LMFDB - Embedded newform 289.3.e.a.214.1

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,-8,-16,8,-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			214.1
Root			$0.382683 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	289.214
Dual form			289.3.e.a.131.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.675577 + 1.63099i) q^{2} +(-3.36482 - 2.24830i) q^{3} +(0.624715 + 0.624715i) q^{4} +(-7.58960 + 1.50967i) q^{5} +(5.94015 - 3.96908i) q^{6} +(-4.01367 - 0.798369i) q^{7} +(-7.96489 + 3.29916i) q^{8} +(2.82302 + 6.81537i) q^{9} +(2.66511 - 13.3984i) q^{10} +(3.85550 + 5.77017i) q^{11} +(-0.697506 - 3.50660i) q^{12} +(-2.37416 + 2.37416i) q^{13} +(4.01367 - 6.00688i) q^{14} +(28.9319 + 11.9840i) q^{15} -11.6855i q^{16} -13.0229 q^{18} +(9.43215 - 22.7712i) q^{19} +(-5.68445 - 3.79823i) q^{20} +(11.7103 + 11.7103i) q^{21} +(-12.0158 + 2.39008i) q^{22} +(9.57836 - 6.40006i) q^{23} +(34.2180 + 6.80638i) q^{24} +(32.2260 - 13.3484i) q^{25} +(-2.26829 - 5.47615i) q^{26} +(-1.28144 + 6.44221i) q^{27} +(-2.00865 - 3.00615i) q^{28} +(2.34344 + 11.7813i) q^{29} +(-39.0914 + 39.0914i) q^{30} +(21.0180 - 31.4557i) q^{31} +(-12.8006 - 5.30218i) q^{32} -28.0839i q^{33} +31.6674 q^{35} +(-2.49408 + 6.02124i) q^{36} +(26.8303 + 17.9275i) q^{37} +(30.7674 + 30.7674i) q^{38} +(13.3265 - 2.65080i) q^{39} +(55.4697 - 37.0637i) q^{40} +(33.1627 + 6.59647i) q^{41} +(-27.0106 + 11.1881i) q^{42} +(1.33189 + 3.21547i) q^{43} +(-1.19612 + 6.01330i) q^{44} +(-31.7145 - 47.4641i) q^{45} +(3.96749 + 19.9459i) q^{46} +(-3.16735 + 3.16735i) q^{47} +(-26.2726 + 39.3198i) q^{48} +(-29.7979 - 12.3427i) q^{49} +61.5781i q^{50} -2.96634 q^{52} +(-11.7603 + 28.3919i) q^{53} +(-9.64145 - 6.44221i) q^{54} +(-37.9728 - 37.9728i) q^{55} +(34.6024 - 6.88284i) q^{56} +(-82.9342 + 55.4148i) q^{57} +(-20.7982 - 4.13703i) q^{58} +(10.8514 - 4.49481i) q^{59} +(10.5876 + 25.5607i) q^{60} +(13.8261 - 69.5084i) q^{61} +(37.1045 + 55.5309i) q^{62} +(-5.88948 - 29.6084i) q^{63} +(50.3473 - 50.3473i) q^{64} +(14.4347 - 21.6031i) q^{65} +(45.8045 + 18.9728i) q^{66} +28.5842i q^{67} -46.6187 q^{69} +(-21.3938 + 51.6491i) q^{70} +(28.5742 + 19.0927i) q^{71} +(-44.9700 - 44.9700i) q^{72} +(-91.8752 + 18.2751i) q^{73} +(-47.3654 + 31.6486i) q^{74} +(-138.446 - 27.5386i) q^{75} +(20.1179 - 8.33312i) q^{76} +(-10.8680 - 26.2377i) q^{77} +(-4.67963 + 23.5261i) q^{78} +(11.9238 + 17.8452i) q^{79} +(17.6413 + 88.6886i) q^{80} +(65.7422 - 65.7422i) q^{81} +(-33.1627 + 49.6315i) q^{82} +(-104.903 - 43.4522i) q^{83} +14.6312i q^{84} -6.14419 q^{86} +(18.6026 - 44.9106i) q^{87} +(-49.7454 - 33.2388i) q^{88} +(28.3238 + 28.3238i) q^{89} +(98.8389 - 19.6603i) q^{90} +(11.4245 - 7.63364i) q^{91} +(9.98195 + 1.98553i) q^{92} +(-141.444 + 58.5880i) q^{93} +(-3.02612 - 7.30570i) q^{94} +(-37.2094 + 187.064i) q^{95} +(31.1508 + 46.6205i) q^{96} +(-32.4513 - 163.144i) q^{97} +(40.2616 - 40.2616i) q^{98} +(-28.4417 + 42.5659i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{2} - 16 q^{3} + 8 q^{4} - 8 q^{5} + 40 q^{6} - 16 q^{7} - 8 q^{8} + 56 q^{9} + 16 q^{10} - 32 q^{12} + 16 q^{14} + 80 q^{15} - 136 q^{18} + 80 q^{19} - 48 q^{20} + 64 q^{21} - 40 q^{22} - 16 q^{23}+ \cdots - 144 q^{99}+O(q^{100}) $ 8 * q - 8 * q^2 - 16 * q^3 + 8 * q^4 - 8 * q^5 + 40 * q^6 - 16 * q^7 - 8 * q^8 + 56 * q^9 + 16 * q^10 - 32 * q^12 + 16 * q^14 + 80 * q^15 - 136 * q^18 + 80 * q^19 - 48 * q^20 + 64 * q^21 - 40 * q^22 - 16 * q^23 + 88 * q^24 + 136 * q^25 - 40 * q^26 - 64 * q^27 - 40 * q^28 + 144 * q^29 - 168 * q^30 + 88 * q^31 - 16 * q^32 + 80 * q^35 + 72 * q^36 - 24 * q^37 - 8 * q^38 + 96 * q^40 + 144 * q^41 - 88 * q^42 - 48 * q^43 - 112 * q^44 - 8 * q^46 + 80 * q^47 + 40 * q^48 - 72 * q^49 + 240 * q^52 - 88 * q^53 + 256 * q^54 + 8 * q^55 + 64 * q^56 - 200 * q^57 - 144 * q^58 + 40 * q^59 + 96 * q^60 + 88 * q^61 - 24 * q^62 - 216 * q^63 + 120 * q^64 - 160 * q^65 + 120 * q^66 - 208 * q^69 - 96 * q^70 - 48 * q^71 - 24 * q^72 - 224 * q^73 + 104 * q^74 - 272 * q^75 - 192 * q^76 - 120 * q^77 + 232 * q^78 + 136 * q^79 + 80 * q^80 + 224 * q^81 - 144 * q^82 - 504 * q^83 + 288 * q^86 - 216 * q^87 - 112 * q^88 - 288 * q^89 + 344 * q^90 + 16 * q^91 - 48 * q^92 - 248 * q^93 - 72 * q^94 + 144 * q^95 + 80 * q^96 - 208 * q^97 - 16 * q^98 - 144 * q^99

Character values

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

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

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 $

$2$	−0.675577	+	1.63099i	−0.337788	+	0.815493i	0.660139	+	0.751143i	$0.270497\pi$
$2$	−0.675577	+	1.63099i	−0.337788	+	0.815493i	−0.997927	+	0.0643498i	$0.979503\pi$
$3$	−3.36482	−	2.24830i	−1.12161	−	0.749434i	−0.150627	−	0.988591i	$-0.548129\pi$
$3$	−3.36482	−	2.24830i	−1.12161	−	0.749434i	−0.970981	+	0.239156i	$0.923129\pi$
$4$	0.624715	+	0.624715i	0.156179	+	0.156179i
$5$	−7.58960	+	1.50967i	−1.51792	+	0.301933i	−0.882529	−	0.470257i	$-0.844161\pi$
$5$	−7.58960	+	1.50967i	−1.51792	+	0.301933i	−0.635391	+	0.772190i	$0.719161\pi$
$6$	5.94015	−	3.96908i	0.990025	−	0.661513i
$7$	−4.01367	−	0.798369i	−0.573381	−	0.114053i	−0.100121	−	0.994975i	$-0.531923\pi$
$7$	−4.01367	−	0.798369i	−0.573381	−	0.114053i	−0.473260	+	0.880923i	$0.656923\pi$
$8$	−7.96489	+	3.29916i	−0.995611	+	0.412396i
$9$	2.82302	+	6.81537i	0.313669	+	0.757263i
$10$	2.66511	−	13.3984i	0.266511	−	1.33984i
$11$	3.85550	+	5.77017i	0.350500	+	0.524561i	0.964269	−	0.264925i	$-0.0853473\pi$
$11$	3.85550	+	5.77017i	0.350500	+	0.524561i	−0.613769	+	0.789486i	$0.710347\pi$
$12$	−0.697506	−	3.50660i	−0.0581255	−	0.292217i
$13$	−2.37416	+	2.37416i	−0.182628	+	0.182628i	−0.792500	−	0.609872i	$-0.791221\pi$
$13$	−2.37416	+	2.37416i	−0.182628	+	0.182628i	0.609872	+	0.792500i	$0.291221\pi$
$14$	4.01367	−	6.00688i	0.286691	−	0.429063i
$15$	28.9319	+	11.9840i	1.92879	+	0.798931i
$16$		−	11.6855i		−	0.730347i
$17$		0			0
$17$		0			0
$18$	−13.0229			−0.723496
$19$	9.43215	−	22.7712i	0.496429	−	1.19849i	−0.454965	−	0.890509i	$-0.650348\pi$
$19$	9.43215	−	22.7712i	0.496429	−	1.19849i	0.951394	−	0.307977i	$-0.0996519\pi$
$20$	−5.68445	−	3.79823i	−0.284222	−	0.189911i
$21$	11.7103	+	11.7103i	0.557634	+	0.557634i
$22$	−12.0158	+	2.39008i	−0.546170	+	0.108640i
$23$	9.57836	−	6.40006i	0.416450	−	0.278263i	−0.329642	−	0.944106i	$-0.606928\pi$
$23$	9.57836	−	6.40006i	0.416450	−	0.278263i	0.746092	+	0.665843i	$0.231928\pi$
$24$	34.2180	+	6.80638i	1.42575	+	0.283599i
$25$	32.2260	−	13.3484i	1.28904	−	0.533938i
$26$	−2.26829	−	5.47615i	−0.0872421	−	0.210621i
$27$	−1.28144	+	6.44221i	−0.0474606	+	0.238600i
$28$	−2.00865	−	3.00615i	−0.0717373	−	0.107363i
$29$	2.34344	+	11.7813i	0.0808082	+	0.406250i	0.999925	+	0.0122647i	$0.00390406\pi$
$29$	2.34344	+	11.7813i	0.0808082	+	0.406250i	−0.919117	+	0.393986i	$0.871096\pi$
$30$	−39.0914	+	39.0914i	−1.30305	+	1.30305i
$31$	21.0180	−	31.4557i	0.678001	−	1.01470i	−0.319739	−	0.947506i	$-0.603595\pi$
$31$	21.0180	−	31.4557i	0.678001	−	1.01470i	0.997740	−	0.0671946i	$-0.0214048\pi$
$32$	−12.8006	−	5.30218i	−0.400019	−	0.165693i
$33$		−	28.0839i		−	0.851028i
$34$		0			0
$35$	31.6674			0.904784
$36$	−2.49408	+	6.02124i	−0.0692800	+	0.167257i
$37$	26.8303	+	17.9275i	0.725145	+	0.484526i	0.862539	−	0.505990i	$-0.168873\pi$
$37$	26.8303	+	17.9275i	0.725145	+	0.484526i	−0.137395	+	0.990516i	$0.543873\pi$
$38$	30.7674	+	30.7674i	0.809669	+	0.809669i
$39$	13.3265	−	2.65080i	0.341704	−	0.0679691i
$40$	55.4697	−	37.0637i	1.38674	−	0.926592i
$41$	33.1627	+	6.59647i	0.808846	+	0.160890i	0.582156	−	0.813077i	$-0.302209\pi$
$41$	33.1627	+	6.59647i	0.808846	+	0.160890i	0.226691	+	0.973967i	$0.427209\pi$
$42$	−27.0106	+	11.1881i	−0.643109	+	0.266384i
$43$	1.33189	+	3.21547i	0.0309742	+	0.0747784i	0.938610	−	0.344981i	$-0.112115\pi$
$43$	1.33189	+	3.21547i	0.0309742	+	0.0747784i	−0.907636	+	0.419759i	$0.862115\pi$
$44$	−1.19612	+	6.01330i	−0.0271845	+	0.136666i
$45$	−31.7145	−	47.4641i	−0.704767	−	1.05476i
$46$	3.96749	+	19.9459i	0.0862497	+	0.433607i
$47$	−3.16735	+	3.16735i	−0.0673905	+	0.0673905i	−0.739999	−	0.672608i	$-0.765174\pi$
$47$	−3.16735	+	3.16735i	−0.0673905	+	0.0673905i	0.672608	+	0.739999i	$0.265174\pi$
$48$	−26.2726	+	39.3198i	−0.547347	+	0.819162i
$49$	−29.7979	−	12.3427i	−0.608121	−	0.251892i
$50$			61.5781i			1.23156i
$51$		0			0
$52$	−2.96634			−0.0570451
$53$	−11.7603	+	28.3919i	−0.221893	+	0.535697i	−0.995147	−	0.0983994i	$-0.968628\pi$
$53$	−11.7603	+	28.3919i	−0.221893	+	0.535697i	0.773254	+	0.634096i	$0.218628\pi$
$54$	−9.64145	−	6.44221i	−0.178545	−	0.119300i
$55$	−37.9728	−	37.9728i	−0.690414	−	0.690414i
$56$	34.6024	−	6.88284i	0.617900	−	0.122908i
$57$	−82.9342	+	55.4148i	−1.45499	+	0.972190i
$58$	−20.7982	−	4.13703i	−0.358590	−	0.0713281i
$59$	10.8514	−	4.49481i	0.183923	−	0.0761832i	−0.288822	−	0.957383i	$-0.593263\pi$
$59$	10.8514	−	4.49481i	0.183923	−	0.0761832i	0.472744	+	0.881200i	$0.343263\pi$
$60$	10.5876	+	25.5607i	0.176460	+	0.426012i
$61$	13.8261	−	69.5084i	0.226657	−	1.13948i	−0.685004	−	0.728539i	$-0.740200\pi$
$61$	13.8261	−	69.5084i	0.226657	−	1.13948i	0.911661	−	0.410942i	$-0.134800\pi$
$62$	37.1045	+	55.5309i	0.598460	+	0.895659i
$63$	−5.88948	−	29.6084i	−0.0934839	−	0.469975i
$64$	50.3473	−	50.3473i	0.786676	−	0.786676i
$65$	14.4347	−	21.6031i	0.222073	−	0.332356i
$66$	45.8045	+	18.9728i	0.694008	+	0.287467i
$67$			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
$70$	−21.3938	+	51.6491i	−0.305625	+	0.737845i
$71$	28.5742	+	19.0927i	0.402454	+	0.268911i	0.740282	−	0.672297i	$-0.234692\pi$
$71$	28.5742	+	19.0927i	0.402454	+	0.268911i	−0.337828	+	0.941208i	$0.609692\pi$
$72$	−44.9700	−	44.9700i	−0.624584	−	0.624584i
$73$	−91.8752	+	18.2751i	−1.25856	+	0.250344i	−0.778922	−	0.627120i	$-0.784233\pi$
$73$	−91.8752	+	18.2751i	−1.25856	+	0.250344i	−0.479642	+	0.877464i	$0.659233\pi$
$74$	−47.3654	+	31.6486i	−0.640073	+	0.427683i
$75$	−138.446	−	27.5386i	−1.84595	−	0.367182i
$76$	20.1179	−	8.33312i	0.264710	−	0.109646i
$77$	−10.8680	−	26.2377i	−0.141143	−	0.340749i
$78$	−4.67963	+	23.5261i	−0.0599952	+	0.301616i
$79$	11.9238	+	17.8452i	0.150934	+	0.225889i	0.899230	−	0.437476i	$-0.144128\pi$
$79$	11.9238	+	17.8452i	0.150934	+	0.225889i	−0.748296	+	0.663365i	$0.769128\pi$
$80$	17.6413	+	88.6886i	0.220516	+	1.10861i
$81$	65.7422	−	65.7422i	0.811632	−	0.811632i
$82$	−33.1627	+	49.6315i	−0.404423	+	0.605262i
$83$	−104.903	−	43.4522i	−1.26389	−	0.523521i	−0.352789	−	0.935703i	$-0.614767\pi$
$83$	−104.903	−	43.4522i	−1.26389	−	0.523521i	−0.911102	+	0.412182i	$0.864767\pi$
$84$			14.6312i			0.174181i
$85$		0			0
$86$	−6.14419			−0.0714440
$87$	18.6026	−	44.9106i	0.213823	−	0.516214i
$88$	−49.7454	−	33.2388i	−0.565288	−	0.377714i
$89$	28.3238	+	28.3238i	0.318245	+	0.318245i	0.848093	−	0.529848i	$-0.177751\pi$
$89$	28.3238	+	28.3238i	0.318245	+	0.318245i	−0.529848	+	0.848093i	$0.677751\pi$
$90$	98.8389	−	19.6603i	1.09821	−	0.218448i
$91$	11.4245	−	7.63364i	0.125544	−	0.0838861i
$92$	9.98195	+	1.98553i	0.108499	+	0.0215819i
$93$	−141.444	+	58.5880i	−1.52090	+	0.629978i
$94$	−3.02612	−	7.30570i	−0.0321928	−	0.0777202i
$95$	−37.2094	+	187.064i	−0.391677	+	1.96910i
$96$	31.1508	+	46.6205i	0.324488	+	0.485630i
$97$	−32.4513	−	163.144i	−0.334550	−	1.68190i	−0.671999	−	0.740552i	$-0.734564\pi$
$97$	−32.4513	−	163.144i	−0.334550	−	1.68190i	0.337449	−	0.941344i	$-0.390436\pi$
$98$	40.2616	−	40.2616i	0.410833	−	0.410833i
$99$	−28.4417	+	42.5659i	−0.287289	+	0.429959i
$100$	28.4710	+	11.7931i	0.284710	+	0.117931i
$101$		−	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	$0.176649\pi$
$104$	11.0772	−	26.7427i	0.106511	−	0.257141i
$105$	−106.555	−	71.1980i	−1.01481	−	0.678076i
$106$	−38.3619	−	38.3619i	−0.361904	−	0.361904i
$107$	39.1003	−	7.77754i	0.365424	−	0.0726873i	−0.00896329	−	0.999960i	$-0.502853\pi$
$107$	39.1003	−	7.77754i	0.365424	−	0.0726873i	0.374387	+	0.927273i	$0.377853\pi$
$108$	−4.82508	+	3.22401i	−0.0446766	+	0.0298520i
$109$	−44.9470	−	8.94051i	−0.412358	−	0.0820231i	−0.0154480	−	0.999881i	$-0.504917\pi$
$109$	−44.9470	−	8.94051i	−0.412358	−	0.0820231i	−0.396910	+	0.917858i	$0.629917\pi$
$110$	87.5866	−	36.2795i	0.796241	−	0.329814i
$111$	−49.9730	−	120.645i	−0.450207	−	1.08690i
$112$	−9.32937	+	46.9019i	−0.0832980	+	0.418767i
$113$	−104.026	−	155.686i	−0.920585	−	1.37775i	−0.925901	−	0.377767i	$-0.876692\pi$
$113$	−104.026	−	155.686i	−0.920585	−	1.37775i	0.00531545	−	0.999986i	$-0.498308\pi$
$114$	−34.3525	−	172.701i	−0.301337	−	1.51493i
$115$	−63.0340	+	63.0340i	−0.548122	+	0.548122i
$116$	−5.89595	+	8.82391i	−0.0508271	+	0.0760682i
$117$	−22.8831	−	9.47847i	−0.195582	−	0.0810126i
$118$			20.7351i			0.175721i
$119$		0			0
$120$	−269.976			−2.24980
$121$	27.8748	−	67.2956i	0.230370	−	0.556162i
$122$	104.027	+	69.5084i	0.852677	+	0.569741i
$123$	−96.7557	−	96.7557i	−0.786632	−	0.786632i
$124$	32.7811	−	6.52057i	0.264364	−	0.0525852i
$125$	−63.5770	+	42.4808i	−0.508616	+	0.339846i
$126$	52.2698	+	10.3971i	0.414839	+	0.0825167i
$127$	37.9454	−	15.7175i	0.298783	−	0.123760i	−0.228256	−	0.973601i	$-0.573302\pi$
$127$	37.9454	−	15.7175i	0.298783	−	0.123760i	0.527039	+	0.849841i	$0.323302\pi$
$128$	26.8936	+	64.9268i	0.210106	+	0.507241i
$129$	2.74777	−	13.8140i	0.0213006	−	0.107085i
$130$	25.4826	+	38.1374i	0.196020	+	0.293365i
$131$	37.5517	+	188.785i	0.286654	+	1.44111i	0.808715	+	0.588200i	$0.200163\pi$
$131$	37.5517	+	188.785i	0.286654	+	1.44111i	−0.522061	+	0.852908i	$0.674837\pi$
$132$	17.5444	−	17.5444i	0.132912	−	0.132912i
$133$	−56.0374	+	83.8659i	−0.421334	+	0.630571i
$134$	−46.6204	−	19.3108i	−0.347913	−	0.144110i
$135$		−	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	$0.438233\pi$
$138$	31.4945	−	76.0345i	0.228221	−	0.550975i
$139$	43.6322	+	29.1541i	0.313900	+	0.209742i	0.702533	−	0.711651i	$-0.252052\pi$
$139$	43.6322	+	29.1541i	0.313900	+	0.209742i	−0.388632	+	0.921393i	$0.627052\pi$
$140$	19.7831	+	19.7831i	0.141308	+	0.141308i
$141$	17.7788	−	3.53641i	0.126090	−	0.0250810i
$142$	−50.4440	+	33.7056i	−0.355239	+	0.237363i
$143$	−22.8529	−	4.54572i	−0.159810	−	0.0317882i
$144$	79.6413	−	32.9885i	0.553064	−	0.229087i
$145$	−35.5715	−	85.8773i	−0.245321	−	0.592257i
$146$	32.2623	−	162.193i	0.220974	−	1.11091i
$147$	72.5147	+	108.526i	0.493297	+	0.738271i
$148$	5.56176	+	27.9609i	0.0375795	+	0.188925i
$149$	−36.5973	+	36.5973i	−0.245620	+	0.245620i	−0.819170	−	0.573551i	$-0.805566\pi$
$149$	−36.5973	+	36.5973i	−0.245620	+	0.245620i	0.573551	+	0.819170i	$0.305566\pi$
$150$	138.446	−	207.199i	0.922974	−	1.38133i
$151$	222.028	+	91.9670i	1.47038	+	0.609053i	0.966947	−	0.254979i	$-0.0820686\pi$
$151$	222.028	+	91.9670i	1.47038	+	0.609053i	0.503437	+	0.864032i	$0.332069\pi$
$152$			212.489i			1.39795i
$153$		0			0
$154$	50.1354			0.325555
$155$	−112.031	+	270.467i	−0.722780	+	1.74495i
$156$	9.98122	+	6.66924i	0.0639822	+	0.0427515i
$157$	190.153	+	190.153i	1.21117	+	1.21117i	0.970644	+	0.240522i	$0.0773185\pi$
$157$	190.153	+	190.153i	1.21117	+	1.21117i	0.240522	+	0.970644i	$0.422681\pi$
$158$	−37.1608	+	7.39174i	−0.235195	+	0.0467832i
$159$	103.405	−	69.0931i	0.650346	−	0.434548i
$160$	105.156	+	20.9168i	0.657225	+	0.130730i
$161$	−43.5540	+	18.0406i	−0.270522	+	0.112054i
$162$	62.8107	+	151.638i	0.387720	+	0.936040i
$163$	7.56986	−	38.0563i	0.0464409	−	0.233474i	−0.950593	−	0.310441i	$-0.899523\pi$
$163$	7.56986	−	38.0563i	0.0464409	−	0.233474i	0.997034	+	0.0769665i	$0.0245234\pi$
$164$	16.5963	+	24.8381i	0.101197	+	0.151452i
$165$	42.3974	+	213.146i	0.256954	+	1.29179i
$166$	141.740	−	141.740i	0.853855	−	0.853855i
$167$	20.0159	−	29.9560i	0.119856	−	0.179377i	−0.766690	−	0.642017i	$-0.778098\pi$
$167$	20.0159	−	29.9560i	0.119856	−	0.179377i	0.886546	+	0.462640i	$0.153098\pi$
$168$	−131.906	−	54.6371i	−0.785152	−	0.325221i
$169$			157.727i			0.933294i
$170$		0			0
$171$	181.821			1.06328
$172$	−1.17670	+	2.84081i	−0.00684128	+	0.0165163i
$173$	160.487	+	107.234i	0.927668	+	0.619848i	0.924925	−	0.380149i	$-0.124127\pi$
$173$	160.487	+	107.234i	0.927668	+	0.619848i	0.00274223	+	0.999996i	$0.499127\pi$
$174$	60.6811	+	60.6811i	0.348742	+	0.348742i
$175$	−140.001	+	27.8480i	−0.800009	+	0.159132i
$176$	67.4275	−	45.0536i	0.383111	−	0.255987i
$177$	−46.6188	−	9.27307i	−0.263383	−	0.0523902i
$178$	−65.3307	+	27.0608i	−0.367026	+	0.152027i
$179$	92.7619	+	223.947i	0.518223	+	1.25110i	0.938994	+	0.343933i	$0.111759\pi$
$179$	92.7619	+	223.947i	0.518223	+	1.25110i	−0.420771	+	0.907167i	$0.638241\pi$
$180$	9.83901	−	49.4640i	0.0546612	−	0.274800i
$181$	−75.8453	−	113.511i	−0.419035	−	0.627130i	0.560560	−	0.828114i	$-0.310586\pi$
$181$	−75.8453	−	113.511i	−0.419035	−	0.627130i	−0.979595	+	0.200984i	$0.935586\pi$
$182$	4.73220	+	23.7904i	0.0260011	+	0.130716i
$183$	−202.798	+	202.798i	−1.10819	+	1.10819i
$184$	−55.1757	+	82.5763i	−0.299868	+	0.448784i
$185$	−230.696	−	95.5575i	−1.24701	−	0.516527i
$186$		−	270.274i		−	1.45308i
$187$		0			0
$188$	−3.95738			−0.0210499
$189$	10.2865	−	24.8339i	0.0544260	−	0.131396i
$190$	−279.961	−	187.064i	−1.47348	−	0.984548i
$191$	−123.244	−	123.244i	−0.645254	−	0.645254i	0.306588	−	0.951842i	$-0.400813\pi$
$191$	−123.244	−	123.244i	−0.645254	−	0.645254i	−0.951842	+	0.306588i	$0.900813\pi$
$192$	−282.606	+	56.2137i	−1.47190	+	0.292780i
$193$	156.042	−	104.264i	0.808507	−	0.540227i	−0.0812325	−	0.996695i	$-0.525886\pi$
$193$	156.042	−	104.264i	0.808507	−	0.540227i	0.889740	+	0.456468i	$0.150886\pi$
$194$	288.009	+	57.2885i	1.48458	+	0.295302i
$195$	−97.1407	+	40.2370i	−0.498157	+	0.206344i
$196$	−10.9045	−	26.3259i	−0.0556354	−	0.134316i
$197$	56.0168	−	281.616i	0.284349	−	1.42952i	−0.529433	−	0.848352i	$-0.677595\pi$
$197$	56.0168	−	281.616i	0.284349	−	1.42952i	0.813783	−	0.581169i	$-0.197405\pi$
$198$	−50.2100	−	75.1445i	−0.253586	−	0.379518i
$199$	−17.8696	−	89.8366i	−0.0897970	−	0.451440i	−0.999357	−	0.0358665i	$-0.988581\pi$
$199$	−17.8696	−	89.8366i	−0.0897970	−	0.451440i	0.909560	−	0.415574i	$-0.136419\pi$
$200$	−212.638	+	212.638i	−1.06319	+	1.06319i
$201$	64.2659	−	96.1807i	0.319731	−	0.478511i
$202$	202.966	+	84.0712i	1.00478	+	0.416194i
$203$		−	49.1570i		−	0.242153i
$204$		0			0
$205$	−261.650			−1.27634
$206$	−118.283	+	285.560i	−0.574188	+	1.38621i
$207$	70.6586	+	47.2126i	0.341346	+	0.228080i
$208$	27.7433	+	27.7433i	0.133381	+	0.133381i
$209$	167.760	−	33.3694i	0.802677	−	0.159662i
$210$	188.109	−	125.691i	0.895758	−	0.598526i
$211$	35.4645	+	7.05432i	0.168078	+	0.0334328i	0.278412	−	0.960462i	$-0.410192\pi$
$211$	35.4645	+	7.05432i	0.168078	+	0.0334328i	−0.110334	+	0.993895i	$0.535192\pi$
$212$	−25.0837	+	10.3900i	−0.118319	+	0.0490095i
$213$	−53.2210	−	128.487i	−0.249864	−	0.603225i
$214$	−13.7302	+	69.0264i	−0.0641599	+	0.322554i
$215$	−14.9628	−	22.3934i	−0.0695945	−	0.104156i
$216$	−11.0474	−	55.5392i	−0.0511455	−	0.257126i
$217$	−109.473	+	109.473i	−0.504482	+	0.504482i
$218$	44.9470	−	67.2679i	0.206179	−	0.308569i
$219$	350.232	+	145.071i	1.59923	+	0.662423i
$220$		−	47.4443i		−	0.215656i
$221$		0			0
$222$	230.532			1.03843
$223$	154.260	−	372.417i	0.691750	−	1.67003i	−0.0494759	−	0.998775i	$-0.515755\pi$
$223$	154.260	−	372.417i	0.691750	−	1.67003i	0.741226	−	0.671256i	$-0.234245\pi$
$224$	47.1443	+	31.5008i	0.210465	+	0.140629i
$225$	181.949	+	181.949i	0.808663	+	0.808663i
$226$	324.200	−	64.4873i	1.43451	−	0.285342i
$227$	−104.967	+	70.1368i	−0.462410	+	0.308973i	−0.764864	−	0.644191i	$-0.777194\pi$
$227$	−104.967	+	70.1368i	−0.462410	+	0.308973i	0.302454	+	0.953164i	$0.402194\pi$
$228$	−86.4286	−	17.1917i	−0.379073	−	0.0754023i
$229$	113.583	−	47.0477i	0.495997	−	0.205449i	−0.120640	−	0.992696i	$-0.538495\pi$
$229$	113.583	−	47.0477i	0.495997	−	0.205449i	0.616637	+	0.787248i	$0.288495\pi$
$230$	−60.2233	−	145.392i	−0.261840	−	0.632139i
$231$	−22.4213	+	112.720i	−0.0970620	+	0.487964i
$232$	−57.5335	−	86.1050i	−0.247989	−	0.371142i
$233$	11.7334	+	58.9878i	0.0503579	+	0.253166i	0.997761	−	0.0668754i	$-0.0213030\pi$
$233$	11.7334	+	58.9878i	0.0503579	+	0.253166i	−0.947403	+	0.320042i	$0.896303\pi$
$234$	30.9185	−	30.9185i	0.132130	−	0.132130i
$235$	19.2573	−	28.8206i	0.0819460	−	0.122641i
$236$	9.58702	+	3.97107i	0.0406230	+	0.0168266i
$237$		−	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	$0.704101\pi$
$240$	140.039	−	338.085i	0.583497	−	1.40869i
$241$	−103.381	−	69.0771i	−0.428967	−	0.286627i	0.322284	−	0.946643i	$-0.395549\pi$
$241$	−103.381	−	69.0771i	−0.428967	−	0.286627i	−0.751251	+	0.660016i	$0.770549\pi$
$242$	90.9267	+	90.9267i	0.375730	+	0.375730i
$243$	−311.039	+	61.8695i	−1.28000	+	0.254607i
$244$	52.0602	−	34.7855i	0.213362	−	0.142564i
$245$	244.788	+	48.6914i	0.999135	+	0.198740i
$246$	223.173	−	92.4414i	0.907208	−	0.375778i
$247$	31.6691	+	76.4560i	0.128215	+	0.309538i
$248$	−63.6287	+	319.883i	−0.256567	+	1.28985i
$249$	255.286	+	382.063i	1.02525	+	1.53439i
$250$	−26.3344	−	132.392i	−0.105338	−	0.529569i
$251$	99.6747	−	99.6747i	0.397110	−	0.397110i	−0.480102	−	0.877213i	$-0.659400\pi$
$251$	99.6747	−	99.6747i	0.397110	−	0.397110i	0.877213	+	0.480102i	$0.159400\pi$
$252$	14.8176	−	22.1761i	0.0587999	−	0.0880003i
$253$	73.8588	+	30.5933i	0.291932	+	0.120922i
$254$			72.5069i			0.285460i
$255$		0			0
$256$	160.744			0.627906
$257$	150.400	−	363.098i	0.585214	−	1.41283i	−0.302818	−	0.953048i	$-0.597927\pi$
$257$	150.400	−	363.098i	0.585214	−	1.41283i	0.888032	−	0.459783i	$-0.152073\pi$
$258$	20.6741	+	13.8140i	0.0801322	+	0.0535426i
$259$	−93.3754	−	93.3754i	−0.360523	−	0.360523i
$260$	22.5134	−	4.47819i	0.0865899	−	0.0172238i
$261$	−73.6780	+	49.2301i	−0.282291	+	0.188621i
$262$	−333.275	−	66.2926i	−1.27204	−	0.253025i
$263$	269.286	−	111.542i	1.02390	−	0.424113i	0.193393	−	0.981121i	$-0.438051\pi$
$263$	269.286	−	111.542i	1.02390	−	0.424113i	0.830507	+	0.557008i	$0.188051\pi$
$264$	92.6535	+	223.685i	0.350960	+	0.847293i
$265$	46.3939	−	233.238i	0.175071	−	0.880142i
$266$	−98.9266	−	148.054i	−0.371904	−	0.556594i
$267$	−31.6241	−	158.985i	−0.118442	−	0.595450i
$268$	−17.8569	+	17.8569i	−0.0666304	+	0.0666304i
$269$	56.6082	−	84.7201i	0.210439	−	0.314945i	−0.711202	−	0.702988i	$-0.751849\pi$
$269$	56.6082	−	84.7201i	0.210439	−	0.314945i	0.921641	+	0.388043i	$0.126849\pi$
$270$	82.9004	+	34.3385i	0.307038	+	0.127180i
$271$		−	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
$274$	−35.6948	+	86.1749i	−0.130273	+	0.314507i
$275$	201.270	+	134.484i	0.731892	+	0.489034i
$276$	−29.1234	−	29.1234i	−0.105520	−	0.105520i
$277$	−65.9245	+	13.1132i	−0.237995	+	0.0473401i	−0.312646	−	0.949870i	$-0.601215\pi$
$277$	−65.9245	+	13.1132i	−0.237995	+	0.0473401i	0.0746518	+	0.997210i	$0.476215\pi$
$278$	−77.0268	+	51.4676i	−0.277075	+	0.185135i
$279$	273.716	+	54.4456i	0.981063	+	0.195146i
$280$	−252.228	+	104.476i	−0.900813	+	0.373129i
$281$	−144.294	−	348.356i	−0.513501	−	1.23970i	−0.941834	−	0.336079i	$-0.890899\pi$
$281$	−144.294	−	348.356i	−0.513501	−	1.23970i	0.428333	−	0.903621i	$-0.359101\pi$
$282$	−6.24307	+	31.3860i	−0.0221385	+	0.111298i
$283$	164.909	+	246.804i	0.582717	+	0.872098i	0.999316	−	0.0369928i	$-0.0117778\pi$
$283$	164.909	+	246.804i	0.582717	+	0.872098i	−0.416598	+	0.909091i	$0.636778\pi$
$284$	5.92325	+	29.7782i	0.0208565	+	0.104853i
$285$	545.780	−	545.780i	1.91502	−	1.91502i
$286$	22.8529	−	34.2017i	0.0799051	−	0.119586i
$287$	−127.838	−	52.9521i	−0.445428	−	0.184502i
$288$		−	102.209i		−	0.354892i
$289$		0			0
$290$	164.096			0.565848
$291$	−257.604	+	621.911i	−0.885237	+	2.13715i
$292$	−68.8125	−	45.9790i	−0.235659	−	0.157462i
$293$	−99.8472	−	99.8472i	−0.340776	−	0.340776i	0.515883	−	0.856659i	$-0.327464\pi$
$293$	−99.8472	−	99.8472i	−0.340776	−	0.340776i	−0.856659	+	0.515883i	$0.827464\pi$
$294$	−225.993	+	44.9529i	−0.768685	+	0.152901i
$295$	−75.5724	+	50.4959i	−0.256178	+	0.171172i
$296$	−272.846	−	54.2725i	−0.921778	−	0.183353i
$297$	−42.1132	+	17.4439i	−0.141795	+	0.0587336i
$298$	−34.9654	−	84.4140i	−0.117334	−	0.283269i
$299$	−7.54580	+	37.9353i	−0.0252368	+	0.126874i
$300$	−69.2855	−	103.693i	−0.230952	−	0.345644i
$301$	−2.77864	−	13.9692i	−0.00923138	−	0.0464093i
$302$	−299.994	+	299.994i	−0.993357	+	0.993357i
$303$	−279.787	+	418.731i	−0.923389	+	1.38195i
$304$	−266.094	−	110.220i	−0.875310	−	0.362565i
$305$			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	$0.638976\pi$
$308$	9.60165	−	23.1804i	0.0311742	−	0.0752612i
$309$	−589.127	−	393.642i	−1.90656	−	1.27392i
$310$	−365.442	−	365.442i	−1.17884	−	1.17884i
$311$	553.288	−	110.056i	1.77906	−	0.353877i	0.807355	−	0.590066i	$-0.200898\pi$
$311$	553.288	−	110.056i	1.77906	−	0.353877i	0.971707	+	0.236189i	$0.0758985\pi$
$312$	−97.3983	+	65.0795i	−0.312174	+	0.208588i
$313$	−447.002	−	88.9143i	−1.42812	−	0.284071i	−0.580322	−	0.814387i	$-0.697073\pi$
$313$	−447.002	−	88.9143i	−1.42812	−	0.284071i	−0.847800	+	0.530316i	$0.822073\pi$
$314$	−438.600	+	181.674i	−1.39681	+	0.578580i
$315$	89.3977	+	215.825i	0.283802	+	0.685159i
$316$	−3.69920	+	18.5972i	−0.0117063	+	0.0588518i
$317$	−184.415	−	275.997i	−0.581751	−	0.870653i	0.417526	−	0.908665i	$-0.362897\pi$
$317$	−184.415	−	275.997i	−0.581751	−	0.870653i	−0.999277	+	0.0380125i	$0.987897\pi$
$318$	42.8318	+	215.330i	0.134691	+	0.677138i
$319$	−58.9447	+	58.9447i	−0.184780	+	0.184780i
$320$	−306.108	+	458.123i	−0.956588	+	1.43164i
$321$	−149.052	−	61.7394i	−0.464336	−	0.192334i
$322$		−	83.2238i		−	0.258459i
$323$		0			0
$324$	82.1402			0.253519
$325$	−44.8183	+	108.201i	−0.137903	+	0.332926i
$326$	56.9552	+	38.0563i	0.174709	+	0.116737i
$327$	131.138	+	131.138i	0.401033	+	0.401033i
$328$	−285.900	+	56.8691i	−0.871646	+	0.173381i
$329$	15.2414	−	10.1840i	0.0463265	−	0.0309544i
$330$	−376.281	−	74.8469i	−1.14024	−	0.226809i
$331$	−544.633	+	225.594i	−1.64542	+	0.681554i	−0.996828	−	0.0795855i	$-0.974640\pi$
$331$	−544.633	+	225.594i	−1.64542	+	0.681554i	−0.648588	+	0.761139i	$0.724640\pi$
$332$	−38.3892	−	92.6796i	−0.115630	−	0.279156i
$333$	−46.4397	+	233.468i	−0.139459	+	0.701106i
$334$	35.3355	+	52.8833i	0.105795	+	0.158333i
$335$	−43.1525	−	216.942i	−0.128814	−	0.647590i
$336$	136.841	−	136.841i	0.407266	−	0.407266i
$337$	181.999	−	272.381i	0.540056	−	0.808251i	−0.456625	−	0.889659i	$-0.650942\pi$
$337$	181.999	−	272.381i	0.540056	−	0.808251i	0.996681	+	0.0814084i	$0.0259418\pi$
$338$	−257.250	−	106.557i	−0.761095	−	0.315256i
$339$			757.738i			2.23522i
$340$		0			0
$341$	262.540			0.769911
$342$	−122.834	+	296.548i	−0.359165	+	0.867100i
$343$	276.474	+	184.734i	0.806046	+	0.538583i
$344$	−21.2167	−	21.2167i	−0.0616766	−	0.0616766i
$345$	353.818	−	70.3787i	1.02556	−	0.203996i
$346$	−283.318	+	189.307i	−0.818837	+	0.547129i
$347$	237.412	+	47.2242i	0.684185	+	0.136093i	0.524931	−	0.851145i	$-0.324091\pi$
$347$	237.412	+	47.2242i	0.684185	+	0.136093i	0.159254	+	0.987238i	$0.449091\pi$
$348$	39.6776	−	16.4350i	0.114016	−	0.0472270i
$349$	192.479	+	464.685i	0.551515	+	1.33148i	0.916341	+	0.400399i	$0.131129\pi$
$349$	192.479	+	464.685i	0.551515	+	1.33148i	−0.364826	+	0.931076i	$0.618871\pi$
$350$	49.1620	−	247.154i	0.140463	−	0.706154i
$351$	−12.2525	−	18.3372i	−0.0349074	−	0.0522427i
$352$	−18.7583	−	94.3041i	−0.0532905	−	0.267909i
$353$	231.294	−	231.294i	0.655223	−	0.655223i	−0.299023	−	0.954246i	$-0.596661\pi$
$353$	231.294	−	231.294i	0.655223	−	0.655223i	0.954246	+	0.299023i	$0.0966606\pi$
$354$	46.6188	−	69.7700i	0.131692	−	0.197090i
$355$	−245.691	−	101.768i	−0.692086	−	0.286671i
$356$			35.3886i			0.0994062i
$357$		0			0
$358$	−427.922			−1.19531
$359$	−203.355	+	490.942i	−0.566448	+	1.36753i	0.338082	+	0.941117i	$0.390222\pi$
$359$	−203.355	+	490.942i	−0.566448	+	1.36753i	−0.904530	+	0.426410i	$0.859778\pi$
$360$	409.194	+	273.415i	1.13665	+	0.759486i
$361$	−174.298	−	174.298i	−0.482820	−	0.482820i
$362$	236.374	−	47.0176i	0.652965	−	0.129883i
$363$	−245.095	+	163.767i	−0.675192	+	0.451149i
$364$	11.9059	+	2.36824i	0.0327086	+	0.00650614i
$365$	669.707	−	277.402i	1.83481	−	0.760005i
$366$	−193.755	−	467.767i	−0.529386	−	1.27805i
$367$	−64.5850	+	324.691i	−0.175981	+	0.884716i	0.787372	+	0.616479i	$0.211441\pi$
$367$	−64.5850	+	324.691i	−0.175981	+	0.884716i	−0.963353	+	0.268238i	$0.913559\pi$
$368$	−74.7881	−	111.928i	−0.203229	−	0.304153i
$369$	48.6615	+	244.638i	0.131874	+	0.662975i
$370$	311.706	−	311.706i	0.842448	−	0.842448i
$371$	69.8693	−	104.567i	0.188327	−	0.281851i
$372$	−124.963	−	51.7613i	−0.335922	−	0.139143i
$373$		−	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
$376$	14.7780	−	35.6772i	0.0393032	−	0.0948863i
$377$	−33.5343	−	22.4069i	−0.0889504	−	0.0594347i
$378$	33.5543	+	33.5543i	0.0887681	+	0.0887681i
$379$	42.8446	−	8.52233i	0.113047	−	0.0224864i	−0.138243	−	0.990398i	$-0.544145\pi$
$379$	42.8446	−	8.52233i	0.113047	−	0.0224864i	0.251289	+	0.967912i	$0.419145\pi$
$380$	−140.107	+	93.6164i	−0.368702	+	0.246359i
$381$	−163.017	−	32.4262i	−0.427867	−	0.0851081i
$382$	284.269	−	117.748i	0.744160	−	0.308241i
$383$	75.6230	+	182.570i	0.197449	+	0.476684i	0.991331	−	0.131387i	$-0.0419432\pi$
$383$	75.6230	+	182.570i	0.197449	+	0.476684i	−0.793882	+	0.608072i	$0.791943\pi$
$384$	55.4830	−	278.932i	0.144487	−	0.726385i
$385$	122.094	+	182.726i	0.317127	+	0.474614i
$386$	64.6347	+	324.941i	0.167447	+	0.841815i
$387$	−18.1547	+	18.1547i	−0.0469113	+	0.0469113i
$388$	81.6456	−	122.191i	0.210427	−	0.314926i
$389$	−19.8577	−	8.22534i	−0.0510481	−	0.0211448i	0.357013	−	0.934099i	$-0.383795\pi$
$389$	−19.8577	−	8.22534i	−0.0510481	−	0.0211448i	−0.408061	+	0.912954i	$0.633795\pi$
$390$		−	185.618i		−	0.475944i
$391$		0			0
$392$	278.058			0.709332
$393$	298.092	−	719.657i	0.758503	−	1.83119i
$394$	421.468	+	281.616i	1.06971	+	0.714761i
$395$	−117.437	−	117.437i	−0.297310	−	0.297310i
$396$	−44.3595	+	8.82365i	−0.112019	+	0.0222819i
$397$	29.4981	−	19.7100i	0.0743025	−	0.0496473i	−0.517864	−	0.855463i	$-0.673273\pi$
$397$	29.4981	−	19.7100i	0.0743025	−	0.0496473i	0.592167	+	0.805816i	$0.298273\pi$
$398$	158.594	+	31.5464i	0.398479	+	0.0792623i
$399$	377.112	−	156.205i	0.945142	−	0.391491i
$400$	−155.984	−	376.578i	−0.389960	−	0.941446i
$401$	−29.1786	+	146.691i	−0.0727646	+	0.365812i	−0.999962	−	0.00876160i	$-0.997211\pi$
$401$	−29.1786	+	146.691i	−0.0727646	+	0.365812i	0.927197	+	0.374574i	$0.122211\pi$
$402$	113.453	+	169.794i	0.282221	+	0.422374i
$403$	24.7807	+	124.581i	0.0614906	+	0.309134i
$404$	77.7417	−	77.7417i	0.192430	−	0.192430i
$405$	−399.708	+	598.206i	−0.986934	+	1.47705i
$406$	80.1744	+	33.2093i	0.197474	+	0.0817964i
$407$			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	$0.662143\pi$
$410$	176.765	−	426.748i	0.431134	−	1.04085i
$411$	−177.784	−	118.792i	−0.432565	−	0.289030i
$412$	109.378	+	109.378i	0.265479	+	0.265479i
$413$	−47.1426	+	9.37724i	−0.114147	+	0.0227052i
$414$	−124.738	+	83.3475i	−0.301300	+	0.201322i
$415$	861.770	+	171.417i	2.07655	+	0.413052i
$416$	42.9789	−	17.8024i	0.103315	−	0.0427943i
$417$	−81.2673	−	196.197i	−0.194886	−	0.470496i
$418$	−58.9093	+	296.157i	−0.140931	+	0.708510i
$419$	20.7782	+	31.0967i	0.0495899	+	0.0742166i	0.855436	−	0.517908i	$-0.173289\pi$
$419$	20.7782	+	31.0967i	0.0495899	+	0.0742166i	−0.805846	+	0.592125i	$0.798289\pi$
$420$	−22.0882	−	111.045i	−0.0525910	−	0.264393i
$421$	−312.706	+	312.706i	−0.742769	+	0.742769i	−0.973110	−	0.230341i	$-0.926016\pi$
$421$	−312.706	+	312.706i	−0.742769	+	0.742769i	0.230341	+	0.973110i	$0.426016\pi$
$422$	−35.4645	+	53.0763i	−0.0840390	+	0.125773i
$423$	−30.5282	−	12.6452i	−0.0721706	−	0.0298941i
$424$		−	264.938i		−	0.624853i
$425$		0			0
$426$	245.515			0.576327
$427$	−110.987	+	267.945i	−0.259922	+	0.627507i
$428$	29.2853	+	19.5678i	0.0684236	+	0.0457192i
$429$	66.6757	+	66.6757i	0.155421	+	0.155421i
$430$	46.6319	−	9.27567i	0.108446	−	0.0215713i
$431$	288.433	−	192.725i	0.669218	−	0.447157i	−0.173988	−	0.984748i	$-0.555665\pi$
$431$	288.433	−	192.725i	0.669218	−	0.447157i	0.843206	+	0.537590i	$0.180665\pi$
$432$	75.2808	+	14.9743i	0.174261	+	0.0346627i
$433$	49.6556	−	20.5680i	0.114678	−	0.0475012i	−0.324607	−	0.945849i	$-0.605232\pi$
$433$	49.6556	−	20.5680i	0.114678	−	0.0475012i	0.439285	+	0.898348i	$0.355232\pi$
$434$	−104.591	−	252.506i	−0.240994	−	0.581810i
$435$	−73.3862	+	368.937i	−0.168704	+	0.848132i
$436$	−22.4938	−	33.6643i	−0.0515912	−	0.0772117i
$437$	−55.3926	−	278.477i	−0.126757	−	0.637248i
$438$	−473.217	+	473.217i	−1.08040	+	1.08040i
$439$	135.146	−	202.261i	0.307851	−	0.460731i	−0.644995	−	0.764187i	$-0.723140\pi$
$439$	135.146	−	202.261i	0.307851	−	0.460731i	0.952846	+	0.303456i	$0.0981405\pi$
$440$	427.727	+	177.170i	0.972107	+	0.402660i
$441$		−	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	$0.541285\pi$
$444$	44.1501	−	106.588i	0.0994373	−	0.240063i
$445$	−257.726	−	172.207i	−0.579160	−	0.386982i
$446$	503.192	+	503.192i	1.12823	+	1.12823i
$447$	205.425	−	40.8616i	0.459565	−	0.0914131i
$448$	−242.273	+	161.882i	−0.540788	+	0.361343i
$449$	−532.761	−	105.973i	−1.18655	−	0.236020i	−0.437925	−	0.899012i	$-0.644286\pi$
$449$	−532.761	−	105.973i	−1.18655	−	0.236020i	−0.748626	+	0.662992i	$0.769286\pi$
$450$	−419.677	+	173.836i	−0.932616	+	0.386302i
$451$	89.7961	+	216.787i	0.199104	+	0.480681i
$452$	32.2727	−	162.246i	0.0713999	−	0.358951i
$453$	−540.315	−	808.639i	−1.19275	−	1.78507i
$454$	−43.4788	−	218.583i	−0.0957683	−	0.481460i
$455$	−75.1835	+	75.1835i	−0.165239	+	0.165239i
$456$	477.739	−	714.987i	1.04767	−	1.56795i
$457$	207.434	+	85.9222i	0.453905	+	0.188014i	0.597910	−	0.801563i	$-0.295998\pi$
$457$	207.434	+	85.9222i	0.453905	+	0.188014i	−0.144005	+	0.989577i	$0.545998\pi$
$458$			217.037i			0.473880i
$459$		0			0
$460$	−78.7565			−0.171210
$461$	−96.5408	+	233.070i	−0.209416	+	0.505575i	−0.993332	−	0.115292i	$-0.963219\pi$
$461$	−96.5408	+	233.070i	−0.209416	+	0.505575i	0.783916	+	0.620867i	$0.213219\pi$
$462$	−168.697	−	112.720i	−0.365145	−	0.243982i
$463$	−88.6506	−	88.6506i	−0.191470	−	0.191470i	0.604861	−	0.796331i	$-0.293229\pi$
$463$	−88.6506	−	88.6506i	−0.191470	−	0.191470i	−0.796331	+	0.604861i	$0.793229\pi$
$464$	137.670	−	27.3844i	0.296704	−	0.0590180i
$465$	985.055	−	658.193i	2.11840	−	1.41547i
$466$	−104.135	−	20.7138i	−0.223466	−	0.0444501i
$467$	−640.133	+	265.152i	−1.37074	+	0.567777i	−0.941988	−	0.335647i	$-0.891045\pi$
$467$	−640.133	+	265.152i	−1.37074	+	0.567777i	−0.428748	+	0.903424i	$0.641045\pi$
$468$	−8.37404	−	20.2167i	−0.0178932	−	0.0431981i
$469$	22.8207	−	114.727i	0.0486582	−	0.244621i
$470$	33.9962	+	50.8789i	0.0723324	+	0.108253i
$471$	−212.310	−	1067.35i	−0.450764	−	2.26614i
$472$	−71.6013	+	71.6013i	−0.151698	+	0.151698i
$473$	−13.4187	+	20.0825i	−0.0283693	+	0.0424577i
$474$	141.658	+	58.6768i	0.298857	+	0.123791i
$475$		−	859.730i		−	1.80996i
$476$		0			0
$477$	−226.701			−0.475264
$478$	193.161	−	466.332i	0.404103	−	0.975591i
$479$	−398.019	−	265.948i	−0.830938	−	0.555215i	0.0657717	−	0.997835i	$-0.479049\pi$
$479$	−398.019	−	265.948i	−0.830938	−	0.555215i	−0.896709	+	0.442620i	$0.854049\pi$
$480$	−306.804	−	306.804i	−0.639175	−	0.639175i
$481$	−106.262	+	21.1369i	−0.220919	+	0.0439436i
$482$	182.506	−	121.946i	0.378642	−	0.253001i
$483$	187.112	+	37.2189i	0.387396	+	0.0770579i
$484$	59.4543	−	24.6268i	0.122840	−	0.0508818i
$485$	492.586	+	1189.21i	1.01564	+	2.45197i
$486$	109.222	−	549.098i	0.224737	−	1.12983i
$487$	225.375	+	337.297i	0.462782	+	0.692602i	0.987312	−	0.158790i	$-0.0507592\pi$
$487$	225.375	+	337.297i	0.462782	+	0.692602i	−0.524531	+	0.851392i	$0.675759\pi$
$488$	119.196	+	599.241i	0.244255	+	1.22795i
$489$	−111.033	+	111.033i	−0.227062	+	0.227062i
$490$	−244.788	+	366.351i	−0.499567	+	0.747655i
$491$	57.3172	+	23.7416i	0.116736	+	0.0483535i	0.440287	−	0.897857i	$-0.354877\pi$
$491$	57.3172	+	23.7416i	0.116736	+	0.0483535i	−0.323551	+	0.946211i	$0.604877\pi$
$492$		−	120.889i		−	0.245710i
$493$		0			0
$494$	−146.094			−0.295736
$495$	151.601	−	365.996i	0.306264	−	0.739386i
$496$	−367.577	−	245.607i	−0.741083	−	0.495176i
$497$	−99.4445	−	99.4445i	−0.200089	−	0.200089i
$498$	−795.604	+	158.256i	−1.59760	+	0.317782i
$499$	426.744	−	285.141i	0.855199	−	0.571426i	−0.0488735	−	0.998805i	$-0.515563\pi$
$499$	426.744	−	285.141i	0.855199	−	0.571426i	0.904072	+	0.427379i	$0.140563\pi$
$500$	−66.2558	−	13.1791i	−0.132512	−	0.0263582i
$501$	−134.700	+	55.7947i	−0.268863	+	0.111367i
$502$	95.2302	+	229.906i	0.189702	+	0.457980i
$503$	64.5518	−	324.524i	0.128334	−	0.645176i	−0.862050	−	0.506824i	$-0.830819\pi$
$503$	64.5518	−	324.524i	0.128334	−	0.645176i	0.990383	−	0.138352i	$-0.0441806\pi$
$504$	144.592	+	216.398i	0.286889	+	0.429360i
$505$	187.868	+	944.477i	0.372016	+	1.87025i
$506$	−99.7945	+	99.7945i	−0.197222	+	0.197222i
$507$	354.617	−	530.723i	0.699443	−	1.04679i
$508$	33.5240	+	13.8861i	0.0659922	+	0.0273349i
$509$		−	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
$512$	−216.169	+	521.878i	−0.422205	+	1.01929i
$513$	134.610	+	89.9438i	0.262399	+	0.175329i
$514$	490.601	+	490.601i	0.954476	+	0.954476i
$515$	−1328.82	+	264.318i	−2.58023	+	0.513239i
$516$	10.3464	−	6.91323i	0.0200511	−	0.0133977i
$517$	−30.4879	−	6.06442i	−0.0589708	−	0.0117300i
$518$	215.376	−	89.2118i	0.415784	−	0.172224i
$519$	−298.915	−	721.645i	−0.575944	−	1.39045i
$520$	−43.6989	+	219.689i	−0.0840363	+	0.422479i
$521$	176.947	+	264.820i	0.339629	+	0.508291i	0.961491	−	0.274836i	$-0.0886235\pi$
$521$	176.947	+	264.820i	0.339629	+	0.508291i	−0.621862	+	0.783127i	$0.713623\pi$
$522$	−30.5184	−	153.427i	−0.0584645	−	0.293921i
$523$	167.575	−	167.575i	0.320410	−	0.320410i	−0.528514	−	0.848924i	$-0.677251\pi$
$523$	167.575	−	167.575i	0.320410	−	0.320410i	0.848924	+	0.528514i	$0.177251\pi$
$524$	−94.4778	+	141.396i	−0.180301	+	0.269840i
$525$	533.691	+	221.062i	1.01655	+	0.421071i
$526$			514.556i			0.978244i
$527$		0			0
$528$	−328.176			−0.621545
$529$	−151.655	+	366.128i	−0.286683	+	0.692114i
$530$	349.065	+	233.238i	0.658613	+	0.440071i
$531$	61.2676	+	61.2676i	0.115381	+	0.115381i
$532$	−87.3996	+	17.3849i	−0.164285	+	0.0326783i
$533$	−94.3946	+	63.0724i	−0.177101	+	0.118335i
$534$	280.667	+	55.8282i	0.525594	+	0.104547i
$535$	−285.015	+	118.057i	−0.532738	+	0.220667i
$536$	−94.3039	−	227.670i	−0.175940	−	0.424757i
$537$	191.373	−	962.098i	0.356375	−	1.79162i
$538$	99.9342	+	149.562i	0.185751	+	0.277996i
$539$	−43.6665	−	219.526i	−0.0810140	−	0.407285i
$540$	31.7532	−	31.7532i	0.0588023	−	0.0588023i
$541$	147.180	−	220.270i	0.272051	−	0.407153i	−0.670137	−	0.742237i	$-0.733765\pi$
$541$	147.180	−	220.270i	0.272051	−	0.407153i	0.942188	+	0.335084i	$0.108765\pi$
$542$	621.502	+	257.435i	1.14668	+	0.474972i
$543$			552.466i			1.01743i
$544$		0			0
$545$	354.627			0.650692
$546$	37.5650	−	90.6899i	0.0688003	−	0.166099i
$547$	−299.987	−	200.445i	−0.548423	−	0.366444i	0.250277	−	0.968174i	$-0.419478\pi$
$547$	−299.987	−	200.445i	−0.548423	−	0.366444i	−0.798700	+	0.601730i	$0.794478\pi$
$548$	33.0075	+	33.0075i	0.0602326	+	0.0602326i
$549$	512.756	−	101.994i	0.933982	−	0.185781i
$550$	−355.316	+	237.414i	−0.646029	+	0.431662i
$551$	290.378	+	57.7597i	0.527001	+	0.104827i
$552$	371.313	−	153.803i	0.672669	−	0.278629i
$553$	−33.6111	−	81.1445i	−0.0607797	−	0.146735i
$554$	23.1496	−	116.381i	0.0417863	−	0.210074i
$555$	561.410	+	840.209i	1.01155	+	1.51389i
$556$	9.04467	+	45.4706i	0.0162674	+	0.0817817i
$557$	367.145	−	367.145i	0.659147	−	0.659147i	−0.296031	−	0.955178i	$-0.595663\pi$
$557$	367.145	−	367.145i	0.659147	−	0.659147i	0.955178	+	0.296031i	$0.0956632\pi$
$558$	−273.716	+	409.646i	−0.490531	+	0.734132i
$559$	−10.7962	−	4.47192i	−0.0193134	−	0.00799986i
$560$		−	370.051i		−	0.660806i
$561$		0			0
$562$	665.645			1.18442
$563$	168.267	−	406.232i	0.298875	−	0.721549i	−0.701089	−	0.713074i	$-0.747302\pi$
$563$	168.267	−	406.232i	0.298875	−	0.721549i	0.999964	−	0.00847487i	$-0.00269767\pi$
$564$	13.3159	+	8.89740i	0.0236097	+	0.0157755i
$565$	1024.55	+	1024.55i	1.81336	+	1.81336i
$566$	−513.942	+	102.229i	−0.908025	+	0.180617i
$567$	−316.354	+	211.381i	−0.557943	+	0.372806i
$568$	−290.580	−	57.8000i	−0.511585	−	0.101761i
$569$	443.238	−	183.595i	0.778977	−	0.322663i	0.0424747	−	0.999098i	$-0.486476\pi$
$569$	443.238	−	183.595i	0.778977	−	0.322663i	0.736503	+	0.676435i	$0.236476\pi$
$570$	521.443	+	1258.87i	0.914812	+	2.20855i
$571$	106.163	−	533.718i	0.185925	−	0.934707i	−0.769314	−	0.638871i	$-0.779402\pi$
$571$	106.163	−	533.718i	0.185925	−	0.934707i	0.955239	−	0.295836i	$-0.0955982\pi$
$572$	−11.4367	−	17.1163i	−0.0199943	−	0.0299236i
$573$	137.604	+	691.781i	0.240146	+	1.20730i
$574$	172.728	−	172.728i	0.300920	−	0.300920i
$575$	223.241	−	334.104i	0.388246	−	0.581051i
$576$	485.266	+	201.004i	0.842476	+	0.348965i
$577$			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
$580$	31.4267	−	75.8709i	0.0541840	−	0.130812i
$581$	386.355	+	258.154i	0.664983	+	0.444327i
$582$	−840.297	−	840.297i	−1.44381	−	1.44381i
$583$	−209.168	+	41.6061i	−0.358779	+	0.0713656i
$584$	671.483	−	448.671i	1.14980	−	0.768272i
$585$	187.983	+	37.3921i	0.321338	+	0.0639181i
$586$	230.304	−	95.3950i	0.393010	−	0.162790i
$587$	−244.317	−	589.834i	−0.416213	−	1.00483i	−0.983435	−	0.181263i	$-0.941982\pi$
$587$	−244.317	−	589.834i	−0.416213	−	1.00483i	0.567221	−	0.823565i	$-0.308018\pi$
$588$	−22.4967	+	113.099i	−0.0382597	+	0.192345i
$589$	−518.040	−	775.302i	−0.879525	−	1.31630i
$590$	−31.3031	−	157.371i	−0.0530561	−	0.266731i
$591$	−821.644	+	821.644i	−1.39026	+	1.39026i
$592$	209.492	−	313.527i	0.353872	−	0.529607i
$593$	−594.149	−	246.104i	−1.00194	−	0.415016i	−0.179430	−	0.983771i	$-0.557425\pi$
$593$	−594.149	−	246.104i	−1.00194	−	0.415016i	−0.822507	+	0.568755i	$0.807425\pi$
$594$		−	80.4708i		−	0.135473i
$595$		0			0
$596$	−45.7258			−0.0767211
$597$	−141.852	+	342.460i	−0.237608	+	0.573636i
$598$	−56.7742	−	37.9353i	−0.0949401	−	0.0634370i
$599$	−354.327	−	354.327i	−0.591530	−	0.591530i	0.346514	−	0.938045i	$-0.387365\pi$
$599$	−354.327	−	354.327i	−0.591530	−	0.591530i	−0.938045	+	0.346514i	$0.887365\pi$
$600$	1193.56	−	237.414i	1.98927	−	0.395691i
$601$	−473.731	+	316.537i	−0.788238	+	0.526684i	−0.883312	−	0.468786i	$-0.844691\pi$
$601$	−473.731	+	316.537i	−0.788238	+	0.526684i	0.0950732	+	0.995470i	$0.469691\pi$
$602$	24.6607	+	4.90533i	0.0409647	+	0.00814838i
$603$	−194.812	+	80.6936i	−0.323071	+	0.133820i
$604$	81.2510	+	196.157i	0.134521	+	0.324764i
$605$	−109.964	+	552.829i	−0.181759	+	0.913767i
$606$	−493.926	−	739.213i	−0.815060	−	1.21982i
$607$	35.3853	+	177.894i	0.0582955	+	0.293071i	0.998925	−	0.0463651i	$-0.0147638\pi$
$607$	35.3853	+	177.894i	0.0582955	+	0.293071i	−0.940629	+	0.339436i	$0.889764\pi$
$608$	−241.474	+	241.474i	−0.397162	+	0.397162i
$609$	−110.520	+	165.405i	−0.181478	+	0.271600i
$610$	−894.455	−	370.495i	−1.46632	−	0.607370i
$611$		−	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	$0.540402\pi$
$614$	175.407	−	423.470i	0.285679	−	0.689691i
$615$	880.407	+	588.269i	1.43156	+	0.956535i
$616$	173.125	+	173.125i	0.281047	+	0.281047i
$617$	458.417	−	91.1849i	0.742978	−	0.147787i	0.190934	−	0.981603i	$-0.438848\pi$
$617$	458.417	−	91.1849i	0.742978	−	0.147787i	0.552043	+	0.833815i	$0.313848\pi$
$618$	1040.02	−	694.922i	1.68289	−	1.12447i
$619$	376.303	+	74.8513i	0.607921	+	0.120923i	0.489445	−	0.872034i	$-0.337199\pi$
$619$	376.303	+	74.8513i	0.607921	+	0.120923i	0.118475	+	0.992957i	$0.462199\pi$
$620$	−238.952	+	98.9771i	−0.385406	+	0.159640i
$621$	28.9565	+	69.9071i	0.0466288	+	0.112572i
$622$	−194.289	+	976.757i	−0.312362	+	1.57035i
$623$	−91.0696	−	136.295i	−0.146179	−	0.218773i
$624$	−30.9760	−	155.727i	−0.0496410	−	0.249562i
$625$	−198.226	+	198.226i	−0.317161	+	0.317161i
$626$	447.002	−	668.986i	0.714061	−	1.06867i
$627$	−639.506	−	264.892i	−1.01995	−	0.422475i
$628$			237.583i			0.378316i
$629$		0			0
$630$	−412.403			−0.654608
$631$	−127.804	+	308.547i	−0.202542	+	0.488980i	−0.992213	−	0.124550i	$-0.960251\pi$
$631$	−127.804	+	308.547i	−0.202542	+	0.488980i	0.789671	+	0.613531i	$0.210251\pi$
$632$	−153.846	−	102.797i	−0.243428	−	0.162653i
$633$	−103.471	−	103.471i	−0.163462	−	0.163462i
$634$	574.734	−	114.322i	0.906520	−	0.180318i
$635$	−264.263	+	176.575i	−0.416162	+	0.278070i
$636$	107.762	+	21.4352i	0.169437	+	0.0337032i
$637$	100.049	−	41.4415i	0.157062	−	0.0650573i
$638$	−56.3163	−	135.960i	−0.0882701	−	0.213103i
$639$	−49.4581	+	248.643i	−0.0773992	+	0.389112i
$640$	−302.129	−	452.168i	−0.472077	−	0.706513i
$641$	−187.412	−	942.185i	−0.292375	−	1.46987i	−0.795658	−	0.605746i	$-0.792875\pi$
$641$	−187.412	−	942.185i	−0.292375	−	1.46987i	0.503284	−	0.864121i	$-0.332125\pi$
$642$	201.392	−	201.392i	0.313695	−	0.313695i
$643$	−581.812	+	870.743i	−0.904840	+	1.35419i	0.0301622	+	0.999545i	$0.490398\pi$
$643$	−581.812	+	870.743i	−0.904840	+	1.35419i	−0.935002	+	0.354643i	$0.884602\pi$
$644$	−38.4791	−	15.9385i	−0.0597501	−	0.0247493i
$645$			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	$0.418361\pi$
$648$	−306.735	+	740.523i	−0.473356	+	1.14278i
$649$	67.7735	+	45.2848i	0.104428	+	0.0697763i
$650$	−146.196	−	146.196i	−0.224917	−	0.224917i
$651$	614.484	−	122.228i	0.943908	−	0.187755i
$652$	28.5033	−	19.0453i	0.0437167	−	0.0292106i
$653$	−48.9018	−	9.72717i	−0.0748879	−	0.0148961i	0.157504	−	0.987518i	$-0.449655\pi$
$653$	−48.9018	−	9.72717i	−0.0748879	−	0.0148961i	−0.232392	+	0.972622i	$0.574655\pi$
$654$	−302.477	+	125.290i	−0.462504	+	0.191575i
$655$	−570.005	−	1376.11i	−0.870237	−	2.10094i
$656$	77.0833	−	387.524i	0.117505	−	0.590738i
$657$	−383.917	−	574.572i	−0.584348	−	0.874539i
$658$	6.31321	+	31.7386i	0.00959454	+	0.0482350i
$659$	−61.2456	+	61.2456i	−0.0929371	+	0.0929371i	−0.752047	−	0.659110i	$-0.770933\pi$
$659$	−61.2456	+	61.2456i	−0.0929371	+	0.0929371i	0.659110	+	0.752047i	$0.270933\pi$
$660$	−106.669	+	159.642i	−0.161620	+	0.241881i
$661$	758.170	+	314.044i	1.14700	+	0.475105i	0.873528	−	0.486774i	$-0.161827\pi$
$661$	758.170	+	314.044i	1.14700	+	0.475105i	0.273476	+	0.961879i	$0.411827\pi$
$662$		−	1040.69i		−	1.57205i
$663$		0			0
$664$	978.896			1.47424
$665$	298.692	−	721.107i	0.449161	−	1.08437i
$666$	−349.410	−	233.468i	−0.524639	−	0.350553i
$667$	97.8470	+	97.8470i	0.146697	+	0.146697i
$668$	31.2182	−	6.20969i	0.0467338	−	0.00929594i
$669$	−1356.36	+	906.294i	−2.02745	+	1.35470i
$670$	382.983	+	76.1801i	0.571617	+	0.113702i
$671$	454.381	−	188.211i	0.677170	−	0.280493i
$672$	−87.8088	−	211.989i	−0.130668	−	0.315460i
$673$	−107.266	+	539.262i	−0.159385	+	0.801281i	0.815532	+	0.578712i	$0.196444\pi$
$673$	−107.266	+	539.262i	−0.159385	+	0.801281i	−0.974917	+	0.222569i	$0.928556\pi$
$674$	321.295	+	480.852i	0.476698	+	0.713430i
$675$	44.6980	+	224.712i	0.0662192	+	0.332907i
$676$	−98.5342	+	98.5342i	−0.145761	+	0.145761i
$677$	−301.014	+	450.499i	−0.444629	+	0.665434i	−0.984313	−	0.176434i	$-0.943544\pi$
$677$	−301.014	+	450.499i	−0.444629	+	0.665434i	0.539684	+	0.841868i	$0.318544\pi$
$678$	−1235.86	−	511.910i	−1.82280	−	0.755030i
$679$			680.714i			1.00252i
$680$		0			0
$681$	510.884			0.750197
$682$	−177.366	+	428.199i	−0.260067	+	0.627857i
$683$	−329.272	−	220.012i	−0.482096	−	0.322126i	0.290663	−	0.956825i	$-0.406124\pi$
$683$	−329.272	−	220.012i	−0.482096	−	0.322126i	−0.772759	+	0.634699i	$0.781124\pi$
$684$	113.587	+	113.587i	0.166062	+	0.166062i
$685$	−401.005	+	79.7648i	−0.585409	+	0.116445i
$686$	−488.078	+	326.123i	−0.711483	+	0.475398i
$687$	−487.965	−	97.0623i	−0.710284	−	0.141284i
$688$	37.5745	−	15.5639i	0.0546142	−	0.0226219i
$689$	−39.4861	−	95.3279i	−0.0573093	−	0.138357i
$690$	−124.244	+	624.618i	−0.180064	+	0.905244i
$691$	518.707	+	776.300i	0.750661	+	1.12344i	0.988364	+	0.152106i	$0.0486055\pi$
$691$	518.707	+	776.300i	0.750661	+	1.12344i	−0.237703	+	0.971338i	$0.576395\pi$
$692$	33.2678	+	167.249i	0.0480749	+	0.241689i
$693$	148.139	−	148.139i	0.213764	−	0.213764i
$694$	−237.412	+	355.313i	−0.342093	+	0.511978i
$695$	−375.164	−	155.398i	−0.539804	−	0.223594i
$696$			419.081i			0.602128i
$697$		0			0
$698$	−887.929			−1.27210
$699$	93.1416	−	224.864i	0.133250	−	0.321693i
$700$	−104.858	−	70.0639i	−0.149797	−	0.100091i
$701$	411.177	+	411.177i	0.586558	+	0.586558i	0.936697	−	0.350140i	$-0.113866\pi$
$701$	411.177	+	411.177i	0.586558	+	0.586558i	−0.350140	+	0.936697i	$0.613866\pi$
$702$	38.1852	−	7.59550i	0.0543948	−	0.0108198i
$703$	661.299	−	441.866i	0.940681	−	0.628543i
$704$	484.626	+	96.3981i	0.688389	+	0.136929i
$705$	−129.595	+	53.6800i	−0.183823	+	0.0761418i
$706$	220.980	+	533.494i	0.313003	+	0.755657i
$707$	−99.3518	+	499.475i	−0.140526	+	0.706472i
$708$	−23.3305	−	34.9165i	−0.0329526	−	0.0493171i
$709$	226.937	+	1140.89i	0.320080	+	1.60915i	0.720931	+	0.693007i	$0.243715\pi$
$709$	226.937	+	1140.89i	0.320080	+	1.60915i	−0.400851	+	0.916143i	$0.631285\pi$
$710$	331.966	−	331.966i	0.467557	−	0.467557i
$711$	−87.9607	+	131.643i	−0.123714	+	0.185151i
$712$	−319.041	−	132.151i	−0.448091	−	0.185605i
$713$		−	435.811i		−	0.611235i
$714$		0			0
$715$	180.307			0.252177
$716$	−81.9532	+	197.853i	−0.114460	+	0.276330i
$717$	962.072	+	642.836i	1.34180	+	0.896563i
$718$	−663.338	−	663.338i	−0.923869	−	0.923869i
$719$	−14.5626	+	2.89668i	−0.0202540	+	0.00402876i	−0.205207	−	0.978719i	$-0.565787\pi$
$719$	−14.5626	+	2.89668i	−0.0202540	+	0.00402876i	0.184953	+	0.982747i	$0.440787\pi$
$720$	−554.644	+	370.601i	−0.770339	+	0.514724i
$721$	−702.729	−	139.782i	−0.974659	−	0.193872i
$722$	402.030	−	166.526i	0.556828	−	0.230646i
$723$	192.553	+	464.864i	0.266325	+	0.642966i
$724$	23.5300	−	118.293i	0.0325000	−	0.163389i
$725$	232.781	+	348.382i	0.321077	+	0.480526i
$726$	−101.522	−	510.383i	−0.139837	−	0.703007i
$727$	880.136	−	880.136i	1.21064	−	1.21064i	0.239825	−	0.970816i	$-0.422910\pi$
$727$	880.136	−	880.136i	1.21064	−	1.21064i	0.970816	−	0.239825i	$-0.0770901\pi$
$728$	−65.8106	+	98.4925i	−0.0903992	+	0.135292i
$729$	412.626	+	170.915i	0.566017	+	0.234452i
$730$			1279.69i			1.75300i
$731$		0			0
$732$	−253.382			−0.346150
$733$	208.728	−	503.915i	0.284759	−	0.687469i	−0.715175	−	0.698945i	$-0.753653\pi$
$733$	208.728	−	503.915i	0.284759	−	0.687469i	0.999934	+	0.0114762i	$0.00365305\pi$
$734$	−485.934	−	324.691i	−0.662036	−	0.442358i
$735$	−714.195	−	714.195i	−0.971694	−	0.971694i
$736$	−156.543	+	31.1383i	−0.212694	+	0.0423075i
$737$	−164.935	+	110.206i	−0.223793	+	0.149534i
$738$	−431.876	−	85.9054i	−0.585197	−	0.116403i
$739$	152.427	−	63.1371i	0.206261	−	0.0854359i	−0.277161	−	0.960823i	$-0.589394\pi$
$739$	152.427	−	63.1371i	0.206261	−	0.0854359i	0.483422	+	0.875387i	$0.339394\pi$
$740$	−84.4231	−	203.815i	−0.114085	−	0.275426i
$741$	65.3353	−	328.463i	0.0881717	−	0.443269i
$742$	123.345	+	184.599i	0.166233	+	0.248785i
$743$	0.449762	+	2.26111i	0.000605333	+	0.00304321i	0.981087	−	0.193568i	$-0.0620062\pi$
$743$	0.449762	+	2.26111i	0.000605333	+	0.00304321i	−0.980481	+	0.196612i	$0.937006\pi$
$744$	933.294	−	933.294i	1.25443	−	1.25443i
$745$	222.509	−	333.009i	0.298670	−	0.446992i
$746$	241.151	+	99.8879i	0.323258	+	0.133898i
$747$		−	837.618i		−	1.12131i
$748$		0			0
$749$	−163.145			−0.217817
$750$	−209.047	+	504.684i	−0.278729	+	0.672912i
$751$	1199.39	+	801.406i	1.59706	+	1.06712i	0.953359	+	0.301839i	$0.0976003\pi$
$751$	1199.39	+	801.406i	1.59706	+	1.06712i	0.643697	+	0.765280i	$0.277400\pi$
$752$	37.0123	+	37.0123i	0.0492184	+	0.0492184i
$753$	−559.487	+	111.289i	−0.743010	+	0.147794i
$754$	59.2003	−	39.5564i	0.0785150	−	0.0524620i
$755$	−1823.94	−	362.805i	−2.41582	−	0.480536i
$756$	21.9402	−	9.08793i	0.0290214	−	0.0120211i
$757$	−115.414	−	278.634i	−0.152463	−	0.368077i	0.829132	−	0.559052i	$-0.188835\pi$
$757$	−115.414	−	278.634i	−0.152463	−	0.368077i	−0.981595	+	0.190975i	$0.938835\pi$
$758$	−15.0450	+	75.6365i	−0.0198483	+	0.0997843i
$759$	−179.739	−	268.998i	−0.236810	−	0.354411i
$760$	−320.787	−	1612.70i	−0.422088	−	2.12198i
$761$	811.549	−	811.549i	1.06642	−	1.06642i	0.0687929	−	0.997631i	$-0.478085\pi$
$761$	811.549	−	811.549i	1.06642	−	1.06642i	0.997631	−	0.0687929i	$-0.0219148\pi$
$762$	163.017	−	243.973i	0.213934	−	0.320174i
$763$	173.265	+	71.7685i	0.227083	+	0.0940610i
$764$		−	153.984i		−	0.201550i
$765$		0			0
$766$	−348.859			−0.455429
$767$	−15.0916	+	36.4344i	−0.0196762	+	0.0475025i
$768$	−540.875	−	361.401i	−0.704264	−	0.470574i
$769$	−870.130	−	870.130i	−1.13151	−	1.13151i	−0.989927	−	0.141582i	$-0.954781\pi$
$769$	−870.130	−	870.130i	−1.13151	−	1.13151i	−0.141582	−	0.989927i	$-0.545219\pi$
$770$	−380.508	+	75.6877i	−0.494166	+	0.0982958i
$771$	−1322.42	+	883.615i	−1.71520	+	1.14606i
$772$	162.617	+	32.3465i	0.210644	+	0.0418996i
$773$	−1306.77	+	541.282i	−1.69052	+	0.700235i	−0.999739	−	0.0228308i	$-0.992732\pi$
$773$	−1306.77	+	541.282i	−1.69052	+	0.700235i	−0.690779	+	0.723066i	$0.742732\pi$
$774$	−17.3451	−	41.8749i	−0.0224098	−	0.0541019i
$775$	257.442	−	1294.25i	0.332184	−	1.67000i
$776$	796.710	+	1192.36i	1.02669	+	1.53655i
$777$	104.256	+	524.128i	0.134177	+	0.674553i
$778$	26.8308	−	26.8308i	0.0344869	−	0.0344869i
$779$	463.005	−	692.937i	0.594359	−	0.889521i
$780$	−85.8218	−	35.5486i	−0.110028	−	0.0455751i
$781$			238.490i			0.305365i
$782$		0			0
$783$	−78.9004			−0.100767
$784$	−144.231	+	348.205i	−0.183969	+	0.444139i
$785$	−1730.25	−	1156.12i	−2.20414	−	1.47276i
$786$	972.366	+	972.366i	1.23711	+	1.23711i
$787$	1513.12	−	300.978i	1.92264	−	0.382437i	0.922645	−	0.385650i	$-0.126023\pi$
$787$	1513.12	−	300.978i	1.92264	−	0.382437i	0.999995	+	0.00321327i	$0.00102282\pi$
$788$	210.924	−	140.935i	0.267670	−	0.178851i
$789$	−1156.88	−	230.117i	−1.46626	−	0.291657i
$790$	270.877	−	112.201i	0.342882	−	0.142026i
$791$	293.232	+	707.924i	0.370710	+	0.894973i
$792$	86.1025	−	432.867i	0.108715	−	0.546549i
$793$	132.199	+	197.849i	0.166707	+	0.249495i
$794$	12.2185	+	61.4266i	0.0153885	+	0.0773634i
$795$	−680.496	+	680.496i	−0.855970	+	0.855970i
$796$	44.9588	−	67.2856i	0.0564809	−	0.0845297i
$797$	1040.17	+	430.853i	1.30511	+	0.540593i	0.923453	−	0.383712i	$-0.125355\pi$
$797$	1040.17	+	430.853i	1.30511	+	0.540593i	0.381654	+	0.924305i	$0.375355\pi$
$798$			720.593i			0.902998i
$799$		0			0
$800$	−483.288			−0.604110
$801$	−113.079	+	272.996i	−0.141172	+	0.340819i
$802$	−219.538	−	146.691i	−0.273739	−	0.182906i
$803$	−459.675	−	459.675i	−0.572448	−	0.572448i
$804$	100.233	−	19.9376i	0.124668	−	0.0247981i
$805$	303.322	−	202.673i	0.376798	−	0.251768i
$806$	−219.931	−	43.7470i	−0.272868	−	0.0542767i
$807$	−380.953	+	157.796i	−0.472061	+	0.195534i
$808$	410.560	+	991.179i	0.508119	+	1.22671i
$809$	−64.1132	+	322.319i	−0.0792500	+	0.398417i	0.920717	+	0.390232i	$0.127605\pi$
$809$	−64.1132	+	322.319i	−0.0792500	+	0.398417i	−0.999967	+	0.00818445i	$0.997395\pi$
$810$	−705.632	−	1056.05i	−0.871150	−	1.30377i
$811$	−56.9327	−	286.220i	−0.0702006	−	0.352922i	0.929680	−	0.368368i	$-0.120083\pi$
$811$	−56.9327	−	286.220i	−0.0702006	−	0.352922i	−0.999881	+	0.0154457i	$0.995083\pi$
$812$	30.7091	−	30.7091i	0.0378191	−	0.0378191i
$813$	−856.736	+	1282.20i	−1.05380	+	1.57712i
$814$	−365.235	−	151.285i	−0.448692	−	0.185854i
$815$			300.260i			0.368417i
$816$		0			0
$817$	85.7829			0.104997
$818$	269.482	−	650.588i	0.329441	−	0.795340i
$819$	84.2777	+	56.3126i	0.102903	+	0.0687577i
$820$	−163.457	−	163.457i	−0.199337	−	0.199337i
$821$	−1059.59	+	210.765i	−1.29061	+	0.256718i	−0.792219	−	0.610237i	$-0.791074\pi$
$821$	−1059.59	+	210.765i	−1.29061	+	0.256718i	−0.498388	+	0.866954i	$0.666074\pi$
$822$	313.854	−	209.711i	0.381818	−	0.255122i
$823$	89.0135	+	17.7059i	0.108157	+	0.0215138i	0.248872	−	0.968536i	$-0.419940\pi$
$823$	89.0135	+	17.7059i	0.108157	+	0.0215138i	−0.140715	+	0.990050i	$0.544940\pi$
$824$	−1394.52	+	577.631i	−1.69238	+	0.701008i
$825$	−374.877	−	905.033i	−0.454396	−	1.09701i
$826$	16.5543	−	83.2240i	0.0200415	−	0.100755i
$827$	−270.056	−	404.167i	−0.326549	−	0.488715i	0.631478	−	0.775394i	$-0.282449\pi$
$827$	−270.056	−	404.167i	−0.326549	−	0.488715i	−0.958027	+	0.286679i	$0.907449\pi$
$828$	14.6471	+	73.6358i	0.0176897	+	0.0889322i
$829$	−743.445	+	743.445i	−0.896797	+	0.896797i	−0.995151	−	0.0983544i	$-0.968642\pi$
$829$	−743.445	+	743.445i	−0.896797	+	0.896797i	0.0983544	+	0.995151i	$0.468642\pi$
$830$	−861.770	+	1289.73i	−1.03828	+	1.55389i
$831$	251.307	+	104.095i	0.302415	+	0.125264i
$832$			239.065i			0.287338i
$833$		0			0
$834$	374.896			0.449516
$835$	−106.690	+	257.571i	−0.127772	+	0.308469i
$836$	125.648	+	83.9554i	0.150297	+	0.100425i
$837$	175.711	+	175.711i	0.209930	+	0.209930i
$838$	−64.7556	+	12.8807i	−0.0772740	+	0.0153708i
$839$	381.369	−	254.822i	0.454551	−	0.303721i	−0.307137	−	0.951665i	$-0.599371\pi$
$839$	381.369	−	254.822i	0.454551	−	0.303721i	0.761688	+	0.647944i	$0.224371\pi$
$840$	1083.60	+	215.540i	1.28999	+	0.256596i
$841$	643.676	−	266.619i	0.765370	−	0.317027i
$842$	−298.762	−	721.276i	−0.354824	−	0.856622i
$843$	−297.687	+	1496.57i	−0.353128	+	1.77529i
$844$	17.7482	+	26.5621i	0.0210287	+	0.0314717i
$845$	−238.115	−	1197.08i	−0.281793	−	1.41667i
$846$	41.2482	−	41.2482i	0.0487568	−	0.0487568i
$847$	−165.607	+	247.848i	−0.195522	+	0.292619i
$848$	331.775	+	137.426i	0.391244	+	0.162059i
$849$		−	1201.22i		−	1.41486i
$850$		0			0
$851$	371.728			0.436813
$852$	47.0197	−	113.516i	0.0551875	−	0.133234i
$853$	−6.26033	−	4.18302i	−0.00733919	−	0.00490389i	0.551895	−	0.833913i	$-0.313905\pi$
$853$	−6.26033	−	4.18302i	−0.00733919	−	0.00490389i	−0.559234	+	0.829010i	$0.688905\pi$
$854$	−362.035	−	362.035i	−0.423929	−	0.423929i
$855$	−1379.95	+	274.490i	−1.61398	+	0.321041i
$856$	−285.770	+	190.946i	−0.333844	+	0.223067i
$857$	−49.7272	−	9.89135i	−0.0580247	−	0.0115418i	0.165993	−	0.986127i	$-0.446917\pi$
$857$	−49.7272	−	9.89135i	−0.0580247	−	0.0115418i	−0.224017	+	0.974585i	$0.571917\pi$
$858$	−153.792	+	63.7026i	−0.179244	+	0.0742455i
$859$	−192.547	−	464.849i	−0.224152	−	0.541151i	0.771294	−	0.636479i	$-0.219610\pi$
$859$	−192.547	−	464.849i	−0.224152	−	0.541151i	−0.995446	+	0.0953281i	$0.969610\pi$
$860$	4.64202	−	23.3370i	0.00539770	−	0.0271361i
$861$	311.099	+	465.592i	0.361323	+	0.540758i
$862$	119.473	+	600.631i	0.138600	+	0.696787i
$863$	98.9573	−	98.9573i	0.114667	−	0.114667i	−0.647445	−	0.762112i	$-0.724163\pi$
$863$	98.9573	−	98.9573i	0.114667	−	0.114667i	0.762112	+	0.647445i	$0.224163\pi$
$864$	50.5609	−	75.6697i	0.0585196	−	0.0875807i
$865$	−1379.92	−	571.580i	−1.59528	−	0.660786i
$866$			94.8830i			0.109565i
$867$		0			0
$868$	−136.778			−0.157579
$869$	−56.9977	+	137.605i	−0.0655900	+	0.158348i
$870$	−552.154	−	368.937i	−0.634660	−	0.424066i
$871$	−67.8634	−	67.8634i	−0.0779143	−	0.0779143i
$872$	387.494	−	77.0774i	0.444374	−	0.0883915i
$873$	1020.28	−	681.726i	1.16870	−	0.780900i
$874$	491.615	+	97.7883i	0.562488	+	0.111886i
$875$	289.092	−	119.746i	0.330391	−	0.136853i
$876$	128.167	+	309.423i	0.146309	+	0.353222i
$877$	185.255	−	931.342i	0.211238	−	1.06196i	−0.719001	−	0.695009i	$-0.755400\pi$
$877$	185.255	−	931.342i	0.211238	−	1.06196i	0.930239	−	0.366955i	$-0.119600\pi$
$878$	238.583	+	357.065i	0.271735	+	0.406680i
$879$	111.481	+	560.455i	0.126828	+	0.637605i
$880$	−443.732	+	443.732i	−0.504241	+	0.504241i
$881$	581.184	−	869.803i	0.659686	−	0.987290i	−0.339228	−	0.940704i	$-0.610166\pi$
$881$	581.184	−	869.803i	0.659686	−	0.987290i	0.998914	−	0.0465861i	$-0.0148342\pi$
$882$	388.057	+	160.738i	0.439974	+	0.182243i
$883$		−	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
$886$	77.4157	−	186.898i	0.0873766	−	0.210946i
$887$	−649.952	−	434.284i	−0.732753	−	0.489610i	0.132351	−	0.991203i	$-0.457747\pi$
$887$	−649.952	−	434.284i	−0.732753	−	0.489610i	−0.865104	+	0.501593i	$0.832747\pi$
$888$	796.059	+	796.059i	0.896463	+	0.896463i
$889$	−164.849	+	32.7905i	−0.185432	+	0.0368847i
$890$	454.981	−	304.009i	0.511215	−	0.341583i
$891$	632.812	+	125.874i	0.710227	+	0.141273i
$892$	329.023	−	136.286i	0.368860	−	0.152787i
$893$	42.2496	+	102.000i	0.0473120	+	0.114221i
$894$	−72.1358	+	362.651i	−0.0806888	+	0.405650i
$895$	−1042.11	−	1559.63i	−1.16437	−	1.74260i
$896$	−56.1063	−	282.066i	−0.0626187	−	0.314805i
$897$	110.680	−	110.680i	0.123389	−	0.123389i
$898$	532.761	−	797.334i	0.593276	−	0.887900i
$899$	419.842	+	173.904i	0.467010	+	0.193442i
$900$			227.333i			0.252592i
$901$		0			0
$902$	−414.241			−0.459247
$903$	−22.0573	+	53.2511i	−0.0244267	+	0.0589713i
$904$	1342.19	+	896.823i	1.48472	+	0.992061i
$905$	746.999	+	746.999i	0.825413	+	0.825413i
$906$	1683.90	−	334.949i	1.85861	−	0.369701i
$907$	310.763	−	207.645i	0.342628	−	0.228936i	−0.372336	−	0.928098i	$-0.621443\pi$
$907$	310.763	−	207.645i	0.342628	−	0.228936i	0.714964	+	0.699161i	$0.246443\pi$
$908$	−109.390	−	21.7590i	−0.120474	−	0.0239637i
$909$	848.129	−	351.306i	0.933035	−	0.386476i
$910$	−71.8311	−	173.416i	−0.0789352	−	0.190567i
$911$	−23.7829	+	119.565i	−0.0261064	+	0.131246i	−0.991641	−	0.129030i	$-0.958814\pi$
$911$	−23.7829	+	119.565i	−0.0261064	+	0.131246i	0.965534	+	0.260276i	$0.0838136\pi$
$912$	647.553	+	969.131i	0.710036	+	1.06264i
$913$	−153.727	−	772.838i	−0.168376	−	0.846482i
$914$	−280.276	+	280.276i	−0.306647	+	0.306647i
$915$	1233.00	−	1845.31i	1.34754	−	2.01674i
$916$	100.349	+	41.5657i	0.109551	+	0.0453774i
$917$		−	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	$0.166582\pi$
$920$	294.099	−	710.018i	0.319673	−	0.771759i
$921$	873.645	+	583.751i	0.948583	+	0.633823i
$922$	−314.913	−	314.913i	−0.341555	−	0.341555i
$923$	−113.169	+	22.5107i	−0.122610	+	0.0243886i
$924$	−84.4245	+	56.4107i	−0.0913685	+	0.0610505i
$925$	1103.94	+	219.587i	1.19345	+	0.237391i
$926$	204.478	−	84.6976i	0.220819	−	0.0914661i
$927$	494.265	+	1193.26i	0.533188	+	1.28723i
$928$	32.4690	−	163.232i	0.0349881	−	0.175897i
$929$	−377.264	−	564.616i	−0.406097	−	0.607767i	0.570900	−	0.821020i	$-0.306594\pi$
$929$	−377.264	−	564.616i	−0.406097	−	0.607767i	−0.976997	+	0.213252i	$0.931594\pi$
$930$	408.023	+	2051.27i	0.438735	+	2.20567i
$931$	−562.118	+	562.118i	−0.603778	+	0.603778i
$932$	−29.5205	+	44.1806i	−0.0316744	+	0.0474040i
$933$	−2109.16	−	873.641i	−2.26062	−	0.936378i
$934$		−	1223.18i		−	1.30961i
$935$		0			0
$936$	213.532			0.228133
$937$	112.652	−	271.967i	0.120227	−	0.290253i	−0.852296	−	0.523059i	$-0.824791\pi$
$937$	112.652	−	271.967i	0.120227	−	0.290253i	0.972523	+	0.232806i	$0.0747907\pi$
$938$	171.702	+	114.727i	0.183051	+	0.122311i
$939$	1304.18	+	1304.18i	1.38890	+	1.38890i
$940$	30.0350	−	5.97433i	0.0319521	−	0.00635567i
$941$	−694.344	+	463.946i	−0.737879	+	0.493035i	−0.866822	−	0.498617i	$-0.833841\pi$
$941$	−694.344	+	463.946i	−0.737879	+	0.493035i	0.128943	+	0.991652i	$0.458841\pi$
$942$	1884.27	+	374.804i	2.00029	+	0.397882i
$943$	359.862	−	149.060i	0.381614	−	0.158070i
$944$	−52.5243	−	126.805i	−0.0556402	−	0.134327i
$945$	−40.5798	+	204.008i	−0.0429416	+	0.215882i
$946$	−23.6889	−	35.4530i	−0.0250412	−	0.0374767i
$947$	121.512	+	610.881i	0.128312	+	0.645070i	0.990391	+	0.138295i	$0.0441624\pi$
$947$	121.512	+	610.881i	0.128312	+	0.645070i	−0.862079	+	0.506775i	$0.830838\pi$
$948$	54.2592	−	54.2592i	0.0572355	−	0.0572355i
$949$	174.738	−	261.514i	0.184129	−	0.275568i
$950$	1402.21	+	580.814i	1.47601	+	0.611383i
$951$			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	$0.562734\pi$
$954$	153.154	−	369.746i	0.160539	−	0.387575i
$955$	1121.43	+	749.313i	1.17427	+	0.784621i
$956$	−178.619	−	178.619i	−0.186840	−	0.186840i
$957$	330.864	−	65.8130i	0.345730	−	0.0687701i
$958$	702.650	−	469.496i	0.733455	−	0.490079i
$959$	−212.067	−	42.1827i	−0.221133	−	0.0439861i
$960$	2060.00	−	853.280i	2.14583	−	0.888833i
$961$	−179.945	−	434.426i	−0.187248	−	0.452056i
$962$	37.3143	−	187.592i	0.0387883	−	0.195002i
$963$	163.388	+	244.527i	0.169665	+	0.253922i
$964$	−21.4303	−	107.737i	−0.0222306	−	0.111761i
$965$	−1026.89	+	1026.89i	−1.06414	+	1.06414i
$966$	−187.112	+	280.033i	−0.193698	+	0.289890i
$967$	947.512	+	392.472i	0.979847	+	0.405866i	0.814369	−	0.580348i	$-0.197083\pi$
$967$	947.512	+	392.472i	0.979847	+	0.405866i	0.165478	+	0.986213i	$0.447083\pi$
$968$			627.966i			0.648725i
$969$		0			0
$970$	−2272.36			−2.34264
$971$	376.591	−	909.171i	0.387838	−	0.936325i	−0.602559	−	0.798074i	$-0.705852\pi$
$971$	376.591	−	909.171i	0.387838	−	0.936325i	0.990397	−	0.138250i	$-0.0441478\pi$
$972$	−232.961	−	155.660i	−0.239672	−	0.160144i
$973$	−151.849	−	151.849i	−0.156063	−	0.156063i
$974$	−702.385	+	139.713i	−0.721134	+	0.143443i
$975$	394.074	−	263.312i	0.404179	−	0.270064i
$976$	−812.243	−	161.565i	−0.832216	−	0.165538i
$977$	−525.837	+	217.809i	−0.538216	+	0.222936i	−0.635197	−	0.772350i	$-0.719081\pi$
$977$	−525.837	+	217.809i	−0.538216	+	0.222936i	0.0969814	+	0.995286i	$0.469081\pi$
$978$	−106.082	−	256.105i	−0.108469	−	0.261866i
$979$	−54.2306	+	272.636i	−0.0553939	+	0.278484i
$980$	122.504	+	183.341i	0.125004	+	0.187082i
$981$	−65.9533	−	331.570i	−0.0672307	−	0.337991i
$982$	−77.4444	+	77.4444i	−0.0788639	+	0.0788639i
$983$	−798.843	+	1195.55i	−0.812658	+	1.21623i	0.160715	+	0.987001i	$0.448620\pi$
$983$	−798.843	+	1195.55i	−0.812658	+	1.21623i	−0.973373	+	0.229228i	$0.926380\pi$
$984$	1089.86	+	451.436i	1.10758	+	0.458776i
$985$			2221.92i			2.25575i
$986$		0			0
$987$	−74.1814			−0.0751585
$988$	−27.9790	+	67.5473i	−0.0283188	+	0.0683677i
$989$	33.3365	+	22.2748i	0.0337073	+	0.0225225i
$990$	494.517	+	494.517i	0.499512	+	0.499512i
$991$	82.3495	−	16.3803i	0.0830973	−	0.0165291i	−0.153367	−	0.988169i	$-0.549012\pi$
$991$	82.3495	−	16.3803i	0.0830973	−	0.0165291i	0.236464	+	0.971640i	$0.424012\pi$
$992$	−435.827	+	291.210i	−0.439342	+	0.293559i
$993$	2339.80	+	465.415i	2.35629	+	0.468696i
$994$	229.375	−	95.0102i	0.230759	−	0.0955837i
$995$	271.246	+	654.847i	0.272609	+	0.658137i
$996$	−79.1992	+	398.161i	−0.0795172	+	0.399760i
$997$	−418.521	−	626.361i	−0.419780	−	0.628246i	0.559959	−	0.828520i	$-0.310817\pi$
$997$	−418.521	−	626.361i	−0.419780	−	0.628246i	−0.979740	+	0.200274i	$0.935817\pi$
$998$	176.763	+	888.649i	0.177118	+	0.890430i
$999$	−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.a.214.1		8
17.2	even	8		289.3.e.g.40.1		8
17.3	odd	16		289.3.e.j.158.1		8
17.4	even	4		289.3.e.j.75.1		8
17.5	odd	16		289.3.e.e.131.1		8
17.6	odd	16		289.3.e.g.224.1		8
17.7	odd	16		289.3.e.h.65.1		8
17.8	even	8		289.3.e.f.249.1		8
17.9	even	8		289.3.e.h.249.1		8
17.10	odd	16		289.3.e.f.65.1		8
17.11	odd	16		17.3.e.b.3.1	✓	8
17.12	odd	16	inner	289.3.e.a.131.1		8
17.13	even	4		289.3.e.n.75.1		8
17.14	odd	16		289.3.e.n.158.1		8
17.15	even	8		17.3.e.b.6.1	yes	8
17.16	even	2		289.3.e.e.214.1		8
51.11	even	16		153.3.p.a.37.1		8
51.32	odd	8		153.3.p.a.91.1		8
68.11	even	16		272.3.bh.b.241.1		8
68.15	odd	8		272.3.bh.b.193.1		8
85.28	even	16		425.3.t.d.224.1		8
85.32	odd	8		425.3.t.d.74.1		8
85.49	even	8		425.3.u.a.176.1		8
85.62	even	16		425.3.t.b.224.1		8
85.79	odd	16		425.3.u.a.326.1		8
85.83	odd	8		425.3.t.b.74.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.3.e.b.3.1	✓	8	17.11	odd	16
17.3.e.b.6.1	yes	8	17.15	even	8
153.3.p.a.37.1		8	51.11	even	16
153.3.p.a.91.1		8	51.32	odd	8
272.3.bh.b.193.1		8	68.15	odd	8
272.3.bh.b.241.1		8	68.11	even	16
289.3.e.a.131.1		8	17.12	odd	16	inner
289.3.e.a.214.1		8	1.1	even	1	trivial
289.3.e.e.131.1		8	17.5	odd	16
289.3.e.e.214.1		8	17.16	even	2
289.3.e.f.65.1		8	17.10	odd	16
289.3.e.f.249.1		8	17.8	even	8
289.3.e.g.40.1		8	17.2	even	8
289.3.e.g.224.1		8	17.6	odd	16
289.3.e.h.65.1		8	17.7	odd	16
289.3.e.h.249.1		8	17.9	even	8
289.3.e.j.75.1		8	17.4	even	4
289.3.e.j.158.1		8	17.3	odd	16
289.3.e.n.75.1		8	17.13	even	4
289.3.e.n.158.1		8	17.14	odd	16
425.3.t.b.74.1		8	85.83	odd	8
425.3.t.b.224.1		8	85.62	even	16
425.3.t.d.74.1		8	85.32	odd	8
425.3.t.d.224.1		8	85.28	even	16
425.3.u.a.176.1		8	85.49	even	8
425.3.u.a.326.1		8	85.79	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+(-0.675577 + 1.63099i) q^{2} +(-3.36482 - 2.24830i) q^{3} +(0.624715 + 0.624715i) q^{4} +(-7.58960 + 1.50967i) q^{5} +(5.94015 - 3.96908i) q^{6} +(-4.01367 - 0.798369i) q^{7} +(-7.96489 + 3.29916i) q^{8} +(2.82302 + 6.81537i) q^{9} +(2.66511 - 13.3984i) q^{10} +(3.85550 + 5.77017i) q^{11} +(-0.697506 - 3.50660i) q^{12} +(-2.37416 + 2.37416i) q^{13} +(4.01367 - 6.00688i) q^{14} +(28.9319 + 11.9840i) q^{15} -11.6855i q^{16} -13.0229 q^{18} +(9.43215 - 22.7712i) q^{19} +(-5.68445 - 3.79823i) q^{20} +(11.7103 + 11.7103i) q^{21} +(-12.0158 + 2.39008i) q^{22} +(9.57836 - 6.40006i) q^{23} +(34.2180 + 6.80638i) q^{24} +(32.2260 - 13.3484i) q^{25} +(-2.26829 - 5.47615i) q^{26} +(-1.28144 + 6.44221i) q^{27} +(-2.00865 - 3.00615i) q^{28} +(2.34344 + 11.7813i) q^{29} +(-39.0914 + 39.0914i) q^{30} +(21.0180 - 31.4557i) q^{31} +(-12.8006 - 5.30218i) q^{32} -28.0839i q^{33} +31.6674 q^{35} +(-2.49408 + 6.02124i) q^{36} +(26.8303 + 17.9275i) q^{37} +(30.7674 + 30.7674i) q^{38} +(13.3265 - 2.65080i) q^{39} +(55.4697 - 37.0637i) q^{40} +(33.1627 + 6.59647i) q^{41} +(-27.0106 + 11.1881i) q^{42} +(1.33189 + 3.21547i) q^{43} +(-1.19612 + 6.01330i) q^{44} +(-31.7145 - 47.4641i) q^{45} +(3.96749 + 19.9459i) q^{46} +(-3.16735 + 3.16735i) q^{47} +(-26.2726 + 39.3198i) q^{48} +(-29.7979 - 12.3427i) q^{49} +61.5781i q^{50} -2.96634 q^{52} +(-11.7603 + 28.3919i) q^{53} +(-9.64145 - 6.44221i) q^{54} +(-37.9728 - 37.9728i) q^{55} +(34.6024 - 6.88284i) q^{56} +(-82.9342 + 55.4148i) q^{57} +(-20.7982 - 4.13703i) q^{58} +(10.8514 - 4.49481i) q^{59} +(10.5876 + 25.5607i) q^{60} +(13.8261 - 69.5084i) q^{61} +(37.1045 + 55.5309i) q^{62} +(-5.88948 - 29.6084i) q^{63} +(50.3473 - 50.3473i) q^{64} +(14.4347 - 21.6031i) q^{65} +(45.8045 + 18.9728i) q^{66} +28.5842i q^{67} -46.6187 q^{69} +(-21.3938 + 51.6491i) q^{70} +(28.5742 + 19.0927i) q^{71} +(-44.9700 - 44.9700i) q^{72} +(-91.8752 + 18.2751i) q^{73} +(-47.3654 + 31.6486i) q^{74} +(-138.446 - 27.5386i) q^{75} +(20.1179 - 8.33312i) q^{76} +(-10.8680 - 26.2377i) q^{77} +(-4.67963 + 23.5261i) q^{78} +(11.9238 + 17.8452i) q^{79} +(17.6413 + 88.6886i) q^{80} +(65.7422 - 65.7422i) q^{81} +(-33.1627 + 49.6315i) q^{82} +(-104.903 - 43.4522i) q^{83} +14.6312i q^{84} -6.14419 q^{86} +(18.6026 - 44.9106i) q^{87} +(-49.7454 - 33.2388i) q^{88} +(28.3238 + 28.3238i) q^{89} +(98.8389 - 19.6603i) q^{90} +(11.4245 - 7.63364i) q^{91} +(9.98195 + 1.98553i) q^{92} +(-141.444 + 58.5880i) q^{93} +(-3.02612 - 7.30570i) q^{94} +(-37.2094 + 187.064i) q^{95} +(31.1508 + 46.6205i) q^{96} +(-32.4513 - 163.144i) q^{97} +(40.2616 - 40.2616i) q^{98} +(-28.4417 + 42.5659i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{2} - 16 q^{3} + 8 q^{4} - 8 q^{5} + 40 q^{6} - 16 q^{7} - 8 q^{8} + 56 q^{9} + 16 q^{10} - 32 q^{12} + 16 q^{14} + 80 q^{15} - 136 q^{18} + 80 q^{19} - 48 q^{20} + 64 q^{21} - 40 q^{22} - 16 q^{23}+ \cdots - 144 q^{99}+O(q^{100}) \) 8 * q - 8 * q^2 - 16 * q^3 + 8 * q^4 - 8 * q^5 + 40 * q^6 - 16 * q^7 - 8 * q^8 + 56 * q^9 + 16 * q^10 - 32 * q^12 + 16 * q^14 + 80 * q^15 - 136 * q^18 + 80 * q^19 - 48 * q^20 + 64 * q^21 - 40 * q^22 - 16 * q^23 + 88 * q^24 + 136 * q^25 - 40 * q^26 - 64 * q^27 - 40 * q^28 + 144 * q^29 - 168 * q^30 + 88 * q^31 - 16 * q^32 + 80 * q^35 + 72 * q^36 - 24 * q^37 - 8 * q^38 + 96 * q^40 + 144 * q^41 - 88 * q^42 - 48 * q^43 - 112 * q^44 - 8 * q^46 + 80 * q^47 + 40 * q^48 - 72 * q^49 + 240 * q^52 - 88 * q^53 + 256 * q^54 + 8 * q^55 + 64 * q^56 - 200 * q^57 - 144 * q^58 + 40 * q^59 + 96 * q^60 + 88 * q^61 - 24 * q^62 - 216 * q^63 + 120 * q^64 - 160 * q^65 + 120 * q^66 - 208 * q^69 - 96 * q^70 - 48 * q^71 - 24 * q^72 - 224 * q^73 + 104 * q^74 - 272 * q^75 - 192 * q^76 - 120 * q^77 + 232 * q^78 + 136 * q^79 + 80 * q^80 + 224 * q^81 - 144 * q^82 - 504 * q^83 + 288 * q^86 - 216 * q^87 - 112 * q^88 - 288 * q^89 + 344 * q^90 + 16 * q^91 - 48 * q^92 - 248 * q^93 - 72 * q^94 + 144 * q^95 + 80 * q^96 - 208 * q^97 - 16 * q^98 - 144 * q^99

Introduction

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