$	4.98156	+	18.7132i	0.257247	+	0.966346i
$376$	−3.01048	−	0.281050i	−0.155254	−	0.0144941i
$377$	−1.08388			−0.0558224
$378$	−7.34580	+	4.13779i	−0.377827	+	0.212825i
$379$		−	6.92628i		−	0.355779i	−0.984050	−	0.177889i	$-0.943073\pi$
$379$		−	6.92628i		−	0.355779i	0.984050	−	0.177889i	$-0.0569270\pi$
$380$	−5.49755	+	15.2468i	−0.282018	+	0.782143i
$381$	−1.16003	−	17.8261i	−0.0594302	−	0.913259i
$382$	−7.11621	−	21.6159i	−0.364097	−	1.10597i
$383$	1.25094	+	0.722230i	0.0639200	+	0.0369042i	0.531619	−	0.846983i	$-0.321584\pi$
$383$	1.25094	+	0.722230i	0.0639200	+	0.0369042i	−0.467699	+	0.883888i	$0.654917\pi$
$384$	19.2175	−	3.83250i	0.980688	−	0.195576i
$385$	1.42995	−	2.89682i	0.0728769	−	0.147636i
$386$	−12.7875	−	11.4244i	−0.650865	−	0.581488i
$387$	5.16567	+	6.74506i	0.262586	+	0.342871i
$388$	−15.3699	+	1.73606i	−0.780290	+	0.0881349i
$389$	0.707497	−	0.408474i	0.0358715	−	0.0207104i	−0.481957	−	0.876195i	$-0.660074\pi$
$389$	0.707497	−	0.408474i	0.0358715	−	0.0207104i	0.517829	+	0.855484i	$0.326741\pi$
$390$	15.6837	−	22.9683i	0.794173	−	1.16305i
$391$	−10.2222	−	5.90178i	−0.516958	−	0.298466i
$392$	−14.6090	+	6.70902i	−0.737864	+	0.338856i
$393$	−22.3315	−	11.0256i	−1.12648	−	0.556170i
$394$	−4.95827	−	1.03383i	−0.249794	−	0.0520838i
$395$	12.4241	−	8.29454i	0.625122	−	0.417344i
$396$	1.81384	+	7.33443i	0.0911491	+	0.368569i
$397$			29.4855i			1.47984i	0.672697	+	0.739918i	$0.265136\pi$
$397$			29.4855i			1.47984i	−0.672697	+	0.739918i	$0.734864\pi$
$398$	−1.84557	+	8.85134i	−0.0925100	+	0.443677i
$399$	−3.99838	−	5.99004i	−0.200169	−	0.299877i
$400$	15.3979	+	12.7635i	0.769893	+	0.638173i
$401$	−1.19058	−	0.687380i	−0.0594546	−	0.0343261i	0.469978	−	0.882678i	$-0.344262\pi$
$401$	−1.19058	−	0.687380i	−0.0594546	−	0.0343261i	−0.529433	+	0.848352i	$0.677595\pi$
$402$	−28.6389	−	22.4191i	−1.42838	−	1.11816i
$403$	−26.7468	−	46.3268i	−1.33235	−	2.30770i
$404$	−37.8289	+	4.27282i	−1.88206	+	0.212581i
$405$	19.0711	−	6.42588i	0.947652	−	0.319305i
$406$	0.258277	+	0.230747i	0.0128181	+	0.0114518i
$407$	−5.15737	+	2.97761i	−0.255642	+	0.147595i
$408$	−8.46883	+	13.7604i	−0.419270	+	0.681240i
$409$	−1.66076	+	2.87653i	−0.0821195	+	0.142235i	−0.904160	−	0.427194i	$-0.859502\pi$
$409$	−1.66076	+	2.87653i	−0.0821195	+	0.142235i	0.822041	+	0.569429i	$0.192836\pi$
$410$	−16.7069	−	13.0764i	−0.825094	−	0.645795i
$411$	−10.6560	+	7.11292i	−0.525621	+	0.350854i
$412$	−12.3526	+	9.12188i	−0.608569	+	0.449403i
$413$	11.1753			0.549899
$414$	12.5386	+	8.56327i	0.616236	+	0.420862i
$415$	−10.5973	+	7.07498i	−0.520202	+	0.347297i
$416$	−0.556851	−	28.7190i	−0.0273019	−	1.40806i
$417$	−1.28289	+	2.59839i	−0.0628235	+	0.127244i
$418$	−6.13028	+	2.01816i	−0.299842	+	0.0987115i
$419$	17.6346	−	30.5441i	0.861508	−	1.49218i	−0.00896441	−	0.999960i	$-0.502853\pi$
$419$	17.6346	−	30.5441i	0.861508	−	1.49218i	0.870473	−	0.492217i	$-0.163813\pi$
$420$	−8.62700	+	2.13423i	−0.420955	+	0.104140i
$421$	−14.6171	−	25.3175i	−0.712392	−	1.23390i	−0.963957	−	0.266059i	$-0.914278\pi$
$421$	−14.6171	−	25.3175i	−0.712392	−	1.23390i	0.251565	−	0.967841i	$-0.419055\pi$
$422$	−15.3643	−	13.7266i	−0.747923	−	0.668200i
$423$	−2.54609	+	1.94991i	−0.123795	+	0.0948079i
$424$	21.0551	+	14.9264i	1.02253	+	0.724888i
$425$	−16.3514	+	2.13983i	−0.793159	+	0.103797i
$426$	3.32436	−	23.4916i	0.161066	−	1.13817i
$427$	6.01792	−	10.4233i	0.291227	−	0.504421i
$428$	9.47233	−	21.7271i	0.457862	−	1.05022i
$429$	11.0516	−	0.719179i	0.533575	−	0.0347223i
$430$	3.34752	+	8.30627i	0.161432	+	0.400564i
$431$	−15.7242			−0.757408			−0.378704	−	0.925518i	$-0.623630\pi$
$431$	−15.7242			−0.757408			−0.378704	+	0.925518i	$0.623630\pi$
$432$	12.1997	−	16.8276i	0.586960	−	0.809616i
$433$		−	40.6371i		−	1.95289i	−0.215758	−	0.976447i	$-0.569222\pi$
$433$		−	40.6371i		−	1.95289i	0.215758	−	0.976447i	$-0.430778\pi$
$434$	−3.48902	+	16.7333i	−0.167479	+	0.803226i
$435$	−0.502705	−	0.656297i	−0.0241028	−	0.0314670i
$436$	2.54041	+	1.10754i	0.121663	+	0.0530414i
$437$	−6.48509	+	11.2325i	−0.310224	+	0.537324i
$438$	22.0272	+	3.11712i	1.05250	+	0.148942i
$439$	−19.5385	+	11.2806i	−0.932523	+	0.538392i	−0.887608	−	0.460599i	$-0.847635\pi$
$439$	−19.5385	+	11.2806i	−0.932523	+	0.538392i	−0.0449140	+	0.998991i	$0.514301\pi$
$440$	−0.223161	+	7.96095i	−0.0106388	+	0.379523i
$441$	−6.53983	+	15.7470i	−0.311421	+	0.749856i
$442$	17.6623	+	15.7796i	0.840108	+	0.750559i
$443$	12.4768	−	7.20347i	0.592789	−	0.342247i	−0.173410	−	0.984850i	$-0.555479\pi$
$443$	12.4768	−	7.20347i	0.592789	−	0.342247i	0.766200	+	0.642603i	$0.222145\pi$
$444$	15.4109	+	5.55813i	0.731371	+	0.263777i
$445$	−0.329005	−	5.04958i	−0.0155963	−	0.239373i
$446$	−0.551210	−	1.67433i	−0.0261005	−	0.0792819i
$447$	−3.42722	+	6.94154i	−0.162102	+	0.328324i
$448$	−5.98130	+	6.96200i	−0.282590	+	0.328924i
$449$			14.7482i			0.696008i	0.937493	+	0.348004i	$0.113140\pi$
$449$			14.7482i			0.696008i	−0.937493	+	0.348004i	$0.886860\pi$
$450$	21.1817	−	1.15618i	0.998514	−	0.0545031i
$451$		−	8.44822i		−	0.397811i
$452$	−0.938067	+	0.692723i	−0.0441229	+	0.0325829i
$453$	−12.4836	−	18.7020i	−0.586532	−	0.878695i
$454$	14.5704	−	4.79674i	0.683822	−	0.225122i
$455$	0.846975	+	12.9994i	0.0397068	+	0.609422i
$456$	15.1204	+	9.30585i	0.708077	+	0.435786i
$457$	0.883921	−	0.510332i	0.0413481	−	0.0238723i	−0.479183	−	0.877715i	$-0.659067\pi$
$457$	0.883921	−	0.510332i	0.0413481	−	0.0238723i	0.520532	+	0.853842i	$0.325734\pi$
$458$	22.7749	−	25.4921i	1.06420	−	1.19117i
$459$	3.31988	+	16.8131i	0.154959	+	0.784769i
$460$	10.3246	+	12.2296i	0.481388	+	0.570208i
$461$	0.679602	−	0.392368i	0.0316522	−	0.0182744i	−0.484090	−	0.875018i	$-0.660849\pi$
$461$	0.679602	−	0.392368i	0.0316522	−	0.0182744i	0.515743	+	0.856744i	$0.327516\pi$
$462$	−2.78659	−	2.18140i	−0.129644	−	0.101488i
$463$	−16.2867	+	28.2095i	−0.756909	+	1.31101i	0.187510	+	0.982263i	$0.439958\pi$
$463$	−16.2867	+	28.2095i	−0.756909	+	1.31101i	−0.944420	+	0.328743i	$0.893375\pi$
$464$	−0.816020	−	0.251218i	−0.0378828	−	0.0116625i
$465$	15.6461	−	37.6819i	0.725569	−	1.74746i
$466$	12.3858	+	2.58253i	0.573762	+	0.119634i
$467$			26.0874i			1.20718i	0.797295	+	0.603590i	$0.206264\pi$
$467$			26.0874i			1.20718i	−0.797295	+	0.603590i	$0.793736\pi$
$468$	−21.1222	−	21.9563i	−0.976375	−	1.01493i
$469$	17.0355			0.786627
$470$	−3.13541	+	1.26360i	−0.144626	+	0.0582857i
$471$	5.64165	−	11.4267i	0.259954	−	0.526514i
$472$	−25.0360	+	11.4975i	−1.15238	+	0.529217i
$473$	−1.78305	+	3.08833i	−0.0819845	+	0.142001i
$474$	−6.11569	−	15.1785i	−0.280903	−	0.697171i
$475$	2.35132	+	17.9675i	0.107886	+	0.824405i
$476$	−0.849422	−	7.52025i	−0.0389332	−	0.344690i
$477$	27.1439	−	3.54780i	1.24284	−	0.162443i
$478$	14.3106	−	16.0180i	0.654551	−	0.732646i
$479$	15.0858	+	26.1294i	0.689288	+	1.19388i	0.972068	+	0.234698i	$0.0754101\pi$
$479$	15.0858	+	26.1294i	0.689288	+	1.19388i	−0.282780	+	0.959185i	$0.591257\pi$
$480$	17.1313	−	13.6571i	0.781935	−	0.623360i
$481$	12.0071	−	20.7969i	0.547477	−	0.948257i
$482$	0.208663	+	0.633826i	0.00950434	+	0.0288700i
$483$	−7.09688	+	0.461829i	−0.322919	+	0.0210139i
$484$	15.1464	−	11.1850i	0.688474	−	0.508410i
$485$	−14.3826	+	9.60212i	−0.653082	+	0.436010i
$486$	−2.62497	−	21.8886i	−0.119071	−	0.992886i
$487$	−22.2802			−1.00961			−0.504806	−	0.863233i	$-0.668436\pi$
$487$	−22.2802			−1.00961			−0.504806	+	0.863233i	$0.668436\pi$
$488$	−2.75805	+	29.5429i	−0.124851	+	1.33735i
$489$	0.729018	+	11.2028i	0.0329673	+	0.506606i
$490$	−11.0778	+	14.1535i	−0.500446	+	0.639390i
$491$	10.7024	−	18.5371i	0.482992	−	0.836566i	−0.516817	−	0.856096i	$-0.672883\pi$
$491$	10.7024	−	18.5371i	0.482992	−	0.836566i	0.999809	+	0.0195292i	$0.00621675\pi$
$492$	−17.7597	+	14.9909i	−0.800669	+	0.675841i
$493$	0.609686	−	0.352002i	0.0274589	−	0.0158534i
$494$	17.3392	−	19.4079i	0.780126	−	0.873203i
$495$	5.56122	+	6.35827i	0.249958	+	0.285783i
$496$	−9.39943	−	41.0775i	−0.422047	−	1.84443i
$497$	5.55644	+	9.62404i	0.249240	+	0.431697i
$498$	5.21649	+	12.9468i	0.233757	+	0.580158i
$499$	14.4771	+	8.35834i	0.648083	+	0.374171i	0.787721	−	0.616032i	$-0.211261\pi$
$499$	14.4771	+	8.35834i	0.648083	+	0.374171i	−0.139638	+	0.990203i	$0.544594\pi$
$500$	21.8414	+	4.79103i	0.976776	+	0.214261i
$501$	−10.0186	+	20.2918i	−0.447598	+	0.906572i
$502$	−33.4412	−	6.97274i	−1.49255	−	0.311209i
$503$			37.4827i			1.67127i	0.549285	+	0.835635i	$0.314900\pi$
$503$			37.4827i			1.67127i	−0.549285	+	0.835635i	$0.685100\pi$
$504$	0.358947	+	9.72868i	0.0159888	+	0.433350i
$505$	−35.3989	+	23.6330i	−1.57523	+	1.05165i
$506$	−1.30089	+	6.23908i	−0.0578318	+	0.277361i
$507$	−18.4167	+	12.2932i	−0.817912	+	0.545960i
$508$	−18.9085	−	8.24351i	−0.838930	−	0.365747i
$509$	23.3737	+	13.4948i	1.03602	+	0.598148i	0.918704	−	0.394947i	$-0.129237\pi$
$509$	23.3737	+	13.4948i	1.03602	+	0.598148i	0.117318	+	0.993094i	$0.462570\pi$
$510$	−1.36288	+	18.0133i	−0.0603495	+	0.797642i
$511$	−9.02407	+	5.21005i	−0.399201	+	0.230479i
$512$	6.23717	−	21.7508i	0.275647	−	0.961259i
$513$	18.4748	−	3.64800i	0.815684	−	0.161063i
$514$	−13.8950	+	15.5528i	−0.612881	+	0.686004i
$515$	−7.59922	+	15.3947i	−0.334862	+	0.678371i
$516$	9.65613	−	1.73177i	0.425088	−	0.0762371i
$517$	−1.16577	−	0.673055i	−0.0512703	−	0.0296009i
$518$	−7.28864	+	2.39951i	−0.320244	+	0.105428i
$519$	8.11309	−	5.41552i	0.356125	−	0.237715i
$520$	−15.2718	−	28.2513i	−0.669712	−	1.23890i
$521$			26.5168i			1.16172i	0.814003	+	0.580860i	$0.197284\pi$
$521$			26.5168i			1.16172i	−0.814003	+	0.580860i	$0.802716\pi$
$522$	−0.816236	+	0.392279i	−0.0357257	+	0.0171696i
$523$	31.5217			1.37835			0.689174	−	0.724596i	$-0.257974\pi$
$523$	31.5217			1.37835			0.689174	+	0.724596i	$0.257974\pi$
$524$	−23.1338	+	17.0834i	−1.01061	+	0.746290i
$525$	−7.47844	+	6.54202i	−0.326386	+	0.285517i
$526$	1.75927	−	0.579172i	0.0767077	−	0.0252531i
$527$	30.0904	+	17.3727i	1.31076	+	0.756767i
$528$	8.48712	+	2.02005i	0.369354	+	0.0879115i
$529$	−5.09598	−	8.82649i	−0.221564	−	0.383760i
$530$	28.5712	+	4.04086i	1.24106	+	0.175524i
$531$	−11.2076	+	26.9863i	−0.486369	+	1.17111i
$532$	−8.26352	+	0.933375i	−0.358269	+	0.0404669i
$533$	17.0336	+	29.5030i	0.737805	+	1.27792i
$534$	−5.48859	−	0.776702i	−0.237514	−	0.0336112i
$535$	−1.72294	−	26.4437i	−0.0744891	−	1.14326i
$536$	−38.1648	+	17.5268i	−1.64847	+	0.757042i
$537$	−1.61774	−	24.8596i	−0.0698105	−	1.07277i
$538$	−6.22289	+	29.8449i	−0.268288	+	1.28671i
$539$	−7.15705			−0.308276
$540$	3.49817	−	22.9731i	0.150537	−	0.988604i
$541$	−0.0570124			−0.00245116			−0.00122558	−	0.999999i	$-0.500390\pi$
$541$	−0.0570124			−0.00245116			−0.00122558	+	0.999999i	$0.500390\pi$
$542$	−0.456411	+	2.18894i	−0.0196045	+	0.0940232i
$543$	−1.28197	−	19.7000i	−0.0550147	−	0.845406i
$544$	9.64009	+	15.9737i	0.413315	+	0.684869i
$545$	3.09189	−	0.201452i	0.132442	−	0.00862924i
$546$	14.1296	+	1.99951i	0.604690	+	0.0855710i
$547$	1.78811	+	3.09710i	0.0764541	+	0.132422i	0.901718	−	0.432325i	$-0.142307\pi$
$547$	1.78811	+	3.09710i	0.0764541	+	0.132422i	−0.825264	+	0.564748i	$0.808973\pi$
$548$	1.66043	+	14.7004i	0.0709300	+	0.627970i
$549$	19.1352	+	24.9857i	0.816670	+	1.06636i
$550$	3.85824	+	8.02478i	0.164516	+	0.342178i
$551$	−0.386793	−	0.669944i	−0.0164779	−	0.0285406i
$552$	15.4240	−	8.33618i	0.656491	−	0.354812i
$553$	6.63795	+	3.83242i	0.282274	+	0.162971i
$554$	−10.6661	+	3.51142i	−0.453161	+	0.149186i
$555$	18.1617	−	2.37526i	0.770919	−	0.100824i
$556$	1.98774	+	2.69174i	0.0842989	+	0.114155i
$557$	15.0861			0.639217			0.319609	−	0.947550i	$-0.396449\pi$
$557$	15.0861			0.639217			0.319609	+	0.947550i	$0.396449\pi$
$558$	−36.9090	−	25.2071i	−1.56248	−	1.06710i
$559$		−	14.3801i		−	0.608214i
$560$	−2.37531	+	9.98322i	−0.100375	+	0.421868i
$561$	−5.98301	+	3.99368i	−0.252603	+	0.168613i
$562$	9.12594	−	3.00437i	0.384954	−	0.126732i
$563$	−7.29553	−	4.21208i	−0.307470	−	0.177518i	0.338324	−	0.941030i	$-0.390140\pi$
$563$	−7.29553	−	4.21208i	−0.307470	−	0.177518i	−0.645794	+	0.763512i	$0.723473\pi$
$564$	0.653701	+	3.64495i	0.0275258	+	0.153480i
$565$	−0.577091	+	1.16908i	−0.0242784	+	0.0491837i
$566$	7.16884	−	8.02416i	0.301329	−	0.337280i
$567$	7.28784	+	7.31509i	0.306060	+	0.307205i
$568$	−22.3497	−	15.8441i	−0.937773	−	0.664804i
$569$	−3.05453	+	1.76353i	−0.128053	+	0.0739312i	−0.562658	−	0.826690i	$-0.690221\pi$
$569$	−3.05453	+	1.76353i	−0.128053	+	0.0739312i	0.434605	+	0.900621i	$0.356888\pi$
$570$	19.7936	+	1.49758i	0.829064	+	0.0627269i
$571$	−29.6633	−	17.1261i	−1.24137	−	0.716705i	−0.271997	−	0.962298i	$-0.587684\pi$
$571$	−29.6633	−	17.1261i	−1.24137	−	0.716705i	−0.969373	+	0.245593i	$0.921017\pi$
$572$	5.11069	−	11.7226i	0.213689	−	0.490148i
$573$	−23.1817	+	15.4739i	−0.968429	+	0.646430i
$574$	2.22197	−	10.6566i	0.0927432	−	0.444796i
$575$	16.5267	+	6.86059i	0.689213	+	0.286107i
$576$	−10.8134	−	21.4259i	−0.450558	−	0.892747i
$577$			1.78616i			0.0743587i	0.999309	+	0.0371793i	$0.0118373\pi$
$577$			1.78616i			0.0743587i	−0.999309	+	0.0371793i	$0.988163\pi$
$578$	8.47572	+	1.76725i	0.352544	+	0.0735079i
$579$	−9.29744	+	18.8312i	−0.386388	+	0.782597i
$580$	−0.939589	+	0.168587i	−0.0390143	+	0.00700021i
$581$	−5.66196	−	3.26893i	−0.234898	−	0.135618i
$582$	7.07980	+	17.5713i	0.293467	+	0.728353i
$583$	5.74520	+	9.95098i	0.237942	+	0.412127i
$584$	14.8564	−	20.9564i	0.614762	−	0.867183i
$585$	−32.2407	−	10.9917i	−1.33299	−	0.454453i
$586$	−9.33714	+	10.4512i	−0.385714	+	0.431733i
$587$	13.5891	−	7.84570i	0.560884	−	0.323826i	−0.192616	−	0.981274i	$-0.561697\pi$
$587$	13.5891	−	7.84570i	0.560884	−	0.323826i	0.753500	+	0.657448i	$0.228364\pi$
$588$	12.6998	+	15.0454i	0.523730	+	0.620462i
$589$	19.0898	−	33.0644i	0.786579	−	1.36240i
$590$	−18.9846	+	24.2555i	−0.781584	+	0.998584i
$591$	0.402821	+	6.19012i	0.0165698	+	0.254627i
$592$	13.8601	−	12.8745i	0.569646	−	0.529137i
$593$	46.6356			1.91510			0.957548	−	0.288273i	$-0.0930810\pi$
$593$	46.6356			1.91510			0.957548	+	0.288273i	$0.0930810\pi$
$594$	8.06234	−	4.54141i	0.330802	−	0.186336i
$595$	−4.69816	−	7.03718i	−0.192606	−	0.288496i
$596$	5.31020	+	7.19093i	0.217514	+	0.294552i
$597$	11.0504	−	0.719103i	0.452263	−	0.0294309i
$598$	−8.03643	−	24.4111i	−0.328634	−	0.998245i
$599$	21.3211	−	36.9292i	0.871156	−	1.50889i	0.0103549	−	0.999946i	$-0.496704\pi$
$599$	21.3211	−	36.9292i	0.871156	−	1.50889i	0.860802	−	0.508941i	$-0.169963\pi$
$600$	10.0233	−	22.3502i	0.409200	−	0.912445i
$601$	10.7999	+	18.7061i	0.440539	+	0.763036i	0.997729	−	0.0673489i	$-0.0214541\pi$
$601$	10.7999	+	18.7061i	0.440539	+	0.763036i	−0.557191	+	0.830385i	$0.688121\pi$
$602$	−3.06139	+	3.42664i	−0.124773	+	0.139660i
$603$	−17.0848	+	41.1377i	−0.695747	+	1.67526i
$604$	−25.8001	+	2.91416i	−1.04979	+	0.118576i
$605$	9.31797	−	18.8766i	0.378829	−	0.767441i
$606$	17.4250	+	43.2469i	0.707841	+	1.75678i
$607$	1.49873	−	2.59588i	0.0608316	−	0.105363i	−0.834006	−	0.551756i	$-0.813958\pi$
$607$	1.49873	−	2.59588i	0.0608316	−	0.105363i	0.894837	+	0.446392i	$0.147291\pi$
$608$	17.5525	−	10.5929i	0.711848	−	0.429598i
$609$	0.187786	−	0.380346i	0.00760949	−	0.0154124i
$610$	12.4002	+	30.7689i	0.502070	+	1.24580i
$611$	5.42814			0.219599
$612$	19.0119	+	5.49081i	0.768513	+	0.221953i
$613$		−	14.2081i		−	0.573858i	−0.957952	−	0.286929i	$-0.907366\pi$
$613$		−	14.2081i		−	0.573858i	0.957952	−	0.286929i	$-0.0926344\pi$
$614$	−11.0409	−	2.30211i	−0.445575	−	0.0929057i
$615$	−9.96412	+	23.9976i	−0.401792	+	0.967675i
$616$	−3.71346	+	1.70537i	−0.149620	+	0.0687114i
$617$	−13.2631	+	22.9723i	−0.533952	+	0.924832i	0.465262	+	0.885173i	$0.345960\pi$
$617$	−13.2631	+	22.9723i	−0.533952	+	0.924832i	−0.999213	+	0.0396583i	$0.987373\pi$
$618$	14.8089	+	11.5927i	0.595700	+	0.466326i
$619$	13.2974	−	7.67724i	0.534466	−	0.308574i	−0.208367	−	0.978051i	$-0.566815\pi$
$619$	13.2974	−	7.67724i	0.534466	−	0.308574i	0.742833	+	0.669476i	$0.233481\pi$
$620$	−30.3920	−	35.9995i	−1.22057	−	1.44577i
$621$	6.00219	−	17.6009i	0.240859	−	0.706299i
$622$	6.60115	−	7.38874i	0.264682	−	0.296261i
$623$	2.24856	−	1.29821i	0.0900866	−	0.0520115i
$624$	−33.7117	+	10.0575i	−1.34955	+	0.402624i
$625$	24.1581	−	6.43309i	0.966325	−	0.257324i
$626$	19.7472	−	6.50100i	0.789255	−	0.259832i
$627$	4.38840	+	6.57434i	0.175256	+	0.262554i
$628$	−8.74130	−	11.8372i	−0.348816	−	0.472357i
$629$			15.5978i			0.621927i
$630$	5.34262	+	9.48296i	0.212855	+	0.377810i
$631$		−	4.30213i		−	0.171265i	−0.996327	−	0.0856326i	$-0.972709\pi$
$631$		−	4.30213i		−	0.171265i	0.996327	−	0.0856326i	$-0.0272911\pi$
$632$	−18.8140	−	1.75642i	−0.748380	−	0.0698667i
$633$	−11.1710	+	22.6259i	−0.444007	+	0.899299i
$634$	1.02779	+	3.12196i	0.0408186	+	0.123989i
$635$	−23.0133	+	1.49943i	−0.913254	+	0.0595029i
$636$	10.7242	−	29.7349i	0.425243	−	1.17907i
$637$	24.9939	−	14.4303i	0.990296	−	0.571748i
$638$	−0.283470	−	0.253255i	−0.0112227	−	0.0100264i
$639$	−28.8129	+	3.76593i	−1.13982	+	0.148978i
$640$	−4.94971	−	24.8093i	−0.195654	−	0.980673i
$641$	26.3204	−	15.1961i	1.03959	−	0.600209i	0.119875	−	0.992789i	$-0.461751\pi$
$641$	26.3204	−	15.1961i	1.03959	−	0.600209i	0.919718	+	0.392580i	$0.128417\pi$
$642$	−28.7427	−	4.06745i	−1.13438	−	0.160529i
$643$	13.4062	−	23.2202i	0.528688	−	0.915714i	−0.470753	−	0.882265i	$-0.656018\pi$
$643$	13.4062	−	23.2202i	0.528688	−	0.915714i	0.999440	−	0.0334490i	$-0.0106491\pi$
$644$	−3.28189	+	7.52781i	−0.129324	+	0.296637i
$645$	8.70730	−	6.66955i	0.342850	−	0.262613i
$646$	−3.45042	+	16.5482i	−0.135755	+	0.651079i
$647$		−	9.51887i		−	0.374225i	−0.982338	−	0.187113i	$-0.940087\pi$
$647$		−	9.51887i		−	0.374225i	0.982338	−	0.187113i	$-0.0599130\pi$
$648$	−23.8530	−	8.89004i	−0.937036	−	0.349234i
$649$	−12.2654			−0.481457
$650$	−29.6536	−	20.2451i	−1.16311	−	0.794080i
$651$	20.8907	−	1.35946i	0.818769	−	0.0532813i
$652$	11.8830	+	5.18061i	0.465374	+	0.202888i
$653$	−7.71208	+	13.3577i	−0.301797	+	0.522728i	−0.976543	−	0.215322i	$-0.930920\pi$
$653$	−7.71208	+	13.3577i	−0.301797	+	0.522728i	0.674746	+	0.738050i	$0.264253\pi$
$654$	0.475580	−	3.36070i	0.0185966	−	0.131414i
$655$	−14.2318	+	28.8310i	−0.556081	+	1.12652i
$656$	5.98598	+	26.1600i	0.233713	+	1.02138i
$657$	−3.53116	−	27.0167i	−0.137764	−	1.05402i
$658$	−1.29347	−	1.15560i	−0.0504248	−	0.0450499i
$659$	−17.3345	−	30.0242i	−0.675256	−	1.16958i	−0.976394	−	0.215998i	$-0.930700\pi$
$659$	−17.3345	−	30.0242i	−0.675256	−	1.16958i	0.301137	−	0.953581i	$-0.402634\pi$
$660$	9.46852	−	2.34242i	0.368562	−	0.0911785i
$661$	−10.7043	+	18.5404i	−0.416350	+	0.721139i	−0.995569	−	0.0940328i	$-0.970024\pi$
$661$	−10.7043	+	18.5404i	−0.416350	+	0.721139i	0.579219	+	0.815172i	$0.303357\pi$
$662$	20.2728	−	6.67404i	0.787923	−	0.259394i
$663$	12.8418	−	26.0099i	0.498733	−	1.01014i
$664$	16.0477	+	1.49817i	0.622772	+	0.0581403i
$665$	−7.73270	+	5.16250i	−0.299861	+	0.200193i
$666$	1.51535	−	20.0072i	0.0587185	−	0.775264i
$667$	−0.763915			−0.0295789
$668$	15.5230	+	21.0208i	0.600604	+	0.813321i
$669$	−1.79561	+	1.19858i	−0.0694225	+	0.0463398i
$670$	−28.9400	+	36.9750i	−1.11805	+	1.42847i
$671$	−6.60493	+	11.4401i	−0.254981	+	0.441639i
$672$	10.1743	+	4.78029i	0.392483	+	0.184404i
$673$	−22.3026	+	12.8764i	−0.859702	+	0.496349i	−0.863913	−	0.503642i	$-0.831993\pi$
$673$	−22.3026	+	12.8764i	−0.859702	+	0.496349i	0.00421032	+	0.999991i	$0.498660\pi$
$674$	−22.9399	−	20.4947i	−0.883613	−	0.789427i
$675$	−8.29774	−	24.6201i	−0.319380	−	0.947627i
$676$	2.86970	+	25.4065i	0.110373	+	0.977175i
$677$	−14.5489	−	25.1994i	−0.559159	−	0.968492i	−0.997567	−	0.0697156i	$-0.977791\pi$
$677$	−14.5489	−	25.1994i	−0.559159	−	0.968492i	0.438408	−	0.898776i	$-0.355542\pi$
$678$	1.12460	+	0.880358i	0.0431899	+	0.0338100i
$679$	−7.68438	−	4.43658i	−0.294899	−	0.170260i
$680$	17.7654	+	10.9318i	0.681273	+	0.419215i
$681$	−10.4303	−	15.6258i	−0.399690	−	0.598783i
$682$	3.82936	−	18.3656i	0.146634	−	0.703255i
$683$		−	0.973163i		−	0.0372370i	−0.999827	−	0.0186185i	$-0.994073\pi$
$683$		−	0.973163i		−	0.0372370i	0.999827	−	0.0186185i	$-0.00592680\pi$
$684$	6.03349	−	20.8910i	0.230696	−	0.798787i
$685$	9.18383	+	13.7561i	0.350896	+	0.525594i
$686$	−20.1466	−	4.20071i	−0.769201	−	0.160384i
$687$	−37.5404	−	18.5347i	−1.43225	−	0.707141i
$688$	3.33299	−	10.8264i	0.127069	−	0.412753i
$689$	−40.1269	−	23.1673i	−1.52871	−	0.882604i
$690$	11.0538	−	16.1881i	0.420812	−	0.616270i
$691$	14.2382	−	8.22045i	0.541648	−	0.312721i	−0.204099	−	0.978950i	$-0.565426\pi$
$691$	14.2382	−	8.22045i	0.541648	−	0.312721i	0.745747	+	0.666230i	$0.232093\pi$
$692$	−1.26419	−	11.1924i	−0.0480573	−	0.425469i
$693$	−1.66237	+	4.00274i	−0.0631481	+	0.152051i
$694$	28.8102	+	25.7392i	1.09362	+	0.977048i
$695$	3.35464	+	1.65594i	0.127249	+	0.0628133i
$696$	−0.0293848	+	1.04529i	−0.00111383	+	0.0396217i
$697$	−19.1629	−	11.0637i	−0.725848	−	0.419069i
$698$	1.57212	+	4.77540i	0.0595055	+	0.180751i
$699$	−1.00625	−	15.4630i	−0.0380600	−	0.584865i
$700$	2.75617	+	11.1372i	0.104173	+	0.420946i
$701$		−	12.3225i		−	0.465415i	−0.972547	−	0.232707i	$-0.925242\pi$
$701$		−	12.3225i		−	0.465415i	0.972547	−	0.232707i	$-0.0747585\pi$
$702$	−18.9989	+	32.1151i	−0.717068	+	1.21211i
$703$	17.1395			0.646427
$704$	6.56474	−	7.64111i	0.247418	−	0.287985i
$705$	2.51759	+	3.28679i	0.0948178	+	0.123788i
$706$	−1.15778	−	3.51682i	−0.0435736	−	0.132357i
$707$	−18.9130	−	10.9194i	−0.711296	−	0.410667i
$708$	21.7642	+	25.7840i	0.817948	+	0.969022i
$709$	2.75578	+	4.77314i	0.103495	+	0.179259i	0.913122	−	0.407685i	$-0.133664\pi$
$709$	2.75578	+	4.77314i	0.103495	+	0.179259i	−0.809627	+	0.586945i	$0.800331\pi$
$710$	−30.3279	−	4.28931i	−1.13819	−	0.160975i
$711$	−15.9118	+	12.1860i	−0.596738	+	0.457009i
$712$	−3.70182	+	5.22178i	−0.138731	+	0.195695i
$713$	−18.8511	−	32.6511i	−0.705980	−	1.22279i
$714$	−8.59733	+	3.46402i	−0.321747	+	0.129638i
$715$	−0.929593	−	14.2674i	−0.0347648	−	0.533572i
$716$	−26.3691	−	11.4961i	−0.985460	−	0.429629i
$717$	−23.5885	−	11.6463i	−0.880929	−	0.434937i
$718$	30.4033	+	6.33932i	1.13464	+	0.236581i
$719$	13.7828			0.514012			0.257006	−	0.966410i	$-0.417264\pi$
$719$	13.7828			0.514012			0.257006	+	0.966410i	$0.417264\pi$
$720$	−21.7255	−	15.7481i	−0.809663	−	0.586895i
$721$	−8.80888			−0.328060
$722$	−8.12062	−	1.69321i	−0.302218	−	0.0630147i
$723$	0.679738	−	0.453728i	0.0252797	−	0.0168743i
$724$	−20.8962	−	9.11006i	−0.776599	−	0.338573i
$725$	−0.847224	+	0.649056i	−0.0314651	+	0.0241053i
$726$	−18.1583	−	14.2147i	−0.673916	−	0.527555i
$727$	−23.1299	−	40.0622i	−0.857842	−	1.48583i	−0.873983	−	0.485956i	$-0.838472\pi$
$727$	−23.1299	−	40.0622i	−0.857842	−	1.48583i	0.0161416	−	0.999870i	$-0.494862\pi$
$728$	9.52979	−	13.4427i	0.353197	−	0.498220i
$729$	−24.9736	+	10.2626i	−0.924947	+	0.380095i
$730$	4.02191	−	28.4373i	0.148858	−	1.05251i
$731$	4.67013	+	8.08890i	0.172731	+	0.299179i
$732$	35.7692	−	6.41500i	1.32207	−	0.237105i
$733$	25.8707	+	14.9365i	0.955556	+	0.551690i	0.894802	−	0.446462i	$-0.147316\pi$
$733$	25.8707	+	14.9365i	0.955556	+	0.551690i	0.0607534	+	0.998153i	$0.480650\pi$
$734$	−8.96344	−	27.2270i	−0.330847	−	1.00497i
$735$	20.3299	+	8.44127i	0.749880	+	0.311361i
$736$	−0.392468	−	20.2411i	−0.0144666	−	0.746098i
$737$	−18.6972			−0.688721
$738$	23.5053	+	16.0531i	0.865242	+	0.590921i
$739$			37.3592i			1.37428i	0.726526	+	0.687139i	$0.241134\pi$
$739$			37.3592i			1.37428i	−0.726526	+	0.687139i	$0.758866\pi$
$740$	7.17393	−	19.8960i	0.263719	−	0.731392i
$741$	−28.5806	−	14.1110i	−1.04994	−	0.518380i
$742$	4.62977	+	14.0632i	0.169964	+	0.516276i
$743$	−21.2072	−	12.2440i	−0.778016	−	0.449188i	0.0577104	−	0.998333i	$-0.481620\pi$
$743$	−21.2072	−	12.2440i	−0.778016	−	0.449188i	−0.835727	+	0.549145i	$0.814953\pi$
$744$	−45.4028	+	24.5387i	−1.66455	+	0.899632i
$745$	8.96185	+	4.42381i	0.328337	+	0.162076i
$746$	13.0375	+	11.6478i	0.477337	+	0.426456i
$747$	13.5722	−	10.3942i	0.496582	−	0.380305i
$748$	0.932279	+	8.25381i	0.0340875	+	0.301789i
$749$	11.7753	−	6.79847i	0.430260	−	0.248411i
$750$	−1.49481	−	27.3453i	−0.0545826	−	0.998509i
$751$	20.1320	+	11.6232i	0.734629	+	0.424138i	0.820113	−	0.572201i	$-0.193910\pi$
$751$	20.1320	+	11.6232i	0.734629	+	0.424138i	−0.0854843	+	0.996340i	$0.527244\pi$
$752$	4.08670	+	1.25812i	0.149027	+	0.0458789i
$753$	2.71684	+	41.7495i	0.0990072	+	1.52144i
$754$	1.50056	+	0.312877i	0.0546471	+	0.0113943i
$755$	−24.1429	+	16.1182i	−0.878648	+	0.586602i
$756$	11.3643	−	3.60804i	0.413314	−	0.131223i
$757$			31.5549i			1.14688i	0.819246	+	0.573442i	$0.194392\pi$
$757$			31.5549i			1.14688i	−0.819246	+	0.573442i	$0.805608\pi$
$758$	−1.99938	+	9.58901i	−0.0726207	+	0.348289i
$759$	7.78915	−	0.506878i	0.282728	−	0.0183985i
$760$	12.0122	−	19.5213i	0.435730	−	0.708111i
$761$	22.9687	+	13.2610i	0.832616	+	0.480711i	0.854747	−	0.519044i	$-0.173712\pi$
$761$	22.9687	+	13.2610i	0.832616	+	0.480711i	−0.0221316	+	0.999755i	$0.507045\pi$
$762$	−3.53979	+	25.0140i	−0.128233	+	0.906162i
$763$	0.794900	+	1.37681i	0.0287773	+	0.0498438i
$764$	3.61220	+	31.9801i	0.130685	+	1.15700i
$765$	21.7053	−	4.28767i	0.784757	−	0.155021i
$766$	−1.52337	−	1.36099i	−0.0550415	−	0.0491745i
$767$	42.8332	−	24.7298i	1.54662	−	0.892941i
$768$	−27.7118	−	0.241569i	−0.999962	−	0.00871688i
$769$	2.70091	−	4.67812i	0.0973974	−	0.168697i	−0.813209	−	0.581971i	$-0.802282\pi$
$769$	2.70091	−	4.67812i	0.0973974	−	0.168697i	0.910607	+	0.413274i	$0.135615\pi$
$770$	−2.81589	+	3.59769i	−0.101478	+	0.129652i
$771$	22.9035	+	11.3080i	0.824848	+	0.407249i
$772$	14.4056	+	19.5077i	0.518471	+	0.702099i
$773$	−10.0058			−0.359884			−0.179942	−	0.983677i	$-0.557591\pi$
$773$	−10.0058			−0.359884			−0.179942	+	0.983677i	$0.557591\pi$
$774$	−5.20449	−	10.8293i	−0.187072	−	0.389250i
$775$	−48.6488	−	20.1951i	−1.74751	−	0.725429i
$776$	21.7799	+	2.03331i	0.781852	+	0.0729916i
$777$	5.21761	+	7.81660i	0.187181	+	0.280419i
$778$	−1.09740	+	0.361277i	−0.0393437	+	0.0129524i
$779$	−12.1572	+	21.0569i	−0.435578	+	0.754443i
$780$	−28.3432	+	27.2709i	−1.01485	+	0.976456i
$781$	−6.09844	−	10.5628i	−0.218219	−	0.377967i
$782$	12.4484	+	11.1215i	0.445152	+	0.397702i
$783$	0.730137	+	0.834917i	0.0260930	+	0.0298375i
$784$	22.1619	−	5.07112i	0.791495	−	0.181112i
$785$	−14.7524	−	7.28217i	−0.526535	−	0.259912i
$786$	27.7339	+	21.7107i	0.989236	+	0.774394i
$787$	−1.15191	+	1.99517i	−0.0410613	+	0.0711202i	−0.885826	−	0.464018i	$-0.846407\pi$
$787$	−1.15191	+	1.99517i	−0.0410613	+	0.0711202i	0.844764	+	0.535138i	$0.179741\pi$
$788$	6.56599	+	2.86256i	0.233904	+	0.101975i
$789$	−1.25938	−	1.88670i	−0.0448352	−	0.0671684i
$790$	−19.5947	+	7.89689i	−0.697148	+	0.280959i
$791$	−0.668954			−0.0237853
$792$	−0.393960	−	10.6777i	−0.0139988	−	0.379414i
$793$		−	53.2683i		−	1.89161i
$794$	8.51146	−	40.8209i	0.302061	−	1.44868i
$795$	−4.58298	−	35.0423i	−0.162541	−	1.24282i
$796$	5.11015	−	11.7214i	0.181125	−	0.415454i
$797$	−4.90786	+	8.50066i	−0.173845	+	0.301109i	−0.939761	−	0.341832i	$-0.888953\pi$
$797$	−4.90786	+	8.50066i	−0.173845	+	0.301109i	0.765916	+	0.642941i	$0.222286\pi$
$798$	3.80639	+	9.44705i	0.134745	+	0.334422i
$799$	−3.05336	+	1.76286i	−0.108020	+	0.0623654i
$800$	−17.6330	−	22.1151i	−0.623422	−	0.781886i
$801$	0.879872	+	6.73183i	0.0310888	+	0.237858i
$802$	1.44986	+	1.29532i	0.0511963	+	0.0457392i
$803$	9.90432	−	5.71826i	0.349516	−	0.201793i
$804$	33.1772	+	39.3050i	1.17007	+	1.38618i
$805$	0.596948	+	9.16199i	0.0210396	+	0.322918i
$806$	23.6563	+	71.8575i	0.833259	+	2.53107i
$807$	37.2597	−	2.42467i	1.31161	−	0.0853525i
$808$	53.6052	+	5.00443i	1.88582	+	0.176055i
$809$		−	2.25430i		−	0.0792571i	−0.999214	−	0.0396285i	$-0.987383\pi$
$809$		−	2.25430i		−	0.0792571i	0.999214	−	0.0396285i	$-0.0126175\pi$
$810$	−28.2578	+	3.39107i	−0.992876	+	0.119150i
$811$			43.2702i			1.51942i	0.650260	+	0.759711i	$0.274660\pi$
$811$			43.2702i			1.51942i	−0.650260	+	0.759711i	$0.725340\pi$
$812$	−0.290960	−	0.394010i	−0.0102107	−	0.0138271i
$813$	2.73278	−	0.177835i	0.0958426	−	0.00623694i
$814$	7.99960	−	2.63357i	0.280386	−	0.0923064i
$815$	14.4626	−	0.942309i	0.506603	−	0.0330077i
$816$	15.6967	−	16.6057i	0.549495	−	0.581317i
$817$	8.88837	−	5.13170i	0.310965	−	0.179536i
$818$	3.12958	−	3.50297i	0.109423	−	0.122478i
$819$	−2.26510	−	17.3301i	−0.0791491	−	0.605564i
$820$	19.3550	+	22.9261i	0.675905	+	0.800615i
$821$	14.9032	−	8.60434i	0.520124	−	0.300293i	−0.216862	−	0.976202i	$-0.569582\pi$
$821$	14.9032	−	8.60434i	0.520124	−	0.300293i	0.736985	+	0.675909i	$0.236249\pi$
$822$	16.8058	−	6.77138i	0.586171	−	0.236179i
$823$	−7.68986	+	13.3192i	−0.268052	+	0.464279i	−0.968359	−	0.249563i	$-0.919713\pi$
$823$	−7.68986	+	13.3192i	−0.268052	+	0.464279i	0.700307	+	0.713842i	$0.253046\pi$
$824$	19.7346	−	9.06292i	0.687487	−	0.315722i
$825$	8.20792	−	7.18016i	0.285763	−	0.249981i
$826$	−15.4715	−	3.22592i	−0.538322	−	0.112244i
$827$		−	0.827927i		−	0.0287899i	−0.999896	−	0.0143949i	$-0.995418\pi$
$827$		−	0.827927i		−	0.0287899i	0.999896	−	0.0143949i	$-0.00458221\pi$
$828$	−14.8869	−	15.4748i	−0.517357	−	0.537785i
$829$	30.8355			1.07096			0.535481	−	0.844547i	$-0.320130\pi$
$829$	30.8355			1.07096			0.535481	+	0.844547i	$0.320130\pi$
$830$	16.7137	−	6.73579i	0.580140	−	0.233803i
$831$	7.63542	+	11.4388i	0.264870	+	0.396807i
$832$	−7.51926	+	39.9204i	−0.260683	+	1.38399i
$833$	−9.37282	+	16.2342i	−0.324749	+	0.562482i
$834$	2.52615	−	3.22699i	0.0874735	−	0.111741i
$835$	26.1977	+	12.9319i	0.906607	+	0.447526i
$836$	9.06958	−	1.02442i	0.313678	−	0.0354303i
$837$	−17.6683	+	51.8106i	−0.610704	+	1.79084i
$838$	−33.2311	+	37.1959i	−1.14795	+	1.28491i
$839$	7.49176	+	12.9761i	0.258644	+	0.447985i	0.965879	−	0.258994i	$-0.0833909\pi$
$839$	7.49176	+	12.9761i	0.258644	+	0.447985i	−0.707235	+	0.706979i	$0.750058\pi$
$840$	12.5596	−	0.464399i	0.433349	−	0.0160233i
$841$	−14.4772	+	25.0753i	−0.499214	+	0.864665i
$842$	12.9281	+	39.2700i	0.445533	+	1.35333i
$843$	−6.53286	−	9.78699i	−0.225004	−	0.337082i
$844$	17.3086	+	23.4388i	0.595785	+	0.806796i
$845$	15.8723	+	23.7745i	0.546025	+	0.817869i
$846$	4.08778	−	1.96457i	0.140541	−	0.0675431i
$847$	10.8012			0.371134
$848$	−24.8408	−	26.7425i	−0.853038	−	0.918343i
$849$	−11.8166	−	5.83415i	−0.405544	−	0.200228i
$850$	23.2552	+	1.75762i	0.797647	+	0.0602859i
$851$	8.46260	−	14.6577i	0.290094	−	0.502458i
$852$	−11.3836	+	31.5631i	−0.389996	+	1.08134i
$853$	2.52471	−	1.45764i	0.0864445	−	0.0499088i	−0.456155	−	0.889901i	$-0.650774\pi$
$853$	2.52471	−	1.45764i	0.0864445	−	0.0499088i	0.542599	+	0.839992i	$0.317440\pi$
$854$	−11.3403	+	12.6933i	−0.388057	+	0.434356i
$855$	−4.71144	−	23.8505i	−0.161128	−	0.815672i
$856$	−19.3857	+	27.3455i	−0.662591	+	0.934650i
$857$	−26.1654	−	45.3198i	−0.893794	−	1.54810i	−0.835291	−	0.549809i	$-0.814701\pi$
$857$	−26.1654	−	45.3198i	−0.893794	−	1.54810i	−0.0585032	−	0.998287i	$-0.518633\pi$
$858$	−15.5078	−	2.19455i	−0.529429	−	0.0749206i
$859$	−1.52668	−	0.881431i	−0.0520897	−	0.0300740i	0.473729	−	0.880671i	$-0.342908\pi$
$859$	−1.52668	−	0.881431i	−0.0520897	−	0.0300740i	−0.525819	+	0.850597i	$0.676241\pi$
$860$	−2.23670	−	12.4658i	−0.0762709	−	0.425081i
$861$	−13.3041	+	0.865763i	−0.453403	+	0.0295051i
$862$	21.7692	+	4.53904i	0.741462	+	0.154600i
$863$		−	16.9992i		−	0.578658i	−0.957230	−	0.289329i	$-0.906568\pi$
$863$		−	16.9992i		−	0.578658i	0.957230	−	0.289329i	$-0.0934322\pi$
$864$	−21.7473	+	19.7751i	−0.739859	+	0.672762i
$865$	−6.99224	−	10.4734i	−0.237743	−	0.356106i
$866$	−11.7305	+	56.2596i	−0.398620	+	1.91178i
$867$	−0.688587	−	10.5815i	−0.0233857	−	0.359365i
$868$	9.66069	−	22.1591i	0.327905	−	0.752130i
$869$	−7.28544	−	4.20625i	−0.247142	−	0.142687i
$870$	0.506514	+	1.05372i	0.0171724	+	0.0357243i
$871$	65.2947	−	37.6979i	2.21243	−	1.27735i
$872$	−3.19733	−	2.26665i	−0.108275	−	0.0767583i
$873$	18.4202	−	14.1070i	0.623428	−	0.477450i
$874$	12.2207	−	13.6787i	0.413370	−	0.462689i
$875$	8.44648	+	9.65395i	0.285543	+	0.326363i
$876$	−29.5955	−	10.6739i	−0.999939	−	0.360639i
$877$	−32.5343	−	18.7837i	−1.09860	−	0.634279i	−0.162750	−	0.986667i	$-0.552036\pi$
$877$	−32.5343	−	18.7837i	−1.09860	−	0.634279i	−0.935854	+	0.352388i	$0.885370\pi$
$878$	30.3062	−	9.97716i	1.02278	−	0.336713i
$879$	15.3907	+	7.59876i	0.519114	+	0.256300i
$880$	2.60700	−	10.9570i	0.0878821	−	0.369361i
$881$		−	32.8340i		−	1.10620i	−0.833114	−	0.553102i	$-0.813444\pi$
$881$		−	32.8340i		−	1.10620i	0.833114	−	0.553102i	$-0.186556\pi$
$882$	13.5996	−	19.9129i	0.457923	−	0.670502i
$883$	−57.6883			−1.94137			−0.970683	−	0.240363i	$-0.922734\pi$
$883$	−57.6883			−1.94137			−0.970683	+	0.240363i	$0.922734\pi$
$884$	−19.8973	−	26.9444i	−0.669219	−	0.906237i
$885$	34.8403	+	14.4662i	1.17114	+	0.486275i
$886$	−19.3527	+	6.37115i	−0.650168	+	0.214043i
$887$	−32.5642	−	18.8010i	−1.09340	−	0.631275i	−0.158920	−	0.987291i	$-0.550801\pi$
$887$	−32.5642	−	18.8010i	−1.09340	−	0.631275i	−0.934479	+	0.356017i	$0.884135\pi$
$888$	−19.7311	−	12.1435i	−0.662132	−	0.407509i
$889$	−5.91652	−	10.2477i	−0.198434	−	0.343698i
$890$	−1.00215	+	7.08581i	−0.0335923	+	0.237517i
$891$	−7.99873	−	8.02864i	−0.267967	−	0.268970i
$892$	0.279795	+	2.47712i	0.00936821	+	0.0829403i
$893$	1.93709	+	3.35514i	0.0648222	+	0.112275i
$894$	6.74856	−	8.62083i	0.225706	−	0.288324i
$895$	−32.0935	+	2.09104i	−1.07277	+	0.0698959i
$896$	10.2904	−	7.91187i	0.343779	−	0.264317i
$897$	−26.1794	+	17.4748i	−0.874104	+	0.583468i
$898$	4.25728	−	20.4179i	0.142067	−	0.681355i
$899$	2.24869			0.0749980
$900$	−29.6585	−	4.51375i	−0.988616	−	0.150458i
$901$	30.0955			1.00263
$902$	−2.43871	+	11.6960i	−0.0812002	+	0.389436i
$903$	5.04617	+	2.49142i	0.167926	+	0.0829094i
$904$	1.49866	−	0.688245i	0.0498447	−	0.0228907i
$905$	−25.4324	+	1.65704i	−0.845402	+	0.0550820i
$906$	11.8842	+	29.4953i	0.394827	+	0.979917i
$907$	12.8060	+	22.1806i	0.425215	+	0.736494i	0.996441	−	0.0842990i	$-0.0268651\pi$
$907$	12.8060	+	22.1806i	0.425215	+	0.736494i	−0.571225	+	0.820793i	$0.693532\pi$
$908$	−21.5565	+	2.43483i	−0.715376	+	0.0808027i
$909$	45.3362	−	34.7205i	1.50371	−	1.15161i
$910$	2.57990	−	18.2414i	0.0855229	−	0.604696i
$911$	0.996781	+	1.72648i	0.0330248	+	0.0572007i	0.882065	−	0.471127i	$-0.156153\pi$
$911$	0.996781	+	1.72648i	0.0330248	+	0.0572007i	−0.849041	+	0.528328i	$0.822819\pi$
$912$	−18.2470	−	17.2481i	−0.604218	−	0.571142i
$913$	6.21425	+	3.58780i	0.205662	+	0.118739i
$914$	−1.37105	+	0.451366i	−0.0453503	+	0.0149299i
$915$	32.2544	−	24.7060i	1.06630	−	0.816755i
$916$	−38.8891	+	28.7180i	−1.28493	+	0.948869i
$917$	−16.4972			−0.544785
$918$	0.257202	−	24.2351i	0.00848893	−	0.799876i
$919$			13.2072i			0.435667i	0.975986	+	0.217833i	$0.0698989\pi$
$919$			13.2072i			0.435667i	−0.975986	+	0.217833i	$0.930101\pi$
$920$	−10.7636	−	19.9115i	−0.354864	−	0.656463i
$921$	0.896990	+	13.7840i	0.0295568	+	0.454197i
$922$	−1.05413	+	0.347032i	−0.0347159	+	0.0114289i
$923$	42.5941	+	24.5917i	1.40200	+	0.809446i
$924$	3.22817	+	3.82441i	0.106199	+	0.125814i
$925$	−3.06831	−	23.4464i	−0.100885	−	0.770911i
$926$	30.6911	−	34.3529i	1.00857	−	1.12891i
$927$	8.83437	−	21.2719i	0.290159	−	0.698661i
$928$	1.05721	+	0.583353i	0.0347047	+	0.0191495i
$929$	−14.7794	+	8.53291i	−0.484897	+	0.279956i	−0.722455	−	0.691418i	$-0.756986\pi$
$929$	−14.7794	+	8.53291i	−0.484897	+	0.279956i	0.237558	+	0.971373i	$0.423653\pi$
$930$	−32.5385	+	47.6518i	−1.06698	+	1.56257i
$931$	17.8387	+	10.2992i	0.584640	+	0.337542i
$932$	−16.4019	−	7.15072i	−0.537263	−	0.234230i
$933$	−10.8808	−	5.37215i	−0.356223	−	0.175876i
$934$	7.53053	−	36.1164i	0.246406	−	1.18176i
$935$	5.15644	+	7.72362i	0.168633	+	0.252589i
$936$	22.9044	+	36.4944i	0.748655	+	1.19286i
$937$			20.0658i			0.655523i	0.944761	+	0.327761i	$0.106294\pi$
$937$			20.0658i			0.655523i	−0.944761	+	0.327761i	$0.893706\pi$
$938$	−23.5846	−	4.91757i	−0.770065	−	0.160564i
$939$	−14.1361	−	21.1776i	−0.461315	−	0.691104i
$940$	4.70554	−	0.844299i	0.153478	−	0.0275380i
$941$	−28.5447	−	16.4803i	−0.930532	−	0.537243i	−0.0435520	−	0.999051i	$-0.513867\pi$
$941$	−28.5447	−	16.4803i	−0.930532	−	0.537243i	−0.886980	+	0.461808i	$0.847201\pi$
$942$	−11.1090	+	14.1910i	−0.361951	+	0.462368i
$943$	12.0053	+	20.7937i	0.390945	+	0.677136i
$944$	37.9798	−	8.69061i	1.23614	−	0.282855i
$945$	9.44299	−	9.40931i	0.307181	−	0.306085i
$946$	3.36001	−	3.76090i	0.109243	−	0.122277i
$947$	−44.3874	+	25.6271i	−1.44240	+	0.832767i	−0.998009	−	0.0630680i	$-0.979912\pi$
$947$	−44.3874	+	25.6271i	−1.44240	+	0.832767i	−0.444386	+	0.895835i	$0.646578\pi$
$948$	4.08530	+	22.7791i	0.132684	+	0.739830i
$949$	−23.0587	+	39.9388i	−0.748516	+	1.29647i
$950$	1.93134	−	25.5536i	0.0626609	−	0.829069i
$951$	3.34810	−	2.23487i	0.108570	−	0.0724707i
$952$	−0.994864	+	10.6565i	−0.0322437	+	0.345380i
$953$	23.0185			0.745641			0.372821	−	0.927903i	$-0.378391\pi$
$953$	23.0185			0.745641			0.372821	+	0.927903i	$0.378391\pi$
$954$	−38.6032	−	2.92381i	−1.24983	−	0.0946618i
$955$	19.9791	+	29.9258i	0.646507	+	0.968377i
$956$	−24.4360	+	18.0450i	−0.790316	+	0.583616i
$957$	−0.206104	+	0.417446i	−0.00666239	+	0.0134941i
$958$	−13.3427	−	40.5293i	−0.431084	−	1.30944i
$959$	−4.24331	+	7.34963i	−0.137024	+	0.237332i
$960$	−27.6596	+	13.9622i	−0.892711	+	0.450629i
$961$	39.9909	+	69.2662i	1.29003	+	2.23439i
$962$	−22.6265	+	25.3260i	−0.729506	+	0.816544i
$963$	4.60773	+	35.2534i	0.148482	+	1.13602i
$964$	−0.105918	−	0.937727i	−0.00341137	−	0.0302022i
$965$	24.3119	+	12.0010i	0.782628	+	0.386326i
$966$	9.95852	+	1.40925i	0.320410	+	0.0453420i
$967$	22.4438	−	38.8737i	0.721743	−	1.25010i	−0.238558	−	0.971128i	$-0.576675\pi$
$967$	22.4438	−	38.8737i	0.721743	−	1.25010i	0.960301	−	0.278967i	$-0.0899920\pi$
$968$	−24.1980	+	11.1127i	−0.777755	+	0.357176i
$969$	20.6595	−	1.34441i	0.663678	−	0.0431888i
$970$	22.6837	−	9.14178i	0.728330	−	0.293525i
$971$	−49.5015			−1.58858			−0.794290	−	0.607539i	$-0.792157\pi$
$971$	−49.5015			−1.58858			−0.794290	+	0.607539i	$0.792157\pi$
$972$	−2.68437	+	31.0611i	−0.0861013	+	0.996286i
$973$			1.91954i			0.0615375i
$974$	30.8456	+	6.43153i	0.988357	+	0.206080i
$975$	−14.1870	+	41.6237i	−0.454346	+	1.33303i
$976$	12.3464	−	40.1042i	0.395198	−	1.28371i
$977$	15.6589	−	27.1220i	0.500972	−	0.867710i	−0.499027	−	0.866586i	$-0.666309\pi$
$977$	15.6589	−	27.1220i	0.500972	−	0.867710i	0.999999	−	0.00112320i	$-0.000357524\pi$
$978$	2.22457	−	15.7200i	0.0711339	−	0.502669i
$979$	−2.46789	+	1.42484i	−0.0788742	+	0.0455380i
$980$	19.4222	−	16.3969i	0.620420	−	0.523779i
$981$	−4.12195	+	0.538752i	−0.131604	+	0.0172010i
$982$	−20.1678	+	22.5740i	−0.643581	+	0.720367i
$983$	−48.0135	+	27.7206i	−1.53139	+	0.884149i	−0.532094	+	0.846686i	$0.678595\pi$
$983$	−48.0135	+	27.7206i	−1.53139	+	0.884149i	−0.999298	+	0.0374637i	$0.988072\pi$
$984$	28.9146	−	15.6274i	0.921763	−	0.498182i
$985$	7.99137	−	0.520676i	0.254626	−	0.0165901i
$986$	−0.945684	+	0.311330i	−0.0301167	+	0.00991478i
$987$	−0.940450	+	1.90480i	−0.0299348	+	0.0606305i
$988$	−29.6074	+	21.8639i	−0.941938	+	0.695582i
$989$		−	10.1351i		−	0.322278i
$990$	−5.86376	−	10.4080i	−0.186363	−	0.330787i
$991$		−	5.66060i		−	0.179815i	−0.995950	−	0.0899075i	$-0.971343\pi$
$991$		−	5.66060i		−	0.179815i	0.995950	−	0.0899075i	$-0.0286571\pi$
$992$	1.15528	+	59.5826i	0.0366803	+	1.89175i
$993$	−14.5124	−	21.7413i	−0.460536	−	0.689938i
$994$	−4.91442	−	14.9278i	−0.155876	−	0.473483i
$995$	−0.929494	−	14.2659i	−0.0294669	−	0.452260i
$996$	−3.48463	−	19.4298i	−0.110415	−	0.615658i
$997$	−16.2323	+	9.37172i	−0.514082	+	0.296805i	−0.734510	−	0.678598i	$-0.762588\pi$
$997$	−16.2323	+	9.37172i	−0.514082	+	0.296805i	0.220428	+	0.975403i	$0.429255\pi$
$998$	−17.6299	−	15.7507i	−0.558064	−	0.498578i
$999$	−24.1084	+	4.76039i	−0.762757	+	0.150612i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	180.2.n.d.59.3	✓	48
3.2	odd	2		540.2.n.d.179.22		48
4.3	odd	2	inner	180.2.n.d.59.16	yes	48
5.2	odd	4		900.2.r.g.851.15		48
5.3	odd	4		900.2.r.g.851.10		48
5.4	even	2	inner	180.2.n.d.59.22	yes	48
9.2	odd	6	inner	180.2.n.d.119.9	yes	48
9.7	even	3		540.2.n.d.359.16		48
12.11	even	2		540.2.n.d.179.9		48
15.14	odd	2		540.2.n.d.179.3		48
20.3	even	4		900.2.r.g.851.4		48
20.7	even	4		900.2.r.g.851.21		48
20.19	odd	2	inner	180.2.n.d.59.9	yes	48
36.7	odd	6		540.2.n.d.359.3		48
36.11	even	6	inner	180.2.n.d.119.22	yes	48
45.2	even	12		900.2.r.g.551.21		48
45.29	odd	6	inner	180.2.n.d.119.16	yes	48
45.34	even	6		540.2.n.d.359.9		48
45.38	even	12		900.2.r.g.551.4		48
60.59	even	2		540.2.n.d.179.16		48
180.47	odd	12		900.2.r.g.551.15		48
180.79	odd	6		540.2.n.d.359.22		48
180.83	odd	12		900.2.r.g.551.10		48
180.119	even	6	inner	180.2.n.d.119.3	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.n.d.59.3	✓	48	1.1	even	1	trivial
180.2.n.d.59.9	yes	48	20.19	odd	2	inner
180.2.n.d.59.16	yes	48	4.3	odd	2	inner
180.2.n.d.59.22	yes	48	5.4	even	2	inner
180.2.n.d.119.3	yes	48	180.119	even	6	inner
180.2.n.d.119.9	yes	48	9.2	odd	6	inner
180.2.n.d.119.16	yes	48	45.29	odd	6	inner
180.2.n.d.119.22	yes	48	36.11	even	6	inner
540.2.n.d.179.3		48	15.14	odd	2
540.2.n.d.179.9		48	12.11	even	2
540.2.n.d.179.16		48	60.59	even	2
540.2.n.d.179.22		48	3.2	odd	2
540.2.n.d.359.3		48	36.7	odd	6
540.2.n.d.359.9		48	45.34	even	6
540.2.n.d.359.16		48	9.7	even	3
540.2.n.d.359.22		48	180.79	odd	6
900.2.r.g.551.4		48	45.38	even	12
900.2.r.g.551.10		48	180.83	odd	12
900.2.r.g.551.15		48	180.47	odd	12
900.2.r.g.551.21		48	45.2	even	12
900.2.r.g.851.4		48	20.3	even	4
900.2.r.g.851.10		48	5.3	odd	4
900.2.r.g.851.15		48	5.2	odd	4
900.2.r.g.851.21		48	20.7	even	4

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:	\( N \)	\(=\)	\( 180 = 2^{2} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	180.n (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38444 - 0.288666i) q^{2} +(0.112475 + 1.72840i) q^{3} +(1.83334 + 0.799280i) q^{4} +(2.23134 - 0.145382i) q^{5} +(0.343213 - 2.42533i) q^{6} +(0.573658 + 0.993605i) q^{7} +(-2.30743 - 1.63578i) q^{8} +(-2.97470 + 0.388803i) q^{9} +(-3.13112 - 0.442837i) q^{10} +(-0.629615 - 1.09053i) q^{11} +(-1.17527 + 3.25864i) q^{12} +(4.39750 + 2.53890i) q^{13} +(-0.507375 - 1.54118i) q^{14} +(0.502248 + 3.84028i) q^{15} +(2.72230 + 2.93071i) q^{16} -3.29816 q^{17} +(4.23052 + 0.320420i) q^{18} +3.62414i q^{19} +(4.20701 + 1.51693i) q^{20} +(-1.65282 + 1.10326i) q^{21} +(0.556867 + 1.69152i) q^{22} +(3.09936 + 1.78942i) q^{23} +(2.56774 - 4.17213i) q^{24} +(4.95773 - 0.648794i) q^{25} +(-5.35518 - 4.78436i) q^{26} +(-1.00658 - 5.09772i) q^{27} +(0.257544 + 2.28013i) q^{28} +(-0.184856 + 0.106727i) q^{29} +(0.413225 - 5.46162i) q^{30} +(-9.12339 - 5.26739i) q^{31} +(-2.92287 - 4.84323i) q^{32} +(1.81404 - 1.21088i) q^{33} +(4.56610 + 0.952066i) q^{34} +(1.42448 + 2.13367i) q^{35} +(-5.76441 - 1.66481i) q^{36} -4.72925i q^{37} +(1.04616 - 5.01740i) q^{38} +(-3.89361 + 7.88619i) q^{39} +(-5.38647 - 3.31451i) q^{40} +(5.81019 + 3.35452i) q^{41} +(2.60670 - 1.05029i) q^{42} +(-1.41598 - 2.45255i) q^{43} +(-0.282666 - 2.50255i) q^{44} +(-6.58103 + 1.30002i) q^{45} +(-3.77433 - 3.37202i) q^{46} +(0.925776 - 0.534497i) q^{47} +(-4.75924 + 5.03485i) q^{48} +(2.84183 - 4.92220i) q^{49} +(-7.05096 - 0.532910i) q^{50} +(-0.370961 - 5.70053i) q^{51} +(6.03285 + 8.16951i) q^{52} -9.12493 q^{53} +(-0.0779834 + 7.34806i) q^{54} +(-1.56343 - 2.34180i) q^{55} +(0.301642 - 3.23105i) q^{56} +(-6.26394 + 0.407625i) q^{57} +(0.286731 - 0.0943952i) q^{58} +(4.87018 - 8.43539i) q^{59} +(-2.14867 + 7.44199i) q^{60} +(-5.24521 - 9.08497i) q^{61} +(11.1103 + 9.92600i) q^{62} +(-2.09278 - 2.73264i) q^{63} +(2.64846 + 7.54889i) q^{64} +(10.1814 + 5.02582i) q^{65} +(-2.86097 + 1.15274i) q^{66} +(7.42407 - 12.8589i) q^{67} +(-6.04666 - 2.63615i) q^{68} +(-2.74422 + 5.55818i) q^{69} +(-1.35619 - 3.36513i) q^{70} +9.68598 q^{71} +(7.49990 + 3.96881i) q^{72} +9.08215i q^{73} +(-1.36517 + 6.54736i) q^{74} +(1.67899 + 8.49594i) q^{75} +(-2.89670 + 6.64429i) q^{76} +(0.722368 - 1.25118i) q^{77} +(7.66694 - 9.79399i) q^{78} +(5.78563 - 3.34033i) q^{79} +(6.50045 + 6.14363i) q^{80} +(8.69767 - 2.31314i) q^{81} +(-7.07552 - 6.32133i) q^{82} +(-4.93496 + 2.84920i) q^{83} +(-3.91200 + 0.701596i) q^{84} +(-7.35931 + 0.479494i) q^{85} +(1.25237 + 3.80415i) q^{86} +(-0.205258 - 0.307501i) q^{87} +(-0.331066 + 3.54622i) q^{88} -2.26303i q^{89} +(9.48631 + 0.0999207i) q^{90} +5.82584i q^{91} +(4.25195 + 5.75787i) q^{92} +(8.07798 - 16.3613i) q^{93} +(-1.43597 + 0.472739i) q^{94} +(0.526885 + 8.08667i) q^{95} +(8.04226 - 5.59661i) q^{96} +(-6.69770 + 3.86692i) q^{97} +(-5.35521 + 5.99415i) q^{98} +(2.29692 + 2.99919i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 2 q^{4} - 18 q^{5} - 12 q^{9} - 16 q^{10} - 42 q^{14} + 30 q^{16} - 12 q^{21} - 6 q^{24} - 26 q^{25} - 12 q^{30} - 4 q^{34} + 96 q^{36} + 10 q^{40} + 96 q^{41} - 66 q^{45} + 4 q^{46} + 32 q^{49}+ \cdots + 54 q^{96}+O(q^{100}) \) 48 * q - 2 * q^4 - 18 * q^5 - 12 * q^9 - 16 * q^10 - 42 * q^14 + 30 * q^16 - 12 * q^21 - 6 * q^24 - 26 * q^25 - 12 * q^30 - 4 * q^34 + 96 * q^36 + 10 * q^40 + 96 * q^41 - 66 * q^45 + 4 * q^46 + 32 * q^49 - 90 * q^50 - 30 * q^54 + 6 * q^56 - 42 * q^60 + 8 * q^61 - 20 * q^64 - 6 * q^65 + 36 * q^66 - 96 * q^69 + 4 * q^70 + 72 * q^74 + 36 * q^81 - 6 * q^84 - 4 * q^85 + 108 * q^86 - 6 * q^90 - 62 * q^94 + 54 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more