LMFDB - Embedded newform 180.2.n.d.119.9

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			119.9
Character	$\chi$	$=$	180.119
Dual form			180.2.n.d.59.9

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.442228 - 1.34329i) q^{2} +(0.112475 - 1.72840i) q^{3} +(-1.60887 + 1.18808i) q^{4} +(0.989764 - 2.00509i) q^{5} +(-2.37148 + 0.613258i) 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} +(1.87252 + 2.91439i) q^{12} +(-4.39750 + 2.53890i) q^{13} +(-1.58839 - 0.331191i) q^{14} +(-3.35426 - 1.93622i) q^{15} +(1.17692 - 3.82294i) q^{16} +3.29816 q^{17} +(0.793219 + 4.16783i) q^{18} +3.62414i q^{19} +(0.789807 + 4.40184i) q^{20} +(-1.65282 - 1.10326i) q^{21} +(-1.74333 - 0.363497i) q^{22} +(3.09936 - 1.78942i) q^{23} +(3.08680 - 3.80416i) q^{24} +(-3.04074 - 3.96912i) 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} +(-1.11757 + 5.36200i) q^{30} +(9.12339 - 5.26739i) q^{31} +(-5.65579 + 0.109664i) q^{32} +(-1.81404 - 1.21088i) q^{33} +(-1.45854 - 4.43039i) q^{34} +(-1.42448 - 2.13367i) q^{35} +(5.24783 - 2.90866i) q^{36} -4.72925i q^{37} +(4.86827 - 1.60269i) q^{38} +(3.89361 + 7.88619i) q^{39} +(5.56368 - 3.00756i) q^{40} +(5.81019 - 3.35452i) q^{41} +(-0.751083 + 2.70811i) q^{42} +(-1.41598 + 2.45255i) q^{43} +(0.282666 + 2.50255i) q^{44} +(-3.72383 + 5.57970i) q^{45} +(-3.77433 - 3.37202i) q^{46} +(0.925776 + 0.534497i) q^{47} +(-6.47517 - 2.46417i) q^{48} +(2.84183 + 4.92220i) q^{49} +(-3.98699 + 5.83985i) q^{50} +(0.370961 - 5.70053i) q^{51} +(4.05858 - 9.30936i) q^{52} +9.12493 q^{53} +(7.29287 - 0.902219i) q^{54} +(-1.56343 - 2.34180i) q^{55} +(2.94899 - 1.35430i) q^{56} +(6.26394 + 0.407625i) q^{57} +(-0.0616167 + 0.295514i) q^{58} +(-4.87018 - 8.43539i) q^{59} +(7.69695 - 0.870002i) 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} +(0.738222 + 11.3303i) q^{65} +(-0.824347 + 2.97228i) q^{66} +(7.42407 + 12.8589i) q^{67} +(-5.30631 + 3.91849i) q^{68} +(-2.74422 - 5.55818i) q^{69} +(-2.23620 + 2.85706i) q^{70} -9.68598 q^{71} +(-6.22791 - 5.76308i) q^{72} +9.08215i q^{73} +(-6.35277 + 2.09141i) q^{74} +(-7.20222 + 4.80917i) q^{75} +(-4.30577 - 5.83076i) q^{76} +(-0.722368 - 1.25118i) q^{77} +(8.87159 - 8.71775i) 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} +(3.96994 - 0.188680i) q^{84} +(3.26440 - 6.61309i) q^{85} +(3.92068 + 0.817489i) q^{86} +(-0.205258 + 0.307501i) q^{87} +(3.23665 - 1.48640i) q^{88} +2.26303i q^{89} +(9.14195 + 2.53469i) q^{90} +5.82584i q^{91} +(-2.86049 + 6.56123i) q^{92} +(-8.07798 - 16.3613i) q^{93} +(0.308582 - 1.47996i) q^{94} +(7.26670 + 3.58704i) q^{95} +(-0.446593 + 9.78778i) 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 $\left(\mathbb{Z}/180\mathbb{Z}\right)^\times$.

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

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 $

$2$	−0.442228	−	1.34329i	−0.312702	−	0.949851i
$2$	−0.442228	−	1.34329i	−0.312702	−	0.949851i
$3$	0.112475	−	1.72840i	0.0649375	−	0.997889i
$3$	0.112475	−	1.72840i	0.0649375	−	0.997889i
$4$	−1.60887	+	1.18808i	−0.804435	+	0.594041i
$5$	0.989764	−	2.00509i	0.442636	−	0.896702i
$5$	0.989764	−	2.00509i	0.442636	−	0.896702i
$6$	−2.37148	+	0.613258i	−0.968152	+	0.250361i
$7$	0.573658	−	0.993605i	0.216822	−	0.375547i	−0.737012	−	0.675879i	$-0.763764\pi$
$7$	0.573658	−	0.993605i	0.216822	−	0.375547i	0.953835	+	0.300332i	$0.0970974\pi$
$8$	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	$-0.772538\pi$
$11$	0.629615	−	1.09053i	0.189836	−	0.328806i	0.945196	+	0.326505i	$0.105871\pi$
$12$	1.87252	+	2.91439i	0.540550	+	0.841312i
$13$	−4.39750	+	2.53890i	−1.21965	+	0.704164i	−0.964843	−	0.262828i	$-0.915345\pi$
$13$	−4.39750	+	2.53890i	−1.21965	+	0.704164i	−0.254805	+	0.966992i	$0.582011\pi$
$14$	−1.58839	−	0.331191i	−0.424515	−	0.0885145i
$15$	−3.35426	−	1.93622i	−0.866065	−	0.499931i
$16$	1.17692	−	3.82294i	0.294230	−	0.955735i
$17$	3.29816			0.799922			0.399961	−	0.916532i	$-0.369024\pi$
$17$	3.29816			0.799922			0.399961	+	0.916532i	$0.369024\pi$
$18$	0.793219	+	4.16783i	0.186964	+	0.982367i
$19$			3.62414i			0.831434i	0.909494	+	0.415717i	$0.136469\pi$
$19$			3.62414i			0.831434i	−0.909494	+	0.415717i	$0.863531\pi$
$20$	0.789807	+	4.40184i	0.176606	+	0.984282i
$21$	−1.65282	−	1.10326i	−0.360675	−	0.240752i
$22$	−1.74333	−	0.363497i	−0.371679	−	0.0774978i
$23$	3.09936	−	1.78942i	0.646261	−	0.373119i	−0.140761	−	0.990044i	$-0.544955\pi$
$23$	3.09936	−	1.78942i	0.646261	−	0.373119i	0.787022	+	0.616924i	$0.211622\pi$
$24$	3.08680	−	3.80416i	0.630090	−	0.776522i
$25$	−3.04074	−	3.96912i	−0.608147	−	0.793824i
$26$	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	0.482738	−	0.875765i	$-0.339642\pi$
$29$	−0.184856	−	0.106727i	−0.0343270	−	0.0198187i	−0.517065	+	0.855946i	$0.672976\pi$
$30$	−1.11757	+	5.36200i	−0.204039	+	0.978963i
$31$	9.12339	−	5.26739i	1.63861	−	0.946052i	0.657297	−	0.753632i	$-0.271700\pi$
$31$	9.12339	−	5.26739i	1.63861	−	0.946052i	0.981313	−	0.192420i	$-0.0616337\pi$
$32$	−5.65579	+	0.109664i	−0.999812	+	0.0193860i
$33$	−1.81404	−	1.21088i	−0.315784	−	0.210787i
$34$	−1.45854	−	4.43039i	−0.250137	−	0.759806i
$35$	−1.42448	−	2.13367i	−0.240781	−	0.360656i
$36$	5.24783	−	2.90866i	0.874638	−	0.484776i
$37$		−	4.72925i		−	0.777484i	−0.921347	−	0.388742i	$-0.872910\pi$
$37$		−	4.72925i		−	0.777484i	0.921347	−	0.388742i	$-0.127090\pi$
$38$	4.86827	−	1.60269i	0.789738	−	0.259991i
$39$	3.89361	+	7.88619i	0.623477	+	1.26280i
$40$	5.56368	−	3.00756i	0.879696	−	0.475537i
$41$	5.81019	−	3.35452i	0.907399	−	0.523887i	0.0278059	−	0.999613i	$-0.491148\pi$
$41$	5.81019	−	3.35452i	0.907399	−	0.523887i	0.879594	+	0.475726i	$0.157815\pi$
$42$	−0.751083	+	2.70811i	−0.115895	+	0.417871i
$43$	−1.41598	+	2.45255i	−0.215935	+	0.374010i	−0.953561	−	0.301199i	$-0.902613\pi$
$43$	−1.41598	+	2.45255i	−0.215935	+	0.374010i	0.737626	+	0.675209i	$0.235947\pi$
$44$	0.282666	+	2.50255i	0.0426135	+	0.377273i
$45$	−3.72383	+	5.57970i	−0.555116	+	0.831773i
$46$	−3.77433	−	3.37202i	−0.556495	−	0.497177i
$47$	0.925776	+	0.534497i	0.135038	+	0.0779644i	0.565997	−	0.824407i	$-0.308491\pi$
$47$	0.925776	+	0.534497i	0.135038	+	0.0779644i	−0.430959	+	0.902372i	$0.641825\pi$
$48$	−6.47517	−	2.46417i	−0.934611	−	0.355672i
$49$	2.84183	+	4.92220i	0.405976	+	0.703171i
$50$	−3.98699	+	5.83985i	−0.563846	+	0.825880i
$51$	0.370961	−	5.70053i	0.0519449	−	0.798233i
$52$	4.05858	−	9.30936i	0.562824	−	1.29098i
$53$	9.12493			1.25341			0.626703	−	0.779258i	$-0.284404\pi$
$53$	9.12493			1.25341			0.626703	+	0.779258i	$0.284404\pi$
$54$	7.29287	−	0.902219i	0.992434	−	0.122776i
$55$	−1.56343	−	2.34180i	−0.210813	−	0.315768i
$56$	2.94899	−	1.35430i	0.394076	−	0.180975i
$57$	6.26394	+	0.407625i	0.829679	+	0.0539912i
$58$	−0.0616167	+	0.295514i	−0.00809067	+	0.0388028i
$59$	−4.87018	−	8.43539i	−0.634043	−	1.09819i	−0.986717	−	0.162449i	$-0.948061\pi$
$59$	−4.87018	−	8.43539i	−0.634043	−	1.09819i	0.352674	−	0.935746i	$-0.385272\pi$
$60$	7.69695	−	0.870002i	0.993672	−	0.112317i
$61$	−5.24521	+	9.08497i	−0.671580	+	1.16321i	0.305876	+	0.952072i	$0.401051\pi$
$61$	−5.24521	+	9.08497i	−0.671580	+	1.16321i	−0.977456	+	0.211140i	$0.932282\pi$
$62$	−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
$65$	0.738222	+	11.3303i	0.0915652	+	1.40535i
$66$	−0.824347	+	2.97228i	−0.101470	+	0.365862i
$67$	7.42407	+	12.8589i	0.906994	+	1.57096i	0.818218	+	0.574909i	$0.194962\pi$
$67$	7.42407	+	12.8589i	0.906994	+	1.57096i	0.0887767	+	0.996052i	$0.471704\pi$
$68$	−5.30631	+	3.91849i	−0.643484	+	0.475186i
$69$	−2.74422	−	5.55818i	−0.330365	−	0.669127i
$70$	−2.23620	+	2.85706i	−0.267277	+	0.341484i
$71$	−9.68598			−1.14951			−0.574757	−	0.818324i	$-0.694903\pi$
$71$	−9.68598			−1.14951			−0.574757	+	0.818324i	$0.694903\pi$
$72$	−6.22791	−	5.76308i	−0.733966	−	0.679186i
$73$			9.08215i			1.06299i	0.847063	+	0.531493i	$0.178369\pi$
$73$			9.08215i			1.06299i	−0.847063	+	0.531493i	$0.821631\pi$
$74$	−6.35277	+	2.09141i	−0.738494	+	0.243121i
$75$	−7.20222	+	4.80917i	−0.831640	+	0.555315i
$76$	−4.30577	−	5.83076i	−0.493906	−	0.668834i
$77$	−0.722368	−	1.25118i	−0.0823215	−	0.142585i
$78$	8.87159	−	8.71775i	1.00451	−	0.987091i
$79$	−5.78563	−	3.34033i	−0.650934	−	0.375817i	0.137880	−	0.990449i	$-0.455971\pi$
$79$	−5.78563	−	3.34033i	−0.650934	−	0.375817i	−0.788814	+	0.614632i	$0.789305\pi$
$80$	−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	0.204078	−	0.978955i	$-0.434580\pi$
$83$	−4.93496	−	2.84920i	−0.541682	−	0.312740i	−0.745760	+	0.666214i	$0.767914\pi$
$84$	3.96994	−	0.188680i	0.433156	−	0.0205867i
$85$	3.26440	−	6.61309i	0.354074	−	0.717291i
$86$	3.92068	+	0.817489i	0.422777	+	0.0881521i
$87$	−0.205258	+	0.307501i	−0.0220060	+	0.0329675i
$88$	3.23665	−	1.48640i	0.345028	−	0.158451i
$89$			2.26303i			0.239881i	0.992781	+	0.119940i	$0.0382703\pi$
$89$			2.26303i			0.239881i	−0.992781	+	0.119940i	$0.961730\pi$
$90$	9.14195	+	2.53469i	0.963647	+	0.267180i
$91$			5.82584i			0.610714i
$92$	−2.86049	+	6.56123i	−0.298227	+	0.684056i
$93$	−8.07798	−	16.3613i	−0.837648	−	1.69659i
$94$	0.308582	−	1.47996i	0.0318278	−	0.152646i
$95$	7.26670	+	3.58704i	0.745548	+	0.368022i
$96$	−0.446593	+	9.78778i	−0.0455802	+	0.998961i
$97$	6.69770	+	3.86692i	0.680048	+	0.392626i	0.799873	−	0.600169i	$-0.204900\pi$
$97$	6.69770	+	3.86692i	0.680048	+	0.392626i	−0.119825	+	0.992795i	$0.538233\pi$
$98$	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	−0.980735	−	0.195341i	$-0.937419\pi$
$101$	−16.4845	−	9.51736i	−1.64027	−	0.947012i	−0.659538	−	0.751671i	$-0.729248\pi$
$102$	−7.82152	+	2.02262i	−0.774446	+	0.200269i
$103$	−3.83891	−	6.64918i	−0.378259	−	0.655164i	0.612550	−	0.790432i	$-0.290144\pi$
$103$	−3.83891	−	6.64918i	−0.378259	−	0.655164i	−0.990809	+	0.135268i	$0.956810\pi$
$104$	−14.3000	−	1.33501i	−1.40223	−	0.130908i
$105$	−3.84804	+	2.22208i	−0.375530	+	0.216852i
$106$	−4.03530	−	12.2575i	−0.391943	−	1.19055i
$107$			11.8511i			1.14569i	0.819665	+	0.572843i	$0.194160\pi$
$107$			11.8511i			1.14569i	−0.819665	+	0.572843i	$0.805840\pi$
$108$	−4.43706	−	9.39747i	−0.426956	−	0.904272i
$109$	1.38567			0.132723			0.0663615	−	0.997796i	$-0.478861\pi$
$109$	1.38567			0.132723			0.0663615	+	0.997796i	$0.478861\pi$
$110$	−2.45433	+	3.13575i	−0.234011	+	0.298982i
$111$	−8.17402	−	0.531923i	−0.775843	−	0.0504879i
$112$	−3.12334	−	3.36245i	−0.295128	−	0.317722i
$113$	0.291530	+	0.504944i	0.0274248	+	0.0475012i	0.879412	−	0.476061i	$-0.157936\pi$
$113$	0.291530	+	0.504944i	0.0274248	+	0.0475012i	−0.851987	+	0.523563i	$0.824603\pi$
$114$	−2.22253	−	8.59456i	−0.208159	−	0.804955i
$115$	−0.520299	−	7.98558i	−0.0485182	−	0.744659i
$116$	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
$120$	−4.57247	−	9.95452i	−0.417408	−	0.908719i
$121$	4.70717	+	8.15306i	0.427924	+	0.741187i
$122$	14.5234	+	3.02822i	1.31488	+	0.274163i
$123$	−5.14443	−	10.4196i	−0.463857	−	0.939504i
$124$	−8.42025	+	19.3139i	−0.756160	+	1.73444i
$125$	−10.9680	+	2.16844i	−0.981011	+	0.193952i
$126$	4.59621	+	1.60276i	0.409463	+	0.142785i
$127$	−10.3137			−0.915191			−0.457595	−	0.889161i	$-0.651289\pi$
$127$	−10.3137			−0.915191			−0.457595	+	0.889161i	$0.651289\pi$
$128$	8.96914	−	6.89598i	0.792767	−	0.609524i
$129$	4.07971	+	2.72322i	0.359199	+	0.239766i
$130$	14.8934	−	6.00221i	1.30624	−	0.526429i
$131$	7.18947	+	12.4525i	0.628147	+	1.08798i	0.987923	+	0.154944i	$0.0495196\pi$
$131$	7.18947	+	12.4525i	0.628147	+	1.08798i	−0.359776	+	0.933039i	$0.617147\pi$
$132$	4.35719	−	0.207085i	0.379244	−	0.0180244i
$133$	3.60096	+	2.07902i	0.312243	+	0.180274i
$134$	13.9901	−	15.6592i	1.20856	−	1.35275i
$135$	9.22509	+	7.06383i	0.793970	+	0.607958i
$136$	7.61027	+	5.39506i	0.652576	+	0.462623i
$137$	−3.69847	+	6.40593i	−0.315981	+	0.547296i	−0.979646	−	0.200735i	$-0.935667\pi$
$137$	−3.69847	+	6.40593i	−0.315981	+	0.547296i	0.663664	+	0.748031i	$0.269000\pi$
$138$	−6.25270	+	6.14427i	−0.532265	+	0.523035i
$139$	−1.44892	+	0.836533i	−0.122896	+	0.0709538i	−0.560188	−	0.828366i	$-0.689271\pi$
$139$	−1.44892	+	0.836533i	−0.122896	+	0.0709538i	0.437292	+	0.899320i	$0.355938\pi$
$140$	4.82677	+	1.74040i	0.407937	+	0.147090i
$141$	1.02795	−	1.53999i	0.0865689	−	0.129690i
$142$	4.28341	+	13.0111i	0.359456	+	1.09187i
$143$			6.39412i			0.534703i
$144$	−4.98735	+	10.9145i	−0.415612	+	0.909542i
$145$	−0.396960	+	0.265018i	−0.0329658	+	0.0220086i
$146$	12.2000	−	4.01638i	1.00968	−	0.332398i
$147$	8.82714	−	4.35818i	0.728050	−	0.359457i
$148$	5.61874	+	7.60875i	0.461858	+	0.625435i
$149$	3.87075	−	2.23478i	0.317104	−	0.183080i	−0.332997	−	0.942928i	$-0.608060\pi$
$149$	3.87075	−	2.23478i	0.317104	−	0.183080i	0.650101	+	0.759848i	$0.274727\pi$
$150$	9.64514	+	7.54794i	0.787522	+	0.616286i
$151$	11.2428	+	6.49105i	0.914928	+	0.528234i	0.882014	−	0.471224i	$-0.156188\pi$
$151$	11.2428	+	6.49105i	0.914928	+	0.528234i	0.0329149	+	0.999458i	$0.489521\pi$
$152$	−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
$155$	−1.53157	−	23.5067i	−0.123019	−	1.88810i
$156$	−15.6338	−	8.06191i	−1.25170	−	0.645469i
$157$	6.37177	−	3.67874i	0.508522	−	0.293595i	−0.223704	−	0.974657i	$-0.571815\pi$
$157$	6.37177	−	3.67874i	0.508522	−	0.293595i	0.732226	+	0.681062i	$0.238481\pi$
$158$	−1.92848	+	9.24898i	−0.153422	+	0.735809i
$159$	1.02633	−	15.7715i	0.0813930	−	1.25076i
$160$	−5.37801	+	11.4489i	−0.425169	+	0.905114i
$161$		−	4.10605i		−	0.323602i
$162$	−0.739125	−	12.7064i	−0.0580711	−	0.998312i
$163$	6.48159			0.507678			0.253839	−	0.967247i	$-0.418307\pi$
$163$	6.48159			0.507678			0.253839	+	0.967247i	$0.418307\pi$
$164$	−5.36240	+	12.3000i	−0.418733	+	0.960466i
$165$	−4.22339	+	2.43883i	−0.328791	+	0.189862i
$166$	−1.64493	+	7.88909i	−0.127671	+	0.612312i
$167$	11.3151	−	6.53280i	0.875592	−	0.505523i	0.00638974	−	0.999980i	$-0.497966\pi$
$167$	11.3151	−	6.53280i	0.875592	−	0.505523i	0.869203	+	0.494456i	$0.164633\pi$
$168$	−2.00907	−	5.24935i	−0.155003	−	0.404996i
$169$	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	$-0.764656\pi$
$173$	2.81588	−	4.87725i	0.214087	−	0.370810i	0.952990	+	0.303002i	$0.0979889\pi$
$174$	0.503834	+	0.139736i	0.0381956	+	0.0105934i
$175$	−5.68808	+	0.744372i	−0.429979	+	0.0562692i
$176$	−3.42801	−	3.69044i	−0.258396	−	0.278178i
$177$	−15.1275	+	7.46882i	−1.13705	+	0.561391i
$178$	3.03991	−	1.00078i	0.227851	−	0.0750113i
$179$	14.3831			1.07504			0.537520	−	0.843251i	$-0.319361\pi$
$179$	14.3831			1.07504			0.537520	+	0.843251i	$0.319361\pi$
$180$	−0.637992	−	13.4012i	−0.0475531	−	0.998869i
$181$	−11.3978			−0.847194			−0.423597	−	0.905851i	$-0.639233\pi$
$181$	−11.3978			−0.847194			−0.423597	+	0.905851i	$0.639233\pi$
$182$	7.82581	−	2.57635i	0.580088	−	0.190972i
$183$	15.1125	+	10.0876i	1.11715	+	0.745699i
$184$	10.0786	+	0.940914i	0.743007	+	0.0693651i
$185$	−9.48256	−	4.68084i	−0.697171	−	0.344142i
$186$	−18.4057	+	18.0865i	−1.34957	+	1.32617i
$187$	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	0.413042	+	0.910712i	$0.364466\pi$
$191$	−8.04586	+	13.9358i	−0.582178	+	1.00836i	−0.995221	+	0.0976507i	$0.968867\pi$
$192$	13.3453	−	3.72852i	0.963117	−	0.269083i
$193$	−10.5007	+	6.06256i	−0.755854	+	0.436393i	−0.827805	−	0.561016i	$-0.810411\pi$
$193$	−10.5007	+	6.06256i	−0.755854	+	0.436393i	0.0719511	+	0.997408i	$0.477077\pi$
$194$	2.23249	−	10.7070i	0.160284	−	0.768720i
$195$	19.6662	−	0.00156616i	1.40833	−	0.000112155i
$196$	−10.4201	−	4.54284i	−0.744294	−	0.324489i
$197$	−3.58143			−0.255166			−0.127583	−	0.991828i	$-0.540722\pi$
$197$	−3.58143			−0.255166			−0.127583	+	0.991828i	$0.540722\pi$
$198$	5.04455	+	1.75910i	0.358501	+	0.125014i
$199$		−	6.39345i		−	0.453219i	−0.973986	−	0.226610i	$-0.927236\pi$
$199$		−	6.39345i		−	0.453219i	0.973986	−	0.226610i	$-0.0727642\pi$
$200$	−0.523681	−	14.1324i	−0.0370298	−	0.999314i
$201$	23.0602	−	11.3854i	1.62654	−	0.803066i
$202$	−5.49467	+	26.3524i	−0.386603	+	1.85415i
$203$	−0.212089	+	0.122449i	−0.0148857	+	0.00859427i
$204$	6.17587	+	9.61213i	0.432397	+	0.672984i
$205$	−0.975375	−	14.9701i	−0.0681231	−	1.04556i
$206$	−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
$210$	4.68661	+	4.18638i	0.323407	+	0.288888i
$211$	−12.6167	+	7.28424i	−0.868568	+	0.501468i	−0.866872	−	0.498531i	$-0.833873\pi$
$211$	−12.6167	+	7.28424i	−0.868568	+	0.501468i	−0.00169595	+	0.999999i	$0.500540\pi$
$212$	−14.6808	+	10.8412i	−1.00828	+	0.744575i
$213$	−1.08943	+	16.7412i	−0.0746466	+	1.14709i
$214$	15.9195	−	5.24088i	1.08823	−	0.358259i
$215$	3.51609	+	5.26660i	0.239795	+	0.359179i
$216$	−10.6614	+	10.1161i	−0.725414	+	0.688313i
$217$		−	12.0867i		−	0.820501i
$218$	−0.612781	−	1.86136i	−0.0415028	−	0.126067i
$219$	15.6975	+	1.02152i	1.06074	+	0.0690276i
$220$	5.29760	+	1.91016i	0.357164	+	0.128783i
$221$	−14.5037	+	8.37370i	−0.975623	+	0.563276i
$222$	2.90025	+	11.2153i	0.194652	+	0.752723i
$223$	0.623219	−	1.07945i	0.0417338	−	0.0722851i	−0.844404	−	0.535707i	$-0.820045\pi$
$223$	0.623219	−	1.07945i	0.0417338	−	0.0722851i	0.886138	+	0.463422i	$0.153379\pi$
$224$	−3.13553	+	5.68253i	−0.209501	+	0.379680i
$225$	7.50207	+	12.9892i	0.500138	+	0.865946i
$226$	0.549365	−	0.614910i	0.0365432	−	0.0409032i
$227$	−9.39358	−	5.42338i	−0.623474	−	0.359963i	0.154747	−	0.987954i	$-0.450544\pi$
$227$	−9.39358	−	5.42338i	−0.623474	−	0.359963i	−0.778220	+	0.627992i	$0.783877\pi$
$228$	−10.5621	+	6.78626i	−0.699495	+	0.449431i
$229$	−12.0859	−	20.9333i	−0.798656	−	1.38331i	−0.920492	−	0.390762i	$-0.872212\pi$
$229$	−12.0859	−	20.9333i	−0.798656	−	1.38331i	0.121836	−	0.992550i	$-0.461122\pi$
$230$	−10.4969	+	4.23036i	−0.692144	+	0.278942i
$231$	−2.24378	+	1.10781i	−0.147630	+	0.0728886i
$232$	−0.251961	−	0.548649i	−0.0165421	−	0.0360205i
$233$	8.94645			0.586102			0.293051	−	0.956097i	$-0.405329\pi$
$233$	8.94645			0.586102			0.293051	+	0.956097i	$0.405329\pi$
$234$	−14.0699	−	16.3141i	−0.919777	−	1.06649i
$235$	1.98801	−	1.32723i	0.129684	−	0.0865792i
$236$	17.8574	+	7.78527i	1.16242	+	0.506778i
$237$	−6.42416	+	9.62415i	−0.417294	+	0.625156i
$238$	−5.23877	−	1.09232i	−0.339579	−	0.0708046i
$239$	7.59415	+	13.1535i	0.491225	+	0.850826i	0.999949	−	0.0101033i	$-0.00321605\pi$
$239$	7.59415	+	13.1535i	0.491225	+	0.850826i	−0.508724	+	0.860930i	$0.669883\pi$
$240$	−11.3498	+	10.5443i	−0.732624	+	0.680634i
$241$	−0.235922	+	0.408630i	−0.0151971	+	0.0263222i	−0.873524	−	0.486781i	$-0.838171\pi$
$241$	−0.235922	+	0.408630i	−0.0151971	+	0.0263222i	0.858327	+	0.513103i	$0.171504\pi$
$242$	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
$245$	12.6822	−	0.826305i	0.810234	−	0.0527907i
$246$	−11.7216	+	11.5183i	−0.747340	+	0.734381i
$247$	−9.20132	−	15.9372i	−0.585466	−	1.01406i
$248$	29.6679	+	2.76971i	1.88391	+	0.175877i
$249$	−5.47960	+	8.20909i	−0.347256	+	0.520230i
$250$	7.76323	+	13.7743i	0.490990	+	0.871165i
$251$	−24.1551			−1.52465			−0.762327	−	0.647192i	$-0.775943\pi$
$251$	−24.1551			−1.52465			−0.762327	+	0.647192i	$0.775943\pi$
$252$	0.120406	−	6.88285i	0.00758484	−	0.433579i
$253$		−	4.50658i		−	0.283326i
$254$	4.56099	+	13.8543i	0.286182	+	0.869295i
$255$	−11.0629	−	6.38598i	−0.692784	−	0.399906i
$256$	−13.2297	−	8.99858i	−0.826858	−	0.562411i
$257$	−7.37360	−	12.7715i	−0.459953	−	0.796661i	0.539005	−	0.842302i	$-0.318800\pi$
$257$	−7.37360	−	12.7715i	−0.459953	−	0.796661i	−0.998958	+	0.0456410i	$0.985467\pi$
$258$	1.85392	−	6.68453i	0.115420	−	0.416161i
$259$	−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	0.464623	−	0.885509i	$-0.346190\pi$
$263$	−1.13421	−	0.654834i	−0.0699381	−	0.0403788i	−0.534561	+	0.845130i	$0.679523\pi$
$264$	−2.20504	−	5.76140i	−0.135711	−	0.354589i
$265$	9.03153	−	18.2963i	0.554802	−	1.12393i
$266$	1.20028	−	5.75654i	0.0735939	−	0.352956i
$267$	3.91141	+	0.254534i	0.239374	+	0.0155773i
$268$	−27.2217	−	11.8678i	−1.66283	−	0.724942i
$269$			21.5574i			1.31438i	0.753725	+	0.657190i	$0.228255\pi$
$269$			21.5574i			1.31438i	−0.753725	+	0.657190i	$0.771745\pi$
$270$	5.40919	−	15.5158i	0.329193	−	0.944263i
$271$		−	1.58111i		−	0.0960453i	−0.998846	−	0.0480227i	$-0.984708\pi$
$271$		−	1.58111i		−	0.0960453i	0.998846	−	0.0480227i	$-0.0152920\pi$
$272$	3.88167	−	12.6087i	0.235361	−	0.764513i
$273$	10.0694	+	0.655262i	0.609425	+	0.0396583i
$274$	10.2406	+	2.13524i	0.618658	+	0.128995i
$275$	−6.24292	+	0.816981i	−0.376463	+	0.0492658i
$276$	11.0187	+	5.68203i	0.663246	+	0.342018i
$277$	−6.87650	−	3.97015i	−0.413169	−	0.238543i	0.278981	−	0.960297i	$-0.410003\pi$
$277$	−6.87650	−	3.97015i	−0.413169	−	0.238543i	−0.692150	+	0.721753i	$0.743337\pi$
$278$	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	0.314136	−	0.949378i	$-0.398285\pi$
$281$	−5.88352	−	3.39685i	−0.350982	−	0.202639i	−0.665118	+	0.746739i	$0.731619\pi$
$282$	−2.52324	−	0.699809i	−0.150257	−	0.0416730i
$283$	−3.80426	−	6.58918i	−0.226140	−	0.391686i	0.730521	−	0.682890i	$-0.239277\pi$
$283$	−3.80426	−	6.58918i	−0.226140	−	0.391686i	−0.956661	+	0.291204i	$0.905944\pi$
$284$	15.5835	−	11.5077i	0.924709	−	0.682859i
$285$	7.01714	−	12.1563i	0.415660	−	0.720076i
$286$	8.58918	−	2.82766i	0.507889	−	0.167203i
$287$		−	7.69738i		−	0.454362i
$288$	16.8669	+	1.87277i	0.993892	+	0.110354i
$289$	−6.12213			−0.360126
$290$	0.531544	+	0.416036i	0.0312133	+	0.0244304i
$291$	7.43689	−	11.1413i	0.435958	−	0.653117i
$292$	−10.7903	−	14.6120i	−0.631457	−	0.855102i
$293$	−4.95491	−	8.58215i	−0.289469	−	0.501375i	0.684214	−	0.729281i	$-0.260145\pi$
$293$	−4.95491	−	8.58215i	−0.289469	−	0.501375i	−0.973683	+	0.227906i	$0.926812\pi$
$294$	−9.75792	−	9.93012i	−0.569094	−	0.579136i
$295$	−21.7340	+	1.41608i	−1.26540	+	0.0824471i
$296$	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
$300$	5.87374	−	16.2941i	0.339120	−	0.940743i
$301$	1.62458	+	2.81385i	0.0936391	+	0.162188i
$302$	3.74749	−	17.9729i	0.215644	−	1.03423i
$303$	−18.3039	+	27.4213i	−1.05153	+	1.57531i
$304$	13.8549	+	4.26531i	0.794630	+	0.244633i
$305$	13.0246	+	19.5091i	0.745788	+	1.11709i
$306$	2.61616	+	13.7462i	0.149556	+	0.785816i
$307$	7.97501			0.455158			0.227579	−	0.973760i	$-0.426919\pi$
$307$	7.97501			0.455158			0.227579	+	0.973760i	$0.426919\pi$
$308$	2.64870	+	1.15475i	0.150924	+	0.0657979i
$309$	−11.9242	+	5.88728i	−0.678344	+	0.334916i
$310$	−30.8990	+	12.4526i	−1.75495	+	0.707263i
$311$	3.50301	+	6.06739i	0.198637	+	0.344050i	0.948087	−	0.318011i	$-0.103015\pi$
$311$	3.50301	+	6.06739i	0.198637	+	0.344050i	−0.749449	+	0.662062i	$0.769682\pi$
$312$	−3.91582	+	24.5659i	−0.221689	+	1.39077i
$313$	12.7311	+	7.35028i	0.719602	+	0.415462i	0.814606	−	0.580014i	$-0.196953\pi$
$313$	12.7311	+	7.35028i	0.719602	+	0.415462i	−0.0950041	+	0.995477i	$0.530286\pi$
$314$	−7.75940	−	6.93230i	−0.437888	−	0.391212i
$315$	3.40782	+	6.90086i	0.192009	+	0.388819i
$316$	13.2769	−	1.49965i	0.746885	−	0.0843616i
$317$	1.16205	−	2.01274i	0.0652675	−	0.113047i	−0.831545	−	0.555457i	$-0.812543\pi$
$317$	1.16205	−	2.01274i	0.0652675	−	0.113047i	0.896813	+	0.442411i	$0.145877\pi$
$318$	−21.6396	+	5.59593i	−1.21349	+	0.313804i
$319$	−0.232777	+	0.134394i	−0.0130330	+	0.00752460i
$320$	17.7575	+	2.16122i	0.992675	+	0.120816i
$321$	20.4833	+	1.33295i	1.14327	+	0.0743980i
$322$	−5.51563	+	1.81581i	−0.307374	+	0.101191i
$323$			11.9530i			0.665082i
$324$	−16.7416	+	6.61200i	−0.930089	+	0.367334i
$325$	23.4488	+	9.73410i	1.30071	+	0.539951i
$326$	−2.86634	−	8.70668i	−0.158752	−	0.482218i
$327$	0.155853	−	2.39498i	0.00861870	−	0.132443i
$328$	18.8938	+	1.76388i	1.04324	+	0.0973938i
$329$	1.06216	−	0.613237i	0.0585587	−	0.0338089i
$330$	5.14376	+	4.59474i	0.283155	+	0.252932i
$331$	13.0699	+	7.54592i	0.718388	+	0.414762i	0.814159	−	0.580642i	$-0.197198\pi$
$331$	13.0699	+	7.54592i	0.718388	+	0.414762i	−0.0957711	+	0.995403i	$0.530532\pi$
$332$	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
$335$	33.1312	−	2.15866i	1.81015	−	0.117940i
$336$	−6.16295	+	5.02018i	−0.336216	+	0.273873i
$337$	−18.8375	+	10.8759i	−1.02615	+	0.592445i	−0.915878	−	0.401456i	$-0.868504\pi$
$337$	−18.8375	+	10.8759i	−1.02615	+	0.592445i	−0.110268	+	0.993902i	$0.535171\pi$
$338$	−17.6987	−	3.69032i	−0.962685	−	0.200727i
$339$	0.905533	−	0.447085i	0.0491818	−	0.0242823i
$340$	2.60491	+	14.5180i	0.141271	+	0.787348i
$341$		−	13.2657i		−	0.718380i
$342$	−15.1048	+	2.87473i	−0.816773	+	0.155448i
$343$	14.5522			0.785744
$344$	−7.27910	+	3.34285i	−0.392463	+	0.180235i
$345$	−13.8608	+	0.00110383i	−0.746238	+	5.94281e-5i
$346$	−7.79683	−	1.62570i	−0.419160	−	0.0873979i
$347$	−23.6580	+	13.6590i	−1.27003	+	0.733251i	−0.974993	−	0.222236i	$-0.928665\pi$
$347$	−23.6580	+	13.6590i	−1.27003	+	0.733251i	−0.295035	+	0.955487i	$0.595331\pi$
$348$	−0.0351032	−	0.738592i	−0.00188173	−	0.0395927i
$349$	−1.77750	+	3.07872i	−0.0951472	+	0.164800i	−0.909670	−	0.415332i	$-0.863666\pi$
$349$	−1.77750	+	3.07872i	−0.0951472	+	0.164800i	0.814523	+	0.580132i	$0.196999\pi$
$350$	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	$-0.855529\pi$
$353$	−1.30903	+	2.26731i	−0.0696727	+	0.120677i	0.829085	+	0.559123i	$0.188862\pi$
$354$	16.7226	+	17.0177i	0.888796	+	0.904480i
$355$	−9.58683	+	19.4212i	−0.508816	+	1.03077i
$356$	−2.68867	−	3.64092i	−0.142499	−	0.192968i
$357$	−5.45127	−	3.63874i	−0.288512	−	0.192583i
$358$	−6.36059	−	19.3207i	−0.336168	−	1.02113i
$359$	21.9608			1.15904			0.579522	−	0.814956i	$-0.303239\pi$
$359$	21.9608			1.15904			0.579522	+	0.814956i	$0.303239\pi$
$360$	−17.7196	+	6.78341i	−0.933907	+	0.357517i
$361$	5.86564			0.308718
$362$	5.04044	+	15.3106i	0.264920	+	0.804709i
$363$	14.6211	−	7.21883i	0.767411	−	0.378890i
$364$	−6.92158	−	9.37302i	−0.362790	−	0.491280i
$365$	18.2105	+	8.98918i	0.953180	+	0.470515i
$366$	6.86748	−	24.7615i	0.358969	−	1.29430i
$367$	10.1344	−	17.5533i	0.529012	−	0.916276i	−0.470415	−	0.882445i	$-0.655896\pi$
$367$	10.1344	−	17.5533i	0.529012	−	0.916276i	0.999428	−	0.0338310i	$-0.0107708\pi$
$368$	−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
$372$	32.4350	+	16.7258i	1.68167	+	0.867194i
$373$	10.7060	−	6.18110i	0.554334	−	0.320045i	−0.196534	−	0.980497i	$-0.562969\pi$
$373$	10.7060	−	6.18110i	0.554334	−	0.320045i	0.750868	+	0.660452i	$0.229635\pi$
$374$	−5.74978	−	1.19887i	−0.297314	−	0.0619921i
$375$	2.51430	+	19.2010i	0.129838	+	0.991535i
$376$	1.26184	+	2.74768i	0.0650746	+	0.141701i
$377$	1.08388			0.0558224
$378$	3.28717	−	7.76380i	0.169074	−	0.399327i
$379$		−	6.92628i		−	0.355779i	−0.984050	−	0.177889i	$-0.943073\pi$
$379$		−	6.92628i		−	0.355779i	0.984050	−	0.177889i	$-0.0569270\pi$
$380$	−15.9529	+	2.86237i	−0.818365	+	0.146836i
$381$	−1.16003	+	17.8261i	−0.0594302	+	0.913259i
$382$	22.2780	+	4.64513i	1.13984	+	0.237665i
$383$	1.25094	−	0.722230i	0.0639200	−	0.0369042i	−0.467699	−	0.883888i	$-0.654917\pi$
$383$	1.25094	−	0.722230i	0.0639200	−	0.0369042i	0.531619	+	0.846983i	$0.321584\pi$
$384$	−10.9102	−	16.2778i	−0.556758	−	0.830675i
$385$	−3.22369	+	0.210039i	−0.164295	+	0.0107046i
$386$	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	0.517829	−	0.855484i	$-0.326741\pi$
$389$	0.707497	+	0.408474i	0.0358715	+	0.0207104i	−0.481957	+	0.876195i	$0.660074\pi$
$390$	−8.69906	−	26.4168i	−0.440494	−	1.33767i
$391$	10.2222	−	5.90178i	0.516958	−	0.298466i
$392$	−1.49430	+	16.0062i	−0.0754734	+	0.808437i
$393$	22.3315	−	11.0256i	1.12648	−	0.556170i
$394$	1.58381	+	4.81090i	0.0797910	+	0.242370i
$395$	−12.4241	+	8.29454i	−0.625122	+	0.417344i
$396$	0.132151	−	7.55423i	0.00664082	−	0.379614i
$397$			29.4855i			1.47984i	0.672697	+	0.739918i	$0.265136\pi$
$397$			29.4855i			1.47984i	−0.672697	+	0.739918i	$0.734864\pi$
$398$	−8.58827	+	2.82736i	−0.430491	+	0.141723i
$399$	3.99838	−	5.99004i	0.200169	−	0.299877i
$400$	−18.7524	+	6.95321i	−0.937620	+	0.347661i
$401$	−1.19058	+	0.687380i	−0.0594546	+	0.0343261i	−0.529433	−	0.848352i	$-0.677595\pi$
$401$	−1.19058	+	0.687380i	−0.0594546	+	0.0343261i	0.469978	+	0.882678i	$0.344262\pi$
$402$	−25.4918	−	25.9417i	−1.27142	−	1.29385i
$403$	−26.7468	+	46.3268i	−1.33235	+	2.30770i
$404$	37.8289	−	4.27282i	1.88206	−	0.212581i
$405$	13.2467	−	15.1501i	0.658233	−	0.752814i
$406$	0.258277	+	0.230747i	0.0128181	+	0.0114518i
$407$	−5.15737	−	2.97761i	−0.255642	−	0.147595i
$408$	10.1808	−	12.5467i	0.504023	−	0.621157i
$409$	−1.66076	−	2.87653i	−0.0821195	−	0.142235i	0.822041	−	0.569429i	$-0.192836\pi$
$409$	−1.66076	−	2.87653i	−0.0821195	−	0.142235i	−0.904160	+	0.427194i	$0.859502\pi$
$410$	−19.6779	+	7.93041i	−0.971822	+	0.391655i
$411$	10.6560	+	7.11292i	0.525621	+	0.350854i
$412$	14.0761	+	6.13673i	0.693479	+	0.302335i
$413$	−11.1753			−0.549899
$414$	9.91646	+	11.4982i	0.487367	+	0.565106i
$415$	−10.5973	+	7.07498i	−0.520202	+	0.347297i
$416$	24.5929	−	14.8417i	1.20577	−	0.727676i
$417$	1.28289	+	2.59839i	0.0628235	+	0.127244i
$418$	1.31736	−	6.31806i	0.0644343	−	0.309026i
$419$	−17.6346	−	30.5441i	−0.861508	−	1.49218i	−0.870473	−	0.492217i	$-0.836187\pi$
$419$	−17.6346	−	30.5441i	−0.861508	−	1.49218i	0.00896441	−	0.999960i	$-0.497147\pi$
$420$	3.55098	−	8.14682i	0.173270	−	0.397524i
$421$	−14.6171	+	25.3175i	−0.712392	+	1.23390i	0.251565	+	0.967841i	$0.419055\pi$
$421$	−14.6171	+	25.3175i	−0.712392	+	1.23390i	−0.963957	+	0.266059i	$0.914278\pi$
$422$	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
$425$	−10.0288	−	13.0908i	−0.486470	−	0.634997i
$426$	22.9701	−	5.94000i	1.11290	−	0.287794i
$427$	6.01792	+	10.4233i	0.291227	+	0.504421i
$428$	−14.0801	−	19.0668i	−0.680585	−	0.921630i
$429$	11.0516	+	0.719179i	0.533575	+	0.0347223i
$430$	5.51968	−	7.05217i	0.266183	−	0.340086i
$431$	15.7242			0.757408			0.378704	−	0.925518i	$-0.376370\pi$
$431$	15.7242			0.757408			0.378704	+	0.925518i	$0.376370\pi$
$432$	18.3036	+	9.84772i	0.880633	+	0.473798i
$433$		−	40.6371i		−	1.95289i	−0.215758	−	0.976447i	$-0.569222\pi$
$433$		−	40.6371i		−	1.95289i	0.215758	−	0.976447i	$-0.430778\pi$
$434$	−16.2360	+	5.34509i	−0.779354	+	0.256573i
$435$	0.413408	+	0.715913i	0.0198214	+	0.0343254i
$436$	−2.22936	+	1.64629i	−0.106767	+	0.0788429i
$437$	6.48509	+	11.2325i	0.310224	+	0.537324i
$438$	−5.56970	−	21.5381i	−0.266130	−	1.02913i
$439$	19.5385	+	11.2806i	0.932523	+	0.538392i	0.887608	−	0.460599i	$-0.152365\pi$
$439$	19.5385	+	11.2806i	0.932523	+	0.538392i	0.0449140	+	0.998991i	$0.485699\pi$
$440$	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	0.766200	−	0.642603i	$-0.222145\pi$
$443$	12.4768	+	7.20347i	0.592789	+	0.342247i	−0.173410	+	0.984850i	$0.555479\pi$
$444$	13.7829	−	8.85561i	0.654107	−	0.420269i
$445$	4.53757	+	2.23987i	0.215101	+	0.106180i
$446$	−1.72562	−	0.359804i	−0.0817104	−	0.0170372i
$447$	−3.42722	−	6.94154i	−0.162102	−	0.328324i
$448$	9.01992	+	1.69896i	0.426151	+	0.0802682i
$449$		−	14.7482i		−	0.696008i	−0.937493	−	0.348004i	$-0.886860\pi$
$449$		−	14.7482i		−	0.696008i	0.937493	−	0.348004i	$-0.113140\pi$
$450$	14.1307	−	15.8217i	0.666125	−	0.745840i
$451$		−	8.44822i		−	0.397811i
$452$	−1.06895	−	0.466028i	−0.0502791	−	0.0219201i
$453$	12.4836	−	18.7020i	0.586532	−	0.878695i
$454$	−3.13109	+	15.0167i	−0.146949	+	0.704768i
$455$	11.6813	+	5.76621i	0.547628	+	0.270324i
$456$	13.7868	+	11.1870i	0.645627	+	0.523878i
$457$	−0.883921	−	0.510332i	−0.0413481	−	0.0238723i	0.479183	−	0.877715i	$-0.340933\pi$
$457$	−0.883921	−	0.510332i	−0.0413481	−	0.0238723i	−0.520532	+	0.853842i	$0.674266\pi$
$458$	−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	0.515743	−	0.856744i	$-0.327516\pi$
$461$	0.679602	+	0.392368i	0.0316522	+	0.0182744i	−0.484090	+	0.875018i	$0.660849\pi$
$462$	2.48038	+	2.52415i	0.115398	+	0.117434i
$463$	−16.2867	−	28.2095i	−0.756909	−	1.31101i	−0.944420	−	0.328743i	$-0.893375\pi$
$463$	−16.2867	−	28.2095i	−0.756909	−	1.31101i	0.187510	−	0.982263i	$-0.439958\pi$
$464$	−0.625571	+	0.581086i	−0.0290414	+	0.0269762i
$465$	−40.8011	+	0.00324927i	−1.89210	+	0.000150681i
$466$	−3.95637	−	12.0177i	−0.183275	−	0.556709i
$467$		−	26.0874i		−	1.20718i	−0.797295	−	0.603590i	$-0.793736\pi$
$467$		−	26.0874i		−	1.20718i	0.797295	−	0.603590i	$-0.206264\pi$
$468$	−15.6926	+	26.1145i	−0.725389	+	1.20714i
$469$	17.0355			0.786627
$470$	−2.66202	−	2.08354i	−0.122790	−	0.0961066i
$471$	−5.64165	−	11.4267i	−0.259954	−	0.526514i
$472$	2.56085	−	27.4306i	0.117872	−	1.26260i
$473$	1.78305	+	3.08833i	0.0819845	+	0.142001i
$474$	15.7690	+	4.37345i	0.724294	+	0.200879i
$475$	14.3846	−	11.0200i	0.660012	−	0.505634i
$476$	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	0.282780	+	0.959185i	$0.408743\pi$
$479$	−15.0858	+	26.1294i	−0.689288	+	1.19388i	−0.972068	+	0.234698i	$0.924590\pi$
$480$	19.1833	+	10.5830i	0.875594	+	0.483048i
$481$	12.0071	+	20.7969i	0.547477	+	0.948257i
$482$	0.653241	+	0.136205i	0.0297543	+	0.00620399i
$483$	−7.09688	−	0.461829i	−0.322919	−	0.0210139i
$484$	−17.2597	−	7.52469i	−0.784533	−	0.342031i
$485$	14.3826	−	9.60212i	0.653082	−	0.436010i
$486$	−22.0449	−	0.151658i	−0.999976	−	0.00687935i
$487$	−22.2802			−1.00961			−0.504806	−	0.863233i	$-0.668436\pi$
$487$	−22.2802			−1.00961			−0.504806	+	0.863233i	$0.668436\pi$
$488$	−26.9639	+	12.3829i	−1.22060	+	0.560549i
$489$	0.729018	−	11.2028i	0.0329673	−	0.506606i
$490$	−6.71838	−	16.6704i	−0.303505	−	0.753094i
$491$	−10.7024	−	18.5371i	−0.482992	−	0.836566i	0.516817	−	0.856096i	$-0.327117\pi$
$491$	−10.7024	−	18.5371i	−0.482992	−	0.836566i	−0.999809	+	0.0195292i	$0.993783\pi$
$492$	20.6561	+	10.6518i	0.931247	+	0.480219i
$493$	−0.609686	−	0.352002i	−0.0274589	−	0.0158534i
$494$	−17.3392	+	19.4079i	−0.780126	+	0.873203i
$495$	3.74023	+	7.57400i	0.168111	+	0.340426i
$496$	−9.39943	−	41.0775i	−0.422047	−	1.84443i
$497$	−5.55644	+	9.62404i	−0.249240	+	0.431697i
$498$	13.4504	+	3.73042i	0.602729	+	0.167164i
$499$	−14.4771	+	8.35834i	−0.648083	+	0.374171i	−0.787721	−	0.616032i	$-0.788739\pi$
$499$	−14.4771	+	8.35834i	−0.648083	+	0.374171i	0.139638	+	0.990203i	$0.455406\pi$
$500$	15.0698	−	16.5197i	0.673944	−	0.738782i
$501$	−10.0186	−	20.2918i	−0.447598	−	0.906572i
$502$	10.6820	+	32.4473i	0.476763	+	1.44819i
$503$		−	37.4827i		−	1.67127i	−0.549285	−	0.835635i	$-0.685100\pi$
$503$		−	37.4827i		−	1.67127i	0.549285	−	0.835635i	$-0.314900\pi$
$504$	−9.29892	+	2.88205i	−0.414207	+	0.128377i
$505$	−35.3989	+	23.6330i	−1.57523	+	1.05165i
$506$	−6.05365	+	1.99293i	−0.269118	+	0.0885967i
$507$	−18.4167	−	12.2932i	−0.817912	−	0.545960i
$508$	16.5934	−	12.2535i	0.736211	−	0.543661i
$509$	23.3737	−	13.4948i	1.03602	−	0.598148i	0.117318	−	0.993094i	$-0.462570\pi$
$509$	23.3737	−	13.4948i	1.03602	−	0.598148i	0.918704	+	0.394947i	$0.129237\pi$
$510$	−3.68593	+	17.6847i	−0.163216	+	0.783093i
$511$	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
$515$	−17.1318	+	1.11622i	−0.754917	+	0.0491865i
$516$	−9.79913	+	0.465725i	−0.431383	+	0.0205024i
$517$	1.16577	−	0.673055i	0.0512703	−	0.0296009i
$518$	−1.56629	+	7.51190i	−0.0688186	+	0.330054i
$519$	−8.11309	−	5.41552i	−0.356125	−	0.237715i
$520$	−16.8304	+	27.3514i	−0.738063	+	1.19944i
$521$		−	26.5168i		−	1.16172i	−0.814003	−	0.580860i	$-0.802716\pi$
$521$		−	26.5168i		−	1.16172i	0.814003	−	0.580860i	$-0.197284\pi$
$522$	0.298188	−	0.855107i	0.0130513	−	0.0374270i
$523$	31.5217			1.37835			0.689174	−	0.724596i	$-0.257974\pi$
$523$	31.5217			1.37835			0.689174	+	0.724596i	$0.257974\pi$
$524$	−26.3615	−	11.4928i	−1.15161	−	0.502065i
$525$	0.646802	+	9.91498i	0.0282287	+	0.432725i
$526$	−0.378056	+	1.81316i	−0.0164840	+	0.0790574i
$527$	30.0904	−	17.3727i	1.31076	−	0.756767i
$528$	−6.76411	+	5.50987i	−0.294370	+	0.239786i
$529$	−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
$534$	−1.38782	−	5.36673i	−0.0600569	−	0.232241i
$535$	23.7624	+	11.7298i	1.02734	+	0.507122i
$536$	−3.90374	+	41.8150i	−0.168616	+	1.80613i
$537$	1.61774	−	24.8596i	0.0698105	−	1.07277i
$538$	28.9579	−	9.53329i	1.24846	−	0.411009i
$539$	7.15705			0.308276
$540$	−23.2344	−	0.404602i	−0.999848	−	0.0174113i
$541$	−0.0570124			−0.00245116			−0.00122558	−	0.999999i	$-0.500390\pi$
$541$	−0.0570124			−0.00245116			−0.00122558	+	0.999999i	$0.500390\pi$
$542$	−2.12389	+	0.699209i	−0.0912288	+	0.0300336i
$543$	−1.28197	+	19.7000i	−0.0550147	+	0.845406i
$544$	−18.6537	+	0.361689i	−0.799771	+	0.0155073i
$545$	1.37148	−	2.77838i	0.0587479	−	0.119013i
$546$	−3.57274	−	13.8159i	−0.152899	−	0.591265i
$547$	1.78811	−	3.09710i	0.0764541	−	0.132422i	−0.825264	−	0.564748i	$-0.808973\pi$
$547$	1.78811	−	3.09710i	0.0764541	−	0.132422i	0.901718	+	0.432325i	$0.142307\pi$
$548$	−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
$552$	2.75987	−	17.3140i	0.117468	−	0.736935i
$553$	−6.63795	+	3.83242i	−0.282274	+	0.162971i
$554$	−2.29209	+	10.9929i	−0.0973817	+	0.467042i
$555$	−9.15690	+	15.8631i	−0.388689	+	0.673352i
$556$	1.33725	−	3.06730i	0.0567119	−	0.130083i
$557$	−15.0861			−0.639217			−0.319609	−	0.947550i	$-0.603551\pi$
$557$	−15.0861			−0.639217			−0.319609	+	0.947550i	$0.603551\pi$
$558$	29.1904	+	33.8466i	1.23573	+	1.43284i
$559$		−	14.3801i		−	0.608214i
$560$	−9.83338	+	2.93454i	−0.415536	+	0.124007i
$561$	−5.98301	−	3.99368i	−0.252603	−	0.168613i
$562$	−1.96111	+	9.40548i	−0.0827244	+	0.396746i
$563$	−7.29553	+	4.21208i	−0.307470	+	0.177518i	−0.645794	−	0.763512i	$-0.723473\pi$
$563$	−7.29553	+	4.21208i	−0.307470	+	0.177518i	0.338324	+	0.941030i	$0.390140\pi$
$564$	0.175800	+	3.69893i	0.00740250	+	0.155753i
$565$	1.30100	−	0.0847666i	0.0547336	−	0.00356616i
$566$	−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	0.434605	−	0.900621i	$-0.356888\pi$
$569$	−3.05453	−	1.76353i	−0.128053	−	0.0739312i	−0.562658	+	0.826690i	$0.690221\pi$
$570$	−19.4326	−	4.05023i	−0.813943	−	0.169645i
$571$	29.6633	−	17.1261i	1.24137	−	0.716705i	0.271997	−	0.962298i	$-0.412316\pi$
$571$	29.6633	−	17.1261i	1.24137	−	0.716705i	0.969373	+	0.245593i	$0.0789826\pi$
$572$	−7.59675	−	10.2873i	−0.317636	−	0.430134i
$573$	23.1817	+	15.4739i	0.968429	+	0.646430i
$574$	−10.3398	+	3.40400i	−0.431576	+	0.142080i
$575$	−16.5267	−	6.86059i	−0.689213	−	0.286107i
$576$	−4.94334	−	23.4854i	−0.205973	−	0.978558i
$577$			1.78616i			0.0743587i	0.999309	+	0.0371793i	$0.0118373\pi$
$577$			1.78616i			0.0743587i	−0.999309	+	0.0371793i	$0.988163\pi$
$578$	2.70738	+	8.22382i	0.112612	+	0.342066i
$579$	9.29744	+	18.8312i	0.386388	+	0.782597i
$580$	0.323794	−	0.898002i	0.0134448	−	0.0372875i
$581$	−5.66196	+	3.26893i	−0.234898	+	0.135618i
$582$	−18.2549	−	5.06290i	−0.756689	−	0.209864i
$583$	5.74520	−	9.95098i	0.237942	−	0.412127i
$584$	−14.8564	+	20.9564i	−0.614762	+	0.867183i
$585$	2.20925	−	33.9912i	0.0913414	−	1.40536i
$586$	−9.33714	+	10.4512i	−0.385714	+	0.431733i
$587$	13.5891	+	7.84570i	0.560884	+	0.323826i	0.753500	−	0.657448i	$-0.228364\pi$
$587$	13.5891	+	7.84570i	0.560884	+	0.323826i	−0.192616	+	0.981274i	$0.561697\pi$
$588$	−9.02383	+	17.4991i	−0.372136	+	0.721651i
$589$	19.0898	+	33.0644i	0.786579	+	1.36240i
$590$	11.5136	+	28.5689i	0.474007	+	1.17616i
$591$	−0.402821	+	6.19012i	−0.0165698	+	0.254627i
$592$	−18.0796	−	5.56595i	−0.743069	−	0.228759i
$593$	−46.6356			−1.91510			−0.957548	−	0.288273i	$-0.906919\pi$
$593$	−46.6356			−1.91510			−0.957548	+	0.288273i	$0.906919\pi$
$594$	3.60781	−	8.52112i	0.148030	−	0.349626i
$595$	−4.69816	−	7.03718i	−0.192606	−	0.288496i
$596$	−3.57243	+	8.19424i	−0.146332	+	0.335649i
$597$	−11.0504	−	0.719103i	−0.452263	−	0.0294309i
$598$	25.1589	+	5.24580i	1.02882	+	0.214517i
$599$	−21.3211	−	36.9292i	−0.871156	−	1.50889i	−0.860802	−	0.508941i	$-0.830037\pi$
$599$	−21.3211	−	36.9292i	−0.871156	−	1.50889i	−0.0103549	−	0.999946i	$-0.503296\pi$
$600$	−24.4853	−	0.684419i	−0.999610	−	0.0279413i
$601$	10.7999	−	18.7061i	0.440539	−	0.763036i	−0.557191	−	0.830385i	$-0.688121\pi$
$601$	10.7999	−	18.7061i	0.440539	−	0.763036i	0.997729	+	0.0673489i	$0.0214541\pi$
$602$	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
$605$	21.0066	−	1.36868i	0.854038	−	0.0556447i
$606$	44.9294	+	12.4609i	1.82513	+	0.506191i
$607$	1.49873	+	2.59588i	0.0608316	+	0.105363i	0.894837	−	0.446392i	$-0.147291\pi$
$607$	1.49873	+	2.59588i	0.0608316	+	0.105363i	−0.834006	+	0.551756i	$0.813958\pi$
$608$	−0.397436	−	20.4974i	−0.0161182	−	0.831278i
$609$	0.187786	+	0.380346i	0.00760949	+	0.0154124i
$610$	20.4465	−	26.1233i	0.827856	−	1.05770i
$611$	−5.42814			−0.219599
$612$	17.3082	−	9.59321i	0.699642	−	0.387783i
$613$		−	14.2081i		−	0.573858i	−0.957952	−	0.286929i	$-0.907366\pi$
$613$		−	14.2081i		−	0.573858i	0.957952	−	0.286929i	$-0.0926344\pi$
$614$	−3.52677	−	10.7128i	−0.142329	−	0.432332i
$615$	−25.9840	+	0.00206928i	−1.04777	+	8.34415e-5i
$616$	0.379837	−	4.06864i	0.0153041	−	0.163930i
$617$	13.2631	+	22.9723i	0.533952	+	0.924832i	0.999213	+	0.0396583i	$0.0126269\pi$
$617$	13.2631	+	22.9723i	0.533952	+	0.924832i	−0.465262	+	0.885173i	$0.654040\pi$
$618$	13.1816	+	13.4142i	0.530240	+	0.539597i
$619$	−13.2974	−	7.67724i	−0.534466	−	0.308574i	0.208367	−	0.978051i	$-0.433185\pi$
$619$	−13.2974	−	7.67724i	−0.534466	−	0.308574i	−0.742833	+	0.669476i	$0.766519\pi$
$620$	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
$624$	34.7309	−	5.60364i	1.39035	−	0.224325i
$625$	−6.50785	+	24.1381i	−0.260314	+	0.965524i
$626$	4.24355	−	20.3520i	0.169606	−	0.813431i
$627$	4.38840	−	6.57434i	0.175256	−	0.262554i
$628$	−5.88069	+	13.4888i	−0.234665	+	0.538262i
$629$		−	15.5978i		−	0.621927i
$630$	7.76284	−	7.62945i	0.309279	−	0.303964i
$631$		−	4.30213i		−	0.171265i	−0.996327	−	0.0856326i	$-0.972709\pi$
$631$		−	4.30213i		−	0.171265i	0.996327	−	0.0856326i	$-0.0272911\pi$
$632$	−7.88588	−	17.1716i	−0.313684	−	0.683049i
$633$	11.1710	+	22.6259i	0.444007	+	0.899299i
$634$	−3.21759	−	0.670890i	−0.127787	−	0.0266445i
$635$	−10.2081	+	20.6798i	−0.405096	+	0.820653i
$636$	17.0866	+	26.5936i	0.677528	+	1.05451i
$637$	−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	0.919718	−	0.392580i	$-0.128417\pi$
$641$	26.3204	+	15.1961i	1.03959	+	0.600209i	0.119875	+	0.992789i	$0.461751\pi$
$642$	−7.26776	−	28.1046i	−0.286836	−	1.10920i
$643$	13.4062	+	23.2202i	0.528688	+	0.915714i	0.999440	+	0.0334490i	$0.0106491\pi$
$643$	13.4062	+	23.2202i	0.528688	+	0.915714i	−0.470753	+	0.882265i	$0.656018\pi$
$644$	4.87833	+	6.60610i	0.192233	+	0.260317i
$645$	9.49824	−	5.48482i	0.373993	−	0.215965i
$646$	16.0564	−	5.28594i	0.631729	−	0.207973i
$647$			9.51887i			0.374225i	0.982338	+	0.187113i	$0.0599130\pi$
$647$			9.51887i			0.374225i	−0.982338	+	0.187113i	$0.940087\pi$
$648$	16.2855	+	19.5649i	0.639753	+	0.768580i
$649$	−12.2654			−0.481457
$650$	2.70601	−	35.8034i	0.106138	−	1.40432i
$651$	−20.8907	−	1.35946i	−0.818769	−	0.0532813i
$652$	−10.4280	+	7.70067i	−0.408393	+	0.301581i
$653$	7.71208	+	13.3577i	0.301797	+	0.522728i	0.976543	−	0.215322i	$-0.0690802\pi$
$653$	7.71208	+	13.3577i	0.301797	+	0.522728i	−0.674746	+	0.738050i	$0.735747\pi$
$654$	−3.28608	+	0.849772i	−0.128496	+	0.0332287i
$655$	32.0843	−	2.09044i	1.25364	−	0.0816804i
$656$	−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	−0.301137	−	0.953581i	$-0.597366\pi$
$659$	17.3345	−	30.0242i	0.675256	−	1.16958i	0.976394	−	0.215998i	$-0.0693004\pi$
$660$	3.89736	−	8.94149i	0.151705	−	0.348047i
$661$	−10.7043	−	18.5404i	−0.416350	−	0.721139i	0.579219	−	0.815172i	$-0.303357\pi$
$661$	−10.7043	−	18.5404i	−0.416350	−	0.721139i	−0.995569	+	0.0940328i	$0.970024\pi$
$662$	4.35650	−	20.8937i	0.169320	−	0.812059i
$663$	12.8418	+	26.0099i	0.498733	+	1.01014i
$664$	−6.72641	−	14.6468i	−0.261035	−	0.568407i
$665$	7.73270	−	5.16250i	0.299861	−	0.200193i
$666$	19.7107	−	3.75133i	0.763775	−	0.145361i
$667$	−0.763915			−0.0295789
$668$	−10.4431	+	23.9538i	−0.404055	+	0.926799i
$669$	−1.79561	−	1.19858i	−0.0694225	−	0.0463398i
$670$	−17.5512	−	43.5503i	−0.678064	−	1.68249i
$671$	6.60493	+	11.4401i	0.254981	+	0.441639i
$672$	9.46899	+	6.05858i	0.365274	+	0.233715i
$673$	22.3026	+	12.8764i	0.859702	+	0.496349i	0.863913	−	0.503642i	$-0.168007\pi$
$673$	22.3026	+	12.8764i	0.859702	+	0.496349i	−0.00421032	+	0.999991i	$0.501340\pi$
$674$	22.9399	+	20.4947i	0.883613	+	0.789427i
$675$	23.2942	−	11.5056i	0.896596	−	0.442850i
$676$	2.86970	+	25.4065i	0.110373	+	0.977175i
$677$	14.5489	−	25.1994i	0.559159	−	0.968492i	−0.438408	−	0.898776i	$-0.644458\pi$
$677$	14.5489	−	25.1994i	0.559159	−	0.968492i	0.997567	−	0.0697156i	$-0.0222092\pi$
$678$	−1.00102	−	1.01868i	−0.0384439	−	0.0391223i
$679$	7.68438	−	4.43658i	0.294899	−	0.170260i
$680$	18.3499	−	9.91941i	0.703688	−	0.380392i
$681$	−10.4303	+	15.6258i	−0.399690	+	0.598783i
$682$	−17.8198	+	5.86648i	−0.682354	+	0.224639i
$683$			0.973163i			0.0372370i	0.999827	+	0.0186185i	$0.00592680\pi$
$683$			0.973163i			0.0372370i	−0.999827	+	0.0186185i	$0.994073\pi$
$684$	10.5414	+	19.0189i	0.403059	+	0.727204i
$685$	9.18383	+	13.7561i	0.350896	+	0.525594i
$686$	−6.43538	−	19.5478i	−0.245704	−	0.746340i
$687$	−37.5404	+	18.5347i	−1.43225	+	0.707141i
$688$	7.70945	+	8.29966i	0.293920	+	0.316421i
$689$	−40.1269	+	23.1673i	−1.52871	+	0.882604i
$690$	6.13110	+	18.6186i	0.233407	+	0.708797i
$691$	−14.2382	−	8.22045i	−0.541648	−	0.312721i	0.204099	−	0.978950i	$-0.434574\pi$
$691$	−14.2382	−	8.22045i	−0.541648	−	0.312721i	−0.745747	+	0.666230i	$0.767907\pi$
$692$	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
$695$	0.243234	+	3.73317i	0.00922640	+	0.141607i
$696$	−0.976621	+	0.373780i	−0.0370187	+	0.0141681i
$697$	19.1629	−	11.0637i	0.725848	−	0.419069i
$698$	4.92167	+	1.02620i	0.186288	+	0.0388424i
$699$	1.00625	−	15.4630i	0.0380600	−	0.584865i
$700$	8.26700	−	7.95551i	0.312463	−	0.300690i
$701$			12.3225i			0.465415i	0.972547	+	0.232707i	$0.0747585\pi$
$701$			12.3225i			0.465415i	−0.972547	+	0.232707i	$0.925242\pi$
$702$	−29.7798	+	22.4834i	−1.12397	+	0.848581i
$703$	17.1395			0.646427
$704$	9.89977	+	1.86468i	0.373111	+	0.0702778i
$705$	−2.07038	−	3.58535i	−0.0779751	−	0.135032i
$706$	3.62455	+	0.755744i	0.136412	+	0.0284428i
$707$	−18.9130	+	10.9194i	−0.711296	+	0.410667i
$708$	15.4645	−	29.9890i	0.581193	−	1.12706i
$709$	2.75578	−	4.77314i	0.103495	−	0.179259i	−0.809627	−	0.586945i	$-0.800331\pi$
$709$	2.75578	−	4.77314i	0.103495	−	0.179259i	0.913122	+	0.407685i	$0.133664\pi$
$710$	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
$714$	−2.47719	+	8.93180i	−0.0927066	+	0.334264i
$715$	12.8208	+	6.32867i	0.479469	+	0.236679i
$716$	−23.1405	+	17.0883i	−0.864800	+	0.638619i
$717$	23.5885	−	11.6463i	0.880929	−	0.434937i
$718$	−9.71166	−	29.4997i	−0.362436	−	1.10092i
$719$	−13.7828			−0.514012			−0.257006	−	0.966410i	$-0.582736\pi$
$719$	−13.7828			−0.514012			−0.257006	+	0.966410i	$0.582736\pi$
$720$	16.9482	+	20.8028i	0.631623	+	0.775276i
$721$	−8.80888			−0.328060
$722$	−2.59395	−	7.87927i	−0.0965368	−	0.293236i
$723$	0.679738	+	0.453728i	0.0252797	+	0.0168743i
$724$	18.3376	−	13.5416i	0.681512	−	0.503268i
$725$	0.138487	+	1.05825i	0.00514330	+	0.0393022i
$726$	−16.1629	−	16.4481i	−0.599861	−	0.610446i
$727$	−23.1299	+	40.0622i	−0.857842	+	1.48583i	0.0161416	+	0.999870i	$0.494862\pi$
$727$	−23.1299	+	40.0622i	−0.857842	+	1.48583i	−0.873983	+	0.485956i	$0.838472\pi$
$728$	−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
$732$	−36.2989	+	1.72518i	−1.34165	+	0.0637646i
$733$	−25.8707	+	14.9365i	−0.955556	+	0.551690i	−0.894802	−	0.446462i	$-0.852684\pi$
$733$	−25.8707	+	14.9365i	−0.955556	+	0.551690i	−0.0607534	+	0.998153i	$0.519350\pi$
$734$	−28.0610	−	5.85092i	−1.03575	−	0.215961i
$735$	−0.00175303	−	22.0127i	−6.46613e−5	−	0.811952i
$736$	−17.3331	+	10.4605i	−0.638907	+	0.385577i
$737$	18.6972			0.688721
$738$	18.5898	+	21.5550i	0.684300	+	0.793451i
$739$			37.3592i			1.37428i	0.726526	+	0.687139i	$0.241134\pi$
$739$			37.3592i			1.37428i	−0.726526	+	0.687139i	$0.758866\pi$
$740$	20.8174	−	3.73520i	0.765264	−	0.137309i
$741$	−28.5806	+	14.1110i	−1.04994	+	0.518380i
$742$	−14.4940	−	3.02209i	−0.532090	−	0.110945i
$743$	−21.2072	+	12.2440i	−0.778016	+	0.449188i	−0.835727	−	0.549145i	$-0.814953\pi$
$743$	−21.2072	+	12.2440i	−0.778016	+	0.449188i	0.0577104	+	0.998333i	$0.481620\pi$
$744$	8.12405	−	50.9663i	0.297842	−	1.86851i
$745$	−0.649795	−	9.97309i	−0.0238066	−	0.365386i
$746$	−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
$750$	24.6807	−	11.8687i	0.901210	−	0.433382i
$751$	−20.1320	+	11.6232i	−0.734629	+	0.424138i	−0.820113	−	0.572201i	$-0.806090\pi$
$751$	−20.1320	+	11.6232i	−0.734629	+	0.424138i	0.0854843	+	0.996340i	$0.472756\pi$
$752$	3.13291	−	2.91012i	0.114246	−	0.106121i
$753$	−2.71684	+	41.7495i	−0.0990072	+	1.52144i
$754$	−0.479320	−	1.45596i	−0.0174558	−	0.0530230i
$755$	24.1429	−	16.1182i	0.878648	−	0.586602i
$756$	−11.8827	−	0.982257i	−0.432171	−	0.0357243i
$757$			31.5549i			1.14688i	0.819246	+	0.573442i	$0.194392\pi$
$757$			31.5549i			1.14688i	−0.819246	+	0.573442i	$0.805608\pi$
$758$	−9.30402	+	3.06299i	−0.337937	+	0.111253i
$759$	−7.78915	−	0.506878i	−0.282728	−	0.0183985i
$760$	10.8998	+	20.1636i	0.395377	+	0.731409i
$761$	22.9687	−	13.2610i	0.832616	−	0.480711i	−0.0221316	−	0.999755i	$-0.507045\pi$
$761$	22.9687	−	13.2610i	0.832616	−	0.480711i	0.854747	+	0.519044i	$0.173712\pi$
$762$	24.4587	−	6.32494i	0.886044	−	0.229128i
$763$	0.794900	−	1.37681i	0.0287773	−	0.0498438i
$764$	−3.61220	−	31.9801i	−0.130685	−	1.15700i
$765$	−12.2818	+	18.4028i	−0.444049	+	0.665353i
$766$	−1.52337	−	1.36099i	−0.0550415	−	0.0491745i
$767$	42.8332	+	24.7298i	1.54662	+	0.892941i
$768$	−17.0411	+	21.8541i	−0.614918	+	0.788591i
$769$	2.70091	+	4.67812i	0.0973974	+	0.168697i	0.910607	−	0.413274i	$-0.135615\pi$
$769$	2.70091	+	4.67812i	0.0973974	+	0.168697i	−0.813209	+	0.581971i	$0.802282\pi$
$770$	1.70775	+	4.23748i	0.0615431	+	0.152708i
$771$	−22.9035	+	11.3080i	−0.824848	+	0.407249i
$772$	9.69137	−	22.2295i	0.348800	−	0.800058i
$773$	10.0058			0.359884			0.179942	−	0.983677i	$-0.442409\pi$
$773$	10.0058			0.359884			0.179942	+	0.983677i	$0.442409\pi$
$774$	−11.3450	−	3.95615i	−0.407787	−	0.142201i
$775$	−48.6488	−	20.1951i	−1.74751	−	0.725429i
$776$	9.12905	+	19.8786i	0.327714	+	0.713600i
$777$	−5.21761	+	7.81660i	−0.187181	+	0.280419i
$778$	0.235825	−	1.13101i	0.00845472	−	0.0405488i
$779$	12.1572	+	21.0569i	0.435578	+	0.754443i
$780$	−31.6385	+	23.3676i	−1.13284	+	0.836695i
$781$	−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
$785$	−1.06965	−	16.4170i	−0.0381774	−	0.585948i
$786$	−24.6863	−	25.1219i	−0.880531	−	0.896069i
$787$	−1.15191	−	1.99517i	−0.0410613	−	0.0711202i	0.844764	−	0.535138i	$-0.179741\pi$
$787$	−1.15191	−	1.99517i	−0.0410613	−	0.0711202i	−0.885826	+	0.464018i	$0.846407\pi$
$788$	5.76204	−	4.25503i	0.205264	−	0.151579i
$789$	−1.25938	+	1.88670i	−0.0448352	+	0.0671684i
$790$	16.6363	+	13.0211i	0.591892	+	0.463269i
$791$	0.668954			0.0237853
$792$	−10.2060	+	3.16317i	−0.362654	+	0.112398i
$793$		−	53.2683i		−	1.89161i
$794$	39.6077	−	13.0393i	1.40562	−	0.462748i
$795$	−30.6074	−	17.6679i	−1.08553	−	0.626617i
$796$	7.59594	+	10.2862i	0.269231	+	0.364585i
$797$	4.90786	+	8.50066i	0.173845	+	0.301109i	0.939761	−	0.341832i	$-0.111047\pi$
$797$	4.90786	+	8.50066i	0.173845	+	0.301109i	−0.765916	+	0.642941i	$0.777714\pi$
$798$	−9.81458	−	2.72203i	−0.347432	−	0.0963587i
$799$	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
$804$	−23.5740	+	45.7151i	−0.831393	+	1.61225i
$805$	−8.23299	−	4.06402i	−0.290175	−	0.143238i
$806$	74.0586	+	15.4417i	2.60860	+	0.543912i
$807$	37.2597	+	2.42467i	1.31161	+	0.0853525i
$808$	−22.4686	−	48.9257i	−0.790444	−	1.72120i
$809$			2.25430i			0.0792571i	0.999214	+	0.0396285i	$0.0126175\pi$
$809$			2.25430i			0.0792571i	−0.999214	+	0.0396285i	$0.987383\pi$
$810$	−26.2091	−	11.0944i	−0.920893	−	0.389816i
$811$			43.2702i			1.51942i	0.650260	+	0.759711i	$0.274660\pi$
$811$			43.2702i			1.51942i	−0.650260	+	0.759711i	$0.725340\pi$
$812$	0.195743	−	0.448984i	0.00686923	−	0.0157563i
$813$	−2.73278	−	0.177835i	−0.0958426	−	0.00623694i
$814$	−1.71907	+	8.24464i	−0.0602533	+	0.288975i
$815$	6.41525	−	12.9961i	0.224716	−	0.455235i
$816$	−21.3562	−	8.12722i	−0.747615	−	0.284509i
$817$	−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	0.736985	−	0.675909i	$-0.236249\pi$
$821$	14.9032	+	8.60434i	0.520124	+	0.300293i	−0.216862	+	0.976202i	$0.569582\pi$
$822$	4.84235	−	17.4596i	0.168896	−	0.608975i
$823$	−7.68986	−	13.3192i	−0.268052	−	0.464279i	0.700307	−	0.713842i	$-0.253046\pi$
$823$	−7.68986	−	13.3192i	−0.268052	−	0.464279i	−0.968359	+	0.249563i	$0.919713\pi$
$824$	2.01858	−	21.6221i	0.0703206	−	0.753242i
$825$	0.709894	+	10.8821i	0.0247153	+	0.378867i
$826$	4.94202	+	15.0117i	0.171955	+	0.522322i
$827$			0.827927i			0.0287899i	0.999896	+	0.0143949i	$0.00458221\pi$
$827$			0.827927i			0.0287899i	−0.999896	+	0.0143949i	$0.995418\pi$
$828$	11.0601	−	18.4055i	0.384366	−	0.639636i
$829$	30.8355			1.07096			0.535481	−	0.844547i	$-0.320130\pi$
$829$	30.8355			1.07096			0.535481	+	0.844547i	$0.320130\pi$
$830$	14.1902	+	11.1066i	0.492549	+	0.385514i
$831$	−7.63542	+	11.4388i	−0.264870	+	0.396807i
$832$	−30.8125	−	26.4721i	−1.06823	−	0.917754i
$833$	9.37282	+	16.2342i	0.324749	+	0.562482i
$834$	2.92307	−	2.87238i	0.101218	−	0.0994624i
$835$	−1.89951	−	29.1538i	−0.0657352	−	1.00891i
$836$	−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	$-0.916609\pi$
$839$	−7.49176	+	12.9761i	−0.258644	+	0.447985i	0.707235	+	0.706979i	$0.249942\pi$
$840$	−12.5139	−	1.16726i	−0.431771	−	0.0402742i
$841$	−14.4772	−	25.0753i	−0.499214	−	0.864665i
$842$	40.4729	+	8.43889i	1.39479	+	0.290823i
$843$	−6.53286	+	9.78699i	−0.225004	+	0.337082i
$844$	11.6443	−	26.7091i	0.400813	−	0.919364i
$845$	−15.8723	−	23.7745i	−0.546025	−	0.817869i
$846$	−1.49335	+	4.28245i	−0.0513424	+	0.147234i
$847$	10.8012			0.371134
$848$	10.7393	−	34.8841i	0.368789	−	1.19792i
$849$	−11.8166	+	5.83415i	−0.405544	+	0.200228i
$850$	−13.1497	+	19.2608i	−0.451032	+	0.660639i
$851$	−8.46260	−	14.6577i	−0.290094	−	0.502458i
$852$	−18.1372	−	28.2287i	−0.621369	−	0.967100i
$853$	−2.52471	−	1.45764i	−0.0864445	−	0.0499088i	0.456155	−	0.889901i	$-0.349226\pi$
$853$	−2.52471	−	1.45764i	−0.0864445	−	0.0499088i	−0.542599	+	0.839992i	$0.682560\pi$
$854$	11.3403	−	12.6933i	0.388057	−	0.434356i
$855$	−20.2216	−	13.4957i	−0.691564	−	0.461542i
$856$	−19.3857	+	27.3455i	−0.662591	+	0.934650i
$857$	26.1654	−	45.3198i	0.893794	−	1.54810i	0.0585032	−	0.998287i	$-0.481367\pi$
$857$	26.1654	−	45.3198i	0.893794	−	1.54810i	0.835291	−	0.549809i	$-0.185299\pi$
$858$	−3.92124	−	15.1635i	−0.133869	−	0.517674i
$859$	1.52668	−	0.881431i	0.0520897	−	0.0300740i	−0.473729	−	0.880671i	$-0.657092\pi$
$859$	1.52668	−	0.881431i	0.0520897	−	0.0300740i	0.525819	+	0.850597i	$0.323759\pi$
$860$	−11.9141	−	4.29588i	−0.406267	−	0.146488i
$861$	−13.3041	−	0.865763i	−0.453403	−	0.0295051i
$862$	−6.95368	−	21.1222i	−0.236843	−	0.719425i
$863$			16.9992i			0.578658i	0.957230	+	0.289329i	$0.0934322\pi$
$863$			16.9992i			0.578658i	−0.957230	+	0.289329i	$0.906568\pi$
$864$	5.13399	−	28.9420i	0.174662	−	0.984628i
$865$	−6.99224	−	10.4734i	−0.237743	−	0.356106i
$866$	−54.5875	+	17.9709i	−1.85496	+	0.610674i
$867$	−0.688587	+	10.5815i	−0.0233857	+	0.359365i
$868$	14.3600	+	19.4460i	0.487412	+	0.660039i
$869$	−7.28544	+	4.20625i	−0.247142	+	0.142687i
$870$	0.778859	−	0.871925i	0.0264058	−	0.0295610i
$871$	−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
$875$	−4.13733	+	12.1418i	−0.139867	+	0.410469i
$876$	−26.4689	+	17.0065i	−0.894302	+	0.574596i
$877$	32.5343	−	18.7837i	1.09860	−	0.634279i	0.162750	−	0.986667i	$-0.447964\pi$
$877$	32.5343	−	18.7837i	1.09860	−	0.634279i	0.935854	+	0.352388i	$0.114630\pi$
$878$	6.51262	−	31.2345i	0.219790	−	1.05411i
$879$	−15.3907	+	7.59876i	−0.519114	+	0.256300i
$880$	−10.7926	+	3.22078i	−0.363817	+	0.108573i
$881$			32.8340i			1.10620i	0.833114	+	0.553102i	$0.186556\pi$
$881$			32.8340i			1.10620i	−0.833114	+	0.553102i	$0.813444\pi$
$882$	−18.2607	+	15.7487i	−0.614869	+	0.530285i
$883$	−57.6883			−1.94137			−0.970683	−	0.240363i	$-0.922734\pi$
$883$	−57.6883			−1.94137			−0.970683	+	0.240363i	$0.922734\pi$
$884$	13.3859	−	30.7038i	0.450215	−	1.03268i
$885$	0.00300424	+	37.7242i	0.000100986	+	1.26809i
$886$	4.15879	−	19.9455i	0.139717	−	0.670083i
$887$	−32.5642	+	18.8010i	−1.09340	+	0.631275i	−0.934479	−	0.356017i	$-0.884135\pi$
$887$	−32.5642	+	18.8010i	−1.09340	+	0.631275i	−0.158920	+	0.987291i	$0.550801\pi$
$888$	−17.9909	−	14.5983i	−0.603734	−	0.489885i
$889$	−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
$894$	−7.80891	+	7.67350i	−0.261169	+	0.256640i
$895$	14.2358	−	28.8393i	0.475851	−	0.963991i
$896$	−1.70666	−	12.8677i	−0.0570157	−	0.429880i
$897$	26.1794	+	17.4748i	0.874104	+	0.583468i
$898$	−19.8111	+	6.52204i	−0.661104	+	0.217643i
$899$	−2.24869			−0.0749980
$900$	−27.5021	−	11.9848i	−0.916736	−	0.399494i
$901$	30.0955			1.00263
$902$	−11.3484	+	3.73604i	−0.377861	+	0.124396i
$903$	5.04617	−	2.49142i	0.167926	−	0.0829094i
$904$	−0.153293	+	1.64200i	−0.00509844	+	0.0546122i
$905$	−11.2812	+	22.8536i	−0.374998	+	0.759680i
$906$	−30.6428	−	8.49864i	−1.01804	−	0.282349i
$907$	12.8060	−	22.1806i	0.425215	−	0.736494i	−0.571225	−	0.820793i	$-0.693532\pi$
$907$	12.8060	−	22.1806i	0.425215	−	0.736494i	0.996441	+	0.0842990i	$0.0268651\pi$
$908$	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	$-0.843847\pi$
$911$	−0.996781	+	1.72648i	−0.0330248	+	0.0572007i	0.849041	+	0.528328i	$0.177181\pi$
$912$	8.93047	−	23.4669i	0.295718	−	0.777067i
$913$	−6.21425	+	3.58780i	−0.205662	+	0.118739i
$914$	−0.294631	+	1.41305i	−0.00974552	+	0.0467395i
$915$	35.1843	−	20.3174i	1.16316	−	0.671673i
$916$	44.3151	+	19.3200i	1.46421	+	0.638349i
$917$	16.4972			0.544785
$918$	24.0531	−	2.97566i	0.793870	−	0.0982115i
$919$			13.2072i			0.435667i	0.975986	+	0.217833i	$0.0698989\pi$
$919$			13.2072i			0.435667i	−0.975986	+	0.217833i	$0.930101\pi$
$920$	11.8621	−	19.2773i	0.391081	−	0.635552i
$921$	0.896990	−	13.7840i	0.0295568	−	0.454197i
$922$	0.226526	−	1.08642i	0.00746025	−	0.0357793i
$923$	42.5941	−	24.5917i	1.40200	−	0.809446i
$924$	2.29377	−	4.44812i	0.0754597	−	0.146332i
$925$	−18.7710	+	14.3804i	−0.617186	+	0.472825i
$926$	−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	0.237558	−	0.971373i	$-0.423653\pi$
$929$	−14.7794	−	8.53291i	−0.484897	−	0.279956i	−0.722455	+	0.691418i	$0.756986\pi$
$930$	18.0477	+	54.8063i	0.591808	+	1.79717i
$931$	−17.8387	+	10.2992i	−0.584640	+	0.337542i
$932$	−14.3937	+	10.6291i	−0.471480	+	0.348169i
$933$	10.8808	−	5.37215i	0.356223	−	0.175876i
$934$	−35.0430	+	11.5366i	−1.14664	+	0.377488i
$935$	−5.15644	−	7.72362i	−0.168633	−	0.252589i
$936$	42.0192	+	9.53113i	1.37344	+	0.311535i
$937$			20.0658i			0.655523i	0.944761	+	0.327761i	$0.106294\pi$
$937$			20.0658i			0.655523i	−0.944761	+	0.327761i	$0.893706\pi$
$938$	−7.53358	−	22.8837i	−0.245980	−	0.747178i
$939$	14.1361	−	21.1776i	0.461315	−	0.691104i
$940$	−1.62159	+	4.49727i	−0.0528903	+	0.146685i
$941$	−28.5447	+	16.4803i	−0.930532	+	0.537243i	−0.886980	−	0.461808i	$-0.847201\pi$
$941$	−28.5447	+	16.4803i	−0.930532	+	0.537243i	−0.0435520	+	0.999051i	$0.513867\pi$
$942$	−12.8545	+	12.6316i	−0.418822	+	0.411559i
$943$	12.0053	−	20.7937i	0.390945	−	0.677136i
$944$	−37.9798	+	8.69061i	−1.23614	+	0.282855i
$945$	12.3107	−	5.11388i	0.400467	−	0.166354i
$946$	3.36001	−	3.76090i	0.109243	−	0.122277i
$947$	−44.3874	−	25.6271i	−1.44240	−	0.832767i	−0.444386	−	0.895835i	$-0.646578\pi$
$947$	−44.3874	−	25.6271i	−1.44240	−	0.832767i	−0.998009	+	0.0630680i	$0.979912\pi$
$948$	−1.09866	−	23.1164i	−0.0356828	−	0.750787i
$949$	−23.0587	−	39.9388i	−0.748516	−	1.29647i
$950$	−21.1644	−	14.4494i	−0.686665	−	0.468801i
$951$	−3.34810	−	2.23487i	−0.108570	−	0.0724707i
$952$	9.72626	−	4.46669i	0.315230	−	0.144766i
$953$	−23.0185			−0.745641			−0.372821	−	0.927903i	$-0.621609\pi$
$953$	−23.0185			−0.745641			−0.372821	+	0.927903i	$0.621609\pi$
$954$	7.23807	+	38.0312i	0.234341	+	1.23130i
$955$	19.9791	+	29.9258i	0.646507	+	0.968377i
$956$	−27.8454	−	12.1397i	−0.900584	−	0.392626i
$957$	0.206104	+	0.417446i	0.00666239	+	0.0134941i
$958$	41.7708	+	8.70951i	1.34955	+	0.281392i
$959$	4.24331	+	7.34963i	0.137024	+	0.237332i
$960$	5.73273	−	30.4489i	0.185023	−	0.982734i
$961$	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
$965$	1.76278	+	27.0552i	0.0567458	+	0.870939i
$966$	2.51807	+	9.73742i	0.0810175	+	0.313296i
$967$	22.4438	+	38.8737i	0.721743	+	1.25010i	0.960301	+	0.278967i	$0.0899920\pi$
$967$	22.4438	+	38.8737i	0.721743	+	1.25010i	−0.238558	+	0.971128i	$0.576675\pi$
$968$	−2.47513	+	26.5125i	−0.0795538	+	0.852143i
$969$	20.6595	+	1.34441i	0.663678	+	0.0431888i
$970$	−19.2589	−	15.0738i	−0.618365	−	0.483989i
$971$	49.5015			1.58858			0.794290	−	0.607539i	$-0.207843\pi$
$971$	49.5015			1.58858			0.794290	+	0.607539i	$0.207843\pi$
$972$	9.54514	+	29.6798i	0.306161	+	0.951980i
$973$			1.91954i			0.0615375i
$974$	9.85293	+	29.9288i	0.315708	+	0.958982i
$975$	19.4618	−	39.4340i	0.623276	−	1.26290i
$976$	28.5581	+	30.7444i	0.914123	+	0.984104i
$977$	−15.6589	−	27.1220i	−0.500972	−	0.867710i	−0.999999	−	0.00112320i	$-0.999642\pi$
$977$	−15.6589	−	27.1220i	−0.500972	−	0.867710i	0.499027	−	0.866586i	$-0.333691\pi$
$978$	−15.3710	+	3.97489i	−0.491509	+	0.127103i
$979$	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	−0.999298	−	0.0374637i	$-0.988072\pi$
$983$	−48.0135	−	27.7206i	−1.53139	−	0.884149i	−0.532094	−	0.846686i	$-0.678595\pi$
$984$	5.17376	−	32.4576i	0.164934	−	1.03471i
$985$	−3.54476	+	7.18106i	−0.112946	+	0.228808i
$986$	−0.203222	+	0.974652i	−0.00647190	+	0.0310392i
$987$	−0.940450	−	1.90480i	−0.0299348	−	0.0606305i
$988$	33.7384	+	14.7089i	1.07336	+	0.467951i
$989$			10.1351i			0.322278i
$990$	8.52007	−	8.37366i	0.270785	−	0.266132i
$991$		−	5.66060i		−	0.179815i	−0.995950	−	0.0899075i	$-0.971343\pi$
$991$		−	5.66060i		−	0.179815i	0.995950	−	0.0899075i	$-0.0286571\pi$
$992$	−51.0224	+	30.7918i	−1.61996	+	0.977640i
$993$	14.5124	−	21.7413i	0.460536	−	0.689938i
$994$	15.3851	+	3.20791i	0.487986	+	0.101749i
$995$	−12.8194	−	6.32800i	−0.406402	−	0.200611i
$996$	−0.937120	−	19.7176i	−0.0296938	−	0.624775i
$997$	16.2323	+	9.37172i	0.514082	+	0.296805i	0.734510	−	0.678598i	$-0.237412\pi$
$997$	16.2323	+	9.37172i	0.514082	+	0.296805i	−0.220428	+	0.975403i	$0.570745\pi$
$998$	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.119.9	yes	48
3.2	odd	2		540.2.n.d.359.16		48
4.3	odd	2	inner	180.2.n.d.119.22	yes	48
5.2	odd	4		900.2.r.g.551.21		48
5.3	odd	4		900.2.r.g.551.4		48
5.4	even	2	inner	180.2.n.d.119.16	yes	48
9.4	even	3		540.2.n.d.179.22		48
9.5	odd	6	inner	180.2.n.d.59.3	✓	48
12.11	even	2		540.2.n.d.359.3		48
15.14	odd	2		540.2.n.d.359.9		48
20.3	even	4		900.2.r.g.551.10		48
20.7	even	4		900.2.r.g.551.15		48
20.19	odd	2	inner	180.2.n.d.119.3	yes	48
36.23	even	6	inner	180.2.n.d.59.16	yes	48
36.31	odd	6		540.2.n.d.179.9		48
45.4	even	6		540.2.n.d.179.3		48
45.14	odd	6	inner	180.2.n.d.59.22	yes	48
45.23	even	12		900.2.r.g.851.10		48
45.32	even	12		900.2.r.g.851.15		48
60.59	even	2		540.2.n.d.359.22		48
180.23	odd	12		900.2.r.g.851.4		48
180.59	even	6	inner	180.2.n.d.59.9	yes	48
180.139	odd	6		540.2.n.d.179.16		48
180.167	odd	12		900.2.r.g.851.21		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
180.2.n.d.59.3	✓	48	9.5	odd	6	inner
180.2.n.d.59.9	yes	48	180.59	even	6	inner
180.2.n.d.59.16	yes	48	36.23	even	6	inner
180.2.n.d.59.22	yes	48	45.14	odd	6	inner
180.2.n.d.119.3	yes	48	20.19	odd	2	inner
180.2.n.d.119.9	yes	48	1.1	even	1	trivial
180.2.n.d.119.16	yes	48	5.4	even	2	inner
180.2.n.d.119.22	yes	48	4.3	odd	2	inner
540.2.n.d.179.3		48	45.4	even	6
540.2.n.d.179.9		48	36.31	odd	6
540.2.n.d.179.16		48	180.139	odd	6
540.2.n.d.179.22		48	9.4	even	3
540.2.n.d.359.3		48	12.11	even	2
540.2.n.d.359.9		48	15.14	odd	2
540.2.n.d.359.16		48	3.2	odd	2
540.2.n.d.359.22		48	60.59	even	2
900.2.r.g.551.4		48	5.3	odd	4
900.2.r.g.551.10		48	20.3	even	4
900.2.r.g.551.15		48	20.7	even	4
900.2.r.g.551.21		48	5.2	odd	4
900.2.r.g.851.4		48	180.23	odd	12
900.2.r.g.851.10		48	45.23	even	12
900.2.r.g.851.15		48	45.32	even	12
900.2.r.g.851.21		48	180.167	odd	12

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+(-0.442228 - 1.34329i) q^{2} +(0.112475 - 1.72840i) q^{3} +(-1.60887 + 1.18808i) q^{4} +(0.989764 - 2.00509i) q^{5} +(-2.37148 + 0.613258i) 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} +(1.87252 + 2.91439i) q^{12} +(-4.39750 + 2.53890i) q^{13} +(-1.58839 - 0.331191i) q^{14} +(-3.35426 - 1.93622i) q^{15} +(1.17692 - 3.82294i) q^{16} +3.29816 q^{17} +(0.793219 + 4.16783i) q^{18} +3.62414i q^{19} +(0.789807 + 4.40184i) q^{20} +(-1.65282 - 1.10326i) q^{21} +(-1.74333 - 0.363497i) q^{22} +(3.09936 - 1.78942i) q^{23} +(3.08680 - 3.80416i) q^{24} +(-3.04074 - 3.96912i) 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} +(-1.11757 + 5.36200i) q^{30} +(9.12339 - 5.26739i) q^{31} +(-5.65579 + 0.109664i) q^{32} +(-1.81404 - 1.21088i) q^{33} +(-1.45854 - 4.43039i) q^{34} +(-1.42448 - 2.13367i) q^{35} +(5.24783 - 2.90866i) q^{36} -4.72925i q^{37} +(4.86827 - 1.60269i) q^{38} +(3.89361 + 7.88619i) q^{39} +(5.56368 - 3.00756i) q^{40} +(5.81019 - 3.35452i) q^{41} +(-0.751083 + 2.70811i) q^{42} +(-1.41598 + 2.45255i) q^{43} +(0.282666 + 2.50255i) q^{44} +(-3.72383 + 5.57970i) q^{45} +(-3.77433 - 3.37202i) q^{46} +(0.925776 + 0.534497i) q^{47} +(-6.47517 - 2.46417i) q^{48} +(2.84183 + 4.92220i) q^{49} +(-3.98699 + 5.83985i) q^{50} +(0.370961 - 5.70053i) q^{51} +(4.05858 - 9.30936i) q^{52} +9.12493 q^{53} +(7.29287 - 0.902219i) q^{54} +(-1.56343 - 2.34180i) q^{55} +(2.94899 - 1.35430i) q^{56} +(6.26394 + 0.407625i) q^{57} +(-0.0616167 + 0.295514i) q^{58} +(-4.87018 - 8.43539i) q^{59} +(7.69695 - 0.870002i) 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} +(0.738222 + 11.3303i) q^{65} +(-0.824347 + 2.97228i) q^{66} +(7.42407 + 12.8589i) q^{67} +(-5.30631 + 3.91849i) q^{68} +(-2.74422 - 5.55818i) q^{69} +(-2.23620 + 2.85706i) q^{70} -9.68598 q^{71} +(-6.22791 - 5.76308i) q^{72} +9.08215i q^{73} +(-6.35277 + 2.09141i) q^{74} +(-7.20222 + 4.80917i) q^{75} +(-4.30577 - 5.83076i) q^{76} +(-0.722368 - 1.25118i) q^{77} +(8.87159 - 8.71775i) 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} +(3.96994 - 0.188680i) q^{84} +(3.26440 - 6.61309i) q^{85} +(3.92068 + 0.817489i) q^{86} +(-0.205258 + 0.307501i) q^{87} +(3.23665 - 1.48640i) q^{88} +2.26303i q^{89} +(9.14195 + 2.53469i) q^{90} +5.82584i q^{91} +(-2.86049 + 6.56123i) q^{92} +(-8.07798 - 16.3613i) q^{93} +(0.308582 - 1.47996i) q^{94} +(7.26670 + 3.58704i) q^{95} +(-0.446593 + 9.78778i) 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