LMFDB - Embedded newform 289.3.e.h.249.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [289,3,Mod(40,289)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(289, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([15])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("289.40"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 289 = 17^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	289.e (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,8,-8,8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

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

Self dual:	no
Analytic conductor:	$7.87467964001$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	$\Q(\zeta_{16})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 17)
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			249.1
Root			$-0.923880 + 0.382683i$ of defining polynomial
Character	$\chi$	$=$	289.249
Dual form			289.3.e.h.65.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.63099 + 0.675577i) q^{2} +(-0.789499 - 3.96908i) q^{3} +(-0.624715 - 0.624715i) q^{4} +(6.43416 + 4.29916i) q^{5} +(1.39376 - 7.00688i) q^{6} +(3.40262 - 2.27356i) q^{7} +(-3.29916 - 7.96489i) q^{8} +(-6.81537 + 2.82302i) q^{9} +(7.58960 + 11.3586i) q^{10} +(6.80638 + 1.35387i) q^{11} +(-1.98633 + 2.97275i) q^{12} +(2.37416 - 2.37416i) q^{13} +(7.08560 - 1.40941i) q^{14} +(11.9840 - 28.9319i) q^{15} -11.6855i q^{16} -13.0229 q^{18} +(-22.7712 - 9.43215i) q^{19} +(-1.33376 - 6.70526i) q^{20} +(-11.7103 - 11.7103i) q^{21} +(10.1865 + 6.80638i) q^{22} +(2.24740 - 11.2984i) q^{23} +(-29.0086 + 19.3829i) q^{24} +(13.3484 + 32.2260i) q^{25} +(5.47615 - 2.26829i) q^{26} +(-3.64922 - 5.46144i) q^{27} +(-3.54600 - 0.705343i) q^{28} +(6.67355 - 9.98767i) q^{29} +(39.0914 - 39.0914i) q^{30} +(37.1045 - 7.38055i) q^{31} +(-5.30218 + 12.8006i) q^{32} -28.0839i q^{33} +31.6674 q^{35} +(6.02124 + 2.49408i) q^{36} +(6.29529 + 31.6486i) q^{37} +(-30.7674 - 30.7674i) q^{38} +(-11.2976 - 7.54883i) q^{39} +(13.0150 - 65.4310i) q^{40} +(-28.1140 + 18.7852i) q^{41} +(-11.1881 - 27.0106i) q^{42} +(-3.21547 + 1.33189i) q^{43} +(-3.40626 - 5.09783i) q^{44} +(-55.9877 - 11.1367i) q^{45} +(11.2984 - 16.9093i) q^{46} +(3.16735 - 3.16735i) q^{47} +(-46.3809 + 9.22573i) q^{48} +(-12.3427 + 29.7979i) q^{49} +61.5781i q^{50} -2.96634 q^{52} +(28.3919 + 11.7603i) q^{53} +(-2.26220 - 11.3729i) q^{54} +(37.9728 + 37.9728i) q^{55} +(-29.3345 - 19.6007i) q^{56} +(-19.4591 + 97.8275i) q^{57} +(17.6319 - 11.7813i) q^{58} +(4.49481 + 10.8514i) q^{59} +(-25.5607 + 10.5876i) q^{60} +(39.3733 + 58.9263i) q^{61} +(65.5031 + 13.0294i) q^{62} +(-16.7718 + 25.1008i) q^{63} +(-50.3473 + 50.3473i) q^{64} +(25.4826 - 5.06881i) q^{65} +(18.9728 - 45.8045i) q^{66} +28.5842i q^{67} -46.6187 q^{69} +(51.6491 + 21.3938i) q^{70} +(6.70446 + 33.7056i) q^{71} +(44.9700 + 44.9700i) q^{72} +(77.8880 + 52.0431i) q^{73} +(-11.1135 + 55.8713i) q^{74} +(117.369 - 78.4234i) q^{75} +(8.33312 + 20.1179i) q^{76} +(26.2377 - 10.8680i) q^{77} +(-13.3265 - 19.9444i) q^{78} +(21.0499 + 4.18708i) q^{79} +(50.2381 - 75.1866i) q^{80} +(-65.7422 + 65.7422i) q^{81} +(-58.5443 + 11.6452i) q^{82} +(-43.4522 + 104.903i) q^{83} +14.6312i q^{84} -6.14419 q^{86} +(-44.9106 - 18.6026i) q^{87} +(-11.6719 - 58.6787i) q^{88} +(-28.3238 - 28.3238i) q^{89} +(-83.7916 - 55.9877i) q^{90} +(2.68058 - 13.4762i) q^{91} +(-8.46229 + 5.65432i) q^{92} +(-58.5880 - 141.444i) q^{93} +(7.30570 - 3.02612i) q^{94} +(-105.963 - 158.585i) q^{95} +(54.9926 + 10.9387i) q^{96} +(-92.4136 + 138.307i) q^{97} +(-40.2616 + 40.2616i) q^{98} +(-50.2100 + 9.98738i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{3} - 8 q^{4} + 8 q^{5} - 24 q^{6} - 8 q^{7} - 16 q^{8} - 8 q^{9} + 8 q^{10} - 32 q^{12} + 24 q^{14} - 32 q^{15} - 136 q^{18} + 32 q^{19} - 64 q^{21} + 8 q^{22} - 32 q^{23} - 48 q^{24} - 16 q^{25}+ \cdots - 256 q^{99}+O(q^{100}) $ 8 * q + 8 * q^3 - 8 * q^4 + 8 * q^5 - 24 * q^6 - 8 * q^7 - 16 * q^8 - 8 * q^9 + 8 * q^10 - 32 * q^12 + 24 * q^14 - 32 * q^15 - 136 * q^18 + 32 * q^19 - 64 * q^21 + 8 * q^22 - 32 * q^23 - 48 * q^24 - 16 * q^25 - 112 * q^27 - 8 * q^28 + 168 * q^30 - 24 * q^31 + 24 * q^32 + 80 * q^35 + 104 * q^36 + 56 * q^37 + 8 * q^38 - 136 * q^39 - 24 * q^40 + 56 * q^41 + 72 * q^42 - 96 * q^43 + 40 * q^44 - 256 * q^45 + 8 * q^46 - 80 * q^47 - 16 * q^48 - 8 * q^49 + 240 * q^52 - 96 * q^53 - 192 * q^54 - 8 * q^55 - 48 * q^56 + 168 * q^57 - 96 * q^58 - 8 * q^59 - 16 * q^60 + 56 * q^61 + 96 * q^62 + 16 * q^63 - 120 * q^64 + 264 * q^65 - 8 * q^66 - 208 * q^69 + 80 * q^70 + 136 * q^71 + 24 * q^72 + 240 * q^73 - 248 * q^74 + 168 * q^75 + 80 * q^76 + 216 * q^77 + 328 * q^79 + 8 * q^80 - 224 * q^81 - 352 * q^82 + 88 * q^83 + 288 * q^86 - 312 * q^87 - 24 * q^88 + 288 * q^89 + 184 * q^90 + 184 * q^91 + 72 * q^92 - 280 * q^93 + 8 * q^94 + 216 * q^95 + 464 * q^96 + 280 * q^97 + 16 * q^98 - 256 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/289\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{7}{16}\right)$

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 $

$2$	1.63099	+	0.675577i	0.815493	+	0.337788i	0.751143	−	0.660139i	$-0.229503\pi$
$2$	1.63099	+	0.675577i	0.815493	+	0.337788i	0.0643498	+	0.997927i	$0.479503\pi$
$3$	−0.789499	−	3.96908i	−0.263166	−	1.32303i	−0.855696	−	0.517478i	$-0.826871\pi$
$3$	−0.789499	−	3.96908i	−0.263166	−	1.32303i	0.592530	−	0.805548i	$-0.298129\pi$
$4$	−0.624715	−	0.624715i	−0.156179	−	0.156179i
$5$	6.43416	+	4.29916i	1.28683	+	0.859833i	0.995311	−	0.0967316i	$-0.0308388\pi$
$5$	6.43416	+	4.29916i	1.28683	+	0.859833i	0.291521	+	0.956565i	$0.405839\pi$
$6$	1.39376	−	7.00688i	0.232293	−	1.16781i
$7$	3.40262	−	2.27356i	0.486089	−	0.324794i	−0.288261	−	0.957552i	$-0.593077\pi$
$7$	3.40262	−	2.27356i	0.486089	−	0.324794i	0.774350	+	0.632757i	$0.218077\pi$
$8$	−3.29916	−	7.96489i	−0.412396	−	0.995611i
$9$	−6.81537	+	2.82302i	−0.757263	+	0.313669i
$10$	7.58960	+	11.3586i	0.758960	+	1.13586i
$11$	6.80638	+	1.35387i	0.618761	+	0.123079i	0.494511	−	0.869172i	$-0.335347\pi$
$11$	6.80638	+	1.35387i	0.618761	+	0.123079i	0.124251	+	0.992251i	$0.460347\pi$
$12$	−1.98633	+	2.97275i	−0.165528	+	0.247729i
$13$	2.37416	−	2.37416i	0.182628	−	0.182628i	−0.609872	−	0.792500i	$-0.708779\pi$
$13$	2.37416	−	2.37416i	0.182628	−	0.182628i	0.792500	+	0.609872i	$0.208779\pi$
$14$	7.08560	−	1.40941i	0.506114	−	0.100672i
$15$	11.9840	−	28.9319i	0.798931	−	1.92879i
$16$		−	11.6855i		−	0.730347i
$17$		0			0
$17$		0			0
$18$	−13.0229			−0.723496
$19$	−22.7712	−	9.43215i	−1.19849	−	0.496429i	−0.307977	−	0.951394i	$-0.599652\pi$
$19$	−22.7712	−	9.43215i	−1.19849	−	0.496429i	−0.890509	+	0.454965i	$0.849652\pi$
$20$	−1.33376	−	6.70526i	−0.0666880	−	0.335263i
$21$	−11.7103	−	11.7103i	−0.557634	−	0.557634i
$22$	10.1865	+	6.80638i	0.463021	+	0.309381i
$23$	2.24740	−	11.2984i	0.0977131	−	0.491237i	−0.900676	−	0.434492i	$-0.856928\pi$
$23$	2.24740	−	11.2984i	0.0977131	−	0.491237i	0.998389	−	0.0567447i	$-0.0180721\pi$
$24$	−29.0086	+	19.3829i	−1.20869	+	0.807622i
$25$	13.3484	+	32.2260i	0.533938	+	1.28904i
$26$	5.47615	−	2.26829i	0.210621	−	0.0872421i
$27$	−3.64922	−	5.46144i	−0.135156	−	0.202276i
$28$	−3.54600	−	0.705343i	−0.126643	−	0.0251908i
$29$	6.67355	−	9.98767i	0.230122	−	0.344402i	−0.698381	−	0.715726i	$-0.746096\pi$
$29$	6.67355	−	9.98767i	0.230122	−	0.344402i	0.928504	+	0.371324i	$0.121096\pi$
$30$	39.0914	−	39.0914i	1.30305	−	1.30305i
$31$	37.1045	−	7.38055i	1.19692	−	0.238082i	0.443898	−	0.896077i	$-0.353595\pi$
$31$	37.1045	−	7.38055i	1.19692	−	0.238082i	0.753022	+	0.657995i	$0.228595\pi$
$32$	−5.30218	+	12.8006i	−0.165693	+	0.400019i
$33$		−	28.0839i		−	0.851028i
$34$		0			0
$35$	31.6674			0.904784
$36$	6.02124	+	2.49408i	0.167257	+	0.0692800i
$37$	6.29529	+	31.6486i	0.170143	+	0.855366i	0.967696	+	0.252118i	$0.0811272\pi$
$37$	6.29529	+	31.6486i	0.170143	+	0.855366i	−0.797554	+	0.603248i	$0.793873\pi$
$38$	−30.7674	−	30.7674i	−0.809669	−	0.809669i
$39$	−11.2976	−	7.54883i	−0.289683	−	0.193560i
$40$	13.0150	−	65.4310i	0.325376	−	1.63577i
$41$	−28.1140	+	18.7852i	−0.685707	+	0.458175i	−0.848993	−	0.528404i	$-0.822791\pi$
$41$	−28.1140	+	18.7852i	−0.685707	+	0.458175i	0.163286	+	0.986579i	$0.447791\pi$
$42$	−11.1881	−	27.0106i	−0.266384	−	0.643109i
$43$	−3.21547	+	1.33189i	−0.0747784	+	0.0309742i	−0.419759	−	0.907636i	$-0.637885\pi$
$43$	−3.21547	+	1.33189i	−0.0747784	+	0.0309742i	0.344981	+	0.938610i	$0.387885\pi$
$44$	−3.40626	−	5.09783i	−0.0774150	−	0.115860i
$45$	−55.9877	−	11.1367i	−1.24417	−	0.247481i
$46$	11.2984	−	16.9093i	0.245618	−	0.367594i
$47$	3.16735	−	3.16735i	0.0673905	−	0.0673905i	−0.672608	−	0.739999i	$-0.734826\pi$
$47$	3.16735	−	3.16735i	0.0673905	−	0.0673905i	0.739999	+	0.672608i	$0.234826\pi$
$48$	−46.3809	+	9.22573i	−0.966268	+	0.192203i
$49$	−12.3427	+	29.7979i	−0.251892	+	0.608121i
$50$			61.5781i			1.23156i
$51$		0			0
$52$	−2.96634			−0.0570451
$53$	28.3919	+	11.7603i	0.535697	+	0.221893i	0.634096	−	0.773254i	$-0.281372\pi$
$53$	28.3919	+	11.7603i	0.535697	+	0.221893i	−0.0983994	+	0.995147i	$0.531372\pi$
$54$	−2.26220	−	11.3729i	−0.0418927	−	0.210609i
$55$	37.9728	+	37.9728i	0.690414	+	0.690414i
$56$	−29.3345	−	19.6007i	−0.523830	−	0.350012i
$57$	−19.4591	+	97.8275i	−0.341388	+	1.71627i
$58$	17.6319	−	11.7813i	0.303998	−	0.203125i
$59$	4.49481	+	10.8514i	0.0761832	+	0.183923i	0.957383	−	0.288822i	$-0.0932635\pi$
$59$	4.49481	+	10.8514i	0.0761832	+	0.183923i	−0.881200	+	0.472744i	$0.843263\pi$
$60$	−25.5607	+	10.5876i	−0.426012	+	0.176460i
$61$	39.3733	+	58.9263i	0.645464	+	0.966006i	0.999526	+	0.0307835i	$0.00980025\pi$
$61$	39.3733	+	58.9263i	0.645464	+	0.966006i	−0.354062	+	0.935222i	$0.615200\pi$
$62$	65.5031	+	13.0294i	1.05650	+	0.210151i
$63$	−16.7718	+	25.1008i	−0.266220	+	0.398426i
$64$	−50.3473	+	50.3473i	−0.786676	+	0.786676i
$65$	25.4826	−	5.06881i	0.392040	−	0.0779816i
$66$	18.9728	−	45.8045i	0.287467	−	0.694008i
$67$			28.5842i			0.426629i	0.976984	+	0.213315i	$0.0684260\pi$
$67$			28.5842i			0.426629i	−0.976984	+	0.213315i	$0.931574\pi$
$68$		0			0
$69$	−46.6187			−0.675634
$70$	51.6491	+	21.3938i	0.737845	+	0.305625i
$71$	6.70446	+	33.7056i	0.0944290	+	0.474726i	0.998844	+	0.0480724i	$0.0153078\pi$
$71$	6.70446	+	33.7056i	0.0944290	+	0.474726i	−0.904415	+	0.426654i	$0.859692\pi$
$72$	44.9700	+	44.9700i	0.624584	+	0.624584i
$73$	77.8880	+	52.0431i	1.06696	+	0.712919i	0.959619	−	0.281303i	$-0.0907666\pi$
$73$	77.8880	+	52.0431i	1.06696	+	0.712919i	0.107340	+	0.994222i	$0.465767\pi$
$74$	−11.1135	+	55.8713i	−0.150182	+	0.755018i
$75$	117.369	−	78.4234i	1.56492	−	1.04565i
$76$	8.33312	+	20.1179i	0.109646	+	0.264710i
$77$	26.2377	−	10.8680i	0.340749	−	0.141143i
$78$	−13.3265	−	19.9444i	−0.170852	−	0.255698i
$79$	21.0499	+	4.18708i	0.266454	+	0.0530011i	0.326509	−	0.945194i	$-0.394128\pi$
$79$	21.0499	+	4.18708i	0.266454	+	0.0530011i	−0.0600549	+	0.998195i	$0.519128\pi$
$80$	50.2381	−	75.1866i	0.627976	−	0.939833i
$81$	−65.7422	+	65.7422i	−0.811632	+	0.811632i
$82$	−58.5443	+	11.6452i	−0.713955	+	0.142015i
$83$	−43.4522	+	104.903i	−0.523521	+	1.26389i	0.412182	+	0.911102i	$0.364767\pi$
$83$	−43.4522	+	104.903i	−0.523521	+	1.26389i	−0.935703	+	0.352789i	$0.885233\pi$
$84$			14.6312i			0.174181i
$85$		0			0
$86$	−6.14419			−0.0714440
$87$	−44.9106	−	18.6026i	−0.516214	−	0.213823i
$88$	−11.6719	−	58.6787i	−0.132635	−	0.666803i
$89$	−28.3238	−	28.3238i	−0.318245	−	0.318245i	0.529848	−	0.848093i	$-0.322249\pi$
$89$	−28.3238	−	28.3238i	−0.318245	−	0.318245i	−0.848093	+	0.529848i	$0.822249\pi$
$90$	−83.7916	−	55.9877i	−0.931018	−	0.622086i
$91$	2.68058	−	13.4762i	0.0294569	−	0.148090i
$92$	−8.46229	+	5.65432i	−0.0919814	+	0.0614600i
$93$	−58.5880	−	141.444i	−0.629978	−	1.52090i
$94$	7.30570	−	3.02612i	0.0777202	−	0.0321928i
$95$	−105.963	−	158.585i	−1.11540	−	1.66932i
$96$	54.9926	+	10.9387i	0.572840	+	0.113945i
$97$	−92.4136	+	138.307i	−0.952718	+	1.42584i	−0.0484747	+	0.998824i	$0.515436\pi$
$97$	−92.4136	+	138.307i	−0.952718	+	1.42584i	−0.904243	+	0.427018i	$0.859564\pi$
$98$	−40.2616	+	40.2616i	−0.410833	+	0.410833i
$99$	−50.2100	+	9.98738i	−0.507171	+	0.100883i
$100$	11.7931	−	28.4710i	0.117931	−	0.284710i
$101$		−	124.444i		−	1.23211i	−0.787701	−	0.616057i	$-0.788729\pi$
$101$		−	124.444i		−	1.23211i	0.787701	−	0.616057i	$-0.211271\pi$
$102$		0			0
$103$	175.084			1.69984			0.849922	−	0.526908i	$-0.176649\pi$
$103$	175.084			1.69984			0.849922	+	0.526908i	$0.176649\pi$
$104$	−26.7427	−	11.0772i	−0.257141	−	0.106511i
$105$	−25.0014	−	125.691i	−0.238109	−	1.19705i
$106$	38.3619	+	38.3619i	0.361904	+	0.361904i
$107$	−33.1477	−	22.1486i	−0.309791	−	0.206996i	0.390949	−	0.920412i	$-0.372147\pi$
$107$	−33.1477	−	22.1486i	−0.309791	−	0.206996i	−0.700740	+	0.713416i	$0.747147\pi$
$108$	−1.13212	+	5.69157i	−0.0104826	+	0.0526997i
$109$	38.1042	−	25.4604i	0.349580	−	0.233582i	−0.368366	−	0.929681i	$-0.620083\pi$
$109$	38.1042	−	25.4604i	0.349580	−	0.233582i	0.717946	+	0.696099i	$0.245083\pi$
$110$	36.2795	+	87.5866i	0.329814	+	0.796241i
$111$	120.645	−	49.9730i	1.08690	−	0.450207i
$112$	−26.5678	−	39.7615i	−0.237213	−	0.355014i
$113$	−183.644	−	36.5291i	−1.62517	−	0.323267i	−0.703338	−	0.710855i	$-0.748308\pi$
$113$	−183.644	−	36.5291i	−1.62517	−	0.323267i	−0.921832	+	0.387589i	$0.873308\pi$
$114$	−97.8275	+	146.409i	−0.858136	+	1.28429i
$115$	63.0340	−	63.0340i	0.548122	−	0.548122i
$116$	−10.4085	+	2.07038i	−0.0897285	+	0.0178481i
$117$	−9.47847	+	22.8831i	−0.0810126	+	0.195582i
$118$			20.7351i			0.175721i
$119$		0			0
$120$	−269.976			−2.24980
$121$	−67.2956	−	27.8748i	−0.556162	−	0.230370i
$122$	24.4081	+	122.708i	0.200066	+	1.00580i
$123$	96.7557	+	96.7557i	0.786632	+	0.786632i
$124$	−27.7905	−	18.5690i	−0.224117	−	0.149750i
$125$	−14.9173	+	74.9942i	−0.119338	+	0.599953i
$126$	−44.3122	+	29.6084i	−0.351684	+	0.234988i
$127$	15.7175	+	37.9454i	0.123760	+	0.298783i	0.973601	−	0.228256i	$-0.0733023\pi$
$127$	15.7175	+	37.9454i	0.123760	+	0.298783i	−0.849841	+	0.527039i	$0.823302\pi$
$128$	−64.9268	+	26.8936i	−0.507241	+	0.210106i
$129$	7.82500	+	11.7109i	0.0606589	+	0.0907825i
$130$	44.9862	+	8.94830i	0.346047	+	0.0688331i
$131$	106.938	−	160.044i	0.816323	−	1.22171i	−0.155927	−	0.987769i	$-0.549837\pi$
$131$	106.938	−	160.044i	0.816323	−	1.22171i	0.972250	−	0.233944i	$-0.0751634\pi$
$132$	−17.5444	+	17.5444i	−0.132912	+	0.132912i
$133$	−98.9266	+	19.6777i	−0.743809	+	0.147953i
$134$	−19.3108	+	46.6204i	−0.144110	+	0.347913i
$135$		−	50.8284i		−	0.376507i
$136$		0			0
$137$	52.8361			0.385665			0.192832	−	0.981232i	$-0.438233\pi$
$137$	52.8361			0.385665			0.192832	+	0.981232i	$0.438233\pi$
$138$	−76.0345	−	31.4945i	−0.550975	−	0.228221i
$139$	10.2376	+	51.4676i	0.0736514	+	0.370271i	0.999979	−	0.00644773i	$-0.00205239\pi$
$139$	10.2376	+	51.4676i	0.0736514	+	0.370271i	−0.926328	+	0.376719i	$0.877052\pi$
$140$	−19.7831	−	19.7831i	−0.141308	−	0.141308i
$141$	−15.0721	−	10.0709i	−0.106894	−	0.0714245i
$142$	−11.8358	+	59.5027i	−0.0833509	+	0.419033i
$143$	19.3737	−	12.9451i	0.135481	−	0.0905253i
$144$	32.9885	+	79.6413i	0.229087	+	0.553064i
$145$	85.8773	−	35.5715i	0.592257	−	0.245321i
$146$	91.8752	+	137.501i	0.629282	+	0.941787i
$147$	128.015	+	25.4638i	0.870850	+	0.173223i
$148$	15.8386	−	23.7041i	0.107017	−	0.160163i
$149$	36.5973	−	36.5973i	0.245620	−	0.245620i	−0.573551	−	0.819170i	$-0.694434\pi$
$149$	36.5973	−	36.5973i	0.245620	−	0.245620i	0.819170	+	0.573551i	$0.194434\pi$
$150$	244.408	−	48.6158i	1.62939	−	0.324105i
$151$	91.9670	−	222.028i	0.609053	−	1.47038i	−0.254979	−	0.966947i	$-0.582069\pi$
$151$	91.9670	−	222.028i	0.609053	−	1.47038i	0.864032	−	0.503437i	$-0.167931\pi$
$152$			212.489i			1.39795i
$153$		0			0
$154$	50.1354			0.325555
$155$	270.467	+	112.031i	1.74495	+	0.722780i
$156$	2.34193	+	11.7737i	0.0150123	+	0.0754721i
$157$	−190.153	−	190.153i	−1.21117	−	1.21117i	−0.970644	−	0.240522i	$-0.922681\pi$
$157$	−190.153	−	190.153i	−1.21117	−	1.21117i	−0.240522	−	0.970644i	$-0.577319\pi$
$158$	31.5034	+	21.0499i	0.199389	+	0.133227i
$159$	24.2623	−	121.975i	0.152593	−	0.767136i
$160$	−89.1469	+	59.5661i	−0.557168	+	0.372288i
$161$	−18.0406	−	43.5540i	−0.112054	−	0.270522i
$162$	−151.638	+	62.8107i	−0.936040	+	0.387720i
$163$	21.5571	+	32.2626i	0.132252	+	0.197930i	0.891685	−	0.452656i	$-0.149523\pi$
$163$	21.5571	+	32.2626i	0.132252	+	0.197930i	−0.759433	+	0.650586i	$0.774523\pi$
$164$	29.2986	+	5.82785i	0.178650	+	0.0355357i
$165$	120.737	−	180.696i	0.731742	−	1.09513i
$166$	−141.740	+	141.740i	−0.853855	+	0.853855i
$167$	35.3355	−	7.02867i	0.211590	−	0.0420878i	−0.0881571	−	0.996107i	$-0.528098\pi$
$167$	35.3355	−	7.02867i	0.211590	−	0.0420878i	0.299747	+	0.954019i	$0.403098\pi$
$168$	−54.6371	+	131.906i	−0.325221	+	0.785152i
$169$			157.727i			0.933294i
$170$		0			0
$171$	181.821			1.06328
$172$	2.84081	+	1.17670i	0.0165163	+	0.00684128i
$173$	37.6555	+	189.307i	0.217662	+	1.09426i	0.922827	+	0.385215i	$0.125873\pi$
$173$	37.6555	+	189.307i	0.217662	+	1.09426i	−0.705165	+	0.709043i	$0.749127\pi$
$174$	−60.6811	−	60.6811i	−0.348742	−	0.348742i
$175$	118.688	+	79.3045i	0.678215	+	0.453168i
$176$	15.8207	−	79.5362i	0.0898905	−	0.451910i
$177$	39.5216	−	26.4075i	0.223286	−	0.149195i
$178$	−27.0608	−	65.3307i	−0.152027	−	0.367026i
$179$	−223.947	+	92.7619i	−1.25110	+	0.518223i	−0.907167	−	0.420771i	$-0.861759\pi$
$179$	−223.947	+	92.7619i	−1.25110	+	0.518223i	−0.343933	+	0.938994i	$0.611759\pi$
$180$	28.0191	+	41.9336i	0.155662	+	0.232964i
$181$	−133.895	−	26.6333i	−0.739750	−	0.147146i	−0.189190	−	0.981941i	$-0.560586\pi$
$181$	−133.895	−	26.6333i	−0.739750	−	0.147146i	−0.550561	+	0.834795i	$0.685586\pi$
$182$	13.4762	−	20.1685i	0.0740449	−	0.110816i
$183$	202.798	−	202.798i	1.10819	−	1.10819i
$184$	−97.4054	+	19.3751i	−0.529377	+	0.105300i
$185$	−95.5575	+	230.696i	−0.516527	+	1.24701i
$186$		−	270.274i		−	1.45308i
$187$		0			0
$188$	−3.95738			−0.0210499
$189$	−24.8339	−	10.2865i	−0.131396	−	0.0544260i
$190$	−65.6882	−	330.237i	−0.345727	−	1.73809i
$191$	123.244	+	123.244i	0.645254	+	0.645254i	0.951842	−	0.306588i	$-0.0991874\pi$
$191$	123.244	+	123.244i	0.645254	+	0.645254i	−0.306588	+	0.951842i	$0.599187\pi$
$192$	239.581	+	160.083i	1.24782	+	0.833767i
$193$	36.6126	−	184.064i	0.189703	−	0.953700i	−0.762210	−	0.647330i	$-0.775886\pi$
$193$	36.6126	−	184.064i	0.189703	−	0.953700i	0.951913	−	0.306370i	$-0.0991144\pi$
$194$	−244.162	+	163.144i	−1.25857	+	0.840948i
$195$	−40.2370	−	97.1407i	−0.206344	−	0.498157i
$196$	26.3259	−	10.9045i	0.134316	−	0.0556354i
$197$	159.522	+	238.742i	0.809759	+	1.21189i	0.974241	+	0.225509i	$0.0724046\pi$
$197$	159.522	+	238.742i	0.809759	+	1.21189i	−0.164482	+	0.986380i	$0.552595\pi$
$198$	−88.6390	−	17.6314i	−0.447672	−	0.0890474i
$199$	−50.8883	+	76.1598i	−0.255720	+	0.382712i	−0.937011	−	0.349301i	$-0.886419\pi$
$199$	−50.8883	+	76.1598i	−0.255720	+	0.382712i	0.681290	+	0.732013i	$0.261419\pi$
$200$	212.638	−	212.638i	1.06319	−	1.06319i
$201$	113.453	−	22.5672i	0.564442	−	0.112274i
$202$	84.0712	−	202.966i	0.416194	−	1.00478i
$203$		−	49.1570i		−	0.242153i
$204$		0			0
$205$	−261.650			−1.27634
$206$	285.560	+	118.283i	1.38621	+	0.574188i
$207$	16.5788	+	83.3475i	0.0800911	+	0.402645i
$208$	−27.7433	−	27.7433i	−0.133381	−	0.133381i
$209$	−142.220	−	95.0281i	−0.680477	−	0.454680i
$210$	44.1367	−	221.890i	0.210175	−	1.05662i
$211$	−30.0653	+	20.0890i	−0.142490	+	0.0952086i	−0.624772	−	0.780807i	$-0.714808\pi$
$211$	−30.0653	+	20.0890i	−0.142490	+	0.0952086i	0.482282	+	0.876016i	$0.339808\pi$
$212$	−10.3900	−	25.0837i	−0.0490095	−	0.118319i
$213$	128.487	−	53.2210i	0.603225	−	0.249864i
$214$	−39.1003	−	58.5178i	−0.182712	−	0.273448i
$215$	−26.4149	−	5.25425i	−0.122860	−	0.0244384i
$216$	−31.4604	+	47.0838i	−0.145650	+	0.217981i
$217$	109.473	−	109.473i	0.504482	−	0.504482i
$218$	79.3479	−	15.7833i	0.363981	−	0.0724004i
$219$	145.071	−	350.232i	0.662423	−	1.59923i
$220$		−	47.4443i		−	0.215656i
$221$		0			0
$222$	230.532			1.03843
$223$	−372.417	−	154.260i	−1.67003	−	0.691750i	−0.671256	−	0.741226i	$-0.734245\pi$
$223$	−372.417	−	154.260i	−1.67003	−	0.691750i	−0.998775	+	0.0494759i	$0.984245\pi$
$224$	11.0616	+	55.6104i	0.0493822	+	0.248261i
$225$	−181.949	−	181.949i	−0.808663	−	0.808663i
$226$	−274.843	−	183.644i	−1.21612	−	0.812585i
$227$	−24.6288	+	123.817i	−0.108497	+	0.545450i	0.887856	+	0.460121i	$0.152194\pi$
$227$	−24.6288	+	123.817i	−0.108497	+	0.545450i	−0.996353	+	0.0853288i	$0.972806\pi$
$228$	73.2707	−	48.9579i	0.321363	−	0.214728i
$229$	47.0477	+	113.583i	0.205449	+	0.495997i	0.992696	−	0.120640i	$-0.0384947\pi$
$229$	47.0477	+	113.583i	0.205449	+	0.495997i	−0.787248	+	0.616637i	$0.788495\pi$
$230$	145.392	−	60.2233i	0.632139	−	0.261840i
$231$	−63.8505	−	95.5591i	−0.276409	−	0.413676i
$232$	−101.568	−	20.2031i	−0.437792	−	0.0870823i
$233$	33.4139	−	50.0074i	0.143407	−	0.214624i	−0.752812	−	0.658236i	$-0.771303\pi$
$233$	33.4139	−	50.0074i	0.143407	−	0.214624i	0.896219	+	0.443612i	$0.146303\pi$
$234$	−30.9185	+	30.9185i	−0.132130	+	0.132130i
$235$	33.9962	−	6.76227i	0.144665	−	0.0287756i
$236$	3.97107	−	9.58702i	0.0168266	−	0.0406230i
$237$		−	86.8544i		−	0.366474i
$238$		0			0
$239$	−285.920			−1.19632			−0.598160	−	0.801377i	$-0.704101\pi$
$239$	−285.920			−1.19632			−0.598160	+	0.801377i	$0.704101\pi$
$240$	−338.085	−	140.039i	−1.40869	−	0.583497i
$241$	−24.2566	−	121.946i	−0.100650	−	0.506002i	−0.997917	−	0.0645131i	$-0.979451\pi$
$241$	−24.2566	−	121.946i	−0.100650	−	0.506002i	0.897267	−	0.441489i	$-0.145549\pi$
$242$	−90.9267	−	90.9267i	−0.375730	−	0.375730i
$243$	263.686	+	176.189i	1.08513	+	0.725060i
$244$	12.2151	−	61.4092i	0.0500617	−	0.251677i
$245$	−207.521	+	138.661i	−0.847025	+	0.565964i
$246$	92.4414	+	223.173i	0.375778	+	0.907208i
$247$	−76.4560	+	31.6691i	−0.309538	+	0.128215i
$248$	−181.199	−	271.184i	−0.730642	−	1.09348i
$249$	450.674	+	89.6446i	1.80993	+	0.360018i
$250$	−74.9942	+	112.237i	−0.299977	+	0.448947i
$251$	−99.6747	+	99.6747i	−0.397110	+	0.397110i	−0.877213	−	0.480102i	$-0.840600\pi$
$251$	−99.6747	+	99.6747i	−0.397110	+	0.397110i	0.480102	+	0.877213i	$0.340600\pi$
$252$	26.1585	−	5.20324i	0.103803	−	0.0206478i
$253$	30.5933	−	73.8588i	0.120922	−	0.291932i
$254$			72.5069i			0.285460i
$255$		0			0
$256$	160.744			0.627906
$257$	−363.098	−	150.400i	−1.41283	−	0.585214i	−0.459783	−	0.888032i	$-0.652073\pi$
$257$	−363.098	−	150.400i	−1.41283	−	0.585214i	−0.953048	+	0.302818i	$0.902073\pi$
$258$	4.85083	+	24.3868i	0.0188017	+	0.0945224i
$259$	93.3754	+	93.3754i	0.360523	+	0.360523i
$260$	−19.0859	−	12.7528i	−0.0734074	−	0.0490492i
$261$	−17.2873	+	86.9092i	−0.0662349	+	0.332985i
$262$	282.537	−	188.785i	1.07839	−	0.720554i
$263$	111.542	+	269.286i	0.424113	+	1.02390i	0.981121	+	0.193393i	$0.0619493\pi$
$263$	111.542	+	269.286i	0.424113	+	1.02390i	−0.557008	+	0.830507i	$0.688051\pi$
$264$	−223.685	+	92.6535i	−0.847293	+	0.350960i
$265$	132.119	+	197.729i	0.498561	+	0.746149i
$266$	−174.642	−	34.7384i	−0.656548	−	0.130595i
$267$	−90.0578	+	134.781i	−0.337295	+	0.504798i
$268$	17.8569	−	17.8569i	0.0666304	−	0.0666304i
$269$	99.9342	−	19.8781i	0.371503	−	0.0738965i	−0.00580827	−	0.999983i	$-0.501849\pi$
$269$	99.9342	−	19.8781i	0.371503	−	0.0738965i	0.377311	+	0.926087i	$0.376849\pi$
$270$	34.3385	−	82.9004i	0.127180	−	0.307038i
$271$		−	381.059i		−	1.40612i	−0.711129	−	0.703061i	$-0.751816\pi$
$271$		−	381.059i		−	1.40612i	0.711129	−	0.703061i	$-0.248184\pi$
$272$		0			0
$273$	−55.6043			−0.203679
$274$	86.1749	+	35.6948i	0.314507	+	0.130273i
$275$	47.2247	+	237.414i	0.171726	+	0.863325i
$276$	29.1234	+	29.1234i	0.105520	+	0.105520i
$277$	55.8881	+	37.3432i	0.201762	+	0.134813i	0.652347	−	0.757920i	$-0.273785\pi$
$277$	55.8881	+	37.3432i	0.201762	+	0.134813i	−0.450585	+	0.892734i	$0.648785\pi$
$278$	−18.0730	+	90.8593i	−0.0650109	+	0.326832i
$279$	−232.046	+	155.048i	−0.831705	+	0.555727i
$280$	−104.476	−	252.228i	−0.373129	−	0.900813i
$281$	348.356	−	144.294i	1.23970	−	0.513501i	0.336079	−	0.941834i	$-0.390899\pi$
$281$	348.356	−	144.294i	1.23970	−	0.513501i	0.903621	+	0.428333i	$0.140899\pi$
$282$	−17.7788	−	26.6078i	−0.0630452	−	0.0943539i
$283$	291.125	+	57.9083i	1.02871	+	0.204623i	0.680465	−	0.732781i	$-0.261778\pi$
$283$	291.125	+	57.9083i	1.02871	+	0.204623i	0.348245	+	0.937404i	$0.386778\pi$
$284$	16.8680	−	25.2447i	0.0593944	−	0.0888899i
$285$	−545.780	+	545.780i	−1.91502	+	1.91502i
$286$	40.3437	−	8.02486i	0.141062	−	0.0280590i
$287$	−52.9521	+	127.838i	−0.184502	+	0.445428i
$288$		−	102.209i		−	0.354892i
$289$		0			0
$290$	164.096			0.565848
$291$	621.911	+	257.604i	2.13715	+	0.885237i
$292$	−16.1457	−	81.1699i	−0.0552935	−	0.277979i
$293$	99.8472	+	99.8472i	0.340776	+	0.340776i	0.856659	−	0.515883i	$-0.172536\pi$
$293$	99.8472	+	99.8472i	0.340776	+	0.340776i	−0.515883	+	0.856659i	$0.672536\pi$
$294$	191.588	+	128.015i	0.651660	+	0.435425i
$295$	−17.7318	+	89.1437i	−0.0601078	+	0.302182i
$296$	231.308	−	154.555i	0.781446	−	0.522146i
$297$	−17.4439	−	42.1132i	−0.0587336	−	0.141795i
$298$	84.4140	−	34.9654i	0.283269	−	0.117334i
$299$	−21.4886	−	32.1600i	−0.0718683	−	0.107559i
$300$	−122.314	−	24.3298i	−0.407715	−	0.0810995i
$301$	−7.91291	+	11.8425i	−0.0262887	+	0.0393439i
$302$	299.994	−	299.994i	0.993357	−	0.993357i
$303$	−493.926	+	98.2481i	−1.63012	+	0.324251i
$304$	−110.220	+	266.094i	−0.362565	+	0.875310i
$305$			548.414i			1.79808i
$306$		0			0
$307$	−259.641			−0.845735			−0.422868	−	0.906192i	$-0.638976\pi$
$307$	−259.641			−0.845735			−0.422868	+	0.906192i	$0.638976\pi$
$308$	−23.1804	−	9.60165i	−0.0752612	−	0.0311742i
$309$	−138.229	−	694.922i	−0.447342	−	2.24894i
$310$	365.442	+	365.442i	1.17884	+	1.17884i
$311$	−469.055	−	313.413i	−1.50822	−	1.00776i	−0.988126	−	0.153646i	$-0.950898\pi$
$311$	−469.055	−	313.413i	−1.50822	−	1.00776i	−0.520090	−	0.854112i	$-0.674102\pi$
$312$	−22.8529	+	114.889i	−0.0732464	+	0.368234i
$313$	378.950	−	253.206i	1.21070	−	0.808966i	0.224495	−	0.974475i	$-0.427927\pi$
$313$	378.950	−	253.206i	1.21070	−	0.808966i	0.986208	+	0.165509i	$0.0529267\pi$
$314$	−181.674	−	438.600i	−0.578580	−	1.39681i
$315$	−215.825	+	89.3977i	−0.685159	+	0.283802i
$316$	−10.5344	−	15.7659i	−0.0333368	−	0.0498921i
$317$	−325.560	−	64.7580i	−1.02700	−	0.204284i	−0.347288	−	0.937759i	$-0.612897\pi$
$317$	−325.560	−	64.7580i	−1.02700	−	0.204284i	−0.679717	+	0.733475i	$0.737897\pi$
$318$	121.975	−	182.548i	0.383568	−	0.574050i
$319$	58.9447	−	58.9447i	0.184780	−	0.184780i
$320$	−540.393	+	107.491i	−1.68873	+	0.335909i
$321$	−61.7394	+	149.052i	−0.192334	+	0.464336i
$322$		−	83.2238i		−	0.258459i
$323$		0			0
$324$	82.1402			0.253519
$325$	108.201	+	44.8183i	0.332926	+	0.137903i
$326$	13.3636	+	67.1833i	0.0409926	+	0.206084i
$327$	−131.138	−	131.138i	−0.401033	−	0.401033i
$328$	242.374	+	161.949i	0.738946	+	0.493748i
$329$	3.57614	−	17.9785i	0.0108697	−	0.0546459i
$330$	318.995	−	213.146i	0.966653	−	0.645897i
$331$	−225.594	−	544.633i	−0.681554	−	1.64542i	−0.761139	−	0.648588i	$-0.775360\pi$
$331$	−225.594	−	544.633i	−0.681554	−	1.64542i	0.0795855	−	0.996828i	$-0.474640\pi$
$332$	92.6796	−	38.3892i	0.279156	−	0.115630i
$333$	−132.249	−	197.925i	−0.397145	−	0.594369i
$334$	62.3801	+	12.4082i	0.186767	+	0.0371502i
$335$	−122.888	+	183.915i	−0.366830	+	0.549000i
$336$	−136.841	+	136.841i	−0.407266	+	0.407266i
$337$	321.295	−	63.9095i	0.953397	−	0.189642i	0.306202	−	0.951967i	$-0.400942\pi$
$337$	321.295	−	63.9095i	0.953397	−	0.189642i	0.647195	+	0.762324i	$0.275942\pi$
$338$	−106.557	+	257.250i	−0.315256	+	0.761095i
$339$			757.738i			2.23522i
$340$		0			0
$341$	262.540			0.769911
$342$	296.548	+	122.834i	0.867100	+	0.359165i
$343$	64.8699	+	326.123i	0.189125	+	0.950796i
$344$	21.2167	+	21.2167i	0.0616766	+	0.0616766i
$345$	−299.952	−	200.422i	−0.869427	−	0.580932i
$346$	−66.4757	+	334.196i	−0.192126	+	0.965884i
$347$	−201.268	+	134.483i	−0.580024	+	0.387560i	−0.810692	−	0.585473i	$-0.800909\pi$
$347$	−201.268	+	134.483i	−0.580024	+	0.387560i	0.230668	+	0.973033i	$0.425909\pi$
$348$	16.4350	+	39.6776i	0.0472270	+	0.114016i
$349$	−464.685	+	192.479i	−1.33148	+	0.551515i	−0.931076	−	0.364826i	$-0.881129\pi$
$349$	−464.685	+	192.479i	−1.33148	+	0.551515i	−0.400399	+	0.916341i	$0.631129\pi$
$350$	140.001	+	209.527i	0.400004	+	0.598649i
$351$	−21.6302	−	4.30251i	−0.0616244	−	0.0122579i
$352$	−53.4190	+	79.9472i	−0.151759	+	0.227123i
$353$	−231.294	+	231.294i	−0.655223	+	0.655223i	−0.954246	−	0.299023i	$-0.903339\pi$
$353$	−231.294	+	231.294i	−0.655223	+	0.655223i	0.299023	+	0.954246i	$0.403339\pi$
$354$	82.2994	−	16.3704i	0.232484	−	0.0462440i
$355$	−101.768	+	245.691i	−0.286671	+	0.692086i
$356$			35.3886i			0.0994062i
$357$		0			0
$358$	−427.922			−1.19531
$359$	490.942	+	203.355i	1.36753	+	0.566448i	0.941117	−	0.338082i	$-0.109778\pi$
$359$	490.942	+	203.355i	1.36753	+	0.566448i	0.426410	+	0.904530i	$0.359778\pi$
$360$	96.0106	+	482.678i	0.266696	+	1.34077i
$361$	174.298	+	174.298i	0.482820	+	0.482820i
$362$	−200.388	−	133.895i	−0.553557	−	0.369875i
$363$	−57.5073	+	289.109i	−0.158422	+	0.796443i
$364$	−10.0934	+	6.74416i	−0.0277290	+	0.0185279i
$365$	277.402	+	669.707i	0.760005	+	1.83481i
$366$	467.767	−	193.755i	1.27805	−	0.529386i
$367$	−183.923	−	275.260i	−0.501152	−	0.750026i	0.491520	−	0.870866i	$-0.336441\pi$
$367$	−183.923	−	275.260i	−0.501152	−	0.750026i	−0.992672	+	0.120840i	$0.961441\pi$
$368$	−132.028	−	26.2621i	−0.358773	−	0.0713644i
$369$	138.576	−	207.394i	0.375545	−	0.562043i
$370$	−311.706	+	311.706i	−0.842448	+	0.842448i
$371$	123.345	−	24.5348i	0.332466	−	0.0661316i
$372$	−51.7613	+	124.963i	−0.139143	+	0.335922i
$373$		−	147.856i		−	0.396396i	−0.980162	−	0.198198i	$-0.936491\pi$
$373$		−	147.856i		−	0.396396i	0.980162	−	0.198198i	$-0.0635089\pi$
$374$		0			0
$375$	309.435			0.825160
$376$	−35.6772	−	14.7780i	−0.0948863	−	0.0393032i
$377$	−7.86825	−	39.5564i	−0.0208707	−	0.104924i
$378$	−33.5543	−	33.5543i	−0.0887681	−	0.0887681i
$379$	−36.3219	−	24.2695i	−0.0958362	−	0.0640357i	0.506729	−	0.862106i	$-0.330855\pi$
$379$	−36.3219	−	24.2695i	−0.0958362	−	0.0640357i	−0.602565	+	0.798070i	$0.705855\pi$
$380$	−32.8737	+	165.267i	−0.0865098	+	0.434914i
$381$	138.199	−	92.3419i	0.362728	−	0.242367i
$382$	117.748	+	284.269i	0.308241	+	0.744160i
$383$	−182.570	+	75.6230i	−0.476684	+	0.197449i	−0.608072	−	0.793882i	$-0.708057\pi$
$383$	−182.570	+	75.6230i	−0.476684	+	0.197449i	0.131387	+	0.991331i	$0.458057\pi$
$384$	158.002	+	236.467i	0.411464	+	0.615800i
$385$	215.540	+	42.8737i	0.559845	+	0.111360i
$386$	184.064	−	275.471i	0.476850	−	0.713656i
$387$	18.1547	−	18.1547i	0.0469113	−	0.0469113i
$388$	144.134	−	28.6701i	0.371480	−	0.0738920i
$389$	−8.22534	+	19.8577i	−0.0211448	+	0.0510481i	−0.934099	−	0.357013i	$-0.883795\pi$
$389$	−8.22534	+	19.8577i	−0.0211448	+	0.0510481i	0.912954	+	0.408061i	$0.133795\pi$
$390$		−	185.618i		−	0.475944i
$391$		0			0
$392$	278.058			0.709332
$393$	−719.657	−	298.092i	−1.83119	−	0.758503i
$394$	98.8903	+	497.155i	0.250991	+	1.26181i
$395$	117.437	+	117.437i	0.297310	+	0.297310i
$396$	37.6062	+	25.1276i	0.0949650	+	0.0634536i
$397$	6.92123	−	34.7954i	0.0174338	−	0.0876457i	−0.971089	−	0.238718i	$-0.923273\pi$
$397$	6.92123	−	34.7954i	0.0174338	−	0.0876457i	0.988523	+	0.151073i	$0.0482727\pi$
$398$	−134.450	+	89.8366i	−0.337814	+	0.225720i
$399$	156.205	+	377.112i	0.391491	+	0.945142i
$400$	376.578	−	155.984i	0.941446	−	0.389960i
$401$	−83.0937	−	124.358i	−0.207216	−	0.310121i	0.713275	−	0.700884i	$-0.247211\pi$
$401$	−83.0937	−	124.358i	−0.207216	−	0.310121i	−0.920491	+	0.390763i	$0.872211\pi$
$402$	200.286	+	39.8393i	0.498224	+	0.0991028i
$403$	70.5695	−	105.615i	0.175110	−	0.262071i
$404$	−77.7417	+	77.7417i	−0.192430	+	0.192430i
$405$	−705.632	+	140.359i	−1.74230	+	0.346565i
$406$	33.2093	−	80.1744i	0.0817964	−	0.197474i
$407$			223.935i			0.550209i
$408$		0			0
$409$	−398.892			−0.975287			−0.487643	−	0.873043i	$-0.662143\pi$
$409$	−398.892			−0.975287			−0.487643	+	0.873043i	$0.662143\pi$
$410$	−426.748	−	176.765i	−1.04085	−	0.431134i
$411$	−41.7140	−	209.711i	−0.101494	−	0.510245i
$412$	−109.378	−	109.378i	−0.265479	−	0.265479i
$413$	39.9656	+	26.7041i	0.0967689	+	0.0646589i
$414$	−29.2678	+	147.139i	−0.0706951	+	0.355408i
$415$	−730.573	+	488.154i	−1.76042	+	1.17627i
$416$	17.8024	+	42.9789i	0.0427943	+	0.103315i
$417$	196.197	−	81.2673i	0.470496	−	0.194886i
$418$	−167.760	−	251.070i	−0.401339	−	0.600646i
$419$	36.6811	+	7.29632i	0.0875444	+	0.0174137i	0.238668	−	0.971101i	$-0.423289\pi$
$419$	36.6811	+	7.29632i	0.0875444	+	0.0174137i	−0.151124	+	0.988515i	$0.548289\pi$
$420$	−62.9020	+	94.1395i	−0.149767	+	0.224142i
$421$	312.706	−	312.706i	0.742769	−	0.742769i	−0.230341	−	0.973110i	$-0.573984\pi$
$421$	312.706	−	312.706i	0.742769	−	0.742769i	0.973110	+	0.230341i	$0.0739841\pi$
$422$	−62.6078	+	12.4535i	−0.148360	+	0.0295106i
$423$	−12.6452	+	30.5282i	−0.0298941	+	0.0721706i
$424$		−	264.938i		−	0.624853i
$425$		0			0
$426$	245.515			0.576327
$427$	267.945	+	110.987i	0.627507	+	0.259922i
$428$	6.87130	+	34.5444i	0.0160544	+	0.0807111i
$429$	−66.6757	−	66.6757i	−0.155421	−	0.155421i
$430$	−39.5327	−	26.4149i	−0.0919364	−	0.0614299i
$431$	67.6760	−	340.230i	0.157021	−	0.789397i	−0.819350	−	0.573294i	$-0.805665\pi$
$431$	67.6760	−	340.230i	0.157021	−	0.789397i	0.976371	−	0.216103i	$-0.0693347\pi$
$432$	−63.8199	+	42.6431i	−0.147731	+	0.0987109i
$433$	20.5680	+	49.6556i	0.0475012	+	0.114678i	0.945849	−	0.324607i	$-0.105232\pi$
$433$	20.5680	+	49.6556i	0.0475012	+	0.114678i	−0.898348	+	0.439285i	$0.855232\pi$
$434$	252.506	−	104.591i	0.581810	−	0.240994i
$435$	−208.986	−	312.770i	−0.480428	−	0.719012i
$436$	−39.7098	−	7.89876i	−0.0910774	−	0.0181164i
$437$	−157.745	+	236.082i	−0.360972	+	0.540233i
$438$	473.217	−	473.217i	1.08040	−	1.08040i
$439$	238.583	−	47.4571i	0.543469	−	0.108103i	0.0842815	−	0.996442i	$-0.473140\pi$
$439$	238.583	−	47.4571i	0.543469	−	0.108103i	0.459188	+	0.888339i	$0.348140\pi$
$440$	177.170	−	427.727i	0.402660	−	0.972107i
$441$		−	237.928i		−	0.539518i
$442$		0			0
$443$	−114.592			−0.258673			−0.129336	−	0.991601i	$-0.541285\pi$
$443$	−114.592			−0.258673			−0.129336	+	0.991601i	$0.541285\pi$
$444$	−106.588	−	44.1501i	−0.240063	−	0.0994373i
$445$	−60.4711	−	304.009i	−0.135890	−	0.683165i
$446$	−503.192	−	503.192i	−1.12823	−	1.12823i
$447$	−174.151	−	116.364i	−0.389600	−	0.260322i
$448$	−56.8453	+	285.780i	−0.126887	+	0.637903i
$449$	451.653	−	301.785i	1.00591	−	0.672127i	0.0605527	−	0.998165i	$-0.480714\pi$
$449$	451.653	−	301.785i	1.00591	−	0.672127i	0.945357	+	0.326038i	$0.105714\pi$
$450$	−173.836	−	419.677i	−0.386302	−	0.932616i
$451$	−216.787	+	89.7961i	−0.480681	+	0.199104i
$452$	91.9050	+	137.546i	0.203330	+	0.304304i
$453$	−953.854	−	189.733i	−2.10564	−	0.418838i
$454$	−123.817	+	185.305i	−0.272725	+	0.408162i
$455$	75.1835	−	75.1835i	0.165239	−	0.165239i
$456$	843.384	−	167.760i	1.84953	−	0.367894i
$457$	85.9222	−	207.434i	0.188014	−	0.453905i	−0.801563	−	0.597910i	$-0.795998\pi$
$457$	85.9222	−	207.434i	0.188014	−	0.453905i	0.989577	+	0.144005i	$0.0459981\pi$
$458$			217.037i			0.473880i
$459$		0			0
$460$	−78.7565			−0.171210
$461$	233.070	+	96.5408i	0.505575	+	0.209416i	0.620867	−	0.783916i	$-0.286781\pi$
$461$	233.070	+	96.5408i	0.505575	+	0.209416i	−0.115292	+	0.993332i	$0.536781\pi$
$462$	−39.5819	−	198.991i	−0.0856750	−	0.430717i
$463$	88.6506	+	88.6506i	0.191470	+	0.191470i	0.796331	−	0.604861i	$-0.206771\pi$
$463$	88.6506	+	88.6506i	0.191470	+	0.191470i	−0.604861	+	0.796331i	$0.706771\pi$
$464$	−116.711	−	77.9840i	−0.251533	−	0.168069i
$465$	231.127	−	1161.95i	0.497046	−	2.49882i
$466$	88.2815	−	58.9878i	0.189445	−	0.126583i
$467$	−265.152	−	640.133i	−0.567777	−	1.37074i	−0.903424	−	0.428748i	$-0.858955\pi$
$467$	−265.152	−	640.133i	−0.567777	−	1.37074i	0.335647	−	0.941988i	$-0.391045\pi$
$468$	20.2167	−	8.37404i	0.0431981	−	0.0178932i
$469$	64.9879	+	97.2612i	0.138567	+	0.207380i
$470$	60.0158	+	11.9379i	0.127693	+	0.0253998i
$471$	−604.607	+	904.858i	−1.28367	+	1.92114i
$472$	71.6013	−	71.6013i	0.151698	−	0.151698i
$473$	−23.6889	+	4.71202i	−0.0500823	+	0.00996199i
$474$	58.6768	−	141.658i	0.123791	−	0.298857i
$475$		−	859.730i		−	1.80996i
$476$		0			0
$477$	−226.701			−0.475264
$478$	−466.332	−	193.161i	−0.975591	−	0.404103i
$479$	−93.3885	−	469.496i	−0.194965	−	0.980158i	−0.947049	−	0.321090i	$-0.895951\pi$
$479$	−93.3885	−	469.496i	−0.194965	−	0.980158i	0.752083	−	0.659068i	$-0.229049\pi$
$480$	306.804	+	306.804i	0.639175	+	0.639175i
$481$	90.0847	+	60.1927i	0.187286	+	0.125141i
$482$	42.8219	−	215.280i	0.0888421	−	0.446639i
$483$	−158.626	+	105.991i	−0.328418	+	0.219442i
$484$	24.6268	+	59.4543i	0.0508818	+	0.122840i
$485$	−1189.21	+	492.586i	−2.45197	+	1.01564i
$486$	311.039	+	465.503i	0.639998	+	0.957825i
$487$	397.869	+	79.1411i	0.816980	+	0.162507i	0.585854	−	0.810417i	$-0.300759\pi$
$487$	397.869	+	79.1411i	0.816980	+	0.162507i	0.231126	+	0.972924i	$0.425759\pi$
$488$	339.443	−	508.012i	0.695579	−	1.04101i
$489$	111.033	−	111.033i	0.227062	−	0.227062i
$490$	−432.141	+	85.9581i	−0.881919	+	0.175425i
$491$	23.7416	−	57.3172i	0.0483535	−	0.116736i	−0.897857	−	0.440287i	$-0.854877\pi$
$491$	23.7416	−	57.3172i	0.0483535	−	0.116736i	0.946211	+	0.323551i	$0.104877\pi$
$492$		−	120.889i		−	0.245710i
$493$		0			0
$494$	−146.094			−0.295736
$495$	−365.996	−	151.601i	−0.739386	−	0.306264i
$496$	−86.2458	−	433.587i	−0.173883	−	0.874167i
$497$	99.4445	+	99.4445i	0.200089	+	0.200089i
$498$	674.481	+	450.674i	1.35438	+	0.904967i
$499$	100.128	−	503.379i	0.200658	−	1.00878i	−0.740821	−	0.671703i	$-0.765563\pi$
$499$	100.128	−	503.379i	0.200658	−	1.00878i	0.941479	−	0.337073i	$-0.109437\pi$
$500$	56.1690	−	37.5309i	0.112338	−	0.0750618i
$501$	−55.7947	−	134.700i	−0.111367	−	0.268863i
$502$	−229.906	+	95.2302i	−0.457980	+	0.189702i
$503$	183.828	+	275.118i	0.365463	+	0.546954i	0.967940	−	0.251182i	$-0.0808194\pi$
$503$	183.828	+	275.118i	0.365463	+	0.546954i	−0.602477	+	0.798136i	$0.705819\pi$
$504$	255.258	+	50.7740i	0.506465	+	0.100742i
$505$	535.003	−	800.689i	1.05941	−	1.58552i
$506$	99.7945	−	99.7945i	0.197222	−	0.197222i
$507$	626.030	−	124.525i	1.23477	−	0.245612i
$508$	13.8861	−	33.5240i	0.0273349	−	0.0659922i
$509$		−	343.247i		−	0.674355i	−0.941441	−	0.337178i	$-0.890528\pi$
$509$		−	343.247i		−	0.674355i	0.941441	−	0.337178i	$-0.109472\pi$
$510$		0			0
$511$	383.347			0.750190
$512$	521.878	+	216.169i	1.01929	+	0.422205i
$513$	31.5841	+	158.784i	0.0615674	+	0.309520i
$514$	−490.601	−	490.601i	−0.954476	−	0.954476i
$515$	1126.52	+	752.715i	2.18741	+	1.46158i
$516$	2.42760	−	12.2044i	0.00470466	−	0.0236519i
$517$	25.8464	−	17.2700i	0.0499930	−	0.0334043i
$518$	89.2118	+	215.376i	0.172224	+	0.415784i
$519$	721.645	−	298.915i	1.39045	−	0.575944i
$520$	−124.444	−	186.243i	−0.239315	−	0.358160i
$521$	312.376	+	62.1355i	0.599570	+	0.119262i	0.485539	−	0.874215i	$-0.338623\pi$
$521$	312.376	+	62.1355i	0.599570	+	0.119262i	0.114032	+	0.993477i	$0.463623\pi$
$522$	−86.9092	+	130.069i	−0.166493	+	0.249174i
$523$	−167.575	+	167.575i	−0.320410	+	0.320410i	−0.848924	−	0.528514i	$-0.822749\pi$
$523$	−167.575	+	167.575i	−0.320410	+	0.320410i	0.528514	+	0.848924i	$0.322749\pi$
$524$	−166.788	+	33.1762i	−0.318298	+	0.0633133i
$525$	221.062	−	533.691i	0.421071	−	1.01655i
$526$			514.556i			0.978244i
$527$		0			0
$528$	−328.176			−0.621545
$529$	366.128	+	151.655i	0.692114	+	0.286683i
$530$	81.9022	+	411.750i	0.154532	+	0.776887i
$531$	−61.2676	−	61.2676i	−0.115381	−	0.115381i
$532$	74.0938	+	49.5079i	0.139274	+	0.0930600i
$533$	−22.1481	+	111.346i	−0.0415537	+	0.208904i
$534$	−237.938	+	158.985i	−0.445577	+	0.297725i
$535$	−118.057	−	285.015i	−0.220667	−	0.532738i
$536$	227.670	−	94.3039i	0.424757	−	0.175940i
$537$	544.985	+	815.628i	1.01487	+	1.51886i
$538$	176.421	+	35.0922i	0.327919	+	0.0652272i
$539$	−124.352	+	186.106i	−0.230708	+	0.345279i
$540$	−31.7532	+	31.7532i	−0.0588023	+	0.0588023i
$541$	259.826	−	51.6826i	0.480270	−	0.0955316i	0.0509824	−	0.998700i	$-0.483765\pi$
$541$	259.826	−	51.6826i	0.480270	−	0.0955316i	0.429287	+	0.903168i	$0.358765\pi$
$542$	257.435	−	621.502i	0.474972	−	1.14668i
$543$			552.466i			1.01743i
$544$		0			0
$545$	354.627			0.650692
$546$	−90.6899	−	37.5650i	−0.166099	−	0.0688003i
$547$	−70.3869	−	353.859i	−0.128678	−	0.646909i	−0.990253	−	0.139278i	$-0.955522\pi$
$547$	−70.3869	−	353.859i	−0.128678	−	0.646909i	0.861575	−	0.507630i	$-0.169478\pi$
$548$	−33.0075	−	33.0075i	−0.0602326	−	0.0602326i
$549$	−434.694	−	290.453i	−0.791792	−	0.529058i
$550$	−83.3688	+	419.123i	−0.151580	+	0.762043i
$551$	−246.170	+	164.486i	−0.446770	+	0.298522i
$552$	153.803	+	371.313i	0.278629	+	0.672669i
$553$	81.1445	−	33.6111i	0.146735	−	0.0607797i
$554$	65.9245	+	98.6630i	0.118997	+	0.178092i
$555$	991.094	+	197.141i	1.78576	+	0.355209i
$556$	25.7570	−	38.5481i	0.0463256	−	0.0693312i
$557$	−367.145	+	367.145i	−0.659147	+	0.659147i	−0.955178	−	0.296031i	$-0.904337\pi$
$557$	−367.145	+	367.145i	−0.659147	+	0.659147i	0.296031	+	0.955178i	$0.404337\pi$
$558$	−483.210	+	96.1164i	−0.865968	+	0.172252i
$559$	−4.47192	+	10.7962i	−0.00799986	+	0.0193134i
$560$		−	370.051i		−	0.660806i
$561$		0			0
$562$	665.645			1.18442
$563$	−406.232	−	168.267i	−0.721549	−	0.298875i	−0.00847487	−	0.999964i	$-0.502698\pi$
$563$	−406.232	−	168.267i	−0.721549	−	0.298875i	−0.713074	+	0.701089i	$0.752698\pi$
$564$	3.12435	+	15.7072i	0.00553963	+	0.0278496i
$565$	−1024.55	−	1024.55i	−1.81336	−	1.81336i
$566$	435.699	+	291.125i	0.769786	+	0.514355i
$567$	−74.2271	+	373.165i	−0.130912	+	0.658139i
$568$	246.342	−	164.601i	0.433701	−	0.289790i
$569$	183.595	+	443.238i	0.322663	+	0.778977i	0.999098	+	0.0424747i	$0.0135242\pi$
$569$	183.595	+	443.238i	0.322663	+	0.778977i	−0.676435	+	0.736503i	$0.736476\pi$
$570$	−1258.87	+	521.443i	−2.20855	+	0.914812i
$571$	302.327	+	452.464i	0.529469	+	0.792406i	0.995737	−	0.0922371i	$-0.0294018\pi$
$571$	302.327	+	452.464i	0.529469	+	0.792406i	−0.466268	+	0.884643i	$0.654402\pi$
$572$	−20.1901	−	4.01605i	−0.0352973	−	0.00702107i
$573$	391.863	−	586.464i	0.683879	−	1.02350i
$574$	−172.728	+	172.728i	−0.300920	+	0.300920i
$575$	394.103	−	78.3920i	0.685397	−	0.136334i
$576$	201.004	−	485.266i	0.348965	−	0.842476i
$577$			304.419i			0.527589i	0.964579	+	0.263795i	$0.0849741\pi$
$577$			304.419i			0.527589i	−0.964579	+	0.263795i	$0.915026\pi$
$578$		0			0
$579$	−759.470			−1.31169
$580$	−75.8709	−	31.4267i	−0.130812	−	0.0541840i
$581$	90.6517	+	455.737i	0.156027	+	0.784400i
$582$	840.297	+	840.297i	1.44381	+	1.44381i
$583$	177.324	+	118.484i	0.304158	+	0.203232i
$584$	157.552	−	792.068i	0.269781	−	1.35628i
$585$	−159.364	+	106.484i	−0.272417	+	0.182023i
$586$	95.3950	+	230.304i	0.162790	+	0.393010i
$587$	589.834	−	244.317i	1.00483	−	0.416213i	0.181263	−	0.983435i	$-0.441982\pi$
$587$	589.834	−	244.317i	1.00483	−	0.416213i	0.823565	+	0.567221i	$0.191982\pi$
$588$	−64.0652	−	95.8804i	−0.108954	−	0.163062i
$589$	−914.531	−	181.911i	−1.55268	−	0.308848i
$590$	−89.1437	+	133.413i	−0.151091	+	0.226124i
$591$	821.644	−	821.644i	1.39026	−	1.39026i
$592$	369.831	−	73.5639i	0.624714	−	0.124263i
$593$	−246.104	+	594.149i	−0.415016	+	1.00194i	0.568755	+	0.822507i	$0.307425\pi$
$593$	−246.104	+	594.149i	−0.415016	+	1.00194i	−0.983771	+	0.179430i	$0.942575\pi$
$594$		−	80.4708i		−	0.135473i
$595$		0			0
$596$	−45.7258			−0.0767211
$597$	342.460	+	141.852i	0.573636	+	0.237608i
$598$	−13.3211	−	66.9697i	−0.0222761	−	0.111990i
$599$	354.327	+	354.327i	0.591530	+	0.591530i	0.938045	−	0.346514i	$-0.112635\pi$
$599$	354.327	+	354.327i	0.591530	+	0.591530i	−0.346514	+	0.938045i	$0.612635\pi$
$600$	−1011.85	−	676.099i	−1.68642	−	1.12683i
$601$	−111.153	+	558.804i	−0.184947	+	0.929791i	0.771131	+	0.636677i	$0.219691\pi$
$601$	−111.153	+	558.804i	−0.184947	+	0.929791i	−0.956078	+	0.293114i	$0.905309\pi$
$602$	−20.9064	+	13.9692i	−0.0347282	+	0.0232046i
$603$	−80.6936	−	194.812i	−0.133820	−	0.323071i
$604$	−196.157	+	81.2510i	−0.324764	+	0.134521i
$605$	−313.152	−	468.666i	−0.517607	−	0.774654i
$606$	−871.961	−	173.444i	−1.43888	−	0.286211i
$607$	100.769	−	150.811i	0.166011	−	0.248454i	−0.739131	−	0.673561i	$-0.764764\pi$
$607$	100.769	−	150.811i	0.166011	−	0.248454i	0.905143	+	0.425108i	$0.139764\pi$
$608$	241.474	−	241.474i	0.397162	−	0.397162i
$609$	−195.108	+	38.8094i	−0.320375	+	0.0637265i
$610$	−370.495	+	894.455i	−0.607370	+	1.46632i
$611$		−	15.0396i		−	0.0246147i
$612$		0			0
$613$	−155.196			−0.253174			−0.126587	−	0.991956i	$-0.540402\pi$
$613$	−155.196			−0.253174			−0.126587	+	0.991956i	$0.540402\pi$
$614$	−423.470	−	175.407i	−0.689691	−	0.285679i
$615$	206.573	+	1038.51i	0.335890	+	1.68863i
$616$	−173.125	−	173.125i	−0.281047	−	0.281047i
$617$	−388.627	−	259.673i	−0.629866	−	0.420863i	0.199243	−	0.979950i	$-0.436152\pi$
$617$	−388.627	−	259.673i	−0.629866	−	0.420863i	−0.829109	+	0.559087i	$0.811152\pi$
$618$	244.024	−	1226.79i	0.394861	−	1.98510i
$619$	−319.014	+	213.158i	−0.515370	+	0.344359i	−0.785901	−	0.618352i	$-0.787801\pi$
$619$	−319.014	+	213.158i	−0.515370	+	0.344359i	0.270531	+	0.962711i	$0.412801\pi$
$620$	−98.9771	−	238.952i	−0.159640	−	0.385406i
$621$	−69.9071	+	28.9565i	−0.112572	+	0.0466288i
$622$	−553.288	−	828.054i	−0.889531	−	1.33128i
$623$	−160.771	−	31.9794i	−0.258060	−	0.0513313i
$624$	−88.2122	+	132.019i	−0.141366	+	0.211569i
$625$	198.226	−	198.226i	0.317161	−	0.317161i
$626$	789.123	−	156.966i	1.26058	−	0.250745i
$627$	−264.892	+	639.506i	−0.422475	+	1.01995i
$628$			237.583i			0.378316i
$629$		0			0
$630$	−412.403			−0.654608
$631$	308.547	+	127.804i	0.488980	+	0.202542i	0.613531	−	0.789671i	$-0.289749\pi$
$631$	308.547	+	127.804i	0.488980	+	0.202542i	−0.124550	+	0.992213i	$0.539749\pi$
$632$	−36.0974	−	181.474i	−0.0571162	−	0.287142i
$633$	103.471	+	103.471i	0.163462	+	0.163462i
$634$	−487.236	−	325.560i	−0.768511	−	0.513502i
$635$	−62.0048	+	311.719i	−0.0976453	+	0.490896i
$636$	−91.3563	+	61.0423i	−0.143642	+	0.0959785i
$637$	41.4415	+	100.049i	0.0650573	+	0.157062i
$638$	135.960	−	56.3163i	0.213103	−	0.0882701i
$639$	−140.845	−	210.789i	−0.220414	−	0.329873i
$640$	−533.369	−	106.094i	−0.833389	−	0.165771i
$641$	−533.705	+	798.746i	−0.832613	+	1.24609i	0.134289	+	0.990942i	$0.457125\pi$
$641$	−533.705	+	798.746i	−0.832613	+	1.24609i	−0.966901	+	0.255151i	$0.917875\pi$
$642$	−201.392	+	201.392i	−0.313695	+	0.313695i
$643$	−1027.11	+	204.305i	−1.59737	+	0.317737i	−0.911917	−	0.410376i	$-0.865398\pi$
$643$	−1027.11	+	204.305i	−1.59737	+	0.317737i	−0.685457	+	0.728113i	$0.740398\pi$
$644$	−15.9385	+	38.4791i	−0.0247493	+	0.0597501i
$645$			108.991i			0.168978i
$646$		0			0
$647$	328.253			0.507346			0.253673	−	0.967290i	$-0.418361\pi$
$647$	328.253			0.507346			0.253673	+	0.967290i	$0.418361\pi$
$648$	740.523	+	306.735i	1.14278	+	0.473356i
$649$	15.9019	+	79.9443i	0.0245022	+	0.123181i
$650$	146.196	+	146.196i	0.224917	+	0.224917i
$651$	−520.934	−	348.077i	−0.800206	−	0.534681i
$652$	6.68782	−	33.6220i	0.0102574	−	0.0515674i
$653$	41.4569	−	27.7006i	0.0634869	−	0.0424206i	−0.523422	−	0.852074i	$-0.675345\pi$
$653$	41.4569	−	27.7006i	0.0634869	−	0.0424206i	0.586909	+	0.809653i	$0.300345\pi$
$654$	−125.290	−	302.477i	−0.191575	−	0.462504i
$655$	1376.11	−	570.005i	2.10094	−	0.870237i
$656$	219.515	+	328.527i	0.334626	+	0.500804i
$657$	−677.754	−	134.814i	−1.03159	−	0.205196i
$658$	17.9785	−	26.9067i	0.0273229	−	0.0408917i
$659$	61.2456	−	61.2456i	0.0929371	−	0.0929371i	−0.659110	−	0.752047i	$-0.729067\pi$
$659$	61.2456	−	61.2456i	0.0929371	−	0.0929371i	0.752047	+	0.659110i	$0.229067\pi$
$660$	−188.310	+	37.4572i	−0.285318	+	0.0567533i
$661$	314.044	−	758.170i	0.475105	−	1.14700i	−0.486774	−	0.873528i	$-0.661827\pi$
$661$	314.044	−	758.170i	0.475105	−	1.14700i	0.961879	−	0.273476i	$-0.0881734\pi$
$662$		−	1040.69i		−	1.57205i
$663$		0			0
$664$	978.896			1.47424
$665$	−721.107	−	298.692i	−1.08437	−	0.449161i
$666$	−81.9831	−	412.157i	−0.123098	−	0.618854i
$667$	−97.8470	−	97.8470i	−0.146697	−	0.146697i
$668$	−26.4655	−	17.6837i	−0.0396190	−	0.0264726i
$669$	−318.248	+	1599.94i	−0.475707	+	2.39154i
$670$	−324.677	+	216.942i	−0.484593	+	0.323795i
$671$	188.211	+	454.381i	0.280493	+	0.677170i
$672$	211.989	−	87.8088i	0.315460	−	0.130668i
$673$	−305.467	−	457.164i	−0.453889	−	0.679293i	0.531990	−	0.846751i	$-0.321444\pi$
$673$	−305.467	−	457.164i	−0.453889	−	0.679293i	−0.985879	+	0.167457i	$0.946444\pi$
$674$	567.203	+	112.824i	0.841548	+	0.167394i
$675$	127.289	−	190.502i	0.188576	−	0.282225i
$676$	98.5342	−	98.5342i	0.145761	−	0.145761i
$677$	−531.400	+	105.702i	−0.784933	+	0.156133i	−0.571257	−	0.820772i	$-0.693544\pi$
$677$	−531.400	+	105.702i	−0.784933	+	0.156133i	−0.213677	+	0.976904i	$0.568544\pi$
$678$	−511.910	+	1235.86i	−0.755030	+	1.82280i
$679$			680.714i			1.00252i
$680$		0			0
$681$	510.884			0.750197
$682$	428.199	+	177.366i	0.627857	+	0.260067i
$683$	−77.2580	−	388.402i	−0.113116	−	0.568671i	−0.995223	−	0.0976233i	$-0.968876\pi$
$683$	−77.2580	−	388.402i	−0.113116	−	0.568671i	0.882108	−	0.471048i	$-0.156124\pi$
$684$	−113.587	−	113.587i	−0.166062	−	0.166062i
$685$	339.956	+	227.151i	0.496285	+	0.331607i
$686$	−114.519	+	575.727i	−0.166938	+	0.839252i
$687$	413.677	−	276.410i	0.602150	−	0.402344i
$688$	15.5639	+	37.5745i	0.0226219	+	0.0546142i
$689$	95.3279	−	39.4861i	0.138357	−	0.0573093i
$690$	−353.818	−	529.526i	−0.512779	−	0.767429i
$691$	915.708	+	182.146i	1.32519	+	0.263597i	0.806434	−	0.591324i	$-0.201395\pi$
$691$	915.708	+	182.146i	1.32519	+	0.263597i	0.518758	+	0.854921i	$0.326395\pi$
$692$	94.7388	−	141.787i	0.136906	−	0.204894i
$693$	−148.139	+	148.139i	−0.213764	+	0.213764i
$694$	−419.120	+	83.3681i	−0.603919	+	0.120127i
$695$	−155.398	+	375.164i	−0.223594	+	0.539804i
$696$			419.081i			0.602128i
$697$		0			0
$698$	−887.929			−1.27210
$699$	−224.864	−	93.1416i	−0.321693	−	0.133250i
$700$	−24.6032	−	123.689i	−0.0351474	−	0.176698i
$701$	−411.177	−	411.177i	−0.586558	−	0.586558i	0.350140	−	0.936697i	$-0.386134\pi$
$701$	−411.177	−	411.177i	−0.586558	−	0.586558i	−0.936697	+	0.350140i	$0.886134\pi$
$702$	−32.3718	−	21.6302i	−0.0461137	−	0.0308122i
$703$	155.163	−	780.055i	0.220715	−	1.10961i
$704$	−410.846	+	274.519i	−0.583588	+	0.389941i
$705$	−53.6800	−	129.595i	−0.0761418	−	0.183823i
$706$	−533.494	+	220.980i	−0.755657	+	0.313003i
$707$	−282.930	−	423.435i	−0.400184	−	0.598918i
$708$	−41.1868	−	8.19257i	−0.0581735	−	0.0115714i
$709$	646.261	−	967.198i	0.911511	−	1.36417i	−0.0197449	−	0.999805i	$-0.506285\pi$
$709$	646.261	−	967.198i	0.911511	−	1.36417i	0.931255	−	0.364367i	$-0.118715\pi$
$710$	−331.966	+	331.966i	−0.467557	+	0.467557i
$711$	−155.283	+	30.8877i	−0.218401	+	0.0434426i
$712$	−132.151	+	319.041i	−0.185605	+	0.448091i
$713$		−	435.811i		−	0.611235i
$714$		0			0
$715$	180.307			0.252177
$716$	197.853	+	81.9532i	0.276330	+	0.114460i
$717$	225.734	+	1134.84i	0.314831	+	1.58276i
$718$	663.338	+	663.338i	0.923869	+	0.923869i
$719$	12.3456	+	8.24905i	0.0171705	+	0.0114729i	0.564126	−	0.825689i	$-0.309213\pi$
$719$	12.3456	+	8.24905i	0.0171705	+	0.0114729i	−0.546955	+	0.837162i	$0.684213\pi$
$720$	−130.138	+	654.247i	−0.180747	+	0.908677i
$721$	595.745	−	398.064i	0.826276	−	0.552100i
$722$	166.526	+	402.030i	0.230646	+	0.556828i
$723$	−464.864	+	192.553i	−0.642966	+	0.266325i
$724$	67.0078	+	100.284i	0.0925522	+	0.138514i
$725$	410.944	+	81.7419i	0.566820	+	0.112747i
$726$	−289.109	+	432.682i	−0.398222	+	0.595981i
$727$	−880.136	+	880.136i	−1.21064	+	1.21064i	−0.239825	+	0.970816i	$0.577090\pi$
$727$	−880.136	+	880.136i	−1.21064	+	1.21064i	−0.970816	+	0.239825i	$0.922910\pi$
$728$	−116.180	+	23.1096i	−0.159588	+	0.0317440i
$729$	170.915	−	412.626i	0.234452	−	0.566017i
$730$			1279.69i			1.75300i
$731$		0			0
$732$	−253.382			−0.346150
$733$	−503.915	−	208.728i	−0.687469	−	0.284759i	0.0114762	−	0.999934i	$-0.496347\pi$
$733$	−503.915	−	208.728i	−0.687469	−	0.284759i	−0.698945	+	0.715175i	$0.746347\pi$
$734$	−114.016	−	573.199i	−0.155336	−	0.780925i
$735$	714.195	+	714.195i	0.971694	+	0.971694i
$736$	132.711	+	88.6744i	0.180313	+	0.120482i
$737$	−38.6993	+	194.555i	−0.0525092	+	0.263982i
$738$	366.126	−	244.638i	0.496106	−	0.331488i
$739$	63.1371	+	152.427i	0.0854359	+	0.206261i	0.960823	−	0.277161i	$-0.0893937\pi$
$739$	63.1371	+	152.427i	0.0854359	+	0.206261i	−0.875387	+	0.483422i	$0.839394\pi$
$740$	203.815	−	84.4231i	0.275426	−	0.114085i
$741$	186.059	+	278.457i	0.251092	+	0.375786i
$742$	217.749	+	43.3130i	0.293462	+	0.0583733i
$743$	1.28081	−	1.91687i	0.00172384	−	0.00257991i	−0.830607	−	0.556860i	$-0.812006\pi$
$743$	1.28081	−	1.91687i	0.00172384	−	0.00257991i	0.832331	+	0.554280i	$0.187006\pi$
$744$	−933.294	+	933.294i	−1.25443	+	1.25443i
$745$	392.811	−	78.1349i	0.527263	−	0.104879i
$746$	99.8879	−	241.151i	0.133898	−	0.323258i
$747$		−	837.618i		−	1.12131i
$748$		0			0
$749$	−163.145			−0.217817
$750$	504.684	+	209.047i	0.672912	+	0.278729i
$751$	281.416	+	1414.78i	0.374722	+	1.88386i	0.460695	+	0.887559i	$0.347600\pi$
$751$	281.416	+	1414.78i	0.374722	+	1.88386i	−0.0859723	+	0.996298i	$0.527400\pi$
$752$	−37.0123	−	37.0123i	−0.0492184	−	0.0492184i
$753$	474.310	+	316.924i	0.629894	+	0.420881i
$754$	13.8904	−	69.8315i	0.0184222	−	0.0926148i
$755$	1546.26	−	1033.18i	2.04803	−	1.36845i
$756$	9.08793	+	21.9402i	0.0120211	+	0.0290214i
$757$	278.634	−	115.414i	0.368077	−	0.152463i	−0.190975	−	0.981595i	$-0.561165\pi$
$757$	278.634	−	115.414i	0.368077	−	0.152463i	0.559052	+	0.829132i	$0.311165\pi$
$758$	−42.8446	−	64.1215i	−0.0565233	−	0.0845931i
$759$	−317.305	−	63.1158i	−0.418056	−	0.0831566i
$760$	−913.524	+	1367.18i	−1.20200	+	1.79893i
$761$	−811.549	+	811.549i	−1.06642	+	1.06642i	−0.0687929	+	0.997631i	$0.521915\pi$
$761$	−811.549	+	811.549i	−1.06642	+	1.06642i	−0.997631	+	0.0687929i	$0.978085\pi$
$762$	287.786	−	57.2441i	0.377671	−	0.0751235i
$763$	71.7685	−	173.265i	0.0940610	−	0.227083i
$764$		−	153.984i		−	0.201550i
$765$		0			0
$766$	−348.859			−0.455429
$767$	36.4344	+	15.0916i	0.0475025	+	0.0196762i
$768$	−126.907	−	638.005i	−0.165244	−	0.830736i
$769$	870.130	+	870.130i	1.13151	+	1.13151i	0.989927	+	0.141582i	$0.0452189\pi$
$769$	870.130	+	870.130i	1.13151	+	1.13151i	0.141582	+	0.989927i	$0.454781\pi$
$770$	322.579	+	215.540i	0.418934	+	0.279923i
$771$	−310.284	+	1559.90i	−0.402444	+	2.02322i
$772$	−137.860	+	92.1150i	−0.178575	+	0.119320i
$773$	−541.282	−	1306.77i	−0.700235	−	1.69052i	−0.723066	−	0.690779i	$-0.757268\pi$
$773$	−541.282	−	1306.77i	−0.700235	−	1.69052i	0.0228308	−	0.999739i	$-0.492732\pi$
$774$	41.8749	−	17.3451i	0.0541019	−	0.0224098i
$775$	733.134	+	1097.21i	0.945979	+	1.41576i
$776$	1406.49	+	279.767i	1.81248	+	0.360525i
$777$	296.895	−	444.334i	0.382104	−	0.571859i
$778$	−26.8308	+	26.8308i	−0.0344869	+	0.0344869i
$779$	817.375	−	162.586i	1.04926	−	0.208711i
$780$	−35.5486	+	85.8218i	−0.0455751	+	0.110028i
$781$			238.490i			0.305365i
$782$		0			0
$783$	−78.9004			−0.100767
$784$	348.205	+	144.231i	0.444139	+	0.183969i
$785$	−405.975	−	2040.97i	−0.517165	−	2.59997i
$786$	−972.366	−	972.366i	−1.23711	−	1.23711i
$787$	−1282.76	−	857.112i	−1.62994	−	1.08909i	−0.925104	−	0.379713i	$-0.876023\pi$
$787$	−1282.76	−	857.112i	−1.62994	−	1.08909i	−0.704831	−	0.709375i	$-0.748977\pi$
$788$	49.4897	−	248.802i	0.0628042	−	0.315738i
$789$	980.754	−	655.319i	1.24303	−	0.830569i
$790$	112.201	+	270.877i	0.142026	+	0.342882i
$791$	−707.924	+	293.232i	−0.894973	+	0.370710i
$792$	245.199	+	366.967i	0.309595	+	0.463342i
$793$	233.379	+	46.4220i	0.294299	+	0.0585397i
$794$	34.7954	−	52.0749i	0.0438229	−	0.0655856i
$795$	680.496	−	680.496i	0.855970	−	0.855970i
$796$	79.3688	−	15.7874i	0.0997095	−	0.0198335i
$797$	430.853	−	1040.17i	0.540593	−	1.30511i	−0.383712	−	0.923453i	$-0.625355\pi$
$797$	430.853	−	1040.17i	0.540593	−	1.30511i	0.924305	−	0.381654i	$-0.124645\pi$
$798$			720.593i			0.902998i
$799$		0			0
$800$	−483.288			−0.604110
$801$	272.996	+	113.079i	0.340819	+	0.141172i
$802$	−51.5110	−	258.963i	−0.0642281	−	0.322897i
$803$	459.675	+	459.675i	0.572448	+	0.572448i
$804$	−84.9737	−	56.7776i	−0.105689	−	0.0706189i
$805$	71.1694	−	357.793i	0.0884092	−	0.444463i
$806$	186.449	−	124.581i	0.231326	−	0.154567i
$807$	−157.796	−	380.953i	−0.195534	−	0.472061i
$808$	−991.179	+	410.560i	−1.22671	+	0.508119i
$809$	−182.579	−	273.249i	−0.225685	−	0.337761i	0.701296	−	0.712870i	$-0.252605\pi$
$809$	−182.579	−	273.249i	−0.225685	−	0.337761i	−0.926981	+	0.375109i	$0.877605\pi$
$810$	−1245.70	−	247.785i	−1.53790	−	0.305907i
$811$	−162.131	+	242.645i	−0.199914	+	0.299193i	−0.917859	−	0.396908i	$-0.870083\pi$
$811$	−162.131	+	242.645i	−0.199914	+	0.299193i	0.717944	+	0.696101i	$0.245083\pi$
$812$	−30.7091	+	30.7091i	−0.0378191	+	0.0378191i
$813$	−1512.45	+	300.846i	−1.86034	+	0.370044i
$814$	−151.285	+	365.235i	−0.185854	+	0.448692i
$815$			300.260i			0.368417i
$816$		0			0
$817$	85.7829			0.104997
$818$	−650.588	−	269.482i	−0.795340	−	0.329441i
$819$	19.7743	+	99.4124i	0.0241445	+	0.121383i
$820$	163.457	+	163.457i	0.199337	+	0.199337i
$821$	898.276	+	600.209i	1.09412	+	0.731070i	0.965443	−	0.260616i	$-0.0839256\pi$
$821$	898.276	+	600.209i	1.09412	+	0.731070i	0.128681	+	0.991686i	$0.458926\pi$
$822$	73.6406	−	370.216i	0.0895871	−	0.450385i
$823$	−75.4620	+	50.4221i	−0.0916914	+	0.0612662i	−0.600571	−	0.799572i	$-0.705060\pi$
$823$	−75.4620	+	50.4221i	−0.0916914	+	0.0612662i	0.508879	+	0.860838i	$0.330060\pi$
$824$	−577.631	−	1394.52i	−0.701008	−	1.69238i
$825$	905.033	−	374.877i	1.09701	−	0.454396i
$826$	47.1426	+	70.5539i	0.0570733	+	0.0854163i
$827$	−476.748	−	94.8310i	−0.576479	−	0.114669i	−0.101764	−	0.994809i	$-0.532449\pi$
$827$	−476.748	−	94.8310i	−0.576479	−	0.114669i	−0.474715	+	0.880140i	$0.657449\pi$
$828$	41.7114	−	62.4255i	0.0503760	−	0.0753931i
$829$	743.445	−	743.445i	0.896797	−	0.896797i	−0.0983544	−	0.995151i	$-0.531358\pi$
$829$	743.445	−	743.445i	0.896797	−	0.896797i	0.995151	+	0.0983544i	$0.0313579\pi$
$830$	−1521.34	+	302.613i	−1.83294	+	0.364594i
$831$	104.095	−	251.307i	0.125264	−	0.302415i
$832$			239.065i			0.287338i
$833$		0			0
$834$	374.896			0.449516
$835$	257.571	+	106.690i	0.308469	+	0.127772i
$836$	29.4812	+	148.212i	0.0352646	+	0.177287i
$837$	−175.711	−	175.711i	−0.209930	−	0.209930i
$838$	54.8971	+	36.6811i	0.0655097	+	0.0437722i
$839$	89.4817	−	449.855i	0.106653	−	0.536180i	−0.890108	−	0.455751i	$-0.849371\pi$
$839$	89.4817	−	449.855i	0.106653	−	0.536180i	0.996760	−	0.0804292i	$-0.0256291\pi$
$840$	−918.627	+	613.807i	−1.09360	+	0.730723i
$841$	266.619	+	643.676i	0.317027	+	0.765370i
$842$	721.276	−	298.762i	0.856622	−	0.354824i
$843$	−847.739	−	1268.73i	−1.00562	−	1.50502i
$844$	31.3321	+	6.23235i	0.0371234	+	0.00738430i
$845$	−678.093	+	1014.84i	−0.802477	+	1.20099i
$846$	−41.2482	+	41.2482i	−0.0487568	+	0.0487568i
$847$	−292.357	+	58.1534i	−0.345167	+	0.0686581i
$848$	137.426	−	331.775i	0.162059	−	0.391244i
$849$		−	1201.22i		−	1.41486i
$850$		0			0
$851$	371.728			0.436813
$852$	−113.516	−	47.0197i	−0.133234	−	0.0551875i
$853$	−1.46888	−	7.38457i	−0.00172202	−	0.00865717i	0.979915	−	0.199417i	$-0.0639048\pi$
$853$	−1.46888	−	7.38457i	−0.00172202	−	0.00865717i	−0.981637	+	0.190760i	$0.938905\pi$
$854$	362.035	+	362.035i	0.423929	+	0.423929i
$855$	1169.87	+	781.680i	1.36827	+	0.914246i
$856$	−67.0512	+	337.089i	−0.0783309	+	0.393796i
$857$	42.1566	−	28.1682i	0.0491910	−	0.0328683i	−0.530732	−	0.847540i	$-0.678083\pi$
$857$	42.1566	−	28.1682i	0.0491910	−	0.0328683i	0.579923	+	0.814672i	$0.303083\pi$
$858$	−63.7026	−	153.792i	−0.0742455	−	0.179244i
$859$	464.849	−	192.547i	0.541151	−	0.224152i	−0.0953281	−	0.995446i	$-0.530390\pi$
$859$	464.849	−	192.547i	0.541151	−	0.224152i	0.636479	+	0.771294i	$0.280390\pi$
$860$	13.2194	+	19.7842i	0.0153713	+	0.0230048i
$861$	549.204	+	109.243i	0.637867	+	0.126880i
$862$	340.230	−	509.190i	0.394698	−	0.590708i
$863$	−98.9573	+	98.9573i	−0.114667	+	0.114667i	−0.762112	−	0.647445i	$-0.775837\pi$
$863$	−98.9573	+	98.9573i	−0.114667	+	0.114667i	0.647445	+	0.762112i	$0.275837\pi$
$864$	89.2585	−	17.7546i	0.103309	−	0.0205493i
$865$	−571.580	+	1379.92i	−0.660786	+	1.59528i
$866$			94.8830i			0.109565i
$867$		0			0
$868$	−136.778			−0.157579
$869$	137.605	+	56.9977i	0.158348	+	0.0655900i
$870$	−129.554	−	651.310i	−0.148912	−	0.748632i
$871$	67.8634	+	67.8634i	0.0779143	+	0.0779143i
$872$	−328.502	−	219.498i	−0.376722	−	0.251718i
$873$	239.390	−	1203.50i	0.274216	−	1.37858i
$874$	−416.771	+	278.477i	−0.476855	+	0.318624i
$875$	119.746	+	289.092i	0.136853	+	0.330391i
$876$	−309.423	+	128.167i	−0.353222	+	0.146309i
$877$	527.563	+	789.554i	0.601554	+	0.900289i	0.999856	−	0.0169652i	$-0.00540045\pi$
$877$	527.563	+	789.554i	0.601554	+	0.900289i	−0.398302	+	0.917254i	$0.630400\pi$
$878$	421.187	+	83.7792i	0.479711	+	0.0954205i
$879$	317.472	−	475.131i	0.361174	−	0.540536i
$880$	443.732	−	443.732i	0.504241	−	0.504241i
$881$	1026.00	−	204.085i	1.16459	−	0.231651i	0.425308	−	0.905049i	$-0.360166\pi$
$881$	1026.00	−	204.085i	1.16459	−	0.231651i	0.739280	+	0.673398i	$0.235166\pi$
$882$	160.738	−	388.057i	0.182243	−	0.439974i
$883$		−	1264.99i		−	1.43261i	−0.697789	−	0.716303i	$-0.745833\pi$
$883$		−	1264.99i		−	1.43261i	0.697789	−	0.716303i	$-0.254167\pi$
$884$		0			0
$885$	367.818			0.415613
$886$	−186.898	−	77.4157i	−0.210946	−	0.0873766i
$887$	−152.500	−	766.671i	−0.171928	−	0.864341i	−0.966401	−	0.257041i	$-0.917253\pi$
$887$	−152.500	−	766.671i	−0.171928	−	0.864341i	0.794472	−	0.607300i	$-0.207747\pi$
$888$	−796.059	−	796.059i	−0.896463	−	0.896463i
$889$	139.752	+	93.3794i	0.157201	+	0.105039i
$890$	106.754	−	536.687i	0.119948	−	0.603019i
$891$	−536.472	+	358.459i	−0.602101	+	0.402311i
$892$	136.286	+	329.023i	0.152787	+	0.368860i
$893$	−102.000	+	42.2496i	−0.114221	+	0.0473120i
$894$	−205.425	−	307.441i	−0.229782	−	0.343894i
$895$	−1839.71	−	365.941i	−2.05554	−	0.408872i
$896$	−159.777	+	239.124i	−0.178323	+	0.266879i
$897$	−110.680	+	110.680i	−0.123389	+	0.123389i
$898$	940.519	−	187.081i	1.04735	−	0.208331i
$899$	173.904	−	419.842i	0.193442	−	0.467010i
$900$			227.333i			0.252592i
$901$		0			0
$902$	−414.241			−0.459247
$903$	53.2511	+	22.0573i	0.0589713	+	0.0244267i
$904$	314.922	+	1583.22i	0.348365	+	1.75135i
$905$	−746.999	−	746.999i	−0.825413	−	0.825413i
$906$	−1427.54	−	953.854i	−1.57566	−	1.05282i
$907$	72.9154	−	366.570i	0.0803918	−	0.404157i	−0.919546	−	0.392983i	$-0.871443\pi$
$907$	72.9154	−	366.570i	0.0803918	−	0.404157i	0.999938	−	0.0111739i	$-0.00355685\pi$
$908$	92.7363	−	61.9644i	0.102133	−	0.0682428i
$909$	351.306	+	848.129i	0.386476	+	0.933035i
$910$	173.416	−	71.8311i	0.190567	−	0.0789352i
$911$	−67.7280	−	101.362i	−0.0743447	−	0.111265i	0.792434	−	0.609958i	$-0.208814\pi$
$911$	−67.7280	−	101.362i	−0.0743447	−	0.111265i	−0.866779	+	0.498693i	$0.833814\pi$
$912$	1143.17	+	227.390i	1.25347	+	0.249331i
$913$	−437.777	+	655.180i	−0.479493	+	0.717612i
$914$	280.276	−	280.276i	0.306647	−	0.306647i
$915$	2176.70	−	432.972i	2.37890	−	0.473193i
$916$	41.5657	−	100.349i	0.0453774	−	0.109551i
$917$		−	787.702i		−	0.858999i
$918$		0			0
$919$	1592.00			1.73232			0.866158	−	0.499770i	$-0.166582\pi$
$919$	1592.00			1.73232			0.866158	+	0.499770i	$0.166582\pi$
$920$	−710.018	−	294.099i	−0.771759	−	0.319673i
$921$	204.986	+	1030.53i	0.222569	+	1.11893i
$922$	314.913	+	314.913i	0.341555	+	0.341555i
$923$	95.9399	+	64.1050i	0.103944	+	0.0694528i
$924$	−19.8088	+	99.5855i	−0.0214381	+	0.107777i
$925$	−935.874	+	625.331i	−1.01176	+	0.676033i
$926$	84.6976	+	204.478i	0.0914661	+	0.220819i
$927$	−1193.26	+	494.265i	−1.28723	+	0.533188i
$928$	92.4638	+	138.382i	0.0996377	+	0.149118i
$929$	−666.010	−	132.478i	−0.716910	−	0.142602i	−0.176861	−	0.984236i	$-0.556594\pi$
$929$	−666.010	−	132.478i	−0.716910	−	0.142602i	−0.540049	+	0.841633i	$0.681594\pi$
$930$	1161.95	−	1738.98i	1.24941	−	1.86987i
$931$	562.118	−	562.118i	0.603778	−	0.603778i
$932$	−52.1145	+	10.3662i	−0.0559169	+	0.0111226i
$933$	−873.641	+	2109.16i	−0.936378	+	2.26062i
$934$		−	1223.18i		−	1.30961i
$935$		0			0
$936$	213.532			0.228133
$937$	−271.967	−	112.652i	−0.290253	−	0.120227i	0.232806	−	0.972523i	$-0.425209\pi$
$937$	−271.967	−	112.652i	−0.290253	−	0.120227i	−0.523059	+	0.852296i	$0.675209\pi$
$938$	40.2869	+	202.536i	0.0429498	+	0.215923i
$939$	−1304.18	−	1304.18i	−1.38890	−	1.38890i
$940$	−25.4624	−	17.0134i	−0.0270877	−	0.0180994i
$941$	−162.916	+	819.035i	−0.173131	+	0.870388i	0.792381	+	0.610027i	$0.208841\pi$
$941$	−162.916	+	819.035i	−0.173131	+	0.870388i	−0.965511	+	0.260361i	$0.916159\pi$
$942$	−1597.41	+	1067.35i	−1.69576	+	1.13307i
$943$	149.060	+	359.862i	0.158070	+	0.381614i
$944$	126.805	−	52.5243i	0.134327	−	0.0556402i
$945$	−115.561	−	172.950i	−0.122287	−	0.183016i
$946$	−41.8196	−	8.31845i	−0.0442068	−	0.00879328i
$947$	346.036	−	517.880i	0.365403	−	0.546864i	−0.602523	−	0.798102i	$-0.705838\pi$
$947$	346.036	−	517.880i	0.365403	−	0.546864i	0.967925	+	0.251238i	$0.0808376\pi$
$948$	−54.2592	+	54.2592i	−0.0572355	+	0.0572355i
$949$	308.477	−	61.3599i	0.325055	−	0.0646575i
$950$	580.814	−	1402.21i	0.611383	−	1.47601i
$951$			1343.30i			1.41252i
$952$		0			0
$953$	−373.214			−0.391620			−0.195810	−	0.980642i	$-0.562734\pi$
$953$	−373.214			−0.391620			−0.195810	+	0.980642i	$0.562734\pi$
$954$	−369.746	−	153.154i	−0.387575	−	0.160539i
$955$	263.124	+	1322.81i	0.275522	+	1.38514i
$956$	178.619	+	178.619i	0.186840	+	0.186840i
$957$	−280.493	−	187.419i	−0.293096	−	0.195841i
$958$	164.865	−	828.832i	0.172093	−	0.865169i
$959$	179.781	−	120.126i	0.187468	−	0.125262i
$960$	853.280	+	2060.00i	0.888833	+	2.14583i
$961$	434.426	−	179.945i	0.452056	−	0.187248i
$962$	106.262	+	159.033i	0.110460	+	0.165315i
$963$	288.439	+	57.3741i	0.299522	+	0.0595786i
$964$	−61.0282	+	91.3352i	−0.0633073	+	0.0947460i
$965$	1026.89	−	1026.89i	1.06414	−	1.06414i
$966$	−330.322	+	65.7051i	−0.341948	+	0.0680177i
$967$	392.472	−	947.512i	0.405866	−	0.979847i	−0.580348	−	0.814369i	$-0.697083\pi$
$967$	392.472	−	947.512i	0.405866	−	0.979847i	0.986213	−	0.165478i	$-0.0529167\pi$
$968$			627.966i			0.648725i
$969$		0			0
$970$	−2272.36			−2.34264
$971$	−909.171	−	376.591i	−0.936325	−	0.387838i	−0.138250	−	0.990397i	$-0.544148\pi$
$971$	−909.171	−	376.591i	−0.936325	−	0.387838i	−0.798074	+	0.602559i	$0.794148\pi$
$972$	−54.6605	−	274.797i	−0.0562351	−	0.282713i
$973$	151.849	+	151.849i	0.156063	+	0.156063i
$974$	595.453	+	397.869i	0.611348	+	0.408490i
$975$	92.4629	−	464.842i	0.0948337	−	0.476761i
$976$	688.586	−	460.099i	0.705519	−	0.471413i
$977$	−217.809	−	525.837i	−0.222936	−	0.538216i	0.772350	−	0.635197i	$-0.219081\pi$
$977$	−217.809	−	525.837i	−0.222936	−	0.538216i	−0.995286	+	0.0969814i	$0.969081\pi$
$978$	256.105	−	106.082i	0.261866	−	0.108469i
$979$	−154.436	−	231.129i	−0.157748	−	0.236087i
$980$	216.265	+	43.0178i	0.220679	+	0.0438957i
$981$	−187.819	+	281.091i	−0.191457	+	0.286535i
$982$	77.4444	−	77.4444i	0.0788639	−	0.0788639i
$983$	−1410.25	+	280.516i	−1.43464	+	0.285368i	−0.850367	−	0.526190i	$-0.823620\pi$
$983$	−1410.25	+	280.516i	−1.43464	+	0.285368i	−0.584272	+	0.811558i	$0.698620\pi$
$984$	451.436	−	1089.86i	0.458776	−	1.10758i
$985$			2221.92i			2.25575i
$986$		0			0
$987$	−74.1814			−0.0751585
$988$	67.5473	+	27.9790i	0.0683677	+	0.0283188i
$989$	7.82186	+	39.3231i	0.00790886	+	0.0397605i
$990$	−494.517	−	494.517i	−0.499512	−	0.499512i
$991$	−69.8125	−	46.6472i	−0.0704465	−	0.0470709i	0.519848	−	0.854259i	$-0.325988\pi$
$991$	−69.8125	−	46.6472i	−0.0704465	−	0.0470709i	−0.590295	+	0.807188i	$0.700988\pi$
$992$	−102.259	+	514.093i	−0.103084	+	0.518239i
$993$	−1983.58	+	1325.39i	−1.99757	+	1.33473i
$994$	95.0102	+	229.375i	0.0955837	+	0.230759i
$995$	−654.847	+	271.246i	−0.658137	+	0.272609i
$996$	−225.540	−	337.545i	−0.226446	−	0.338900i
$997$	−738.843	−	146.965i	−0.741066	−	0.147407i	−0.189901	−	0.981803i	$-0.560817\pi$
$997$	−738.843	−	146.965i	−0.741066	−	0.147407i	−0.551165	+	0.834396i	$0.685817\pi$
$998$	503.379	−	753.360i	0.504388	−	0.754870i
$999$	149.874	−	149.874i	0.150024	−	0.150024i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	289.3.e.h.249.1		8
17.2	even	8		289.3.e.a.214.1		8
17.3	odd	16		289.3.e.f.65.1		8
17.4	even	4		289.3.e.g.40.1		8
17.5	odd	16		17.3.e.b.3.1	✓	8
17.6	odd	16		289.3.e.j.158.1		8
17.7	odd	16		289.3.e.a.131.1		8
17.8	even	8		289.3.e.j.75.1		8
17.9	even	8		289.3.e.n.75.1		8
17.10	odd	16		289.3.e.e.131.1		8
17.11	odd	16		289.3.e.n.158.1		8
17.12	odd	16		289.3.e.g.224.1		8
17.13	even	4		17.3.e.b.6.1	yes	8
17.14	odd	16	inner	289.3.e.h.65.1		8
17.15	even	8		289.3.e.e.214.1		8
17.16	even	2		289.3.e.f.249.1		8
51.5	even	16		153.3.p.a.37.1		8
51.47	odd	4		153.3.p.a.91.1		8
68.39	even	16		272.3.bh.b.241.1		8
68.47	odd	4		272.3.bh.b.193.1		8
85.13	odd	4		425.3.t.b.74.1		8
85.22	even	16		425.3.t.b.224.1		8
85.39	odd	16		425.3.u.a.326.1		8
85.47	odd	4		425.3.t.d.74.1		8
85.64	even	4		425.3.u.a.176.1		8
85.73	even	16		425.3.t.d.224.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.3.e.b.3.1	✓	8	17.5	odd	16
17.3.e.b.6.1	yes	8	17.13	even	4
153.3.p.a.37.1		8	51.5	even	16
153.3.p.a.91.1		8	51.47	odd	4
272.3.bh.b.193.1		8	68.47	odd	4
272.3.bh.b.241.1		8	68.39	even	16
289.3.e.a.131.1		8	17.7	odd	16
289.3.e.a.214.1		8	17.2	even	8
289.3.e.e.131.1		8	17.10	odd	16
289.3.e.e.214.1		8	17.15	even	8
289.3.e.f.65.1		8	17.3	odd	16
289.3.e.f.249.1		8	17.16	even	2
289.3.e.g.40.1		8	17.4	even	4
289.3.e.g.224.1		8	17.12	odd	16
289.3.e.h.65.1		8	17.14	odd	16	inner
289.3.e.h.249.1		8	1.1	even	1	trivial
289.3.e.j.75.1		8	17.8	even	8
289.3.e.j.158.1		8	17.6	odd	16
289.3.e.n.75.1		8	17.9	even	8
289.3.e.n.158.1		8	17.11	odd	16
425.3.t.b.74.1		8	85.13	odd	4
425.3.t.b.224.1		8	85.22	even	16
425.3.t.d.74.1		8	85.47	odd	4
425.3.t.d.224.1		8	85.73	even	16
425.3.u.a.176.1		8	85.64	even	4
425.3.u.a.326.1		8	85.39	odd	16

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:	\( N \)	\(=\)	\( 289 = 17^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	289.e (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(1.63099 + 0.675577i) q^{2} +(-0.789499 - 3.96908i) q^{3} +(-0.624715 - 0.624715i) q^{4} +(6.43416 + 4.29916i) q^{5} +(1.39376 - 7.00688i) q^{6} +(3.40262 - 2.27356i) q^{7} +(-3.29916 - 7.96489i) q^{8} +(-6.81537 + 2.82302i) q^{9} +(7.58960 + 11.3586i) q^{10} +(6.80638 + 1.35387i) q^{11} +(-1.98633 + 2.97275i) q^{12} +(2.37416 - 2.37416i) q^{13} +(7.08560 - 1.40941i) q^{14} +(11.9840 - 28.9319i) q^{15} -11.6855i q^{16} -13.0229 q^{18} +(-22.7712 - 9.43215i) q^{19} +(-1.33376 - 6.70526i) q^{20} +(-11.7103 - 11.7103i) q^{21} +(10.1865 + 6.80638i) q^{22} +(2.24740 - 11.2984i) q^{23} +(-29.0086 + 19.3829i) q^{24} +(13.3484 + 32.2260i) q^{25} +(5.47615 - 2.26829i) q^{26} +(-3.64922 - 5.46144i) q^{27} +(-3.54600 - 0.705343i) q^{28} +(6.67355 - 9.98767i) q^{29} +(39.0914 - 39.0914i) q^{30} +(37.1045 - 7.38055i) q^{31} +(-5.30218 + 12.8006i) q^{32} -28.0839i q^{33} +31.6674 q^{35} +(6.02124 + 2.49408i) q^{36} +(6.29529 + 31.6486i) q^{37} +(-30.7674 - 30.7674i) q^{38} +(-11.2976 - 7.54883i) q^{39} +(13.0150 - 65.4310i) q^{40} +(-28.1140 + 18.7852i) q^{41} +(-11.1881 - 27.0106i) q^{42} +(-3.21547 + 1.33189i) q^{43} +(-3.40626 - 5.09783i) q^{44} +(-55.9877 - 11.1367i) q^{45} +(11.2984 - 16.9093i) q^{46} +(3.16735 - 3.16735i) q^{47} +(-46.3809 + 9.22573i) q^{48} +(-12.3427 + 29.7979i) q^{49} +61.5781i q^{50} -2.96634 q^{52} +(28.3919 + 11.7603i) q^{53} +(-2.26220 - 11.3729i) q^{54} +(37.9728 + 37.9728i) q^{55} +(-29.3345 - 19.6007i) q^{56} +(-19.4591 + 97.8275i) q^{57} +(17.6319 - 11.7813i) q^{58} +(4.49481 + 10.8514i) q^{59} +(-25.5607 + 10.5876i) q^{60} +(39.3733 + 58.9263i) q^{61} +(65.5031 + 13.0294i) q^{62} +(-16.7718 + 25.1008i) q^{63} +(-50.3473 + 50.3473i) q^{64} +(25.4826 - 5.06881i) q^{65} +(18.9728 - 45.8045i) q^{66} +28.5842i q^{67} -46.6187 q^{69} +(51.6491 + 21.3938i) q^{70} +(6.70446 + 33.7056i) q^{71} +(44.9700 + 44.9700i) q^{72} +(77.8880 + 52.0431i) q^{73} +(-11.1135 + 55.8713i) q^{74} +(117.369 - 78.4234i) q^{75} +(8.33312 + 20.1179i) q^{76} +(26.2377 - 10.8680i) q^{77} +(-13.3265 - 19.9444i) q^{78} +(21.0499 + 4.18708i) q^{79} +(50.2381 - 75.1866i) q^{80} +(-65.7422 + 65.7422i) q^{81} +(-58.5443 + 11.6452i) q^{82} +(-43.4522 + 104.903i) q^{83} +14.6312i q^{84} -6.14419 q^{86} +(-44.9106 - 18.6026i) q^{87} +(-11.6719 - 58.6787i) q^{88} +(-28.3238 - 28.3238i) q^{89} +(-83.7916 - 55.9877i) q^{90} +(2.68058 - 13.4762i) q^{91} +(-8.46229 + 5.65432i) q^{92} +(-58.5880 - 141.444i) q^{93} +(7.30570 - 3.02612i) q^{94} +(-105.963 - 158.585i) q^{95} +(54.9926 + 10.9387i) q^{96} +(-92.4136 + 138.307i) q^{97} +(-40.2616 + 40.2616i) q^{98} +(-50.2100 + 9.98738i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{3} - 8 q^{4} + 8 q^{5} - 24 q^{6} - 8 q^{7} - 16 q^{8} - 8 q^{9} + 8 q^{10} - 32 q^{12} + 24 q^{14} - 32 q^{15} - 136 q^{18} + 32 q^{19} - 64 q^{21} + 8 q^{22} - 32 q^{23} - 48 q^{24} - 16 q^{25}+ \cdots - 256 q^{99}+O(q^{100}) \) 8 * q + 8 * q^3 - 8 * q^4 + 8 * q^5 - 24 * q^6 - 8 * q^7 - 16 * q^8 - 8 * q^9 + 8 * q^10 - 32 * q^12 + 24 * q^14 - 32 * q^15 - 136 * q^18 + 32 * q^19 - 64 * q^21 + 8 * q^22 - 32 * q^23 - 48 * q^24 - 16 * q^25 - 112 * q^27 - 8 * q^28 + 168 * q^30 - 24 * q^31 + 24 * q^32 + 80 * q^35 + 104 * q^36 + 56 * q^37 + 8 * q^38 - 136 * q^39 - 24 * q^40 + 56 * q^41 + 72 * q^42 - 96 * q^43 + 40 * q^44 - 256 * q^45 + 8 * q^46 - 80 * q^47 - 16 * q^48 - 8 * q^49 + 240 * q^52 - 96 * q^53 - 192 * q^54 - 8 * q^55 - 48 * q^56 + 168 * q^57 - 96 * q^58 - 8 * q^59 - 16 * q^60 + 56 * q^61 + 96 * q^62 + 16 * q^63 - 120 * q^64 + 264 * q^65 - 8 * q^66 - 208 * q^69 + 80 * q^70 + 136 * q^71 + 24 * q^72 + 240 * q^73 - 248 * q^74 + 168 * q^75 + 80 * q^76 + 216 * q^77 + 328 * q^79 + 8 * q^80 - 224 * q^81 - 352 * q^82 + 88 * q^83 + 288 * q^86 - 312 * q^87 - 24 * q^88 + 288 * q^89 + 184 * q^90 + 184 * q^91 + 72 * q^92 - 280 * q^93 + 8 * q^94 + 216 * q^95 + 464 * q^96 + 280 * q^97 + 16 * q^98 - 256 * q^99

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