LMFDB - Embedded newform 289.3.e.n.75.1

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 = [8,8,8,8,-16] 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			75.1
Root			$-0.382683 - 0.923880i$ of defining polynomial
Character	$\chi$	$=$	289.75
Dual form			289.3.e.n.158.1

$q$-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} +(2.24830 - 3.36482i) q^{3} +(0.624715 + 0.624715i) q^{4} +(-1.50967 - 7.58960i) q^{5} +(-3.96908 - 5.94015i) q^{6} +(-0.798369 + 4.01367i) q^{7} +(7.96489 - 3.29916i) q^{8} +(-2.82302 - 6.81537i) q^{9} +(-13.3984 - 2.66511i) q^{10} +(5.77017 - 3.85550i) q^{11} +(3.50660 - 0.697506i) q^{12} +(-2.37416 + 2.37416i) q^{13} +(6.00688 + 4.01367i) q^{14} +(-28.9319 - 11.9840i) q^{15} -11.6855i q^{16} -13.0229 q^{18} +(-9.43215 + 22.7712i) q^{19} +(3.79823 - 5.68445i) q^{20} +(11.7103 + 11.7103i) q^{21} +(-2.39008 - 12.0158i) q^{22} +(-6.40006 - 9.57836i) q^{23} +(6.80638 - 34.2180i) q^{24} +(-32.2260 + 13.3484i) q^{25} +(2.26829 + 5.47615i) q^{26} +(6.44221 + 1.28144i) q^{27} +(-3.00615 + 2.00865i) q^{28} +(-11.7813 + 2.34344i) q^{29} +(-39.0914 + 39.0914i) q^{30} +(31.4557 + 21.0180i) q^{31} +(12.8006 + 5.30218i) q^{32} -28.0839i q^{33} +31.6674 q^{35} +(2.49408 - 6.02124i) q^{36} +(-17.9275 + 26.8303i) q^{37} +(30.7674 + 30.7674i) q^{38} +(2.65080 + 13.3265i) q^{39} +(-37.0637 - 55.4697i) q^{40} +(6.59647 - 33.1627i) q^{41} +(27.0106 - 11.1881i) q^{42} +(-1.33189 - 3.21547i) q^{43} +(6.01330 + 1.19612i) q^{44} +(-47.4641 + 31.7145i) q^{45} +(-19.9459 + 3.96749i) q^{46} +(-3.16735 + 3.16735i) q^{47} +(-39.3198 - 26.2726i) q^{48} +(29.7979 + 12.3427i) q^{49} +61.5781i q^{50} -2.96634 q^{52} +(11.7603 - 28.3919i) q^{53} +(6.44221 - 9.64145i) q^{54} +(-37.9728 - 37.9728i) q^{55} +(6.88284 + 34.6024i) q^{56} +(55.4148 + 82.9342i) q^{57} +(-4.13703 + 20.7982i) q^{58} +(-10.8514 + 4.49481i) q^{59} +(-10.5876 - 25.5607i) q^{60} +(-69.5084 - 13.8261i) q^{61} +(55.5309 - 37.1045i) q^{62} +(29.6084 - 5.88948i) q^{63} +(50.3473 - 50.3473i) q^{64} +(21.6031 + 14.4347i) q^{65} +(-45.8045 - 18.9728i) q^{66} +28.5842i q^{67} -46.6187 q^{69} +(21.3938 - 51.6491i) q^{70} +(-19.0927 + 28.5742i) q^{71} +(-44.9700 - 44.9700i) q^{72} +(-18.2751 - 91.8752i) q^{73} +(31.6486 + 47.3654i) q^{74} +(-27.5386 + 138.446i) q^{75} +(-20.1179 + 8.33312i) q^{76} +(10.8680 + 26.2377i) q^{77} +(23.5261 + 4.67963i) q^{78} +(17.8452 - 11.9238i) q^{79} +(-88.6886 + 17.6413i) q^{80} +(65.7422 - 65.7422i) q^{81} +(-49.6315 - 33.1627i) q^{82} +(104.903 + 43.4522i) q^{83} +14.6312i q^{84} -6.14419 q^{86} +(-18.6026 + 44.9106i) q^{87} +(33.2388 - 49.7454i) q^{88} +(28.3238 + 28.3238i) q^{89} +(19.6603 + 98.8389i) q^{90} +(-7.63364 - 11.4245i) q^{91} +(1.98553 - 9.98195i) q^{92} +(141.444 - 58.5880i) q^{93} +(3.02612 + 7.30570i) q^{94} +(187.064 + 37.2094i) q^{95} +(46.6205 - 31.1508i) q^{96} +(163.144 - 32.4513i) q^{97} +(40.2616 - 40.2616i) q^{98} +(-42.5659 - 28.4417i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 16 q^{5} + 8 q^{7} + 8 q^{8} - 56 q^{9} - 48 q^{10} + 24 q^{11} + 24 q^{12} - 8 q^{14} - 80 q^{15} - 136 q^{18} - 80 q^{19} + 48 q^{20} + 64 q^{21} - 16 q^{22} - 104 q^{23}+ \cdots + 120 q^{99}+O(q^{100}) $ 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 16 * q^5 + 8 * q^7 + 8 * q^8 - 56 * q^9 - 48 * q^10 + 24 * q^11 + 24 * q^12 - 8 * q^14 - 80 * q^15 - 136 * q^18 - 80 * q^19 + 48 * q^20 + 64 * q^21 - 16 * q^22 - 104 * q^23 - 136 * q^25 + 40 * q^26 + 32 * q^27 - 168 * q^30 + 144 * q^31 + 16 * q^32 + 80 * q^35 - 72 * q^36 + 48 * q^37 - 8 * q^38 - 96 * q^39 + 8 * q^40 + 208 * q^41 + 88 * q^42 + 48 * q^43 - 56 * q^44 + 48 * q^45 - 80 * q^46 + 80 * q^47 - 256 * q^48 + 72 * q^49 + 240 * q^52 + 88 * q^53 + 32 * q^54 + 8 * q^55 - 8 * q^56 + 40 * q^57 - 120 * q^58 - 40 * q^59 - 96 * q^60 - 16 * q^61 + 256 * q^62 + 96 * q^63 + 120 * q^64 - 72 * q^65 - 120 * q^66 - 208 * q^69 + 96 * q^70 - 328 * q^71 - 24 * q^72 + 160 * q^73 + 168 * q^74 - 264 * q^75 + 192 * q^76 + 120 * q^77 - 168 * q^78 - 352 * q^79 - 328 * q^80 + 224 * q^81 + 320 * q^82 + 504 * q^83 + 288 * q^86 + 216 * q^87 - 56 * q^88 - 288 * q^89 + 392 * q^90 + 32 * q^91 - 200 * q^92 + 248 * q^93 + 72 * q^94 + 800 * q^95 - 408 * q^96 + 504 * q^97 - 16 * q^98 + 120 * q^99

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{11}{16}\right)$

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	$-0.729503\pi$
$2$	0.675577	−	1.63099i	0.337788	−	0.815493i	0.997927	−	0.0643498i	$-0.0204973\pi$
$3$	2.24830	−	3.36482i	0.749434	−	1.12161i	−0.239156	−	0.970981i	$-0.576871\pi$
$3$	2.24830	−	3.36482i	0.749434	−	1.12161i	0.988591	−	0.150627i	$-0.0481291\pi$
$4$	0.624715	+	0.624715i	0.156179	+	0.156179i
$5$	−1.50967	−	7.58960i	−0.301933	−	1.51792i	−0.772190	−	0.635391i	$-0.780839\pi$
$5$	−1.50967	−	7.58960i	−0.301933	−	1.51792i	0.470257	−	0.882529i	$-0.344161\pi$
$6$	−3.96908	−	5.94015i	−0.661513	−	0.990025i
$7$	−0.798369	+	4.01367i	−0.114053	+	0.573381i	0.880923	+	0.473260i	$0.156923\pi$
$7$	−0.798369	+	4.01367i	−0.114053	+	0.573381i	−0.994975	+	0.100121i	$0.968077\pi$
$8$	7.96489	−	3.29916i	0.995611	−	0.412396i
$9$	−2.82302	−	6.81537i	−0.313669	−	0.757263i
$10$	−13.3984	−	2.66511i	−1.33984	−	0.266511i
$11$	5.77017	−	3.85550i	0.524561	−	0.350500i	−0.264925	−	0.964269i	$-0.585347\pi$
$11$	5.77017	−	3.85550i	0.524561	−	0.350500i	0.789486	+	0.613769i	$0.210347\pi$
$12$	3.50660	−	0.697506i	0.292217	−	0.0581255i
$13$	−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	$0.291221\pi$
$14$	6.00688	+	4.01367i	0.429063	+	0.286691i
$15$	−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	$0.349652\pi$
$19$	−9.43215	+	22.7712i	−0.496429	+	1.19849i	−0.951394	+	0.307977i	$0.900348\pi$
$20$	3.79823	−	5.68445i	0.189911	−	0.284222i
$21$	11.7103	+	11.7103i	0.557634	+	0.557634i
$22$	−2.39008	−	12.0158i	−0.108640	−	0.546170i
$23$	−6.40006	−	9.57836i	−0.278263	−	0.416450i	0.665843	−	0.746092i	$-0.268072\pi$
$23$	−6.40006	−	9.57836i	−0.278263	−	0.416450i	−0.944106	+	0.329642i	$0.893072\pi$
$24$	6.80638	−	34.2180i	0.283599	−	1.42575i
$25$	−32.2260	+	13.3484i	−1.28904	+	0.533938i
$26$	2.26829	+	5.47615i	0.0872421	+	0.210621i
$27$	6.44221	+	1.28144i	0.238600	+	0.0474606i
$28$	−3.00615	+	2.00865i	−0.107363	+	0.0717373i
$29$	−11.7813	+	2.34344i	−0.406250	+	0.0808082i	−0.393986	−	0.919117i	$-0.628904\pi$
$29$	−11.7813	+	2.34344i	−0.406250	+	0.0808082i	−0.0122647	+	0.999925i	$0.503904\pi$
$30$	−39.0914	+	39.0914i	−1.30305	+	1.30305i
$31$	31.4557	+	21.0180i	1.01470	+	0.678001i	0.947506	−	0.319739i	$-0.103595\pi$
$31$	31.4557	+	21.0180i	1.01470	+	0.678001i	0.0671946	+	0.997740i	$0.478595\pi$
$32$	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
$37$	−17.9275	+	26.8303i	−0.484526	+	0.725145i	−0.990516	−	0.137395i	$-0.956127\pi$
$37$	−17.9275	+	26.8303i	−0.484526	+	0.725145i	0.505990	+	0.862539i	$0.331127\pi$
$38$	30.7674	+	30.7674i	0.809669	+	0.809669i
$39$	2.65080	+	13.3265i	0.0679691	+	0.341704i
$40$	−37.0637	−	55.4697i	−0.926592	−	1.38674i
$41$	6.59647	−	33.1627i	0.160890	−	0.808846i	−0.813077	−	0.582156i	$-0.802209\pi$
$41$	6.59647	−	33.1627i	0.160890	−	0.808846i	0.973967	−	0.226691i	$-0.0727906\pi$
$42$	27.0106	−	11.1881i	0.643109	−	0.266384i
$43$	−1.33189	−	3.21547i	−0.0309742	−	0.0747784i	0.907636	−	0.419759i	$-0.137885\pi$
$43$	−1.33189	−	3.21547i	−0.0309742	−	0.0747784i	−0.938610	+	0.344981i	$0.887885\pi$
$44$	6.01330	+	1.19612i	0.136666	+	0.0271845i
$45$	−47.4641	+	31.7145i	−1.05476	+	0.704767i
$46$	−19.9459	+	3.96749i	−0.433607	+	0.0862497i
$47$	−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	$0.265174\pi$
$48$	−39.3198	−	26.2726i	−0.819162	−	0.547347i
$49$	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	−0.773254	−	0.634096i	$-0.781372\pi$
$53$	11.7603	−	28.3919i	0.221893	−	0.535697i	0.995147	+	0.0983994i	$0.0313723\pi$
$54$	6.44221	−	9.64145i	0.119300	−	0.178545i
$55$	−37.9728	−	37.9728i	−0.690414	−	0.690414i
$56$	6.88284	+	34.6024i	0.122908	+	0.617900i
$57$	55.4148	+	82.9342i	0.972190	+	1.45499i
$58$	−4.13703	+	20.7982i	−0.0713281	+	0.358590i
$59$	−10.8514	+	4.49481i	−0.183923	+	0.0761832i	−0.472744	−	0.881200i	$-0.656737\pi$
$59$	−10.8514	+	4.49481i	−0.183923	+	0.0761832i	0.288822	+	0.957383i	$0.406737\pi$
$60$	−10.5876	−	25.5607i	−0.176460	−	0.426012i
$61$	−69.5084	−	13.8261i	−1.13948	−	0.226657i	−0.410942	−	0.911661i	$-0.634800\pi$
$61$	−69.5084	−	13.8261i	−1.13948	−	0.226657i	−0.728539	+	0.685004i	$0.759800\pi$
$62$	55.5309	−	37.1045i	0.895659	−	0.598460i
$63$	29.6084	−	5.88948i	0.469975	−	0.0934839i
$64$	50.3473	−	50.3473i	0.786676	−	0.786676i
$65$	21.6031	+	14.4347i	0.332356	+	0.222073i
$66$	−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
$71$	−19.0927	+	28.5742i	−0.268911	+	0.402454i	−0.941208	−	0.337828i	$-0.890308\pi$
$71$	−19.0927	+	28.5742i	−0.268911	+	0.402454i	0.672297	+	0.740282i	$0.265308\pi$
$72$	−44.9700	−	44.9700i	−0.624584	−	0.624584i
$73$	−18.2751	−	91.8752i	−0.250344	−	1.25856i	−0.877464	−	0.479642i	$-0.840767\pi$
$73$	−18.2751	−	91.8752i	−0.250344	−	1.25856i	0.627120	−	0.778922i	$-0.284233\pi$
$74$	31.6486	+	47.3654i	0.427683	+	0.640073i
$75$	−27.5386	+	138.446i	−0.367182	+	1.84595i
$76$	−20.1179	+	8.33312i	−0.264710	+	0.109646i
$77$	10.8680	+	26.2377i	0.141143	+	0.340749i
$78$	23.5261	+	4.67963i	0.301616	+	0.0599952i
$79$	17.8452	−	11.9238i	0.225889	−	0.150934i	−0.437476	−	0.899230i	$-0.644128\pi$
$79$	17.8452	−	11.9238i	0.225889	−	0.150934i	0.663365	+	0.748296i	$0.269128\pi$
$80$	−88.6886	+	17.6413i	−1.10861	+	0.220516i
$81$	65.7422	−	65.7422i	0.811632	−	0.811632i
$82$	−49.6315	−	33.1627i	−0.605262	−	0.404423i
$83$	104.903	+	43.4522i	1.26389	+	0.523521i	0.911102	−	0.412182i	$-0.135233\pi$
$83$	104.903	+	43.4522i	1.26389	+	0.523521i	0.352789	+	0.935703i	$0.385233\pi$
$84$			14.6312i			0.174181i
$85$		0			0
$86$	−6.14419			−0.0714440
$87$	−18.6026	+	44.9106i	−0.213823	+	0.516214i
$88$	33.2388	−	49.7454i	0.377714	−	0.565288i
$89$	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	$0.677751\pi$
$90$	19.6603	+	98.8389i	0.218448	+	1.09821i
$91$	−7.63364	−	11.4245i	−0.0838861	−	0.125544i
$92$	1.98553	−	9.98195i	0.0215819	−	0.108499i
$93$	141.444	−	58.5880i	1.52090	−	0.629978i
$94$	3.02612	+	7.30570i	0.0321928	+	0.0777202i
$95$	187.064	+	37.2094i	1.96910	+	0.391677i
$96$	46.6205	−	31.1508i	0.485630	−	0.324488i
$97$	163.144	−	32.4513i	1.68190	−	0.334550i	0.740552	−	0.671999i	$-0.234564\pi$
$97$	163.144	−	32.4513i	1.68190	−	0.334550i	0.941344	+	0.337449i	$0.109564\pi$
$98$	40.2616	−	40.2616i	0.410833	−	0.410833i
$99$	−42.5659	−	28.4417i	−0.429959	−	0.287289i
$100$	−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
$105$	71.1980	−	106.555i	0.678076	−	1.01481i
$106$	−38.3619	−	38.3619i	−0.361904	−	0.361904i
$107$	7.77754	+	39.1003i	0.0726873	+	0.365424i	0.999960	−	0.00896329i	$-0.00285314\pi$
$107$	7.77754	+	39.1003i	0.0726873	+	0.365424i	−0.927273	+	0.374387i	$0.877853\pi$
$108$	3.22401	+	4.82508i	0.0298520	+	0.0446766i
$109$	−8.94051	+	44.9470i	−0.0820231	+	0.412358i	0.917858	+	0.396910i	$0.129917\pi$
$109$	−8.94051	+	44.9470i	−0.0820231	+	0.412358i	−0.999881	+	0.0154480i	$0.995083\pi$
$110$	−87.5866	+	36.2795i	−0.796241	+	0.329814i
$111$	49.9730	+	120.645i	0.450207	+	1.08690i
$112$	46.9019	+	9.32937i	0.418767	+	0.0832980i
$113$	−155.686	+	104.026i	−1.37775	+	0.920585i	−0.999986	−	0.00531545i	$-0.998308\pi$
$113$	−155.686	+	104.026i	−1.37775	+	0.920585i	−0.377767	+	0.925901i	$0.623308\pi$
$114$	172.701	−	34.3525i	1.51493	−	0.301337i
$115$	−63.0340	+	63.0340i	−0.548122	+	0.548122i
$116$	−8.82391	−	5.89595i	−0.0760682	−	0.0508271i
$117$	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
$122$	−69.5084	+	104.027i	−0.569741	+	0.852677i
$123$	−96.7557	−	96.7557i	−0.786632	−	0.786632i
$124$	6.52057	+	32.7811i	0.0525852	+	0.264364i
$125$	42.4808	+	63.5770i	0.339846	+	0.508616i
$126$	10.3971	−	52.2698i	0.0825167	−	0.414839i
$127$	−37.9454	+	15.7175i	−0.298783	+	0.123760i	−0.527039	−	0.849841i	$-0.676698\pi$
$127$	−37.9454	+	15.7175i	−0.298783	+	0.123760i	0.228256	+	0.973601i	$0.426698\pi$
$128$	−26.8936	−	64.9268i	−0.210106	−	0.507241i
$129$	−13.8140	−	2.74777i	−0.107085	−	0.0213006i
$130$	38.1374	−	25.4826i	0.293365	−	0.196020i
$131$	−188.785	+	37.5517i	−1.44111	+	0.286654i	−0.852908	−	0.522061i	$-0.825163\pi$
$131$	−188.785	+	37.5517i	−1.44111	+	0.286654i	−0.588200	+	0.808715i	$0.700163\pi$
$132$	17.5444	−	17.5444i	0.132912	−	0.132912i
$133$	−83.8659	−	56.0374i	−0.630571	−	0.421334i
$134$	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
$139$	−29.1541	+	43.6322i	−0.209742	+	0.313900i	−0.921393	−	0.388632i	$-0.872948\pi$
$139$	−29.1541	+	43.6322i	−0.209742	+	0.313900i	0.711651	+	0.702533i	$0.247948\pi$
$140$	19.7831	+	19.7831i	0.141308	+	0.141308i
$141$	3.53641	+	17.7788i	0.0250810	+	0.126090i
$142$	33.7056	+	50.4440i	0.237363	+	0.355239i
$143$	−4.54572	+	22.8529i	−0.0317882	+	0.159810i
$144$	−79.6413	+	32.9885i	−0.553064	+	0.229087i
$145$	35.5715	+	85.8773i	0.245321	+	0.592257i
$146$	−162.193	−	32.2623i	−1.11091	−	0.220974i
$147$	108.526	−	72.5147i	0.738271	−	0.493297i
$148$	−27.9609	+	5.56176i	−0.188925	+	0.0375795i
$149$	−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	$0.305566\pi$
$150$	207.199	+	138.446i	1.38133	+	0.922974i
$151$	−222.028	−	91.9670i	−1.47038	−	0.609053i	−0.503437	−	0.864032i	$-0.667931\pi$
$151$	−222.028	−	91.9670i	−1.47038	−	0.609053i	−0.966947	+	0.254979i	$0.917931\pi$
$152$			212.489i			1.39795i
$153$		0			0
$154$	50.1354			0.325555
$155$	112.031	−	270.467i	0.722780	−	1.74495i
$156$	−6.66924	+	9.98122i	−0.0427515	+	0.0639822i
$157$	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	$0.422681\pi$
$158$	−7.39174	−	37.1608i	−0.0467832	−	0.235195i
$159$	−69.0931	−	103.405i	−0.434548	−	0.650346i
$160$	20.9168	−	105.156i	0.130730	−	0.657225i
$161$	43.5540	−	18.0406i	0.270522	−	0.112054i
$162$	−62.8107	−	151.638i	−0.387720	−	0.936040i
$163$	−38.0563	−	7.56986i	−0.233474	−	0.0464409i	0.0769665	−	0.997034i	$-0.475477\pi$
$163$	−38.0563	−	7.56986i	−0.233474	−	0.0464409i	−0.310441	+	0.950593i	$0.600477\pi$
$164$	24.8381	−	16.5963i	0.151452	−	0.101197i
$165$	−213.146	+	42.3974i	−1.29179	+	0.256954i
$166$	141.740	−	141.740i	0.853855	−	0.853855i
$167$	29.9560	+	20.0159i	0.179377	+	0.119856i	0.642017	−	0.766690i	$-0.278098\pi$
$167$	29.9560	+	20.0159i	0.179377	+	0.119856i	−0.462640	+	0.886546i	$0.653098\pi$
$168$	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
$173$	−107.234	+	160.487i	−0.619848	+	0.927668i	0.380149	+	0.924925i	$0.375873\pi$
$173$	−107.234	+	160.487i	−0.619848	+	0.927668i	−0.999996	+	0.00274223i	$0.999127\pi$
$174$	60.6811	+	60.6811i	0.348742	+	0.348742i
$175$	−27.8480	−	140.001i	−0.159132	−	0.800009i
$176$	−45.0536	−	67.4275i	−0.255987	−	0.383111i
$177$	−9.27307	+	46.6188i	−0.0523902	+	0.263383i
$178$	65.3307	−	27.0608i	0.367026	−	0.152027i
$179$	−92.7619	−	223.947i	−0.518223	−	1.25110i	−0.938994	−	0.343933i	$-0.888241\pi$
$179$	−92.7619	−	223.947i	−0.518223	−	1.25110i	0.420771	−	0.907167i	$-0.361759\pi$
$180$	−49.4640	−	9.83901i	−0.274800	−	0.0546612i
$181$	−113.511	+	75.8453i	−0.627130	+	0.419035i	−0.828114	−	0.560560i	$-0.810586\pi$
$181$	−113.511	+	75.8453i	−0.627130	+	0.419035i	0.200984	+	0.979595i	$0.435586\pi$
$182$	−23.7904	+	4.73220i	−0.130716	+	0.0260011i
$183$	−202.798	+	202.798i	−1.10819	+	1.10819i
$184$	−82.5763	−	55.1757i	−0.448784	−	0.299868i
$185$	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
$190$	187.064	−	279.961i	0.984548	−	1.47348i
$191$	−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	$0.900813\pi$
$192$	−56.2137	−	282.606i	−0.292780	−	1.47190i
$193$	−104.264	−	156.042i	−0.540227	−	0.808507i	0.456468	−	0.889740i	$-0.349114\pi$
$193$	−104.264	−	156.042i	−0.540227	−	0.808507i	−0.996695	+	0.0812325i	$0.974114\pi$
$194$	57.2885	−	288.009i	0.295302	−	1.48458i
$195$	97.1407	−	40.2370i	0.498157	−	0.206344i
$196$	10.9045	+	26.3259i	0.0556354	+	0.134316i
$197$	−281.616	−	56.0168i	−1.42952	−	0.284349i	−0.581169	−	0.813783i	$-0.697405\pi$
$197$	−281.616	−	56.0168i	−1.42952	−	0.284349i	−0.848352	+	0.529433i	$0.822405\pi$
$198$	−75.1445	+	50.2100i	−0.379518	+	0.253586i
$199$	89.8366	−	17.8696i	0.451440	−	0.0897970i	0.0358665	−	0.999357i	$-0.488581\pi$
$199$	89.8366	−	17.8696i	0.451440	−	0.0897970i	0.415574	+	0.909560i	$0.363581\pi$
$200$	−212.638	+	212.638i	−1.06319	+	1.06319i
$201$	96.1807	+	64.2659i	0.478511	+	0.319731i
$202$	−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
$207$	−47.2126	+	70.6586i	−0.228080	+	0.341346i
$208$	27.7433	+	27.7433i	0.133381	+	0.133381i
$209$	33.3694	+	167.760i	0.159662	+	0.802677i
$210$	−125.691	−	188.109i	−0.598526	−	0.895758i
$211$	7.05432	−	35.4645i	0.0334328	−	0.168078i	−0.960462	−	0.278412i	$-0.910192\pi$
$211$	7.05432	−	35.4645i	0.0334328	−	0.168078i	0.993895	+	0.110334i	$0.0351920\pi$
$212$	25.0837	−	10.3900i	0.118319	−	0.0490095i
$213$	53.2210	+	128.487i	0.249864	+	0.603225i
$214$	69.0264	+	13.7302i	0.322554	+	0.0641599i
$215$	−22.3934	+	14.9628i	−0.104156	+	0.0695945i
$216$	55.5392	−	11.0474i	0.257126	−	0.0511455i
$217$	−109.473	+	109.473i	−0.504482	+	0.504482i
$218$	67.2679	+	44.9470i	0.308569	+	0.206179i
$219$	−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	$0.484245\pi$
$223$	−154.260	+	372.417i	−0.691750	+	1.67003i	−0.741226	+	0.671256i	$0.765755\pi$
$224$	−31.5008	+	47.1443i	−0.140629	+	0.210465i
$225$	181.949	+	181.949i	0.808663	+	0.808663i
$226$	64.4873	+	324.200i	0.285342	+	1.43451i
$227$	70.1368	+	104.967i	0.308973	+	0.462410i	0.953164	−	0.302454i	$-0.0978059\pi$
$227$	70.1368	+	104.967i	0.308973	+	0.462410i	−0.644191	+	0.764864i	$0.722806\pi$
$228$	−17.1917	+	86.4286i	−0.0754023	+	0.379073i
$229$	−113.583	+	47.0477i	−0.495997	+	0.205449i	−0.616637	−	0.787248i	$-0.711505\pi$
$229$	−113.583	+	47.0477i	−0.495997	+	0.205449i	0.120640	+	0.992696i	$0.461505\pi$
$230$	60.2233	+	145.392i	0.261840	+	0.632139i
$231$	112.720	+	22.4213i	0.487964	+	0.0970620i
$232$	−86.1050	+	57.5335i	−0.371142	+	0.247989i
$233$	−58.9878	+	11.7334i	−0.253166	+	0.0503579i	−0.320042	−	0.947403i	$-0.603697\pi$
$233$	−58.9878	+	11.7334i	−0.253166	+	0.0503579i	0.0668754	+	0.997761i	$0.478697\pi$
$234$	30.9185	−	30.9185i	0.132130	−	0.132130i
$235$	28.8206	+	19.2573i	0.122641	+	0.0819460i
$236$	−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
$241$	69.0771	−	103.381i	0.286627	−	0.428967i	−0.660016	−	0.751251i	$-0.729451\pi$
$241$	69.0771	−	103.381i	0.286627	−	0.428967i	0.946643	+	0.322284i	$0.104451\pi$
$242$	90.9267	+	90.9267i	0.375730	+	0.375730i
$243$	−61.8695	−	311.039i	−0.254607	−	1.28000i
$244$	−34.7855	−	52.0602i	−0.142564	−	0.213362i
$245$	48.6914	−	244.788i	0.198740	−	0.999135i
$246$	−223.173	+	92.4414i	−0.907208	+	0.375778i
$247$	−31.6691	−	76.4560i	−0.128215	−	0.309538i
$248$	319.883	+	63.6287i	1.28985	+	0.256567i
$249$	382.063	−	255.286i	1.53439	−	1.02525i
$250$	132.392	−	26.3344i	0.529569	−	0.105338i
$251$	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	$0.159400\pi$
$252$	22.1761	+	14.8176i	0.0880003	+	0.0587999i
$253$	−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	$0.402073\pi$
$257$	−150.400	+	363.098i	−0.585214	+	1.41283i	−0.888032	+	0.459783i	$0.847927\pi$
$258$	−13.8140	+	20.6741i	−0.0535426	+	0.0801322i
$259$	−93.3754	−	93.3754i	−0.360523	−	0.360523i
$260$	4.47819	+	22.5134i	0.0172238	+	0.0865899i
$261$	49.2301	+	73.6780i	0.188621	+	0.282291i
$262$	−66.2926	+	333.275i	−0.253025	+	1.27204i
$263$	−269.286	+	111.542i	−1.02390	+	0.424113i	−0.830507	−	0.557008i	$-0.811949\pi$
$263$	−269.286	+	111.542i	−1.02390	+	0.424113i	−0.193393	+	0.981121i	$0.561949\pi$
$264$	−92.6535	−	223.685i	−0.350960	−	0.847293i
$265$	−233.238	−	46.3939i	−0.880142	−	0.175071i
$266$	−148.054	+	98.9266i	−0.556594	+	0.371904i
$267$	158.985	−	31.6241i	0.595450	−	0.118442i
$268$	−17.8569	+	17.8569i	−0.0666304	+	0.0666304i
$269$	84.7201	+	56.6082i	0.314945	+	0.210439i	0.702988	−	0.711202i	$-0.251849\pi$
$269$	84.7201	+	56.6082i	0.314945	+	0.210439i	−0.388043	+	0.921641i	$0.626849\pi$
$270$	−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
$275$	−134.484	+	201.270i	−0.489034	+	0.731892i
$276$	−29.1234	−	29.1234i	−0.105520	−	0.105520i
$277$	−13.1132	−	65.9245i	−0.0473401	−	0.237995i	0.949870	−	0.312646i	$-0.101215\pi$
$277$	−13.1132	−	65.9245i	−0.0473401	−	0.237995i	−0.997210	+	0.0746518i	$0.976215\pi$
$278$	51.4676	+	77.0268i	0.185135	+	0.277075i
$279$	54.4456	−	273.716i	0.195146	−	0.981063i
$280$	252.228	−	104.476i	0.900813	−	0.373129i
$281$	144.294	+	348.356i	0.513501	+	1.23970i	0.941834	+	0.336079i	$0.109101\pi$
$281$	144.294	+	348.356i	0.513501	+	1.23970i	−0.428333	+	0.903621i	$0.640899\pi$
$282$	31.3860	+	6.24307i	0.111298	+	0.0221385i
$283$	246.804	−	164.909i	0.872098	−	0.582717i	−0.0369928	−	0.999316i	$-0.511778\pi$
$283$	246.804	−	164.909i	0.872098	−	0.582717i	0.909091	+	0.416598i	$0.136778\pi$
$284$	−29.7782	+	5.92325i	−0.104853	+	0.0208565i
$285$	545.780	−	545.780i	1.91502	−	1.91502i
$286$	34.2017	+	22.8529i	0.119586	+	0.0799051i
$287$	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
$292$	45.9790	−	68.8125i	0.157462	−	0.235659i
$293$	−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	$0.827464\pi$
$294$	−44.9529	−	225.993i	−0.152901	−	0.768685i
$295$	50.4959	+	75.5724i	0.171172	+	0.256178i
$296$	−54.2725	+	272.846i	−0.183353	+	0.921778i
$297$	42.1132	−	17.4439i	0.141795	−	0.0587336i
$298$	34.9654	+	84.4140i	0.117334	+	0.283269i
$299$	37.9353	+	7.54580i	0.126874	+	0.0252368i
$300$	−103.693	+	69.2855i	−0.345644	+	0.230952i
$301$	13.9692	−	2.77864i	0.0464093	−	0.00923138i
$302$	−299.994	+	299.994i	−0.993357	+	0.993357i
$303$	−418.731	−	279.787i	−1.38195	−	0.923389i
$304$	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
$309$	393.642	−	589.127i	1.27392	−	1.90656i
$310$	−365.442	−	365.442i	−1.17884	−	1.17884i
$311$	110.056	+	553.288i	0.353877	+	1.77906i	0.590066	+	0.807355i	$0.299102\pi$
$311$	110.056	+	553.288i	0.353877	+	1.77906i	−0.236189	+	0.971707i	$0.575898\pi$
$312$	65.0795	+	97.3983i	0.208588	+	0.312174i
$313$	−88.9143	+	447.002i	−0.284071	+	1.42812i	0.530316	+	0.847800i	$0.322073\pi$
$313$	−88.9143	+	447.002i	−0.284071	+	1.42812i	−0.814387	+	0.580322i	$0.802927\pi$
$314$	438.600	−	181.674i	1.39681	−	0.578580i
$315$	−89.3977	−	215.825i	−0.283802	−	0.685159i
$316$	18.5972	+	3.69920i	0.0588518	+	0.0117063i
$317$	−275.997	+	184.415i	−0.870653	+	0.581751i	−0.908665	−	0.417526i	$-0.862897\pi$
$317$	−275.997	+	184.415i	−0.870653	+	0.581751i	0.0380125	+	0.999277i	$0.487897\pi$
$318$	−215.330	+	42.8318i	−0.677138	+	0.134691i
$319$	−58.9447	+	58.9447i	−0.184780	+	0.184780i
$320$	−458.123	−	306.108i	−1.43164	−	0.956588i
$321$	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
$326$	−38.0563	+	56.9552i	−0.116737	+	0.174709i
$327$	131.138	+	131.138i	0.401033	+	0.401033i
$328$	−56.8691	−	285.900i	−0.173381	−	0.871646i
$329$	−10.1840	−	15.2414i	−0.0309544	−	0.0463265i
$330$	−74.8469	+	376.281i	−0.226809	+	1.14024i
$331$	544.633	−	225.594i	1.64542	−	0.681554i	0.648588	−	0.761139i	$-0.275360\pi$
$331$	544.633	−	225.594i	1.64542	−	0.681554i	0.996828	+	0.0795855i	$0.0253597\pi$
$332$	38.3892	+	92.6796i	0.115630	+	0.279156i
$333$	233.468	+	46.4397i	0.701106	+	0.139459i
$334$	52.8833	−	35.3355i	0.158333	−	0.105795i
$335$	216.942	−	43.1525i	0.647590	−	0.128814i
$336$	136.841	−	136.841i	0.407266	−	0.407266i
$337$	272.381	+	181.999i	0.808251	+	0.540056i	0.889659	−	0.456625i	$-0.150942\pi$
$337$	272.381	+	181.999i	0.808251	+	0.540056i	−0.0814084	+	0.996681i	$0.525942\pi$
$338$	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
$343$	−184.734	+	276.474i	−0.538583	+	0.806046i
$344$	−21.2167	−	21.2167i	−0.0616766	−	0.0616766i
$345$	70.3787	+	353.818i	0.203996	+	1.02556i
$346$	189.307	+	283.318i	0.547129	+	0.818837i
$347$	47.2242	−	237.412i	0.136093	−	0.684185i	−0.851145	−	0.524931i	$-0.824091\pi$
$347$	47.2242	−	237.412i	0.136093	−	0.684185i	0.987238	−	0.159254i	$-0.0509089\pi$
$348$	−39.6776	+	16.4350i	−0.114016	+	0.0472270i
$349$	−192.479	−	464.685i	−0.551515	−	1.33148i	−0.916341	−	0.400399i	$-0.868871\pi$
$349$	−192.479	−	464.685i	−0.551515	−	1.33148i	0.364826	−	0.931076i	$-0.381129\pi$
$350$	−247.154	−	49.1620i	−0.706154	−	0.140463i
$351$	−18.3372	+	12.2525i	−0.0522427	+	0.0349074i
$352$	94.3041	−	18.7583i	0.267909	−	0.0532905i
$353$	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	$0.0966606\pi$
$354$	69.7700	+	46.6188i	0.197090	+	0.131692i
$355$	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	$-0.609778\pi$
$359$	203.355	−	490.942i	0.566448	−	1.36753i	0.904530	−	0.426410i	$-0.140222\pi$
$360$	−273.415	+	409.194i	−0.759486	+	1.13665i
$361$	−174.298	−	174.298i	−0.482820	−	0.482820i
$362$	47.0176	+	236.374i	0.129883	+	0.652965i
$363$	163.767	+	245.095i	0.451149	+	0.675192i
$364$	2.36824	−	11.9059i	0.00650614	−	0.0327086i
$365$	−669.707	+	277.402i	−1.83481	+	0.760005i
$366$	193.755	+	467.767i	0.529386	+	1.27805i
$367$	324.691	+	64.5850i	0.884716	+	0.175981i	0.616479	−	0.787372i	$-0.288559\pi$
$367$	324.691	+	64.5850i	0.884716	+	0.175981i	0.268238	+	0.963353i	$0.413559\pi$
$368$	−111.928	+	74.7881i	−0.304153	+	0.203229i
$369$	−244.638	+	48.6615i	−0.662975	+	0.131874i
$370$	311.706	−	311.706i	0.842448	−	0.842448i
$371$	104.567	+	69.8693i	0.281851	+	0.188327i
$372$	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
$377$	22.4069	−	33.5343i	0.0594347	−	0.0889504i
$378$	33.5543	+	33.5543i	0.0887681	+	0.0887681i
$379$	8.52233	+	42.8446i	0.0224864	+	0.113047i	0.990398	−	0.138243i	$-0.0441454\pi$
$379$	8.52233	+	42.8446i	0.0224864	+	0.113047i	−0.967912	+	0.251289i	$0.919145\pi$
$380$	93.6164	+	140.107i	0.246359	+	0.368702i
$381$	−32.4262	+	163.017i	−0.0851081	+	0.427867i
$382$	−284.269	+	117.748i	−0.744160	+	0.308241i
$383$	−75.6230	−	182.570i	−0.197449	−	0.476684i	0.793882	−	0.608072i	$-0.208057\pi$
$383$	−75.6230	−	182.570i	−0.197449	−	0.476684i	−0.991331	+	0.131387i	$0.958057\pi$
$384$	−278.932	−	55.4830i	−0.726385	−	0.144487i
$385$	182.726	−	122.094i	0.474614	−	0.317127i
$386$	−324.941	+	64.6347i	−0.841815	+	0.167447i
$387$	−18.1547	+	18.1547i	−0.0469113	+	0.0469113i
$388$	122.191	+	81.6456i	0.314926	+	0.210427i
$389$	19.8577	+	8.22534i	0.0510481	+	0.0211448i	0.408061	−	0.912954i	$-0.366205\pi$
$389$	19.8577	+	8.22534i	0.0510481	+	0.0211448i	−0.357013	+	0.934099i	$0.616205\pi$
$390$		−	185.618i		−	0.475944i
$391$		0			0
$392$	278.058			0.709332
$393$	−298.092	+	719.657i	−0.758503	+	1.83119i
$394$	−281.616	+	421.468i	−0.714761	+	1.06971i
$395$	−117.437	−	117.437i	−0.297310	−	0.297310i
$396$	−8.82365	−	44.3595i	−0.0222819	−	0.112019i
$397$	−19.7100	−	29.4981i	−0.0496473	−	0.0743025i	0.805816	−	0.592167i	$-0.201727\pi$
$397$	−19.7100	−	29.4981i	−0.0496473	−	0.0743025i	−0.855463	+	0.517864i	$0.826727\pi$
$398$	31.5464	−	158.594i	0.0792623	−	0.398479i
$399$	−377.112	+	156.205i	−0.945142	+	0.391491i
$400$	155.984	+	376.578i	0.389960	+	0.941446i
$401$	146.691	+	29.1786i	0.365812	+	0.0727646i	0.374574	−	0.927197i	$-0.377789\pi$
$401$	146.691	+	29.1786i	0.365812	+	0.0727646i	−0.00876160	+	0.999962i	$0.502789\pi$
$402$	169.794	−	113.453i	0.422374	−	0.282221i
$403$	−124.581	+	24.7807i	−0.309134	+	0.0614906i
$404$	77.7417	−	77.7417i	0.192430	−	0.192430i
$405$	−598.206	−	399.708i	−1.47705	−	0.986934i
$406$	−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
$411$	118.792	−	177.784i	0.289030	−	0.432565i
$412$	109.378	+	109.378i	0.265479	+	0.265479i
$413$	−9.37724	−	47.1426i	−0.0227052	−	0.114147i
$414$	83.3475	+	124.738i	0.201322	+	0.301300i
$415$	171.417	−	861.770i	0.413052	−	2.07655i
$416$	−42.9789	+	17.8024i	−0.103315	+	0.0427943i
$417$	81.2673	+	196.197i	0.194886	+	0.470496i
$418$	296.157	+	58.9093i	0.708510	+	0.140931i
$419$	31.0967	−	20.7782i	0.0742166	−	0.0495899i	−0.517908	−	0.855436i	$-0.673289\pi$
$419$	31.0967	−	20.7782i	0.0742166	−	0.0495899i	0.592125	+	0.805846i	$0.298289\pi$
$420$	111.045	−	22.0882i	0.264393	−	0.0525910i
$421$	−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	$0.426016\pi$
$422$	−53.0763	−	35.4645i	−0.125773	−	0.0840390i
$423$	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
$428$	−19.5678	+	29.2853i	−0.0457192	+	0.0684236i
$429$	66.6757	+	66.6757i	0.155421	+	0.155421i
$430$	9.27567	+	46.6319i	0.0215713	+	0.108446i
$431$	−192.725	−	288.433i	−0.447157	−	0.669218i	0.537590	−	0.843206i	$-0.319335\pi$
$431$	−192.725	−	288.433i	−0.447157	−	0.669218i	−0.984748	+	0.173988i	$0.944335\pi$
$432$	14.9743	−	75.2808i	0.0346627	−	0.174261i
$433$	−49.6556	+	20.5680i	−0.114678	+	0.0475012i	−0.439285	−	0.898348i	$-0.644768\pi$
$433$	−49.6556	+	20.5680i	−0.114678	+	0.0475012i	0.324607	+	0.945849i	$0.394768\pi$
$434$	104.591	+	252.506i	0.240994	+	0.581810i
$435$	368.937	+	73.3862i	0.848132	+	0.168704i
$436$	−33.6643	+	22.4938i	−0.0772117	+	0.0515912i
$437$	278.477	−	55.3926i	0.637248	−	0.126757i
$438$	−473.217	+	473.217i	−1.08040	+	1.08040i
$439$	202.261	+	135.146i	0.460731	+	0.307851i	0.764187	−	0.644995i	$-0.223140\pi$
$439$	202.261	+	135.146i	0.460731	+	0.307851i	−0.303456	+	0.952846i	$0.598140\pi$
$440$	−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
$445$	172.207	−	257.726i	0.386982	−	0.579160i
$446$	503.192	+	503.192i	1.12823	+	1.12823i
$447$	40.8616	+	205.425i	0.0914131	+	0.459565i
$448$	161.882	+	242.273i	0.361343	+	0.540788i
$449$	−105.973	+	532.761i	−0.236020	+	1.18655i	0.662992	+	0.748626i	$0.269286\pi$
$449$	−105.973	+	532.761i	−0.236020	+	1.18655i	−0.899012	+	0.437925i	$0.855714\pi$
$450$	419.677	−	173.836i	0.932616	−	0.386302i
$451$	−89.7961	−	216.787i	−0.199104	−	0.480681i
$452$	−162.246	−	32.2727i	−0.358951	−	0.0713999i
$453$	−808.639	+	540.315i	−1.78507	+	1.19275i
$454$	218.583	−	43.4788i	0.481460	−	0.0957683i
$455$	−75.1835	+	75.1835i	−0.165239	+	0.165239i
$456$	714.987	+	477.739i	1.56795	+	1.04767i
$457$	−207.434	−	85.9222i	−0.453905	−	0.188014i	0.144005	−	0.989577i	$-0.454002\pi$
$457$	−207.434	−	85.9222i	−0.453905	−	0.188014i	−0.597910	+	0.801563i	$0.704002\pi$
$458$			217.037i			0.473880i
$459$		0			0
$460$	−78.7565			−0.171210
$461$	96.5408	−	233.070i	0.209416	−	0.505575i	−0.783916	−	0.620867i	$-0.786781\pi$
$461$	96.5408	−	233.070i	0.209416	−	0.505575i	0.993332	+	0.115292i	$0.0367805\pi$
$462$	112.720	−	168.697i	0.243982	−	0.365145i
$463$	−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	$0.793229\pi$
$464$	27.3844	+	137.670i	0.0590180	+	0.296704i
$465$	−658.193	−	985.055i	−1.41547	−	2.11840i
$466$	−20.7138	+	104.135i	−0.0444501	+	0.223466i
$467$	640.133	−	265.152i	1.37074	−	0.567777i	0.428748	−	0.903424i	$-0.358955\pi$
$467$	640.133	−	265.152i	1.37074	−	0.567777i	0.941988	+	0.335647i	$0.108955\pi$
$468$	8.37404	+	20.2167i	0.0178932	+	0.0431981i
$469$	−114.727	−	22.8207i	−0.244621	−	0.0486582i
$470$	50.8789	−	33.9962i	0.108253	−	0.0723324i
$471$	1067.35	−	212.310i	2.26614	−	0.450764i
$472$	−71.6013	+	71.6013i	−0.151698	+	0.151698i
$473$	−20.0825	−	13.4187i	−0.0424577	−	0.0283693i
$474$	−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
$479$	265.948	−	398.019i	0.555215	−	0.830938i	−0.442620	−	0.896709i	$-0.645951\pi$
$479$	265.948	−	398.019i	0.555215	−	0.830938i	0.997835	+	0.0657717i	$0.0209509\pi$
$480$	−306.804	−	306.804i	−0.639175	−	0.639175i
$481$	−21.1369	−	106.262i	−0.0439436	−	0.220919i
$482$	−121.946	−	182.506i	−0.253001	−	0.378642i
$483$	37.2189	−	187.112i	0.0770579	−	0.387396i
$484$	−59.4543	+	24.6268i	−0.122840	+	0.0508818i
$485$	−492.586	−	1189.21i	−1.01564	−	2.45197i
$486$	−549.098	−	109.222i	−1.12983	−	0.224737i
$487$	337.297	−	225.375i	0.692602	−	0.462782i	−0.158790	−	0.987312i	$-0.550759\pi$
$487$	337.297	−	225.375i	0.692602	−	0.462782i	0.851392	+	0.524531i	$0.175759\pi$
$488$	−599.241	+	119.196i	−1.22795	+	0.244255i
$489$	−111.033	+	111.033i	−0.227062	+	0.227062i
$490$	−366.351	−	244.788i	−0.747655	−	0.499567i
$491$	−57.3172	−	23.7416i	−0.116736	−	0.0483535i	0.323551	−	0.946211i	$-0.395123\pi$
$491$	−57.3172	−	23.7416i	−0.116736	−	0.0483535i	−0.440287	+	0.897857i	$0.645123\pi$
$492$		−	120.889i		−	0.245710i
$493$		0			0
$494$	−146.094			−0.295736
$495$	−151.601	+	365.996i	−0.306264	+	0.739386i
$496$	245.607	−	367.577i	0.495176	−	0.741083i
$497$	−99.4445	−	99.4445i	−0.200089	−	0.200089i
$498$	−158.256	−	795.604i	−0.317782	−	1.59760i
$499$	−285.141	−	426.744i	−0.571426	−	0.855199i	0.427379	−	0.904072i	$-0.359437\pi$
$499$	−285.141	−	426.744i	−0.571426	−	0.855199i	−0.998805	+	0.0488735i	$0.984437\pi$
$500$	−13.1791	+	66.2558i	−0.0263582	+	0.132512i
$501$	134.700	−	55.7947i	0.268863	−	0.111367i
$502$	−95.2302	−	229.906i	−0.189702	−	0.457980i
$503$	−324.524	−	64.5518i	−0.645176	−	0.128334i	−0.138352	−	0.990383i	$-0.544181\pi$
$503$	−324.524	−	64.5518i	−0.645176	−	0.128334i	−0.506824	+	0.862050i	$0.669181\pi$
$504$	216.398	−	144.592i	0.429360	−	0.286889i
$505$	−944.477	+	187.868i	−1.87025	+	0.372016i
$506$	−99.7945	+	99.7945i	−0.197222	+	0.197222i
$507$	530.723	+	354.617i	1.04679	+	0.699443i
$508$	−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
$513$	−89.9438	+	134.610i	−0.175329	+	0.262399i
$514$	490.601	+	490.601i	0.954476	+	0.954476i
$515$	−264.318	−	1328.82i	−0.513239	−	2.58023i
$516$	−6.91323	−	10.3464i	−0.0133977	−	0.0200511i
$517$	−6.06442	+	30.4879i	−0.0117300	+	0.0589708i
$518$	−215.376	+	89.2118i	−0.415784	+	0.172224i
$519$	298.915	+	721.645i	0.575944	+	1.39045i
$520$	219.689	+	43.6989i	0.422479	+	0.0840363i
$521$	264.820	−	176.947i	0.508291	−	0.339629i	−0.274836	−	0.961491i	$-0.588623\pi$
$521$	264.820	−	176.947i	0.508291	−	0.339629i	0.783127	+	0.621862i	$0.213623\pi$
$522$	153.427	−	30.5184i	0.293921	−	0.0584645i
$523$	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	$0.177251\pi$
$524$	−141.396	−	94.4778i	−0.269840	−	0.180301i
$525$	−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
$530$	−233.238	+	349.065i	−0.440071	+	0.658613i
$531$	61.2676	+	61.2676i	0.115381	+	0.115381i
$532$	−17.3849	−	87.3996i	−0.0326783	−	0.164285i
$533$	63.0724	+	94.3946i	0.118335	+	0.177101i
$534$	55.8282	−	280.667i	0.104547	−	0.525594i
$535$	285.015	−	118.057i	0.532738	−	0.220667i
$536$	94.3039	+	227.670i	0.175940	+	0.424757i
$537$	−962.098	−	191.373i	−1.79162	−	0.356375i
$538$	149.562	−	99.9342i	0.277996	−	0.185751i
$539$	219.526	−	43.6665i	0.407285	−	0.0810140i
$540$	31.7532	−	31.7532i	0.0588023	−	0.0588023i
$541$	220.270	+	147.180i	0.407153	+	0.272051i	0.742237	−	0.670137i	$-0.233765\pi$
$541$	220.270	+	147.180i	0.407153	+	0.272051i	−0.335084	+	0.942188i	$0.608765\pi$
$542$	−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
$547$	200.445	−	299.987i	0.366444	−	0.548423i	−0.601730	−	0.798700i	$-0.705522\pi$
$547$	200.445	−	299.987i	0.366444	−	0.548423i	0.968174	+	0.250277i	$0.0805217\pi$
$548$	33.0075	+	33.0075i	0.0602326	+	0.0602326i
$549$	101.994	+	512.756i	0.185781	+	0.933982i
$550$	237.414	+	355.316i	0.431662	+	0.646029i
$551$	57.7597	−	290.378i	0.104827	−	0.527001i
$552$	−371.313	+	153.803i	−0.672669	+	0.278629i
$553$	33.6111	+	81.1445i	0.0607797	+	0.146735i
$554$	−116.381	−	23.1496i	−0.210074	−	0.0417863i
$555$	840.209	−	561.410i	1.51389	−	1.01155i
$556$	−45.4706	+	9.04467i	−0.0817817	+	0.0162674i
$557$	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	$0.0956632\pi$
$558$	−409.646	−	273.716i	−0.734132	−	0.490531i
$559$	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	$0.252698\pi$
$563$	−168.267	+	406.232i	−0.298875	+	0.721549i	−0.999964	+	0.00847487i	$0.997302\pi$
$564$	−8.89740	+	13.3159i	−0.0157755	+	0.0236097i
$565$	1024.55	+	1024.55i	1.81336	+	1.81336i
$566$	−102.229	−	513.942i	−0.180617	−	0.908025i
$567$	211.381	+	316.354i	0.372806	+	0.557943i
$568$	−57.8000	+	290.580i	−0.101761	+	0.511585i
$569$	−443.238	+	183.595i	−0.778977	+	0.322663i	−0.736503	−	0.676435i	$-0.763524\pi$
$569$	−443.238	+	183.595i	−0.778977	+	0.322663i	−0.0424747	+	0.999098i	$0.513524\pi$
$570$	−521.443	−	1258.87i	−0.914812	−	2.20855i
$571$	−533.718	−	106.163i	−0.934707	−	0.185925i	−0.295836	−	0.955239i	$-0.595598\pi$
$571$	−533.718	−	106.163i	−0.934707	−	0.185925i	−0.638871	+	0.769314i	$0.720598\pi$
$572$	−17.1163	+	11.4367i	−0.0299236	+	0.0199943i
$573$	−691.781	+	137.604i	−1.20730	+	0.240146i
$574$	172.728	−	172.728i	0.300920	−	0.300920i
$575$	334.104	+	223.241i	0.581051	+	0.388246i
$576$	−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
$581$	−258.154	+	386.355i	−0.444327	+	0.664983i
$582$	−840.297	−	840.297i	−1.44381	−	1.44381i
$583$	−41.6061	−	209.168i	−0.0713656	−	0.358779i
$584$	−448.671	−	671.483i	−0.768272	−	1.14980i
$585$	37.3921	−	187.983i	0.0639181	−	0.321338i
$586$	−230.304	+	95.3950i	−0.393010	+	0.162790i
$587$	244.317	+	589.834i	0.416213	+	1.00483i	0.983435	+	0.181263i	$0.0580184\pi$
$587$	244.317	+	589.834i	0.416213	+	1.00483i	−0.567221	+	0.823565i	$0.691982\pi$
$588$	113.099	+	22.4967i	0.192345	+	0.0382597i
$589$	−775.302	+	518.040i	−1.31630	+	0.879525i
$590$	157.371	−	31.3031i	0.266731	−	0.0530561i
$591$	−821.644	+	821.644i	−1.39026	+	1.39026i
$592$	313.527	+	209.492i	0.529607	+	0.353872i
$593$	594.149	+	246.104i	1.00194	+	0.415016i	0.822507	−	0.568755i	$-0.192575\pi$
$593$	594.149	+	246.104i	1.00194	+	0.415016i	0.179430	+	0.983771i	$0.442575\pi$
$594$		−	80.4708i		−	0.135473i
$595$		0			0
$596$	−45.7258			−0.0767211
$597$	141.852	−	342.460i	0.237608	−	0.573636i
$598$	37.9353	−	56.7742i	0.0634370	−	0.0949401i
$599$	−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	$0.887365\pi$
$600$	237.414	+	1193.56i	0.395691	+	1.98927i
$601$	316.537	+	473.731i	0.526684	+	0.788238i	0.995470	−	0.0950732i	$-0.0303085\pi$
$601$	316.537	+	473.731i	0.526684	+	0.788238i	−0.468786	+	0.883312i	$0.655309\pi$
$602$	4.90533	−	24.6607i	0.00814838	−	0.0409647i
$603$	194.812	−	80.6936i	0.323071	−	0.133820i
$604$	−81.2510	−	196.157i	−0.134521	−	0.324764i
$605$	552.829	+	109.964i	0.913767	+	0.181759i
$606$	−739.213	+	493.926i	−1.21982	+	0.815060i
$607$	−177.894	+	35.3853i	−0.293071	+	0.0582955i	−0.339436	−	0.940629i	$-0.610236\pi$
$607$	−177.894	+	35.3853i	−0.293071	+	0.0582955i	0.0463651	+	0.998925i	$0.485236\pi$
$608$	−241.474	+	241.474i	−0.397162	+	0.397162i
$609$	−165.405	−	110.520i	−0.271600	−	0.181478i
$610$	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
$615$	−588.269	+	880.407i	−0.956535	+	1.43156i
$616$	173.125	+	173.125i	0.281047	+	0.281047i
$617$	91.1849	+	458.417i	0.147787	+	0.742978i	0.981603	+	0.190934i	$0.0611518\pi$
$617$	91.1849	+	458.417i	0.147787	+	0.742978i	−0.833815	+	0.552043i	$0.813848\pi$
$618$	−694.922	−	1040.02i	−1.12447	−	1.68289i
$619$	74.8513	−	376.303i	0.120923	−	0.607921i	−0.872034	−	0.489445i	$-0.837199\pi$
$619$	74.8513	−	376.303i	0.120923	−	0.607921i	0.992957	−	0.118475i	$-0.0378007\pi$
$620$	238.952	−	98.9771i	0.385406	−	0.159640i
$621$	−28.9565	−	69.9071i	−0.0466288	−	0.112572i
$622$	976.757	+	194.289i	1.57035	+	0.312362i
$623$	−136.295	+	91.0696i	−0.218773	+	0.146179i
$624$	155.727	−	30.9760i	0.249562	−	0.0496410i
$625$	−198.226	+	198.226i	−0.317161	+	0.317161i
$626$	668.986	+	447.002i	1.06867	+	0.714061i
$627$	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	−0.789671	−	0.613531i	$-0.789749\pi$
$631$	127.804	−	308.547i	0.202542	−	0.488980i	0.992213	+	0.124550i	$0.0397487\pi$
$632$	102.797	−	153.846i	0.162653	−	0.243428i
$633$	−103.471	−	103.471i	−0.163462	−	0.163462i
$634$	114.322	+	574.734i	0.180318	+	0.906520i
$635$	176.575	+	264.263i	0.278070	+	0.416162i
$636$	21.4352	−	107.762i	0.0337032	−	0.169437i
$637$	−100.049	+	41.4415i	−0.157062	+	0.0650573i
$638$	56.3163	+	135.960i	0.0882701	+	0.213103i
$639$	248.643	+	49.4581i	0.389112	+	0.0773992i
$640$	−452.168	+	302.129i	−0.706513	+	0.472077i
$641$	942.185	−	187.412i	1.46987	−	0.292375i	0.605746	−	0.795658i	$-0.292875\pi$
$641$	942.185	−	187.412i	1.46987	−	0.292375i	0.864121	+	0.503284i	$0.167875\pi$
$642$	201.392	−	201.392i	0.313695	−	0.313695i
$643$	−870.743	−	581.812i	−1.35419	−	0.904840i	−0.354643	−	0.935002i	$-0.615398\pi$
$643$	−870.743	−	581.812i	−1.35419	−	0.904840i	−0.999545	+	0.0301622i	$0.990398\pi$
$644$	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
$649$	−45.2848	+	67.7735i	−0.0697763	+	0.104428i
$650$	−146.196	−	146.196i	−0.224917	−	0.224917i
$651$	122.228	+	614.484i	0.187755	+	0.943908i
$652$	−19.0453	−	28.5033i	−0.0292106	−	0.0437167i
$653$	−9.72717	+	48.9018i	−0.0148961	+	0.0748879i	−0.987518	−	0.157504i	$-0.949655\pi$
$653$	−9.72717	+	48.9018i	−0.0148961	+	0.0748879i	0.972622	+	0.232392i	$0.0746552\pi$
$654$	302.477	−	125.290i	0.462504	−	0.191575i
$655$	570.005	+	1376.11i	0.870237	+	2.10094i
$656$	−387.524	−	77.0833i	−0.590738	−	0.117505i
$657$	−574.572	+	383.917i	−0.874539	+	0.584348i
$658$	−31.7386	+	6.31321i	−0.0482350	+	0.00959454i
$659$	−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	$0.270933\pi$
$660$	−159.642	−	106.669i	−0.241881	−	0.161620i
$661$	−758.170	−	314.044i	−1.14700	−	0.475105i	−0.273476	−	0.961879i	$-0.588173\pi$
$661$	−758.170	−	314.044i	−1.14700	−	0.475105i	−0.873528	+	0.486774i	$0.838173\pi$
$662$		−	1040.69i		−	1.57205i
$663$		0			0
$664$	978.896			1.47424
$665$	−298.692	+	721.107i	−0.449161	+	1.08437i
$666$	233.468	−	349.410i	0.350553	−	0.524639i
$667$	97.8470	+	97.8470i	0.146697	+	0.146697i
$668$	6.20969	+	31.2182i	0.00929594	+	0.0467338i
$669$	906.294	+	1356.36i	1.35470	+	2.02745i
$670$	76.1801	−	382.983i	0.113702	−	0.571617i
$671$	−454.381	+	188.211i	−0.677170	+	0.280493i
$672$	87.8088	+	211.989i	0.130668	+	0.315460i
$673$	539.262	+	107.266i	0.801281	+	0.159385i	0.578712	−	0.815532i	$-0.303556\pi$
$673$	539.262	+	107.266i	0.801281	+	0.159385i	0.222569	+	0.974917i	$0.428556\pi$
$674$	480.852	−	321.295i	0.713430	−	0.476698i
$675$	−224.712	+	44.6980i	−0.332907	+	0.0662192i
$676$	−98.5342	+	98.5342i	−0.145761	+	0.145761i
$677$	−450.499	−	301.014i	−0.665434	−	0.444629i	0.176434	−	0.984313i	$-0.443544\pi$
$677$	−450.499	−	301.014i	−0.665434	−	0.444629i	−0.841868	+	0.539684i	$0.818544\pi$
$678$	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
$683$	220.012	−	329.272i	0.322126	−	0.482096i	−0.634699	−	0.772759i	$-0.718876\pi$
$683$	220.012	−	329.272i	0.322126	−	0.482096i	0.956825	+	0.290663i	$0.0938760\pi$
$684$	113.587	+	113.587i	0.166062	+	0.166062i
$685$	−79.7648	−	401.005i	−0.116445	−	0.585409i
$686$	326.123	+	488.078i	0.475398	+	0.711483i
$687$	−97.0623	+	487.965i	−0.141284	+	0.710284i
$688$	−37.5745	+	15.5639i	−0.0546142	+	0.0226219i
$689$	39.4861	+	95.3279i	0.0573093	+	0.138357i
$690$	624.618	+	124.244i	0.905244	+	0.180064i
$691$	776.300	−	518.707i	1.12344	−	0.750661i	0.152106	−	0.988364i	$-0.451395\pi$
$691$	776.300	−	518.707i	1.12344	−	0.750661i	0.971338	+	0.237703i	$0.0763945\pi$
$692$	−167.249	+	33.2678i	−0.241689	+	0.0480749i
$693$	148.139	−	148.139i	0.213764	−	0.213764i
$694$	−355.313	−	237.412i	−0.511978	−	0.342093i
$695$	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
$700$	70.0639	−	104.858i	0.100091	−	0.149797i
$701$	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	$0.613866\pi$
$702$	7.59550	+	38.1852i	0.0108198	+	0.0543948i
$703$	−441.866	−	661.299i	−0.628543	−	0.940681i
$704$	96.3981	−	484.626i	0.136929	−	0.688389i
$705$	129.595	−	53.6800i	0.183823	−	0.0761418i
$706$	−220.980	−	533.494i	−0.313003	−	0.755657i
$707$	499.475	+	99.3518i	0.706472	+	0.140526i
$708$	−34.9165	+	23.3305i	−0.0493171	+	0.0329526i
$709$	−1140.89	+	226.937i	−1.60915	+	0.320080i	−0.916143	−	0.400851i	$-0.868715\pi$
$709$	−1140.89	+	226.937i	−1.60915	+	0.320080i	−0.693007	+	0.720931i	$0.743715\pi$
$710$	331.966	−	331.966i	0.467557	−	0.467557i
$711$	−131.643	−	87.9607i	−0.185151	−	0.123714i
$712$	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
$717$	−642.836	+	962.072i	−0.896563	+	1.34180i
$718$	−663.338	−	663.338i	−0.923869	−	0.923869i
$719$	−2.89668	−	14.5626i	−0.00402876	−	0.0202540i	0.978719	−	0.205207i	$-0.0657867\pi$
$719$	−2.89668	−	14.5626i	−0.00402876	−	0.0202540i	−0.982747	+	0.184953i	$0.940787\pi$
$720$	370.601	+	554.644i	0.514724	+	0.770339i
$721$	−139.782	+	702.729i	−0.193872	+	0.974659i
$722$	−402.030	+	166.526i	−0.556828	+	0.230646i
$723$	−192.553	−	464.864i	−0.266325	−	0.642966i
$724$	−118.293	−	23.5300i	−0.163389	−	0.0325000i
$725$	348.382	−	232.781i	0.480526	−	0.321077i
$726$	510.383	−	101.522i	0.703007	−	0.139837i
$727$	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	$-0.0770901\pi$
$728$	−98.4925	−	65.8106i	−0.135292	−	0.0903992i
$729$	−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	−0.999934	−	0.0114762i	$-0.996347\pi$
$733$	−208.728	+	503.915i	−0.284759	+	0.687469i	0.715175	+	0.698945i	$0.246347\pi$
$734$	324.691	−	485.934i	0.442358	−	0.662036i
$735$	−714.195	−	714.195i	−0.971694	−	0.971694i
$736$	−31.1383	−	156.543i	−0.0423075	−	0.212694i
$737$	110.206	+	164.935i	0.149534	+	0.223793i
$738$	−85.9054	+	431.876i	−0.116403	+	0.585197i
$739$	−152.427	+	63.1371i	−0.206261	+	0.0854359i	−0.483422	−	0.875387i	$-0.660606\pi$
$739$	−152.427	+	63.1371i	−0.206261	+	0.0854359i	0.277161	+	0.960823i	$0.410606\pi$
$740$	84.4231	+	203.815i	0.114085	+	0.275426i
$741$	−328.463	−	65.3353i	−0.443269	−	0.0881717i
$742$	184.599	−	123.345i	0.248785	−	0.166233i
$743$	−2.26111	+	0.449762i	−0.00304321	+	0.000605333i	−0.196612	−	0.980481i	$-0.562994\pi$
$743$	−2.26111	+	0.449762i	−0.00304321	+	0.000605333i	0.193568	+	0.981087i	$0.437994\pi$
$744$	933.294	−	933.294i	1.25443	−	1.25443i
$745$	333.009	+	222.509i	0.446992	+	0.298670i
$746$	−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
$751$	−801.406	+	1199.39i	−1.06712	+	1.59706i	−0.301839	+	0.953359i	$0.597600\pi$
$751$	−801.406	+	1199.39i	−1.06712	+	1.59706i	−0.765280	+	0.643697i	$0.777400\pi$
$752$	37.0123	+	37.0123i	0.0492184	+	0.0492184i
$753$	−111.289	−	559.487i	−0.147794	−	0.743010i
$754$	−39.5564	−	59.2003i	−0.0524620	−	0.0785150i
$755$	−362.805	+	1823.94i	−0.480536	+	2.41582i
$756$	−21.9402	+	9.08793i	−0.0290214	+	0.0120211i
$757$	115.414	+	278.634i	0.152463	+	0.368077i	0.981595	−	0.190975i	$-0.0611651\pi$
$757$	115.414	+	278.634i	0.152463	+	0.368077i	−0.829132	+	0.559052i	$0.811165\pi$
$758$	75.6365	+	15.0450i	0.0997843	+	0.0198483i
$759$	−268.998	+	179.739i	−0.354411	+	0.236810i
$760$	1612.70	−	320.787i	2.12198	−	0.422088i
$761$	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	$-0.0219148\pi$
$762$	243.973	+	163.017i	0.320174	+	0.213934i
$763$	−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
$768$	361.401	−	540.875i	0.470574	−	0.704264i
$769$	−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	$-0.545219\pi$
$770$	−75.6877	−	380.508i	−0.0982958	−	0.494166i
$771$	883.615	+	1322.42i	1.14606	+	1.71520i
$772$	32.3465	−	162.617i	0.0418996	−	0.210644i
$773$	1306.77	−	541.282i	1.69052	−	0.700235i	0.690779	−	0.723066i	$-0.257268\pi$
$773$	1306.77	−	541.282i	1.69052	−	0.700235i	0.999739	+	0.0228308i	$0.00726789\pi$
$774$	17.3451	+	41.8749i	0.0224098	+	0.0541019i
$775$	−1294.25	−	257.442i	−1.67000	−	0.332184i
$776$	1192.36	−	796.710i	1.53655	−	1.02669i
$777$	−524.128	+	104.256i	−0.674553	+	0.134177i
$778$	26.8308	−	26.8308i	0.0344869	−	0.0344869i
$779$	692.937	+	463.005i	0.889521	+	0.594359i
$780$	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
$785$	1156.12	−	1730.25i	1.47276	−	2.20414i
$786$	972.366	+	972.366i	1.23711	+	1.23711i
$787$	300.978	+	1513.12i	0.382437	+	1.92264i	0.385650	+	0.922645i	$0.373977\pi$
$787$	300.978	+	1513.12i	0.382437	+	1.92264i	−0.00321327	+	0.999995i	$0.501023\pi$
$788$	−140.935	−	210.924i	−0.178851	−	0.267670i
$789$	−230.117	+	1156.88i	−0.291657	+	1.46626i
$790$	−270.877	+	112.201i	−0.342882	+	0.142026i
$791$	−293.232	−	707.924i	−0.370710	−	0.894973i
$792$	−432.867	−	86.1025i	−0.546549	−	0.108715i
$793$	197.849	−	132.199i	0.249495	−	0.166707i
$794$	−61.4266	+	12.2185i	−0.0773634	+	0.0153885i
$795$	−680.496	+	680.496i	−0.855970	+	0.855970i
$796$	67.2856	+	44.9588i	0.0845297	+	0.0564809i
$797$	−1040.17	−	430.853i	−1.30511	−	0.540593i	−0.381654	−	0.924305i	$-0.624645\pi$
$797$	−1040.17	−	430.853i	−1.30511	−	0.540593i	−0.923453	+	0.383712i	$0.874645\pi$
$798$			720.593i			0.902998i
$799$		0			0
$800$	−483.288			−0.604110
$801$	113.079	−	272.996i	0.141172	−	0.340819i
$802$	146.691	−	219.538i	0.182906	−	0.273739i
$803$	−459.675	−	459.675i	−0.572448	−	0.572448i
$804$	19.9376	+	100.233i	0.0247981	+	0.124668i
$805$	−202.673	−	303.322i	−0.251768	−	0.376798i
$806$	−43.7470	+	219.931i	−0.0542767	+	0.272868i
$807$	380.953	−	157.796i	0.472061	−	0.195534i
$808$	−410.560	−	991.179i	−0.508119	−	1.22671i
$809$	322.319	+	64.1132i	0.398417	+	0.0792500i	0.390232	−	0.920717i	$-0.372395\pi$
$809$	322.319	+	64.1132i	0.398417	+	0.0792500i	0.00818445	+	0.999967i	$0.497395\pi$
$810$	−1056.05	+	705.632i	−1.30377	+	0.871150i
$811$	286.220	−	56.9327i	0.352922	−	0.0702006i	−0.0154457	−	0.999881i	$-0.504917\pi$
$811$	286.220	−	56.9327i	0.352922	−	0.0702006i	0.368368	+	0.929680i	$0.379917\pi$
$812$	30.7091	−	30.7091i	0.0378191	−	0.0378191i
$813$	−1282.20	−	856.736i	−1.57712	−	1.05380i
$814$	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
$819$	−56.3126	+	84.2777i	−0.0687577	+	0.102903i
$820$	−163.457	−	163.457i	−0.199337	−	0.199337i
$821$	−210.765	−	1059.59i	−0.256718	−	1.29061i	−0.866954	−	0.498388i	$-0.833926\pi$
$821$	−210.765	−	1059.59i	−0.256718	−	1.29061i	0.610237	−	0.792219i	$-0.291074\pi$
$822$	−209.711	−	313.854i	−0.255122	−	0.381818i
$823$	17.7059	−	89.0135i	0.0215138	−	0.108157i	−0.968536	−	0.248872i	$-0.919940\pi$
$823$	17.7059	−	89.0135i	0.0215138	−	0.108157i	0.990050	+	0.140715i	$0.0449401\pi$
$824$	1394.52	−	577.631i	1.69238	−	0.701008i
$825$	374.877	+	905.033i	0.454396	+	1.09701i
$826$	−83.2240	−	16.5543i	−0.100755	−	0.0200415i
$827$	−404.167	+	270.056i	−0.488715	+	0.326549i	−0.775394	−	0.631478i	$-0.782449\pi$
$827$	−404.167	+	270.056i	−0.488715	+	0.326549i	0.286679	+	0.958027i	$0.407449\pi$
$828$	−73.6358	+	14.6471i	−0.0889322	+	0.0176897i
$829$	−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	$0.468642\pi$
$830$	−1289.73	−	861.770i	−1.55389	−	1.03828i
$831$	−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
$836$	−83.9554	+	125.648i	−0.100425	+	0.150297i
$837$	175.711	+	175.711i	0.209930	+	0.209930i
$838$	−12.8807	−	64.7556i	−0.0153708	−	0.0772740i
$839$	−254.822	−	381.369i	−0.303721	−	0.454551i	0.647944	−	0.761688i	$-0.275629\pi$
$839$	−254.822	−	381.369i	−0.303721	−	0.454551i	−0.951665	+	0.307137i	$0.900629\pi$
$840$	215.540	−	1083.60i	0.256596	−	1.28999i
$841$	−643.676	+	266.619i	−0.765370	+	0.317027i
$842$	298.762	+	721.276i	0.354824	+	0.856622i
$843$	1496.57	+	297.687i	1.77529	+	0.353128i
$844$	26.5621	−	17.7482i	0.0314717	−	0.0210287i
$845$	1197.08	−	238.115i	1.41667	−	0.281793i
$846$	41.2482	−	41.2482i	0.0487568	−	0.0487568i
$847$	−247.848	−	165.607i	−0.292619	−	0.195522i
$848$	−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
$853$	4.18302	−	6.26033i	0.00490389	−	0.00733919i	−0.829010	−	0.559234i	$-0.811095\pi$
$853$	4.18302	−	6.26033i	0.00490389	−	0.00733919i	0.833913	+	0.551895i	$0.186095\pi$
$854$	−362.035	−	362.035i	−0.423929	−	0.423929i
$855$	−274.490	−	1379.95i	−0.321041	−	1.61398i
$856$	190.946	+	285.770i	0.223067	+	0.333844i
$857$	−9.89135	+	49.7272i	−0.0115418	+	0.0580247i	−0.986127	−	0.165993i	$-0.946917\pi$
$857$	−9.89135	+	49.7272i	−0.0115418	+	0.0580247i	0.974585	+	0.224017i	$0.0719172\pi$
$858$	153.792	−	63.7026i	0.179244	−	0.0742455i
$859$	192.547	+	464.849i	0.224152	+	0.541151i	0.995446	−	0.0953281i	$-0.0303900\pi$
$859$	192.547	+	464.849i	0.224152	+	0.541151i	−0.771294	+	0.636479i	$0.780390\pi$
$860$	−23.3370	−	4.64202i	−0.0271361	−	0.00539770i
$861$	465.592	−	311.099i	0.540758	−	0.361323i
$862$	−600.631	+	119.473i	−0.696787	+	0.138600i
$863$	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	$0.224163\pi$
$864$	75.6697	+	50.5609i	0.0875807	+	0.0585196i
$865$	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
$870$	368.937	−	552.154i	0.424066	−	0.634660i
$871$	−67.8634	−	67.8634i	−0.0779143	−	0.0779143i
$872$	77.0774	+	387.494i	0.0883915	+	0.444374i
$873$	−681.726	−	1020.28i	−0.780900	−	1.16870i
$874$	97.7883	−	491.615i	0.111886	−	0.562488i
$875$	−289.092	+	119.746i	−0.330391	+	0.136853i
$876$	−128.167	−	309.423i	−0.146309	−	0.353222i
$877$	−931.342	−	185.255i	−1.06196	−	0.211238i	−0.366955	−	0.930239i	$-0.619600\pi$
$877$	−931.342	−	185.255i	−1.06196	−	0.211238i	−0.695009	+	0.719001i	$0.744600\pi$
$878$	357.065	−	238.583i	0.406680	−	0.271735i
$879$	−560.455	+	111.481i	−0.637605	+	0.126828i
$880$	−443.732	+	443.732i	−0.504241	+	0.504241i
$881$	869.803	+	581.184i	0.987290	+	0.659686i	0.940704	−	0.339228i	$-0.110166\pi$
$881$	869.803	+	581.184i	0.987290	+	0.659686i	0.0465861	+	0.998914i	$0.485166\pi$
$882$	−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
$887$	434.284	−	649.952i	0.489610	−	0.732753i	−0.501593	−	0.865104i	$-0.667253\pi$
$887$	434.284	−	649.952i	0.489610	−	0.732753i	0.991203	+	0.132351i	$0.0422525\pi$
$888$	796.059	+	796.059i	0.896463	+	0.896463i
$889$	−32.7905	−	164.849i	−0.0368847	−	0.185432i
$890$	−304.009	−	454.981i	−0.341583	−	0.511215i
$891$	125.874	−	632.812i	0.141273	−	0.710227i
$892$	−329.023	+	136.286i	−0.368860	+	0.152787i
$893$	−42.2496	−	102.000i	−0.0473120	−	0.114221i
$894$	362.651	+	72.1358i	0.405650	+	0.0806888i
$895$	−1559.63	+	1042.11i	−1.74260	+	1.16437i
$896$	282.066	−	56.1063i	0.314805	−	0.0626187i
$897$	110.680	−	110.680i	0.123389	−	0.123389i
$898$	797.334	+	532.761i	0.887900	+	0.593276i
$899$	−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
$904$	−896.823	+	1342.19i	−0.992061	+	1.48472i
$905$	746.999	+	746.999i	0.825413	+	0.825413i
$906$	334.949	+	1683.90i	0.369701	+	1.85861i
$907$	−207.645	−	310.763i	−0.228936	−	0.342628i	0.699161	−	0.714964i	$-0.253557\pi$
$907$	−207.645	−	310.763i	−0.228936	−	0.342628i	−0.928098	+	0.372336i	$0.878557\pi$
$908$	−21.7590	+	109.390i	−0.0239637	+	0.120474i
$909$	−848.129	+	351.306i	−0.933035	+	0.386476i
$910$	71.8311	+	173.416i	0.0789352	+	0.190567i
$911$	119.565	+	23.7829i	0.131246	+	0.0261064i	0.260276	−	0.965534i	$-0.416186\pi$
$911$	119.565	+	23.7829i	0.131246	+	0.0261064i	−0.129030	+	0.991641i	$0.541186\pi$
$912$	969.131	−	647.553i	1.06264	−	0.710036i
$913$	772.838	−	153.727i	0.846482	−	0.168376i
$914$	−280.276	+	280.276i	−0.306647	+	0.306647i
$915$	1845.31	+	1233.00i	2.01674	+	1.34754i
$916$	−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
$921$	−583.751	+	873.645i	−0.633823	+	0.948583i
$922$	−314.913	−	314.913i	−0.341555	−	0.341555i
$923$	−22.5107	−	113.169i	−0.0243886	−	0.122610i
$924$	56.4107	+	84.4245i	0.0610505	+	0.0913685i
$925$	219.587	−	1103.94i	0.237391	−	1.19345i
$926$	−204.478	+	84.6976i	−0.220819	+	0.0914661i
$927$	−494.265	−	1193.26i	−0.533188	−	1.28723i
$928$	−163.232	−	32.4690i	−0.175897	−	0.0349881i
$929$	−564.616	+	377.264i	−0.607767	+	0.406097i	−0.821020	−	0.570900i	$-0.806594\pi$
$929$	−564.616	+	377.264i	−0.607767	+	0.406097i	0.213252	+	0.976997i	$0.431594\pi$
$930$	−2051.27	+	408.023i	−2.20567	+	0.438735i
$931$	−562.118	+	562.118i	−0.603778	+	0.603778i
$932$	−44.1806	−	29.5205i	−0.0474040	−	0.0316744i
$933$	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	−0.972523	−	0.232806i	$-0.925209\pi$
$937$	−112.652	+	271.967i	−0.120227	+	0.290253i	0.852296	+	0.523059i	$0.175209\pi$
$938$	−114.727	+	171.702i	−0.122311	+	0.183051i
$939$	1304.18	+	1304.18i	1.38890	+	1.38890i
$940$	5.97433	+	30.0350i	0.00635567	+	0.0319521i
$941$	463.946	+	694.344i	0.493035	+	0.737879i	0.991652	−	0.128943i	$-0.0411585\pi$
$941$	463.946	+	694.344i	0.493035	+	0.737879i	−0.498617	+	0.866822i	$0.666159\pi$
$942$	374.804	−	1884.27i	0.397882	−	2.00029i
$943$	−359.862	+	149.060i	−0.381614	+	0.158070i
$944$	52.5243	+	126.805i	0.0556402	+	0.134327i
$945$	204.008	+	40.5798i	0.215882	+	0.0429416i
$946$	−35.4530	+	23.6889i	−0.0374767	+	0.0250412i
$947$	−610.881	+	121.512i	−0.645070	+	0.128312i	−0.506775	−	0.862079i	$-0.669162\pi$
$947$	−610.881	+	121.512i	−0.645070	+	0.128312i	−0.138295	+	0.990391i	$0.544162\pi$
$948$	54.2592	−	54.2592i	0.0572355	−	0.0572355i
$949$	261.514	+	174.738i	0.275568	+	0.184129i
$950$	−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
$955$	−749.313	+	1121.43i	−0.784621	+	1.17427i
$956$	−178.619	−	178.619i	−0.186840	−	0.186840i
$957$	65.8130	+	330.864i	0.0687701	+	0.345730i
$958$	−469.496	−	702.650i	−0.490079	−	0.733455i
$959$	−42.1827	+	212.067i	−0.0439861	+	0.221133i
$960$	−2060.00	+	853.280i	−2.14583	+	0.888833i
$961$	179.945	+	434.426i	0.187248	+	0.452056i
$962$	−187.592	−	37.3143i	−0.195002	−	0.0387883i
$963$	244.527	−	163.388i	0.253922	−	0.169665i
$964$	107.737	−	21.4303i	0.111761	−	0.0222306i
$965$	−1026.89	+	1026.89i	−1.06414	+	1.06414i
$966$	−280.033	−	187.112i	−0.289890	−	0.193698i
$967$	−947.512	−	392.472i	−0.979847	−	0.405866i	−0.165478	−	0.986213i	$-0.552917\pi$
$967$	−947.512	−	392.472i	−0.979847	−	0.405866i	−0.814369	+	0.580348i	$0.802917\pi$
$968$			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	$0.294148\pi$
$971$	−376.591	+	909.171i	−0.387838	+	0.936325i	−0.990397	+	0.138250i	$0.955852\pi$
$972$	155.660	−	232.961i	0.160144	−	0.239672i
$973$	−151.849	−	151.849i	−0.156063	−	0.156063i
$974$	−139.713	−	702.385i	−0.143443	−	0.721134i
$975$	−263.312	−	394.074i	−0.270064	−	0.404179i
$976$	−161.565	+	812.243i	−0.165538	+	0.832216i
$977$	525.837	−	217.809i	0.538216	−	0.222936i	−0.0969814	−	0.995286i	$-0.530919\pi$
$977$	525.837	−	217.809i	0.538216	−	0.222936i	0.635197	+	0.772350i	$0.280919\pi$
$978$	106.082	+	256.105i	0.108469	+	0.261866i
$979$	272.636	+	54.2306i	0.278484	+	0.0553939i
$980$	183.341	−	122.504i	0.187082	−	0.125004i
$981$	331.570	−	65.9533i	0.337991	−	0.0672307i
$982$	−77.4444	+	77.4444i	−0.0788639	+	0.0788639i
$983$	−1195.55	−	798.843i	−1.21623	−	0.812658i	−0.229228	−	0.973373i	$-0.573620\pi$
$983$	−1195.55	−	798.843i	−1.21623	−	0.812658i	−0.987001	+	0.160715i	$0.948620\pi$
$984$	−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
$989$	−22.2748	+	33.3365i	−0.0225225	+	0.0337073i
$990$	494.517	+	494.517i	0.499512	+	0.499512i
$991$	16.3803	+	82.3495i	0.0165291	+	0.0830973i	0.988169	−	0.153367i	$-0.0490115\pi$
$991$	16.3803	+	82.3495i	0.0165291	+	0.0830973i	−0.971640	+	0.236464i	$0.924012\pi$
$992$	291.210	+	435.827i	0.293559	+	0.439342i
$993$	465.415	−	2339.80i	0.468696	−	2.35629i
$994$	−229.375	+	95.0102i	−0.230759	+	0.0955837i
$995$	−271.246	−	654.847i	−0.272609	−	0.658137i
$996$	398.161	+	79.1992i	0.399760	+	0.0795172i
$997$	−626.361	+	418.521i	−0.628246	+	0.419780i	−0.828520	−	0.559959i	$-0.810817\pi$
$997$	−626.361	+	418.521i	−0.628246	+	0.419780i	0.200274	+	0.979740i	$0.435817\pi$
$998$	−888.649	+	176.763i	−0.890430	+	0.177118i
$999$	−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.n.75.1		8
17.2	even	8		289.3.e.h.249.1		8
17.3	odd	16		289.3.e.e.131.1		8
17.4	even	4		289.3.e.a.214.1		8
17.5	odd	16	inner	289.3.e.n.158.1		8
17.6	odd	16		289.3.e.f.65.1		8
17.7	odd	16		289.3.e.g.224.1		8
17.8	even	8		289.3.e.g.40.1		8
17.9	even	8		17.3.e.b.6.1	yes	8
17.10	odd	16		17.3.e.b.3.1	✓	8
17.11	odd	16		289.3.e.h.65.1		8
17.12	odd	16		289.3.e.j.158.1		8
17.13	even	4		289.3.e.e.214.1		8
17.14	odd	16		289.3.e.a.131.1		8
17.15	even	8		289.3.e.f.249.1		8
17.16	even	2		289.3.e.j.75.1		8
51.26	odd	8		153.3.p.a.91.1		8
51.44	even	16		153.3.p.a.37.1		8
68.27	even	16		272.3.bh.b.241.1		8
68.43	odd	8		272.3.bh.b.193.1		8
85.9	even	8		425.3.u.a.176.1		8
85.27	even	16		425.3.t.b.224.1		8
85.43	odd	8		425.3.t.b.74.1		8
85.44	odd	16		425.3.u.a.326.1		8
85.77	odd	8		425.3.t.d.74.1		8
85.78	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	17.10	odd	16
17.3.e.b.6.1	yes	8	17.9	even	8
153.3.p.a.37.1		8	51.44	even	16
153.3.p.a.91.1		8	51.26	odd	8
272.3.bh.b.193.1		8	68.43	odd	8
272.3.bh.b.241.1		8	68.27	even	16
289.3.e.a.131.1		8	17.14	odd	16
289.3.e.a.214.1		8	17.4	even	4
289.3.e.e.131.1		8	17.3	odd	16
289.3.e.e.214.1		8	17.13	even	4
289.3.e.f.65.1		8	17.6	odd	16
289.3.e.f.249.1		8	17.15	even	8
289.3.e.g.40.1		8	17.8	even	8
289.3.e.g.224.1		8	17.7	odd	16
289.3.e.h.65.1		8	17.11	odd	16
289.3.e.h.249.1		8	17.2	even	8
289.3.e.j.75.1		8	17.16	even	2
289.3.e.j.158.1		8	17.12	odd	16
289.3.e.n.75.1		8	1.1	even	1	trivial
289.3.e.n.158.1		8	17.5	odd	16	inner
425.3.t.b.74.1		8	85.43	odd	8
425.3.t.b.224.1		8	85.27	even	16
425.3.t.d.74.1		8	85.77	odd	8
425.3.t.d.224.1		8	85.78	even	16
425.3.u.a.176.1		8	85.9	even	8
425.3.u.a.326.1		8	85.44	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} +(2.24830 - 3.36482i) q^{3} +(0.624715 + 0.624715i) q^{4} +(-1.50967 - 7.58960i) q^{5} +(-3.96908 - 5.94015i) q^{6} +(-0.798369 + 4.01367i) q^{7} +(7.96489 - 3.29916i) q^{8} +(-2.82302 - 6.81537i) q^{9} +(-13.3984 - 2.66511i) q^{10} +(5.77017 - 3.85550i) q^{11} +(3.50660 - 0.697506i) q^{12} +(-2.37416 + 2.37416i) q^{13} +(6.00688 + 4.01367i) q^{14} +(-28.9319 - 11.9840i) q^{15} -11.6855i q^{16} -13.0229 q^{18} +(-9.43215 + 22.7712i) q^{19} +(3.79823 - 5.68445i) q^{20} +(11.7103 + 11.7103i) q^{21} +(-2.39008 - 12.0158i) q^{22} +(-6.40006 - 9.57836i) q^{23} +(6.80638 - 34.2180i) q^{24} +(-32.2260 + 13.3484i) q^{25} +(2.26829 + 5.47615i) q^{26} +(6.44221 + 1.28144i) q^{27} +(-3.00615 + 2.00865i) q^{28} +(-11.7813 + 2.34344i) q^{29} +(-39.0914 + 39.0914i) q^{30} +(31.4557 + 21.0180i) q^{31} +(12.8006 + 5.30218i) q^{32} -28.0839i q^{33} +31.6674 q^{35} +(2.49408 - 6.02124i) q^{36} +(-17.9275 + 26.8303i) q^{37} +(30.7674 + 30.7674i) q^{38} +(2.65080 + 13.3265i) q^{39} +(-37.0637 - 55.4697i) q^{40} +(6.59647 - 33.1627i) q^{41} +(27.0106 - 11.1881i) q^{42} +(-1.33189 - 3.21547i) q^{43} +(6.01330 + 1.19612i) q^{44} +(-47.4641 + 31.7145i) q^{45} +(-19.9459 + 3.96749i) q^{46} +(-3.16735 + 3.16735i) q^{47} +(-39.3198 - 26.2726i) q^{48} +(29.7979 + 12.3427i) q^{49} +61.5781i q^{50} -2.96634 q^{52} +(11.7603 - 28.3919i) q^{53} +(6.44221 - 9.64145i) q^{54} +(-37.9728 - 37.9728i) q^{55} +(6.88284 + 34.6024i) q^{56} +(55.4148 + 82.9342i) q^{57} +(-4.13703 + 20.7982i) q^{58} +(-10.8514 + 4.49481i) q^{59} +(-10.5876 - 25.5607i) q^{60} +(-69.5084 - 13.8261i) q^{61} +(55.5309 - 37.1045i) q^{62} +(29.6084 - 5.88948i) q^{63} +(50.3473 - 50.3473i) q^{64} +(21.6031 + 14.4347i) q^{65} +(-45.8045 - 18.9728i) q^{66} +28.5842i q^{67} -46.6187 q^{69} +(21.3938 - 51.6491i) q^{70} +(-19.0927 + 28.5742i) q^{71} +(-44.9700 - 44.9700i) q^{72} +(-18.2751 - 91.8752i) q^{73} +(31.6486 + 47.3654i) q^{74} +(-27.5386 + 138.446i) q^{75} +(-20.1179 + 8.33312i) q^{76} +(10.8680 + 26.2377i) q^{77} +(23.5261 + 4.67963i) q^{78} +(17.8452 - 11.9238i) q^{79} +(-88.6886 + 17.6413i) q^{80} +(65.7422 - 65.7422i) q^{81} +(-49.6315 - 33.1627i) q^{82} +(104.903 + 43.4522i) q^{83} +14.6312i q^{84} -6.14419 q^{86} +(-18.6026 + 44.9106i) q^{87} +(33.2388 - 49.7454i) q^{88} +(28.3238 + 28.3238i) q^{89} +(19.6603 + 98.8389i) q^{90} +(-7.63364 - 11.4245i) q^{91} +(1.98553 - 9.98195i) q^{92} +(141.444 - 58.5880i) q^{93} +(3.02612 + 7.30570i) q^{94} +(187.064 + 37.2094i) q^{95} +(46.6205 - 31.1508i) q^{96} +(163.144 - 32.4513i) q^{97} +(40.2616 - 40.2616i) q^{98} +(-42.5659 - 28.4417i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} + 8 q^{3} + 8 q^{4} - 16 q^{5} + 8 q^{7} + 8 q^{8} - 56 q^{9} - 48 q^{10} + 24 q^{11} + 24 q^{12} - 8 q^{14} - 80 q^{15} - 136 q^{18} - 80 q^{19} + 48 q^{20} + 64 q^{21} - 16 q^{22} - 104 q^{23}+ \cdots + 120 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 + 8 * q^3 + 8 * q^4 - 16 * q^5 + 8 * q^7 + 8 * q^8 - 56 * q^9 - 48 * q^10 + 24 * q^11 + 24 * q^12 - 8 * q^14 - 80 * q^15 - 136 * q^18 - 80 * q^19 + 48 * q^20 + 64 * q^21 - 16 * q^22 - 104 * q^23 - 136 * q^25 + 40 * q^26 + 32 * q^27 - 168 * q^30 + 144 * q^31 + 16 * q^32 + 80 * q^35 - 72 * q^36 + 48 * q^37 - 8 * q^38 - 96 * q^39 + 8 * q^40 + 208 * q^41 + 88 * q^42 + 48 * q^43 - 56 * q^44 + 48 * q^45 - 80 * q^46 + 80 * q^47 - 256 * q^48 + 72 * q^49 + 240 * q^52 + 88 * q^53 + 32 * q^54 + 8 * q^55 - 8 * q^56 + 40 * q^57 - 120 * q^58 - 40 * q^59 - 96 * q^60 - 16 * q^61 + 256 * q^62 + 96 * q^63 + 120 * q^64 - 72 * q^65 - 120 * q^66 - 208 * q^69 + 96 * q^70 - 328 * q^71 - 24 * q^72 + 160 * q^73 + 168 * q^74 - 264 * q^75 + 192 * q^76 + 120 * q^77 - 168 * q^78 - 352 * q^79 - 328 * q^80 + 224 * q^81 + 320 * q^82 + 504 * q^83 + 288 * q^86 + 216 * q^87 - 56 * q^88 - 288 * q^89 + 392 * q^90 + 32 * q^91 - 200 * q^92 + 248 * q^93 + 72 * q^94 + 800 * q^95 - 408 * q^96 + 504 * q^97 - 16 * q^98 + 120 * q^99

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