LMFDB - Embedded newform 289.3.e.g.40.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

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

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

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

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

Newform invariants

comment:select newform

sage:traces = [8,0,0,-8,24] 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			40.1
Root			$0.923880 - 0.382683i$ of defining polynomial
Character	$\chi$	$=$	289.40
Dual form			289.3.e.g.224.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.63099 - 0.675577i) q^{2} +(-3.96908 + 0.789499i) q^{3} +(-0.624715 - 0.624715i) q^{4} +(4.29916 - 6.43416i) q^{5} +(7.00688 + 1.39376i) q^{6} +(2.27356 + 3.40262i) q^{7} +(3.29916 + 7.96489i) q^{8} +(6.81537 - 2.82302i) q^{9} +(-11.3586 + 7.58960i) q^{10} +(-1.35387 + 6.80638i) q^{11} +(2.97275 + 1.98633i) q^{12} +(2.37416 - 2.37416i) q^{13} +(-1.40941 - 7.08560i) q^{14} +(-11.9840 + 28.9319i) q^{15} -11.6855i q^{16} -13.0229 q^{18} +(22.7712 + 9.43215i) q^{19} +(-6.70526 + 1.33376i) q^{20} +(-11.7103 - 11.7103i) q^{21} +(6.80638 - 10.1865i) q^{22} +(11.2984 + 2.24740i) q^{23} +(-19.3829 - 29.0086i) q^{24} +(-13.3484 - 32.2260i) q^{25} +(-5.47615 + 2.26829i) q^{26} +(5.46144 - 3.64922i) q^{27} +(0.705343 - 3.54600i) q^{28} +(-9.98767 - 6.67355i) q^{29} +(39.0914 - 39.0914i) q^{30} +(-7.38055 - 37.1045i) q^{31} +(5.30218 - 12.8006i) q^{32} -28.0839i q^{33} +31.6674 q^{35} +(-6.02124 - 2.49408i) q^{36} +(31.6486 - 6.29529i) q^{37} +(-30.7674 - 30.7674i) q^{38} +(-7.54883 + 11.2976i) q^{39} +(65.4310 + 13.0150i) q^{40} +(-18.7852 - 28.1140i) q^{41} +(11.1881 + 27.0106i) q^{42} +(3.21547 - 1.33189i) q^{43} +(5.09783 - 3.40626i) q^{44} +(11.1367 - 55.9877i) q^{45} +(-16.9093 - 11.2984i) q^{46} +(3.16735 - 3.16735i) q^{47} +(9.22573 + 46.3809i) q^{48} +(12.3427 - 29.7979i) q^{49} +61.5781i q^{50} -2.96634 q^{52} +(-28.3919 - 11.7603i) q^{53} +(-11.3729 + 2.26220i) q^{54} +(37.9728 + 37.9728i) q^{55} +(-19.6007 + 29.3345i) q^{56} +(-97.8275 - 19.4591i) q^{57} +(11.7813 + 17.6319i) q^{58} +(-4.49481 - 10.8514i) q^{59} +(25.5607 - 10.5876i) q^{60} +(-58.9263 + 39.3733i) q^{61} +(-13.0294 + 65.5031i) q^{62} +(25.1008 + 16.7718i) q^{63} +(-50.3473 + 50.3473i) q^{64} +(-5.06881 - 25.4826i) q^{65} +(-18.9728 + 45.8045i) q^{66} +28.5842i q^{67} -46.6187 q^{69} +(-51.6491 - 21.3938i) q^{70} +(33.7056 - 6.70446i) q^{71} +(44.9700 + 44.9700i) q^{72} +(52.0431 - 77.8880i) q^{73} +(-55.8713 - 11.1135i) q^{74} +(78.4234 + 117.369i) q^{75} +(-8.33312 - 20.1179i) q^{76} +(-26.2377 + 10.8680i) q^{77} +(19.9444 - 13.3265i) q^{78} +(-4.18708 + 21.0499i) q^{79} +(-75.1866 - 50.2381i) q^{80} +(-65.7422 + 65.7422i) q^{81} +(11.6452 + 58.5443i) q^{82} +(43.4522 - 104.903i) q^{83} +14.6312i q^{84} -6.14419 q^{86} +(44.9106 + 18.6026i) q^{87} +(-58.6787 + 11.6719i) q^{88} +(-28.3238 - 28.3238i) q^{89} +(-55.9877 + 83.7916i) q^{90} +(13.4762 + 2.68058i) q^{91} +(-5.65432 - 8.46229i) q^{92} +(58.5880 + 141.444i) q^{93} +(-7.30570 + 3.02612i) q^{94} +(158.585 - 105.963i) q^{95} +(-10.9387 + 54.9926i) q^{96} +(138.307 + 92.4136i) q^{97} +(-40.2616 + 40.2616i) q^{98} +(9.98738 + 50.2100i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4} + 24 q^{5} + 16 q^{7} + 16 q^{8} + 8 q^{9} - 40 q^{11} - 40 q^{12} - 16 q^{14} + 32 q^{15} - 136 q^{18} - 32 q^{19} + 40 q^{20} - 64 q^{21} + 8 q^{23} - 24 q^{24} + 16 q^{25} - 96 q^{27} - 80 q^{28}+ \cdots - 136 q^{99}+O(q^{100}) $ 8 * q - 8 * q^4 + 24 * q^5 + 16 * q^7 + 16 * q^8 + 8 * q^9 - 40 * q^11 - 40 * q^12 - 16 * q^14 + 32 * q^15 - 136 * q^18 - 32 * q^19 + 40 * q^20 - 64 * q^21 + 8 * q^23 - 24 * q^24 + 16 * q^25 - 96 * q^27 - 80 * q^28 - 24 * q^29 + 168 * q^30 - 32 * q^31 - 24 * q^32 + 80 * q^35 - 104 * q^36 + 168 * q^37 + 8 * q^38 + 72 * q^39 + 200 * q^40 - 72 * q^42 + 96 * q^43 + 96 * q^44 + 88 * q^45 - 80 * q^47 - 88 * q^48 + 8 * q^49 + 240 * q^52 + 96 * q^53 - 208 * q^54 - 8 * q^55 - 72 * q^56 - 248 * q^57 + 8 * q^59 + 16 * q^60 - 264 * q^61 + 136 * q^62 - 8 * q^63 - 120 * q^64 + 32 * q^65 + 8 * q^66 - 208 * q^69 - 80 * q^70 - 32 * q^71 + 24 * q^72 - 24 * q^73 - 176 * q^74 + 192 * q^75 - 80 * q^76 - 216 * q^77 + 368 * q^78 + 96 * q^79 - 24 * q^80 - 224 * q^81 + 408 * q^82 - 88 * q^83 + 288 * q^86 + 312 * q^87 - 176 * q^88 + 288 * q^89 - 256 * q^90 + 24 * q^91 - 336 * q^92 + 280 * q^93 - 8 * q^94 + 152 * q^95 - 328 * q^96 + 344 * q^97 + 16 * q^98 - 136 * q^99

Character values

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

$n$	$3$
$\chi(n)$	$e\left(\frac{15}{16}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.63099	−	0.675577i	−0.815493	−	0.337788i	−0.0643498	−	0.997927i	$-0.520497\pi$
$2$	−1.63099	−	0.675577i	−0.815493	−	0.337788i	−0.751143	+	0.660139i	$0.770497\pi$
$3$	−3.96908	+	0.789499i	−1.32303	+	0.263166i	−0.805548	−	0.592530i	$-0.798129\pi$
$3$	−3.96908	+	0.789499i	−1.32303	+	0.263166i	−0.517478	+	0.855696i	$0.673129\pi$
$4$	−0.624715	−	0.624715i	−0.156179	−	0.156179i
$5$	4.29916	−	6.43416i	0.859833	−	1.28683i	−0.0967316	−	0.995311i	$-0.530839\pi$
$5$	4.29916	−	6.43416i	0.859833	−	1.28683i	0.956565	−	0.291521i	$-0.0941612\pi$
$6$	7.00688	+	1.39376i	1.16781	+	0.232293i
$7$	2.27356	+	3.40262i	0.324794	+	0.486089i	0.957552	−	0.288261i	$-0.0930770\pi$
$7$	2.27356	+	3.40262i	0.324794	+	0.486089i	−0.632757	+	0.774350i	$0.718077\pi$
$8$	3.29916	+	7.96489i	0.412396	+	0.995611i
$9$	6.81537	−	2.82302i	0.757263	−	0.313669i
$10$	−11.3586	+	7.58960i	−1.13586	+	0.758960i
$11$	−1.35387	+	6.80638i	−0.123079	+	0.618761i	0.869172	+	0.494511i	$0.164653\pi$
$11$	−1.35387	+	6.80638i	−0.123079	+	0.618761i	−0.992251	+	0.124251i	$0.960347\pi$
$12$	2.97275	+	1.98633i	0.247729	+	0.165528i
$13$	2.37416	−	2.37416i	0.182628	−	0.182628i	−0.609872	−	0.792500i	$-0.708779\pi$
$13$	2.37416	−	2.37416i	0.182628	−	0.182628i	0.792500	+	0.609872i	$0.208779\pi$
$14$	−1.40941	−	7.08560i	−0.100672	−	0.506114i
$15$	−11.9840	+	28.9319i	−0.798931	+	1.92879i
$16$		−	11.6855i		−	0.730347i
$17$		0			0
$17$		0			0
$18$	−13.0229			−0.723496
$19$	22.7712	+	9.43215i	1.19849	+	0.496429i	0.890509	−	0.454965i	$-0.150348\pi$
$19$	22.7712	+	9.43215i	1.19849	+	0.496429i	0.307977	+	0.951394i	$0.400348\pi$
$20$	−6.70526	+	1.33376i	−0.335263	+	0.0666880i
$21$	−11.7103	−	11.7103i	−0.557634	−	0.557634i
$22$	6.80638	−	10.1865i	0.309381	−	0.463021i
$23$	11.2984	+	2.24740i	0.491237	+	0.0977131i	0.434492	−	0.900676i	$-0.356928\pi$
$23$	11.2984	+	2.24740i	0.491237	+	0.0977131i	0.0567447	+	0.998389i	$0.481928\pi$
$24$	−19.3829	−	29.0086i	−0.807622	−	1.20869i
$25$	−13.3484	−	32.2260i	−0.533938	−	1.28904i
$26$	−5.47615	+	2.26829i	−0.210621	+	0.0872421i
$27$	5.46144	−	3.64922i	0.202276	−	0.135156i
$28$	0.705343	−	3.54600i	0.0251908	−	0.126643i
$29$	−9.98767	−	6.67355i	−0.344402	−	0.230122i	0.371324	−	0.928504i	$-0.378904\pi$
$29$	−9.98767	−	6.67355i	−0.344402	−	0.230122i	−0.715726	+	0.698381i	$0.753904\pi$
$30$	39.0914	−	39.0914i	1.30305	−	1.30305i
$31$	−7.38055	−	37.1045i	−0.238082	−	1.19692i	−0.896077	−	0.443898i	$-0.853595\pi$
$31$	−7.38055	−	37.1045i	−0.238082	−	1.19692i	0.657995	−	0.753022i	$-0.271405\pi$
$32$	5.30218	−	12.8006i	0.165693	−	0.400019i
$33$		−	28.0839i		−	0.851028i
$34$		0			0
$35$	31.6674			0.904784
$36$	−6.02124	−	2.49408i	−0.167257	−	0.0692800i
$37$	31.6486	−	6.29529i	0.855366	−	0.170143i	0.252118	−	0.967696i	$-0.418873\pi$
$37$	31.6486	−	6.29529i	0.855366	−	0.170143i	0.603248	+	0.797554i	$0.293873\pi$
$38$	−30.7674	−	30.7674i	−0.809669	−	0.809669i
$39$	−7.54883	+	11.2976i	−0.193560	+	0.289683i
$40$	65.4310	+	13.0150i	1.63577	+	0.325376i
$41$	−18.7852	−	28.1140i	−0.458175	−	0.685707i	0.528404	−	0.848993i	$-0.322791\pi$
$41$	−18.7852	−	28.1140i	−0.458175	−	0.685707i	−0.986579	+	0.163286i	$0.947791\pi$
$42$	11.1881	+	27.0106i	0.266384	+	0.643109i
$43$	3.21547	−	1.33189i	0.0747784	−	0.0309742i	−0.344981	−	0.938610i	$-0.612115\pi$
$43$	3.21547	−	1.33189i	0.0747784	−	0.0309742i	0.419759	+	0.907636i	$0.362115\pi$
$44$	5.09783	−	3.40626i	0.115860	−	0.0774150i
$45$	11.1367	−	55.9877i	0.247481	−	1.24417i
$46$	−16.9093	−	11.2984i	−0.367594	−	0.245618i
$47$	3.16735	−	3.16735i	0.0673905	−	0.0673905i	−0.672608	−	0.739999i	$-0.734826\pi$
$47$	3.16735	−	3.16735i	0.0673905	−	0.0673905i	0.739999	+	0.672608i	$0.234826\pi$
$48$	9.22573	+	46.3809i	0.192203	+	0.966268i
$49$	12.3427	−	29.7979i	0.251892	−	0.608121i
$50$			61.5781i			1.23156i
$51$		0			0
$52$	−2.96634			−0.0570451
$53$	−28.3919	−	11.7603i	−0.535697	−	0.221893i	0.0983994	−	0.995147i	$-0.468628\pi$
$53$	−28.3919	−	11.7603i	−0.535697	−	0.221893i	−0.634096	+	0.773254i	$0.718628\pi$
$54$	−11.3729	+	2.26220i	−0.210609	+	0.0418927i
$55$	37.9728	+	37.9728i	0.690414	+	0.690414i
$56$	−19.6007	+	29.3345i	−0.350012	+	0.523830i
$57$	−97.8275	−	19.4591i	−1.71627	−	0.341388i
$58$	11.7813	+	17.6319i	0.203125	+	0.303998i
$59$	−4.49481	−	10.8514i	−0.0761832	−	0.183923i	0.881200	−	0.472744i	$-0.156737\pi$
$59$	−4.49481	−	10.8514i	−0.0761832	−	0.183923i	−0.957383	+	0.288822i	$0.906737\pi$
$60$	25.5607	−	10.5876i	0.426012	−	0.176460i
$61$	−58.9263	+	39.3733i	−0.966006	+	0.645464i	−0.935222	−	0.354062i	$-0.884800\pi$
$61$	−58.9263	+	39.3733i	−0.966006	+	0.645464i	−0.0307835	+	0.999526i	$0.509800\pi$
$62$	−13.0294	+	65.5031i	−0.210151	+	1.05650i
$63$	25.1008	+	16.7718i	0.398426	+	0.266220i
$64$	−50.3473	+	50.3473i	−0.786676	+	0.786676i
$65$	−5.06881	−	25.4826i	−0.0779816	−	0.392040i
$66$	−18.9728	+	45.8045i	−0.287467	+	0.694008i
$67$			28.5842i			0.426629i	0.976984	+	0.213315i	$0.0684260\pi$
$67$			28.5842i			0.426629i	−0.976984	+	0.213315i	$0.931574\pi$
$68$		0			0
$69$	−46.6187			−0.675634
$70$	−51.6491	−	21.3938i	−0.737845	−	0.305625i
$71$	33.7056	−	6.70446i	0.474726	−	0.0944290i	0.0480724	−	0.998844i	$-0.484692\pi$
$71$	33.7056	−	6.70446i	0.474726	−	0.0944290i	0.426654	+	0.904415i	$0.359692\pi$
$72$	44.9700	+	44.9700i	0.624584	+	0.624584i
$73$	52.0431	−	77.8880i	0.712919	−	1.06696i	−0.281303	−	0.959619i	$-0.590767\pi$
$73$	52.0431	−	77.8880i	0.712919	−	1.06696i	0.994222	−	0.107340i	$-0.0342334\pi$
$74$	−55.8713	−	11.1135i	−0.755018	−	0.150182i
$75$	78.4234	+	117.369i	1.04565	+	1.56492i
$76$	−8.33312	−	20.1179i	−0.109646	−	0.264710i
$77$	−26.2377	+	10.8680i	−0.340749	+	0.141143i
$78$	19.9444	−	13.3265i	0.255698	−	0.170852i
$79$	−4.18708	+	21.0499i	−0.0530011	+	0.266454i	−0.998195	−	0.0600549i	$-0.980872\pi$
$79$	−4.18708	+	21.0499i	−0.0530011	+	0.266454i	0.945194	+	0.326509i	$0.105872\pi$
$80$	−75.1866	−	50.2381i	−0.939833	−	0.627976i
$81$	−65.7422	+	65.7422i	−0.811632	+	0.811632i
$82$	11.6452	+	58.5443i	0.142015	+	0.713955i
$83$	43.4522	−	104.903i	0.523521	−	1.26389i	−0.412182	−	0.911102i	$-0.635233\pi$
$83$	43.4522	−	104.903i	0.523521	−	1.26389i	0.935703	−	0.352789i	$-0.114767\pi$
$84$			14.6312i			0.174181i
$85$		0			0
$86$	−6.14419			−0.0714440
$87$	44.9106	+	18.6026i	0.516214	+	0.213823i
$88$	−58.6787	+	11.6719i	−0.666803	+	0.132635i
$89$	−28.3238	−	28.3238i	−0.318245	−	0.318245i	0.529848	−	0.848093i	$-0.322249\pi$
$89$	−28.3238	−	28.3238i	−0.318245	−	0.318245i	−0.848093	+	0.529848i	$0.822249\pi$
$90$	−55.9877	+	83.7916i	−0.622086	+	0.931018i
$91$	13.4762	+	2.68058i	0.148090	+	0.0294569i
$92$	−5.65432	−	8.46229i	−0.0614600	−	0.0919814i
$93$	58.5880	+	141.444i	0.629978	+	1.52090i
$94$	−7.30570	+	3.02612i	−0.0777202	+	0.0321928i
$95$	158.585	−	105.963i	1.66932	−	1.11540i
$96$	−10.9387	+	54.9926i	−0.113945	+	0.572840i
$97$	138.307	+	92.4136i	1.42584	+	0.952718i	0.998824	+	0.0484747i	$0.0154360\pi$
$97$	138.307	+	92.4136i	1.42584	+	0.952718i	0.427018	+	0.904243i	$0.359564\pi$
$98$	−40.2616	+	40.2616i	−0.410833	+	0.410833i
$99$	9.98738	+	50.2100i	0.100883	+	0.507171i
$100$	−11.7931	+	28.4710i	−0.117931	+	0.284710i
$101$		−	124.444i		−	1.23211i	−0.787701	−	0.616057i	$-0.788729\pi$
$101$		−	124.444i		−	1.23211i	0.787701	−	0.616057i	$-0.211271\pi$
$102$		0			0
$103$	175.084			1.69984			0.849922	−	0.526908i	$-0.176649\pi$
$103$	175.084			1.69984			0.849922	+	0.526908i	$0.176649\pi$
$104$	26.7427	+	11.0772i	0.257141	+	0.106511i
$105$	−125.691	+	25.0014i	−1.19705	+	0.238109i
$106$	38.3619	+	38.3619i	0.361904	+	0.361904i
$107$	−22.1486	+	33.1477i	−0.206996	+	0.309791i	−0.920412	−	0.390949i	$-0.872147\pi$
$107$	−22.1486	+	33.1477i	−0.206996	+	0.309791i	0.713416	+	0.700740i	$0.247147\pi$
$108$	−5.69157	−	1.13212i	−0.0526997	−	0.0104826i
$109$	25.4604	+	38.1042i	0.233582	+	0.349580i	0.929681	−	0.368366i	$-0.120083\pi$
$109$	25.4604	+	38.1042i	0.233582	+	0.349580i	−0.696099	+	0.717946i	$0.745083\pi$
$110$	−36.2795	−	87.5866i	−0.329814	−	0.796241i
$111$	−120.645	+	49.9730i	−1.08690	+	0.450207i
$112$	39.7615	−	26.5678i	0.355014	−	0.237213i
$113$	36.5291	−	183.644i	0.323267	−	1.62517i	−0.387589	−	0.921832i	$-0.626692\pi$
$113$	36.5291	−	183.644i	0.323267	−	1.62517i	0.710855	−	0.703338i	$-0.248308\pi$
$114$	146.409	+	97.8275i	1.28429	+	0.858136i
$115$	63.0340	−	63.0340i	0.548122	−	0.548122i
$116$	2.07038	+	10.4085i	0.0178481	+	0.0897285i
$117$	9.47847	−	22.8831i	0.0810126	−	0.195582i
$118$			20.7351i			0.175721i
$119$		0			0
$120$	−269.976			−2.24980
$121$	67.2956	+	27.8748i	0.556162	+	0.230370i
$122$	122.708	−	24.4081i	1.00580	−	0.200066i
$123$	96.7557	+	96.7557i	0.786632	+	0.786632i
$124$	−18.5690	+	27.7905i	−0.149750	+	0.224117i
$125$	−74.9942	−	14.9173i	−0.599953	−	0.119338i
$126$	−29.6084	−	44.3122i	−0.234988	−	0.351684i
$127$	−15.7175	−	37.9454i	−0.123760	−	0.298783i	0.849841	−	0.527039i	$-0.176698\pi$
$127$	−15.7175	−	37.9454i	−0.123760	−	0.298783i	−0.973601	+	0.228256i	$0.926698\pi$
$128$	64.9268	−	26.8936i	0.507241	−	0.210106i
$129$	−11.7109	+	7.82500i	−0.0907825	+	0.0606589i
$130$	−8.94830	+	44.9862i	−0.0688331	+	0.346047i
$131$	−160.044	−	106.938i	−1.22171	−	0.816323i	−0.233944	−	0.972250i	$-0.575163\pi$
$131$	−160.044	−	106.938i	−1.22171	−	0.816323i	−0.987769	+	0.155927i	$0.950163\pi$
$132$	−17.5444	+	17.5444i	−0.132912	+	0.132912i
$133$	19.6777	+	98.9266i	0.147953	+	0.743809i
$134$	19.3108	−	46.6204i	0.144110	−	0.347913i
$135$		−	50.8284i		−	0.376507i
$136$		0			0
$137$	52.8361			0.385665			0.192832	−	0.981232i	$-0.438233\pi$
$137$	52.8361			0.385665			0.192832	+	0.981232i	$0.438233\pi$
$138$	76.0345	+	31.4945i	0.550975	+	0.228221i
$139$	51.4676	−	10.2376i	0.370271	−	0.0736514i	−0.00644773	−	0.999979i	$-0.502052\pi$
$139$	51.4676	−	10.2376i	0.370271	−	0.0736514i	0.376719	+	0.926328i	$0.377052\pi$
$140$	−19.7831	−	19.7831i	−0.141308	−	0.141308i
$141$	−10.0709	+	15.0721i	−0.0714245	+	0.106894i
$142$	−59.5027	−	11.8358i	−0.419033	−	0.0833509i
$143$	12.9451	+	19.3737i	0.0905253	+	0.135481i
$144$	−32.9885	−	79.6413i	−0.229087	−	0.553064i
$145$	−85.8773	+	35.5715i	−0.592257	+	0.245321i
$146$	−137.501	+	91.8752i	−0.941787	+	0.629282i
$147$	−25.4638	+	128.015i	−0.173223	+	0.870850i
$148$	−23.7041	−	15.8386i	−0.160163	−	0.107017i
$149$	36.5973	−	36.5973i	0.245620	−	0.245620i	−0.573551	−	0.819170i	$-0.694434\pi$
$149$	36.5973	−	36.5973i	0.245620	−	0.245620i	0.819170	+	0.573551i	$0.194434\pi$
$150$	−48.6158	−	244.408i	−0.324105	−	1.62939i
$151$	−91.9670	+	222.028i	−0.609053	+	1.47038i	0.254979	+	0.966947i	$0.417931\pi$
$151$	−91.9670	+	222.028i	−0.609053	+	1.47038i	−0.864032	+	0.503437i	$0.832069\pi$
$152$			212.489i			1.39795i
$153$		0			0
$154$	50.1354			0.325555
$155$	−270.467	−	112.031i	−1.74495	−	0.722780i
$156$	11.7737	−	2.34193i	0.0754721	−	0.0150123i
$157$	−190.153	−	190.153i	−1.21117	−	1.21117i	−0.970644	−	0.240522i	$-0.922681\pi$
$157$	−190.153	−	190.153i	−1.21117	−	1.21117i	−0.240522	−	0.970644i	$-0.577319\pi$
$158$	21.0499	−	31.5034i	0.133227	−	0.199389i
$159$	121.975	+	24.2623i	0.767136	+	0.152593i
$160$	−59.5661	−	89.1469i	−0.372288	−	0.557168i
$161$	18.0406	+	43.5540i	0.112054	+	0.270522i
$162$	151.638	−	62.8107i	0.936040	−	0.387720i
$163$	−32.2626	+	21.5571i	−0.197930	+	0.132252i	−0.650586	−	0.759433i	$-0.725477\pi$
$163$	−32.2626	+	21.5571i	−0.197930	+	0.132252i	0.452656	+	0.891685i	$0.350477\pi$
$164$	−5.82785	+	29.2986i	−0.0355357	+	0.178650i
$165$	−180.696	−	120.737i	−1.09513	−	0.731742i
$166$	−141.740	+	141.740i	−0.853855	+	0.853855i
$167$	−7.02867	−	35.3355i	−0.0420878	−	0.211590i	0.954019	−	0.299747i	$-0.0969022\pi$
$167$	−7.02867	−	35.3355i	−0.0420878	−	0.211590i	−0.996107	+	0.0881571i	$0.971902\pi$
$168$	54.6371	−	131.906i	0.325221	−	0.785152i
$169$			157.727i			0.933294i
$170$		0			0
$171$	181.821			1.06328
$172$	−2.84081	−	1.17670i	−0.0165163	−	0.00684128i
$173$	189.307	−	37.6555i	1.09426	−	0.217662i	0.385215	−	0.922827i	$-0.374127\pi$
$173$	189.307	−	37.6555i	1.09426	−	0.217662i	0.709043	+	0.705165i	$0.249127\pi$
$174$	−60.6811	−	60.6811i	−0.348742	−	0.348742i
$175$	79.3045	−	118.688i	0.453168	−	0.678215i
$176$	79.5362	+	15.8207i	0.451910	+	0.0898905i
$177$	26.4075	+	39.5216i	0.149195	+	0.223286i
$178$	27.0608	+	65.3307i	0.152027	+	0.367026i
$179$	223.947	−	92.7619i	1.25110	−	0.518223i	0.343933	−	0.938994i	$-0.388241\pi$
$179$	223.947	−	92.7619i	1.25110	−	0.518223i	0.907167	+	0.420771i	$0.138241\pi$
$180$	−41.9336	+	28.0191i	−0.232964	+	0.155662i
$181$	26.6333	−	133.895i	0.147146	−	0.739750i	−0.834795	−	0.550561i	$-0.814414\pi$
$181$	26.6333	−	133.895i	0.147146	−	0.739750i	0.981941	−	0.189190i	$-0.0605861\pi$
$182$	−20.1685	−	13.4762i	−0.110816	−	0.0740449i
$183$	202.798	−	202.798i	1.10819	−	1.10819i
$184$	19.3751	+	97.4054i	0.105300	+	0.529377i
$185$	95.5575	−	230.696i	0.516527	−	1.24701i
$186$		−	270.274i		−	1.45308i
$187$		0			0
$188$	−3.95738			−0.0210499
$189$	24.8339	+	10.2865i	0.131396	+	0.0544260i
$190$	−330.237	+	65.6882i	−1.73809	+	0.345727i
$191$	123.244	+	123.244i	0.645254	+	0.645254i	0.951842	−	0.306588i	$-0.0991874\pi$
$191$	123.244	+	123.244i	0.645254	+	0.645254i	−0.306588	+	0.951842i	$0.599187\pi$
$192$	160.083	−	239.581i	0.833767	−	1.24782i
$193$	184.064	+	36.6126i	0.953700	+	0.189703i	0.647330	−	0.762210i	$-0.275886\pi$
$193$	184.064	+	36.6126i	0.953700	+	0.189703i	0.306370	+	0.951913i	$0.400886\pi$
$194$	−163.144	−	244.162i	−0.840948	−	1.25857i
$195$	40.2370	+	97.1407i	0.206344	+	0.498157i
$196$	−26.3259	+	10.9045i	−0.134316	+	0.0556354i
$197$	−238.742	+	159.522i	−1.21189	+	0.809759i	−0.986380	−	0.164482i	$-0.947405\pi$
$197$	−238.742	+	159.522i	−1.21189	+	0.809759i	−0.225509	+	0.974241i	$0.572405\pi$
$198$	17.6314	−	88.6390i	0.0890474	−	0.447672i
$199$	76.1598	+	50.8883i	0.382712	+	0.255720i	0.732013	−	0.681290i	$-0.238581\pi$
$199$	76.1598	+	50.8883i	0.382712	+	0.255720i	−0.349301	+	0.937011i	$0.613581\pi$
$200$	212.638	−	212.638i	1.06319	−	1.06319i
$201$	−22.5672	−	113.453i	−0.112274	−	0.564442i
$202$	−84.0712	+	202.966i	−0.416194	+	1.00478i
$203$		−	49.1570i		−	0.242153i
$204$		0			0
$205$	−261.650			−1.27634
$206$	−285.560	−	118.283i	−1.38621	−	0.574188i
$207$	83.3475	−	16.5788i	0.402645	−	0.0800911i
$208$	−27.7433	−	27.7433i	−0.133381	−	0.133381i
$209$	−95.0281	+	142.220i	−0.454680	+	0.680477i
$210$	221.890	+	44.1367i	1.05662	+	0.210175i
$211$	−20.0890	−	30.0653i	−0.0952086	−	0.142490i	0.780807	−	0.624772i	$-0.214808\pi$
$211$	−20.0890	−	30.0653i	−0.0952086	−	0.142490i	−0.876016	+	0.482282i	$0.839808\pi$
$212$	10.3900	+	25.0837i	0.0490095	+	0.118319i
$213$	−128.487	+	53.2210i	−0.603225	+	0.249864i
$214$	58.5178	−	39.1003i	0.273448	−	0.182712i
$215$	5.25425	−	26.4149i	0.0244384	−	0.122860i
$216$	47.0838	+	31.4604i	0.217981	+	0.145650i
$217$	109.473	−	109.473i	0.504482	−	0.504482i
$218$	−15.7833	−	79.3479i	−0.0724004	−	0.363981i
$219$	−145.071	+	350.232i	−0.662423	+	1.59923i
$220$		−	47.4443i		−	0.215656i
$221$		0			0
$222$	230.532			1.03843
$223$	372.417	+	154.260i	1.67003	+	0.691750i	0.998775	−	0.0494759i	$-0.0157551\pi$
$223$	372.417	+	154.260i	1.67003	+	0.691750i	0.671256	+	0.741226i	$0.265755\pi$
$224$	55.6104	−	11.0616i	0.248261	−	0.0493822i
$225$	−181.949	−	181.949i	−0.808663	−	0.808663i
$226$	−183.644	+	274.843i	−0.812585	+	1.21612i
$227$	−123.817	−	24.6288i	−0.545450	−	0.108497i	−0.0853288	−	0.996353i	$-0.527194\pi$
$227$	−123.817	−	24.6288i	−0.545450	−	0.108497i	−0.460121	+	0.887856i	$0.652194\pi$
$228$	48.9579	+	73.2707i	0.214728	+	0.321363i
$229$	−47.0477	−	113.583i	−0.205449	−	0.495997i	0.787248	−	0.616637i	$-0.211505\pi$
$229$	−47.0477	−	113.583i	−0.205449	−	0.495997i	−0.992696	+	0.120640i	$0.961505\pi$
$230$	−145.392	+	60.2233i	−0.632139	+	0.261840i
$231$	95.5591	−	63.8505i	0.413676	−	0.276409i
$232$	20.2031	−	101.568i	0.0870823	−	0.437792i
$233$	−50.0074	−	33.4139i	−0.214624	−	0.143407i	0.443612	−	0.896219i	$-0.353697\pi$
$233$	−50.0074	−	33.4139i	−0.214624	−	0.143407i	−0.658236	+	0.752812i	$0.728697\pi$
$234$	−30.9185	+	30.9185i	−0.132130	+	0.132130i
$235$	−6.76227	−	33.9962i	−0.0287756	−	0.144665i
$236$	−3.97107	+	9.58702i	−0.0168266	+	0.0406230i
$237$		−	86.8544i		−	0.366474i
$238$		0			0
$239$	−285.920			−1.19632			−0.598160	−	0.801377i	$-0.704101\pi$
$239$	−285.920			−1.19632			−0.598160	+	0.801377i	$0.704101\pi$
$240$	338.085	+	140.039i	1.40869	+	0.583497i
$241$	−121.946	+	24.2566i	−0.506002	+	0.100650i	−0.441489	−	0.897267i	$-0.645549\pi$
$241$	−121.946	+	24.2566i	−0.506002	+	0.100650i	−0.0645131	+	0.997917i	$0.520549\pi$
$242$	−90.9267	−	90.9267i	−0.375730	−	0.375730i
$243$	176.189	−	263.686i	0.725060	−	1.08513i
$244$	61.4092	+	12.2151i	0.251677	+	0.0500617i
$245$	−138.661	−	207.521i	−0.565964	−	0.847025i
$246$	−92.4414	−	223.173i	−0.375778	−	0.907208i
$247$	76.4560	−	31.6691i	0.309538	−	0.128215i
$248$	271.184	−	181.199i	1.09348	−	0.730642i
$249$	−89.6446	+	450.674i	−0.360018	+	1.80993i
$250$	112.237	+	74.9942i	0.448947	+	0.299977i
$251$	−99.6747	+	99.6747i	−0.397110	+	0.397110i	−0.877213	−	0.480102i	$-0.840600\pi$
$251$	−99.6747	+	99.6747i	−0.397110	+	0.397110i	0.480102	+	0.877213i	$0.340600\pi$
$252$	−5.20324	−	26.1585i	−0.0206478	−	0.103803i
$253$	−30.5933	+	73.8588i	−0.120922	+	0.291932i
$254$			72.5069i			0.285460i
$255$		0			0
$256$	160.744			0.627906
$257$	363.098	+	150.400i	1.41283	+	0.585214i	0.953048	−	0.302818i	$-0.0979273\pi$
$257$	363.098	+	150.400i	1.41283	+	0.585214i	0.459783	+	0.888032i	$0.347927\pi$
$258$	24.3868	−	4.85083i	0.0945224	−	0.0188017i
$259$	93.3754	+	93.3754i	0.360523	+	0.360523i
$260$	−12.7528	+	19.0859i	−0.0490492	+	0.0734074i
$261$	−86.9092	−	17.2873i	−0.332985	−	0.0662349i
$262$	188.785	+	282.537i	0.720554	+	1.07839i
$263$	−111.542	−	269.286i	−0.424113	−	1.02390i	−0.981121	−	0.193393i	$-0.938051\pi$
$263$	−111.542	−	269.286i	−0.424113	−	1.02390i	0.557008	−	0.830507i	$-0.311949\pi$
$264$	223.685	−	92.6535i	0.847293	−	0.350960i
$265$	−197.729	+	132.119i	−0.746149	+	0.498561i
$266$	34.7384	−	174.642i	0.130595	−	0.656548i
$267$	134.781	+	90.0578i	0.504798	+	0.337295i
$268$	17.8569	−	17.8569i	0.0666304	−	0.0666304i
$269$	−19.8781	−	99.9342i	−0.0738965	−	0.371503i	0.926087	−	0.377311i	$-0.123151\pi$
$269$	−19.8781	−	99.9342i	−0.0738965	−	0.371503i	−0.999983	+	0.00580827i	$0.998151\pi$
$270$	−34.3385	+	82.9004i	−0.127180	+	0.307038i
$271$		−	381.059i		−	1.40612i	−0.711129	−	0.703061i	$-0.751816\pi$
$271$		−	381.059i		−	1.40612i	0.711129	−	0.703061i	$-0.248184\pi$
$272$		0			0
$273$	−55.6043			−0.203679
$274$	−86.1749	−	35.6948i	−0.314507	−	0.130273i
$275$	237.414	−	47.2247i	0.863325	−	0.171726i
$276$	29.1234	+	29.1234i	0.105520	+	0.105520i
$277$	37.3432	−	55.8881i	0.134813	−	0.201762i	−0.757920	−	0.652347i	$-0.773785\pi$
$277$	37.3432	−	55.8881i	0.134813	−	0.201762i	0.892734	+	0.450585i	$0.148785\pi$
$278$	−90.8593	−	18.0730i	−0.326832	−	0.0650109i
$279$	−155.048	−	232.046i	−0.555727	−	0.831705i
$280$	104.476	+	252.228i	0.373129	+	0.900813i
$281$	−348.356	+	144.294i	−1.23970	+	0.513501i	−0.903621	−	0.428333i	$-0.859101\pi$
$281$	−348.356	+	144.294i	−1.23970	+	0.513501i	−0.336079	+	0.941834i	$0.609101\pi$
$282$	26.6078	−	17.7788i	0.0943539	−	0.0630452i
$283$	−57.9083	+	291.125i	−0.204623	+	1.02871i	0.732781	+	0.680465i	$0.238222\pi$
$283$	−57.9083	+	291.125i	−0.204623	+	1.02871i	−0.937404	+	0.348245i	$0.886778\pi$
$284$	−25.2447	−	16.8680i	−0.0888899	−	0.0593944i
$285$	−545.780	+	545.780i	−1.91502	+	1.91502i
$286$	−8.02486	−	40.3437i	−0.0280590	−	0.141062i
$287$	52.9521	−	127.838i	0.184502	−	0.445428i
$288$		−	102.209i		−	0.354892i
$289$		0			0
$290$	164.096			0.565848
$291$	−621.911	−	257.604i	−2.13715	−	0.885237i
$292$	−81.1699	+	16.1457i	−0.277979	+	0.0552935i
$293$	99.8472	+	99.8472i	0.340776	+	0.340776i	0.856659	−	0.515883i	$-0.172536\pi$
$293$	99.8472	+	99.8472i	0.340776	+	0.340776i	−0.515883	+	0.856659i	$0.672536\pi$
$294$	128.015	−	191.588i	0.435425	−	0.651660i
$295$	−89.1437	−	17.7318i	−0.302182	−	0.0601078i
$296$	154.555	+	231.308i	0.522146	+	0.781446i
$297$	17.4439	+	42.1132i	0.0587336	+	0.141795i
$298$	−84.4140	+	34.9654i	−0.283269	+	0.117334i
$299$	32.1600	−	21.4886i	0.107559	−	0.0718683i
$300$	24.3298	−	122.314i	0.0810995	−	0.407715i
$301$	11.8425	+	7.91291i	0.0393439	+	0.0262887i
$302$	299.994	−	299.994i	0.993357	−	0.993357i
$303$	98.2481	+	493.926i	0.324251	+	1.63012i
$304$	110.220	−	266.094i	0.362565	−	0.875310i
$305$			548.414i			1.79808i
$306$		0			0
$307$	−259.641			−0.845735			−0.422868	−	0.906192i	$-0.638976\pi$
$307$	−259.641			−0.845735			−0.422868	+	0.906192i	$0.638976\pi$
$308$	23.1804	+	9.60165i	0.0752612	+	0.0311742i
$309$	−694.922	+	138.229i	−2.24894	+	0.447342i
$310$	365.442	+	365.442i	1.17884	+	1.17884i
$311$	−313.413	+	469.055i	−1.00776	+	1.50822i	−0.153646	+	0.988126i	$0.549102\pi$
$311$	−313.413	+	469.055i	−1.00776	+	1.50822i	−0.854112	+	0.520090i	$0.825898\pi$
$312$	−114.889	−	22.8529i	−0.368234	−	0.0732464i
$313$	253.206	+	378.950i	0.808966	+	1.21070i	0.974475	+	0.224495i	$0.0720733\pi$
$313$	253.206	+	378.950i	0.808966	+	1.21070i	−0.165509	+	0.986208i	$0.552927\pi$
$314$	181.674	+	438.600i	0.578580	+	1.39681i
$315$	215.825	−	89.3977i	0.685159	−	0.283802i
$316$	15.7659	−	10.5344i	0.0498921	−	0.0333368i
$317$	64.7580	−	325.560i	0.204284	−	1.02700i	−0.733475	−	0.679717i	$-0.762103\pi$
$317$	64.7580	−	325.560i	0.204284	−	1.02700i	0.937759	−	0.347288i	$-0.112897\pi$
$318$	−182.548	−	121.975i	−0.574050	−	0.383568i
$319$	58.9447	−	58.9447i	0.184780	−	0.184780i
$320$	107.491	+	540.393i	0.335909	+	1.68873i
$321$	61.7394	−	149.052i	0.192334	−	0.464336i
$322$		−	83.2238i		−	0.258459i
$323$		0			0
$324$	82.1402			0.253519
$325$	−108.201	−	44.8183i	−0.332926	−	0.137903i
$326$	67.1833	−	13.3636i	0.206084	−	0.0409926i
$327$	−131.138	−	131.138i	−0.401033	−	0.401033i
$328$	161.949	−	242.374i	0.493748	−	0.738946i
$329$	17.9785	+	3.57614i	0.0546459	+	0.0108697i
$330$	213.146	+	318.995i	0.645897	+	0.966653i
$331$	225.594	+	544.633i	0.681554	+	1.64542i	0.761139	+	0.648588i	$0.224640\pi$
$331$	225.594	+	544.633i	0.681554	+	1.64542i	−0.0795855	+	0.996828i	$0.525360\pi$
$332$	−92.6796	+	38.3892i	−0.279156	+	0.115630i
$333$	197.925	−	132.249i	0.594369	−	0.397145i
$334$	−12.4082	+	62.3801i	−0.0371502	+	0.186767i
$335$	183.915	+	122.888i	0.549000	+	0.366830i
$336$	−136.841	+	136.841i	−0.407266	+	0.407266i
$337$	−63.9095	−	321.295i	−0.189642	−	0.953397i	−0.951967	−	0.306202i	$-0.900942\pi$
$337$	−63.9095	−	321.295i	−0.189642	−	0.953397i	0.762324	−	0.647195i	$-0.224058\pi$
$338$	106.557	−	257.250i	0.315256	−	0.761095i
$339$			757.738i			2.23522i
$340$		0			0
$341$	262.540			0.769911
$342$	−296.548	−	122.834i	−0.867100	−	0.359165i
$343$	326.123	−	64.8699i	0.950796	−	0.189125i
$344$	21.2167	+	21.2167i	0.0616766	+	0.0616766i
$345$	−200.422	+	299.952i	−0.580932	+	0.869427i
$346$	−334.196	−	66.4757i	−0.965884	−	0.192126i
$347$	−134.483	−	201.268i	−0.387560	−	0.580024i	0.585473	−	0.810692i	$-0.300909\pi$
$347$	−134.483	−	201.268i	−0.387560	−	0.580024i	−0.973033	+	0.230668i	$0.925909\pi$
$348$	−16.4350	−	39.6776i	−0.0472270	−	0.114016i
$349$	464.685	−	192.479i	1.33148	−	0.551515i	0.400399	−	0.916341i	$-0.368871\pi$
$349$	464.685	−	192.479i	1.33148	−	0.551515i	0.931076	+	0.364826i	$0.118871\pi$
$350$	−209.527	+	140.001i	−0.598649	+	0.400004i
$351$	4.30251	−	21.6302i	0.0122579	−	0.0616244i
$352$	79.9472	+	53.4190i	0.227123	+	0.151759i
$353$	−231.294	+	231.294i	−0.655223	+	0.655223i	−0.954246	−	0.299023i	$-0.903339\pi$
$353$	−231.294	+	231.294i	−0.655223	+	0.655223i	0.299023	+	0.954246i	$0.403339\pi$
$354$	−16.3704	−	82.2994i	−0.0462440	−	0.232484i
$355$	101.768	−	245.691i	0.286671	−	0.692086i
$356$			35.3886i			0.0994062i
$357$		0			0
$358$	−427.922			−1.19531
$359$	−490.942	−	203.355i	−1.36753	−	0.566448i	−0.426410	−	0.904530i	$-0.640222\pi$
$359$	−490.942	−	203.355i	−1.36753	−	0.566448i	−0.941117	+	0.338082i	$0.890222\pi$
$360$	482.678	−	96.0106i	1.34077	−	0.266696i
$361$	174.298	+	174.298i	0.482820	+	0.482820i
$362$	−133.895	+	200.388i	−0.369875	+	0.553557i
$363$	−289.109	−	57.5073i	−0.796443	−	0.158422i
$364$	−6.74416	−	10.0934i	−0.0185279	−	0.0277290i
$365$	−277.402	−	669.707i	−0.760005	−	1.83481i
$366$	−467.767	+	193.755i	−1.27805	+	0.529386i
$367$	275.260	−	183.923i	0.750026	−	0.501152i	−0.120840	−	0.992672i	$-0.538559\pi$
$367$	275.260	−	183.923i	0.750026	−	0.501152i	0.870866	+	0.491520i	$0.163559\pi$
$368$	26.2621	−	132.028i	0.0713644	−	0.358773i
$369$	−207.394	−	138.576i	−0.562043	−	0.375545i
$370$	−311.706	+	311.706i	−0.842448	+	0.842448i
$371$	−24.5348	−	123.345i	−0.0661316	−	0.332466i
$372$	51.7613	−	124.963i	0.139143	−	0.335922i
$373$		−	147.856i		−	0.396396i	−0.980162	−	0.198198i	$-0.936491\pi$
$373$		−	147.856i		−	0.396396i	0.980162	−	0.198198i	$-0.0635089\pi$
$374$		0			0
$375$	309.435			0.825160
$376$	35.6772	+	14.7780i	0.0948863	+	0.0393032i
$377$	−39.5564	+	7.86825i	−0.104924	+	0.0208707i
$378$	−33.5543	−	33.5543i	−0.0887681	−	0.0887681i
$379$	−24.2695	+	36.3219i	−0.0640357	+	0.0958362i	−0.862106	−	0.506729i	$-0.830855\pi$
$379$	−24.2695	+	36.3219i	−0.0640357	+	0.0958362i	0.798070	+	0.602565i	$0.205855\pi$
$380$	−165.267	−	32.8737i	−0.434914	−	0.0865098i
$381$	92.3419	+	138.199i	0.242367	+	0.362728i
$382$	−117.748	−	284.269i	−0.308241	−	0.744160i
$383$	182.570	−	75.6230i	0.476684	−	0.197449i	−0.131387	−	0.991331i	$-0.541943\pi$
$383$	182.570	−	75.6230i	0.476684	−	0.197449i	0.608072	+	0.793882i	$0.291943\pi$
$384$	−236.467	+	158.002i	−0.615800	+	0.411464i
$385$	−42.8737	+	215.540i	−0.111360	+	0.559845i
$386$	−275.471	−	184.064i	−0.713656	−	0.476850i
$387$	18.1547	−	18.1547i	0.0469113	−	0.0469113i
$388$	−28.6701	−	144.134i	−0.0738920	−	0.371480i
$389$	8.22534	−	19.8577i	0.0211448	−	0.0510481i	−0.912954	−	0.408061i	$-0.866205\pi$
$389$	8.22534	−	19.8577i	0.0211448	−	0.0510481i	0.934099	+	0.357013i	$0.116205\pi$
$390$		−	185.618i		−	0.475944i
$391$		0			0
$392$	278.058			0.709332
$393$	719.657	+	298.092i	1.83119	+	0.758503i
$394$	497.155	−	98.8903i	1.26181	−	0.250991i
$395$	117.437	+	117.437i	0.297310	+	0.297310i
$396$	25.1276	−	37.6062i	0.0634536	−	0.0949650i
$397$	34.7954	+	6.92123i	0.0876457	+	0.0174338i	0.238718	−	0.971089i	$-0.423273\pi$
$397$	34.7954	+	6.92123i	0.0876457	+	0.0174338i	−0.151073	+	0.988523i	$0.548273\pi$
$398$	−89.8366	−	134.450i	−0.225720	−	0.337814i
$399$	−156.205	−	377.112i	−0.391491	−	0.945142i
$400$	−376.578	+	155.984i	−0.941446	+	0.389960i
$401$	124.358	−	83.0937i	0.310121	−	0.207216i	−0.390763	−	0.920491i	$-0.627789\pi$
$401$	124.358	−	83.0937i	0.310121	−	0.207216i	0.700884	+	0.713275i	$0.252789\pi$
$402$	−39.8393	+	200.286i	−0.0991028	+	0.498224i
$403$	−105.615	−	70.5695i	−0.262071	−	0.175110i
$404$	−77.7417	+	77.7417i	−0.192430	+	0.192430i
$405$	140.359	+	705.632i	0.346565	+	1.74230i
$406$	−33.2093	+	80.1744i	−0.0817964	+	0.197474i
$407$			223.935i			0.550209i
$408$		0			0
$409$	−398.892			−0.975287			−0.487643	−	0.873043i	$-0.662143\pi$
$409$	−398.892			−0.975287			−0.487643	+	0.873043i	$0.662143\pi$
$410$	426.748	+	176.765i	1.04085	+	0.431134i
$411$	−209.711	+	41.7140i	−0.510245	+	0.101494i
$412$	−109.378	−	109.378i	−0.265479	−	0.265479i
$413$	26.7041	−	39.9656i	0.0646589	−	0.0967689i
$414$	−147.139	−	29.2678i	−0.355408	−	0.0706951i
$415$	−488.154	−	730.573i	−1.17627	−	1.76042i
$416$	−17.8024	−	42.9789i	−0.0427943	−	0.103315i
$417$	−196.197	+	81.2673i	−0.470496	+	0.194886i
$418$	251.070	−	167.760i	0.600646	−	0.401339i
$419$	−7.29632	+	36.6811i	−0.0174137	+	0.0875444i	−0.988515	−	0.151124i	$-0.951711\pi$
$419$	−7.29632	+	36.6811i	−0.0174137	+	0.0875444i	0.971101	+	0.238668i	$0.0767108\pi$
$420$	94.1395	+	62.9020i	0.224142	+	0.149767i
$421$	312.706	−	312.706i	0.742769	−	0.742769i	−0.230341	−	0.973110i	$-0.573984\pi$
$421$	312.706	−	312.706i	0.742769	−	0.742769i	0.973110	+	0.230341i	$0.0739841\pi$
$422$	12.4535	+	62.6078i	0.0295106	+	0.148360i
$423$	12.6452	−	30.5282i	0.0298941	−	0.0721706i
$424$		−	264.938i		−	0.624853i
$425$		0			0
$426$	245.515			0.576327
$427$	−267.945	−	110.987i	−0.627507	−	0.259922i
$428$	34.5444	−	6.87130i	0.0807111	−	0.0160544i
$429$	−66.6757	−	66.6757i	−0.155421	−	0.155421i
$430$	−26.4149	+	39.5327i	−0.0614299	+	0.0919364i
$431$	340.230	+	67.6760i	0.789397	+	0.157021i	0.573294	−	0.819350i	$-0.305665\pi$
$431$	340.230	+	67.6760i	0.789397	+	0.157021i	0.216103	+	0.976371i	$0.430665\pi$
$432$	−42.6431	−	63.8199i	−0.0987109	−	0.147731i
$433$	−20.5680	−	49.6556i	−0.0475012	−	0.114678i	0.898348	−	0.439285i	$-0.144768\pi$
$433$	−20.5680	−	49.6556i	−0.0475012	−	0.114678i	−0.945849	+	0.324607i	$0.894768\pi$
$434$	−252.506	+	104.591i	−0.581810	+	0.240994i
$435$	312.770	−	208.986i	0.719012	−	0.480428i
$436$	7.89876	−	39.7098i	0.0181164	−	0.0910774i
$437$	236.082	+	157.745i	0.540233	+	0.360972i
$438$	473.217	−	473.217i	1.08040	−	1.08040i
$439$	−47.4571	−	238.583i	−0.108103	−	0.543469i	−0.996442	−	0.0842815i	$-0.973140\pi$
$439$	−47.4571	−	238.583i	−0.108103	−	0.543469i	0.888339	−	0.459188i	$-0.151860\pi$
$440$	−177.170	+	427.727i	−0.402660	+	0.972107i
$441$		−	237.928i		−	0.539518i
$442$		0			0
$443$	−114.592			−0.258673			−0.129336	−	0.991601i	$-0.541285\pi$
$443$	−114.592			−0.258673			−0.129336	+	0.991601i	$0.541285\pi$
$444$	106.588	+	44.1501i	0.240063	+	0.0994373i
$445$	−304.009	+	60.4711i	−0.683165	+	0.135890i
$446$	−503.192	−	503.192i	−1.12823	−	1.12823i
$447$	−116.364	+	174.151i	−0.260322	+	0.389600i
$448$	−285.780	−	56.8453i	−0.637903	−	0.126887i
$449$	301.785	+	451.653i	0.672127	+	1.00591i	0.998165	+	0.0605527i	$0.0192863\pi$
$449$	301.785	+	451.653i	0.672127	+	1.00591i	−0.326038	+	0.945357i	$0.605714\pi$
$450$	173.836	+	419.677i	0.386302	+	0.932616i
$451$	216.787	−	89.7961i	0.480681	−	0.199104i
$452$	−137.546	+	91.9050i	−0.304304	+	0.203330i
$453$	189.733	−	953.854i	0.418838	−	2.10564i
$454$	185.305	+	123.817i	0.408162	+	0.272725i
$455$	75.1835	−	75.1835i	0.165239	−	0.165239i
$456$	−167.760	−	843.384i	−0.367894	−	1.84953i
$457$	−85.9222	+	207.434i	−0.188014	+	0.453905i	−0.989577	−	0.144005i	$-0.954002\pi$
$457$	−85.9222	+	207.434i	−0.188014	+	0.453905i	0.801563	+	0.597910i	$0.204002\pi$
$458$			217.037i			0.473880i
$459$		0			0
$460$	−78.7565			−0.171210
$461$	−233.070	−	96.5408i	−0.505575	−	0.209416i	0.115292	−	0.993332i	$-0.463219\pi$
$461$	−233.070	−	96.5408i	−0.505575	−	0.209416i	−0.620867	+	0.783916i	$0.713219\pi$
$462$	−198.991	+	39.5819i	−0.430717	+	0.0856750i
$463$	88.6506	+	88.6506i	0.191470	+	0.191470i	0.796331	−	0.604861i	$-0.206771\pi$
$463$	88.6506	+	88.6506i	0.191470	+	0.191470i	−0.604861	+	0.796331i	$0.706771\pi$
$464$	−77.9840	+	116.711i	−0.168069	+	0.251533i
$465$	1161.95	+	231.127i	2.49882	+	0.497046i
$466$	58.9878	+	88.2815i	0.126583	+	0.189445i
$467$	265.152	+	640.133i	0.567777	+	1.37074i	0.903424	+	0.428748i	$0.141045\pi$
$467$	265.152	+	640.133i	0.567777	+	1.37074i	−0.335647	+	0.941988i	$0.608955\pi$
$468$	−20.2167	+	8.37404i	−0.0431981	+	0.0178932i
$469$	−97.2612	+	64.9879i	−0.207380	+	0.138567i
$470$	−11.9379	+	60.0158i	−0.0253998	+	0.127693i
$471$	904.858	+	604.607i	1.92114	+	1.28367i
$472$	71.6013	−	71.6013i	0.151698	−	0.151698i
$473$	4.71202	+	23.6889i	0.00996199	+	0.0500823i
$474$	−58.6768	+	141.658i	−0.123791	+	0.298857i
$475$		−	859.730i		−	1.80996i
$476$		0			0
$477$	−226.701			−0.475264
$478$	466.332	+	193.161i	0.975591	+	0.404103i
$479$	−469.496	+	93.3885i	−0.980158	+	0.194965i	−0.659068	−	0.752083i	$-0.729049\pi$
$479$	−469.496	+	93.3885i	−0.980158	+	0.194965i	−0.321090	+	0.947049i	$0.604049\pi$
$480$	306.804	+	306.804i	0.639175	+	0.639175i
$481$	60.1927	−	90.0847i	0.125141	−	0.187286i
$482$	215.280	+	42.8219i	0.446639	+	0.0888421i
$483$	−105.991	−	158.626i	−0.219442	−	0.328418i
$484$	−24.6268	−	59.4543i	−0.0508818	−	0.122840i
$485$	1189.21	−	492.586i	2.45197	−	1.01564i
$486$	−465.503	+	311.039i	−0.957825	+	0.639998i
$487$	−79.1411	+	397.869i	−0.162507	+	0.816980i	0.810417	+	0.585854i	$0.199241\pi$
$487$	−79.1411	+	397.869i	−0.162507	+	0.816980i	−0.972924	+	0.231126i	$0.925759\pi$
$488$	−508.012	−	339.443i	−1.04101	−	0.695579i
$489$	111.033	−	111.033i	0.227062	−	0.227062i
$490$	85.9581	+	432.141i	0.175425	+	0.881919i
$491$	−23.7416	+	57.3172i	−0.0483535	+	0.116736i	−0.946211	−	0.323551i	$-0.895123\pi$
$491$	−23.7416	+	57.3172i	−0.0483535	+	0.116736i	0.897857	+	0.440287i	$0.145123\pi$
$492$		−	120.889i		−	0.245710i
$493$		0			0
$494$	−146.094			−0.295736
$495$	365.996	+	151.601i	0.739386	+	0.306264i
$496$	−433.587	+	86.2458i	−0.874167	+	0.173883i
$497$	99.4445	+	99.4445i	0.200089	+	0.200089i
$498$	450.674	−	674.481i	0.904967	−	1.35438i
$499$	503.379	+	100.128i	1.00878	+	0.200658i	0.671703	−	0.740821i	$-0.265563\pi$
$499$	503.379	+	100.128i	1.00878	+	0.200658i	0.337073	+	0.941479i	$0.390563\pi$
$500$	37.5309	+	56.1690i	0.0750618	+	0.112338i
$501$	55.7947	+	134.700i	0.111367	+	0.268863i
$502$	229.906	−	95.2302i	0.457980	−	0.189702i
$503$	−275.118	+	183.828i	−0.546954	+	0.365463i	−0.798136	−	0.602477i	$-0.794181\pi$
$503$	−275.118	+	183.828i	−0.546954	+	0.365463i	0.251182	+	0.967940i	$0.419181\pi$
$504$	−50.7740	+	255.258i	−0.100742	+	0.506465i
$505$	−800.689	−	535.003i	−1.58552	−	1.05941i
$506$	99.7945	−	99.7945i	0.197222	−	0.197222i
$507$	−124.525	−	626.030i	−0.245612	−	1.23477i
$508$	−13.8861	+	33.5240i	−0.0273349	+	0.0659922i
$509$		−	343.247i		−	0.674355i	−0.941441	−	0.337178i	$-0.890528\pi$
$509$		−	343.247i		−	0.674355i	0.941441	−	0.337178i	$-0.109472\pi$
$510$		0			0
$511$	383.347			0.750190
$512$	−521.878	−	216.169i	−1.01929	−	0.422205i
$513$	158.784	−	31.5841i	0.309520	−	0.0615674i
$514$	−490.601	−	490.601i	−0.954476	−	0.954476i
$515$	752.715	−	1126.52i	1.46158	−	2.18741i
$516$	12.2044	+	2.42760i	0.0236519	+	0.00470466i
$517$	17.2700	+	25.8464i	0.0334043	+	0.0499930i
$518$	−89.2118	−	215.376i	−0.172224	−	0.415784i
$519$	−721.645	+	298.915i	−1.39045	+	0.575944i
$520$	186.243	−	124.444i	0.358160	−	0.239315i
$521$	−62.1355	+	312.376i	−0.119262	+	0.599570i	0.874215	+	0.485539i	$0.161377\pi$
$521$	−62.1355	+	312.376i	−0.119262	+	0.599570i	−0.993477	+	0.114032i	$0.963623\pi$
$522$	130.069	+	86.9092i	0.249174	+	0.166493i
$523$	−167.575	+	167.575i	−0.320410	+	0.320410i	−0.848924	−	0.528514i	$-0.822749\pi$
$523$	−167.575	+	167.575i	−0.320410	+	0.320410i	0.528514	+	0.848924i	$0.322749\pi$
$524$	33.1762	+	166.788i	0.0633133	+	0.318298i
$525$	−221.062	+	533.691i	−0.421071	+	1.01655i
$526$			514.556i			0.978244i
$527$		0			0
$528$	−328.176			−0.621545
$529$	−366.128	−	151.655i	−0.692114	−	0.286683i
$530$	411.750	−	81.9022i	0.776887	−	0.154532i
$531$	−61.2676	−	61.2676i	−0.115381	−	0.115381i
$532$	49.5079	−	74.0938i	0.0930600	−	0.139274i
$533$	−111.346	−	22.1481i	−0.208904	−	0.0415537i
$534$	−158.985	−	237.938i	−0.297725	−	0.445577i
$535$	118.057	+	285.015i	0.220667	+	0.532738i
$536$	−227.670	+	94.3039i	−0.424757	+	0.175940i
$537$	−815.628	+	544.985i	−1.51886	+	1.01487i
$538$	−35.0922	+	176.421i	−0.0652272	+	0.327919i
$539$	186.106	+	124.352i	0.345279	+	0.230708i
$540$	−31.7532	+	31.7532i	−0.0588023	+	0.0588023i
$541$	−51.6826	−	259.826i	−0.0955316	−	0.480270i	−0.998700	−	0.0509824i	$-0.983765\pi$
$541$	−51.6826	−	259.826i	−0.0955316	−	0.480270i	0.903168	−	0.429287i	$-0.141235\pi$
$542$	−257.435	+	621.502i	−0.474972	+	1.14668i
$543$			552.466i			1.01743i
$544$		0			0
$545$	354.627			0.650692
$546$	90.6899	+	37.5650i	0.166099	+	0.0688003i
$547$	−353.859	+	70.3869i	−0.646909	+	0.128678i	−0.507630	−	0.861575i	$-0.669478\pi$
$547$	−353.859	+	70.3869i	−0.646909	+	0.128678i	−0.139278	+	0.990253i	$0.544478\pi$
$548$	−33.0075	−	33.0075i	−0.0602326	−	0.0602326i
$549$	−290.453	+	434.694i	−0.529058	+	0.791792i
$550$	−419.123	−	83.3688i	−0.762043	−	0.151580i
$551$	−164.486	−	246.170i	−0.298522	−	0.446770i
$552$	−153.803	−	371.313i	−0.278629	−	0.672669i
$553$	−81.1445	+	33.6111i	−0.146735	+	0.0607797i
$554$	−98.6630	+	65.9245i	−0.178092	+	0.118997i
$555$	−197.141	+	991.094i	−0.355209	+	1.78576i
$556$	−38.5481	−	25.7570i	−0.0693312	−	0.0463256i
$557$	−367.145	+	367.145i	−0.659147	+	0.659147i	−0.955178	−	0.296031i	$-0.904337\pi$
$557$	−367.145	+	367.145i	−0.659147	+	0.659147i	0.296031	+	0.955178i	$0.404337\pi$
$558$	96.1164	+	483.210i	0.172252	+	0.865968i
$559$	4.47192	−	10.7962i	0.00799986	−	0.0193134i
$560$		−	370.051i		−	0.660806i
$561$		0			0
$562$	665.645			1.18442
$563$	406.232	+	168.267i	0.721549	+	0.298875i	0.713074	−	0.701089i	$-0.247302\pi$
$563$	406.232	+	168.267i	0.721549	+	0.298875i	0.00847487	+	0.999964i	$0.497302\pi$
$564$	15.7072	−	3.12435i	0.0278496	−	0.00553963i
$565$	−1024.55	−	1024.55i	−1.81336	−	1.81336i
$566$	291.125	−	435.699i	0.514355	−	0.769786i
$567$	−373.165	−	74.2271i	−0.658139	−	0.130912i
$568$	164.601	+	246.342i	0.289790	+	0.433701i
$569$	−183.595	−	443.238i	−0.322663	−	0.778977i	−0.999098	−	0.0424747i	$-0.986476\pi$
$569$	−183.595	−	443.238i	−0.322663	−	0.778977i	0.676435	−	0.736503i	$-0.263524\pi$
$570$	1258.87	−	521.443i	2.20855	−	0.914812i
$571$	−452.464	+	302.327i	−0.792406	+	0.529469i	−0.884643	−	0.466268i	$-0.845598\pi$
$571$	−452.464	+	302.327i	−0.792406	+	0.529469i	0.0922371	+	0.995737i	$0.470598\pi$
$572$	4.01605	−	20.1901i	0.00702107	−	0.0352973i
$573$	−586.464	−	391.863i	−1.02350	−	0.683879i
$574$	−172.728	+	172.728i	−0.300920	+	0.300920i
$575$	−78.3920	−	394.103i	−0.136334	−	0.685397i
$576$	−201.004	+	485.266i	−0.348965	+	0.842476i
$577$			304.419i			0.527589i	0.964579	+	0.263795i	$0.0849741\pi$
$577$			304.419i			0.527589i	−0.964579	+	0.263795i	$0.915026\pi$
$578$		0			0
$579$	−759.470			−1.31169
$580$	75.8709	+	31.4267i	0.130812	+	0.0541840i
$581$	455.737	−	90.6517i	0.784400	−	0.156027i
$582$	840.297	+	840.297i	1.44381	+	1.44381i
$583$	118.484	−	177.324i	0.203232	−	0.304158i
$584$	792.068	+	157.552i	1.35628	+	0.269781i
$585$	−106.484	−	159.364i	−0.182023	−	0.272417i
$586$	−95.3950	−	230.304i	−0.162790	−	0.393010i
$587$	−589.834	+	244.317i	−1.00483	+	0.416213i	−0.823565	−	0.567221i	$-0.808018\pi$
$587$	−589.834	+	244.317i	−1.00483	+	0.416213i	−0.181263	+	0.983435i	$0.558018\pi$
$588$	95.8804	−	64.0652i	0.163062	−	0.108954i
$589$	181.911	−	914.531i	0.308848	−	1.55268i
$590$	133.413	+	89.1437i	0.226124	+	0.151091i
$591$	821.644	−	821.644i	1.39026	−	1.39026i
$592$	−73.5639	−	369.831i	−0.124263	−	0.624714i
$593$	246.104	−	594.149i	0.415016	−	1.00194i	−0.568755	−	0.822507i	$-0.692575\pi$
$593$	246.104	−	594.149i	0.415016	−	1.00194i	0.983771	−	0.179430i	$-0.0574253\pi$
$594$		−	80.4708i		−	0.135473i
$595$		0			0
$596$	−45.7258			−0.0767211
$597$	−342.460	−	141.852i	−0.573636	−	0.237608i
$598$	−66.9697	+	13.3211i	−0.111990	+	0.0222761i
$599$	354.327	+	354.327i	0.591530	+	0.591530i	0.938045	−	0.346514i	$-0.112635\pi$
$599$	354.327	+	354.327i	0.591530	+	0.591530i	−0.346514	+	0.938045i	$0.612635\pi$
$600$	−676.099	+	1011.85i	−1.12683	+	1.68642i
$601$	−558.804	−	111.153i	−0.929791	−	0.184947i	−0.293114	−	0.956078i	$-0.594691\pi$
$601$	−558.804	−	111.153i	−0.929791	−	0.184947i	−0.636677	+	0.771131i	$0.719691\pi$
$602$	−13.9692	−	20.9064i	−0.0232046	−	0.0347282i
$603$	80.6936	+	194.812i	0.133820	+	0.323071i
$604$	196.157	−	81.2510i	0.324764	−	0.134521i
$605$	468.666	−	313.152i	0.774654	−	0.517607i
$606$	173.444	−	871.961i	0.286211	−	1.43888i
$607$	−150.811	−	100.769i	−0.248454	−	0.166011i	0.425108	−	0.905143i	$-0.360236\pi$
$607$	−150.811	−	100.769i	−0.248454	−	0.166011i	−0.673561	+	0.739131i	$0.735236\pi$
$608$	241.474	−	241.474i	0.397162	−	0.397162i
$609$	38.8094	+	195.108i	0.0637265	+	0.320375i
$610$	370.495	−	894.455i	0.607370	−	1.46632i
$611$		−	15.0396i		−	0.0246147i
$612$		0			0
$613$	−155.196			−0.253174			−0.126587	−	0.991956i	$-0.540402\pi$
$613$	−155.196			−0.253174			−0.126587	+	0.991956i	$0.540402\pi$
$614$	423.470	+	175.407i	0.689691	+	0.285679i
$615$	1038.51	−	206.573i	1.68863	−	0.335890i
$616$	−173.125	−	173.125i	−0.281047	−	0.281047i
$617$	−259.673	+	388.627i	−0.420863	+	0.629866i	−0.979950	−	0.199243i	$-0.936152\pi$
$617$	−259.673	+	388.627i	−0.420863	+	0.629866i	0.559087	+	0.829109i	$0.311152\pi$
$618$	1226.79	+	244.024i	1.98510	+	0.394861i
$619$	−213.158	−	319.014i	−0.344359	−	0.515370i	0.618352	−	0.785901i	$-0.287801\pi$
$619$	−213.158	−	319.014i	−0.344359	−	0.515370i	−0.962711	+	0.270531i	$0.912801\pi$
$620$	98.9771	+	238.952i	0.159640	+	0.385406i
$621$	69.9071	−	28.9565i	0.112572	−	0.0466288i
$622$	828.054	−	553.288i	1.33128	−	0.889531i
$623$	31.9794	−	160.771i	0.0513313	−	0.258060i
$624$	132.019	+	88.2122i	0.211569	+	0.141366i
$625$	198.226	−	198.226i	0.317161	−	0.317161i
$626$	−156.966	−	789.123i	−0.250745	−	1.26058i
$627$	264.892	−	639.506i	0.422475	−	1.01995i
$628$			237.583i			0.378316i
$629$		0			0
$630$	−412.403			−0.654608
$631$	−308.547	−	127.804i	−0.488980	−	0.202542i	0.124550	−	0.992213i	$-0.460251\pi$
$631$	−308.547	−	127.804i	−0.488980	−	0.202542i	−0.613531	+	0.789671i	$0.710251\pi$
$632$	−181.474	+	36.0974i	−0.287142	+	0.0571162i
$633$	103.471	+	103.471i	0.163462	+	0.163462i
$634$	−325.560	+	487.236i	−0.513502	+	0.768511i
$635$	−311.719	−	62.0048i	−0.490896	−	0.0976453i
$636$	−61.0423	−	91.3563i	−0.0959785	−	0.143642i
$637$	−41.4415	−	100.049i	−0.0650573	−	0.157062i
$638$	−135.960	+	56.3163i	−0.213103	+	0.0882701i
$639$	210.789	−	140.845i	0.329873	−	0.220414i
$640$	106.094	−	533.369i	0.165771	−	0.833389i
$641$	798.746	+	533.705i	1.24609	+	0.832613i	0.990942	−	0.134289i	$-0.0428749\pi$
$641$	798.746	+	533.705i	1.24609	+	0.832613i	0.255151	+	0.966901i	$0.417875\pi$
$642$	−201.392	+	201.392i	−0.313695	+	0.313695i
$643$	204.305	+	1027.11i	0.317737	+	1.59737i	0.728113	+	0.685457i	$0.240398\pi$
$643$	204.305	+	1027.11i	0.317737	+	1.59737i	−0.410376	+	0.911917i	$0.634602\pi$
$644$	15.9385	−	38.4791i	0.0247493	−	0.0597501i
$645$			108.991i			0.168978i
$646$		0			0
$647$	328.253			0.507346			0.253673	−	0.967290i	$-0.418361\pi$
$647$	328.253			0.507346			0.253673	+	0.967290i	$0.418361\pi$
$648$	−740.523	−	306.735i	−1.14278	−	0.473356i
$649$	79.9443	−	15.9019i	0.123181	−	0.0245022i
$650$	146.196	+	146.196i	0.224917	+	0.224917i
$651$	−348.077	+	520.934i	−0.534681	+	0.800206i
$652$	33.6220	+	6.68782i	0.0515674	+	0.0102574i
$653$	27.7006	+	41.4569i	0.0424206	+	0.0634869i	0.852074	−	0.523422i	$-0.175345\pi$
$653$	27.7006	+	41.4569i	0.0424206	+	0.0634869i	−0.809653	+	0.586909i	$0.800345\pi$
$654$	125.290	+	302.477i	0.191575	+	0.462504i
$655$	−1376.11	+	570.005i	−2.10094	+	0.870237i
$656$	−328.527	+	219.515i	−0.500804	+	0.334626i
$657$	134.814	−	677.754i	0.205196	−	1.03159i
$658$	−26.9067	−	17.9785i	−0.0408917	−	0.0273229i
$659$	61.2456	−	61.2456i	0.0929371	−	0.0929371i	−0.659110	−	0.752047i	$-0.729067\pi$
$659$	61.2456	−	61.2456i	0.0929371	−	0.0929371i	0.752047	+	0.659110i	$0.229067\pi$
$660$	37.4572	+	188.310i	0.0567533	+	0.285318i
$661$	−314.044	+	758.170i	−0.475105	+	1.14700i	0.486774	+	0.873528i	$0.338173\pi$
$661$	−314.044	+	758.170i	−0.475105	+	1.14700i	−0.961879	+	0.273476i	$0.911827\pi$
$662$		−	1040.69i		−	1.57205i
$663$		0			0
$664$	978.896			1.47424
$665$	721.107	+	298.692i	1.08437	+	0.449161i
$666$	−412.157	+	81.9831i	−0.618854	+	0.123098i
$667$	−97.8470	−	97.8470i	−0.146697	−	0.146697i
$668$	−17.6837	+	26.4655i	−0.0264726	+	0.0396190i
$669$	−1599.94	−	318.248i	−2.39154	−	0.475707i
$670$	−216.942	−	324.677i	−0.323795	−	0.484593i
$671$	−188.211	−	454.381i	−0.280493	−	0.677170i
$672$	−211.989	+	87.8088i	−0.315460	+	0.130668i
$673$	457.164	−	305.467i	0.679293	−	0.453889i	−0.167457	−	0.985879i	$-0.553556\pi$
$673$	457.164	−	305.467i	0.679293	−	0.453889i	0.846751	+	0.531990i	$0.178556\pi$
$674$	−112.824	+	567.203i	−0.167394	+	0.841548i
$675$	−190.502	−	127.289i	−0.282225	−	0.188576i
$676$	98.5342	−	98.5342i	0.145761	−	0.145761i
$677$	105.702	+	531.400i	0.156133	+	0.784933i	0.976904	+	0.213677i	$0.0685439\pi$
$677$	105.702	+	531.400i	0.156133	+	0.784933i	−0.820772	+	0.571257i	$0.806456\pi$
$678$	511.910	−	1235.86i	0.755030	−	1.82280i
$679$			680.714i			1.00252i
$680$		0			0
$681$	510.884			0.750197
$682$	−428.199	−	177.366i	−0.627857	−	0.260067i
$683$	−388.402	+	77.2580i	−0.568671	+	0.113116i	−0.471048	−	0.882108i	$-0.656124\pi$
$683$	−388.402	+	77.2580i	−0.568671	+	0.113116i	−0.0976233	+	0.995223i	$0.531124\pi$
$684$	−113.587	−	113.587i	−0.166062	−	0.166062i
$685$	227.151	−	339.956i	0.331607	−	0.496285i
$686$	−575.727	−	114.519i	−0.839252	−	0.166938i
$687$	276.410	+	413.677i	0.402344	+	0.602150i
$688$	−15.5639	−	37.5745i	−0.0226219	−	0.0546142i
$689$	−95.3279	+	39.4861i	−0.138357	+	0.0573093i
$690$	529.526	−	353.818i	0.767429	−	0.512779i
$691$	−182.146	+	915.708i	−0.263597	+	1.32519i	0.591324	+	0.806434i	$0.298605\pi$
$691$	−182.146	+	915.708i	−0.263597	+	1.32519i	−0.854921	+	0.518758i	$0.826395\pi$
$692$	−141.787	−	94.7388i	−0.204894	−	0.136906i
$693$	−148.139	+	148.139i	−0.213764	+	0.213764i
$694$	83.3681	+	419.120i	0.120127	+	0.603919i
$695$	155.398	−	375.164i	0.223594	−	0.539804i
$696$			419.081i			0.602128i
$697$		0			0
$698$	−887.929			−1.27210
$699$	224.864	+	93.1416i	0.321693	+	0.133250i
$700$	−123.689	+	24.6032i	−0.176698	+	0.0351474i
$701$	−411.177	−	411.177i	−0.586558	−	0.586558i	0.350140	−	0.936697i	$-0.386134\pi$
$701$	−411.177	−	411.177i	−0.586558	−	0.586558i	−0.936697	+	0.350140i	$0.886134\pi$
$702$	−21.6302	+	32.3718i	−0.0308122	+	0.0461137i
$703$	780.055	+	155.163i	1.10961	+	0.220715i
$704$	−274.519	−	410.846i	−0.389941	−	0.583588i
$705$	53.6800	+	129.595i	0.0761418	+	0.183823i
$706$	533.494	−	220.980i	0.755657	−	0.313003i
$707$	423.435	−	282.930i	0.598918	−	0.400184i
$708$	8.19257	−	41.1868i	0.0115714	−	0.0581735i
$709$	−967.198	−	646.261i	−1.36417	−	0.911511i	−0.364367	−	0.931255i	$-0.618715\pi$
$709$	−967.198	−	646.261i	−1.36417	−	0.911511i	−0.999805	+	0.0197449i	$0.993715\pi$
$710$	−331.966	+	331.966i	−0.467557	+	0.467557i
$711$	30.8877	+	155.283i	0.0434426	+	0.218401i
$712$	132.151	−	319.041i	0.185605	−	0.448091i
$713$		−	435.811i		−	0.611235i
$714$		0			0
$715$	180.307			0.252177
$716$	−197.853	−	81.9532i	−0.276330	−	0.114460i
$717$	1134.84	−	225.734i	1.58276	−	0.314831i
$718$	663.338	+	663.338i	0.923869	+	0.923869i
$719$	8.24905	−	12.3456i	0.0114729	−	0.0171705i	−0.825689	−	0.564126i	$-0.809213\pi$
$719$	8.24905	−	12.3456i	0.0114729	−	0.0171705i	0.837162	+	0.546955i	$0.184213\pi$
$720$	−654.247	−	130.138i	−0.908677	−	0.180747i
$721$	398.064	+	595.745i	0.552100	+	0.826276i
$722$	−166.526	−	402.030i	−0.230646	−	0.556828i
$723$	464.864	−	192.553i	0.642966	−	0.266325i
$724$	−100.284	+	67.0078i	−0.138514	+	0.0925522i
$725$	−81.7419	+	410.944i	−0.112747	+	0.566820i
$726$	432.682	+	289.109i	0.595981	+	0.398222i
$727$	−880.136	+	880.136i	−1.21064	+	1.21064i	−0.239825	+	0.970816i	$0.577090\pi$
$727$	−880.136	+	880.136i	−1.21064	+	1.21064i	−0.970816	+	0.239825i	$0.922910\pi$
$728$	23.1096	+	116.180i	0.0317440	+	0.159588i
$729$	−170.915	+	412.626i	−0.234452	+	0.566017i
$730$			1279.69i			1.75300i
$731$		0			0
$732$	−253.382			−0.346150
$733$	503.915	+	208.728i	0.687469	+	0.284759i	0.698945	−	0.715175i	$-0.253653\pi$
$733$	503.915	+	208.728i	0.687469	+	0.284759i	−0.0114762	+	0.999934i	$0.503653\pi$
$734$	−573.199	+	114.016i	−0.780925	+	0.155336i
$735$	714.195	+	714.195i	0.971694	+	0.971694i
$736$	88.6744	−	132.711i	0.120482	−	0.180313i
$737$	−194.555	−	38.6993i	−0.263982	−	0.0525092i
$738$	244.638	+	366.126i	0.331488	+	0.496106i
$739$	−63.1371	−	152.427i	−0.0854359	−	0.206261i	0.875387	−	0.483422i	$-0.160606\pi$
$739$	−63.1371	−	152.427i	−0.0854359	−	0.206261i	−0.960823	+	0.277161i	$0.910606\pi$
$740$	−203.815	+	84.4231i	−0.275426	+	0.114085i
$741$	−278.457	+	186.059i	−0.375786	+	0.251092i
$742$	−43.3130	+	217.749i	−0.0583733	+	0.293462i
$743$	−1.91687	−	1.28081i	−0.00257991	−	0.00172384i	0.554280	−	0.832331i	$-0.312994\pi$
$743$	−1.91687	−	1.28081i	−0.00257991	−	0.00172384i	−0.556860	+	0.830607i	$0.687994\pi$
$744$	−933.294	+	933.294i	−1.25443	+	1.25443i
$745$	−78.1349	−	392.811i	−0.104879	−	0.527263i
$746$	−99.8879	+	241.151i	−0.133898	+	0.323258i
$747$		−	837.618i		−	1.12131i
$748$		0			0
$749$	−163.145			−0.217817
$750$	−504.684	−	209.047i	−0.672912	−	0.278729i
$751$	1414.78	−	281.416i	1.88386	−	0.374722i	0.887559	−	0.460695i	$-0.152400\pi$
$751$	1414.78	−	281.416i	1.88386	−	0.374722i	0.996298	+	0.0859723i	$0.0273997\pi$
$752$	−37.0123	−	37.0123i	−0.0492184	−	0.0492184i
$753$	316.924	−	474.310i	0.420881	−	0.629894i
$754$	69.8315	+	13.8904i	0.0926148	+	0.0184222i
$755$	1033.18	+	1546.26i	1.36845	+	2.04803i
$756$	−9.08793	−	21.9402i	−0.0120211	−	0.0290214i
$757$	−278.634	+	115.414i	−0.368077	+	0.152463i	−0.559052	−	0.829132i	$-0.688835\pi$
$757$	−278.634	+	115.414i	−0.368077	+	0.152463i	0.190975	+	0.981595i	$0.438835\pi$
$758$	64.1215	−	42.8446i	0.0845931	−	0.0565233i
$759$	63.1158	−	317.305i	0.0831566	−	0.418056i
$760$	1367.18	+	913.524i	1.79893	+	1.20200i
$761$	−811.549	+	811.549i	−1.06642	+	1.06642i	−0.0687929	+	0.997631i	$0.521915\pi$
$761$	−811.549	+	811.549i	−1.06642	+	1.06642i	−0.997631	+	0.0687929i	$0.978085\pi$
$762$	−57.2441	−	287.786i	−0.0751235	−	0.377671i
$763$	−71.7685	+	173.265i	−0.0940610	+	0.227083i
$764$		−	153.984i		−	0.201550i
$765$		0			0
$766$	−348.859			−0.455429
$767$	−36.4344	−	15.0916i	−0.0475025	−	0.0196762i
$768$	−638.005	+	126.907i	−0.830736	+	0.165244i
$769$	870.130	+	870.130i	1.13151	+	1.13151i	0.989927	+	0.141582i	$0.0452189\pi$
$769$	870.130	+	870.130i	1.13151	+	1.13151i	0.141582	+	0.989927i	$0.454781\pi$
$770$	215.540	−	322.579i	0.279923	−	0.418934i
$771$	−1559.90	−	310.284i	−2.02322	−	0.402444i
$772$	−92.1150	−	137.860i	−0.119320	−	0.178575i
$773$	541.282	+	1306.77i	0.700235	+	1.69052i	0.723066	+	0.690779i	$0.242732\pi$
$773$	541.282	+	1306.77i	0.700235	+	1.69052i	−0.0228308	+	0.999739i	$0.507268\pi$
$774$	−41.8749	+	17.3451i	−0.0541019	+	0.0224098i
$775$	−1097.21	+	733.134i	−1.41576	+	0.945979i
$776$	−279.767	+	1406.49i	−0.360525	+	1.81248i
$777$	−444.334	−	296.895i	−0.571859	−	0.382104i
$778$	−26.8308	+	26.8308i	−0.0344869	+	0.0344869i
$779$	−162.586	−	817.375i	−0.208711	−	1.04926i
$780$	35.5486	−	85.8218i	0.0455751	−	0.110028i
$781$			238.490i			0.305365i
$782$		0			0
$783$	−78.9004			−0.100767
$784$	−348.205	−	144.231i	−0.444139	−	0.183969i
$785$	−2040.97	+	405.975i	−2.59997	+	0.517165i
$786$	−972.366	−	972.366i	−1.23711	−	1.23711i
$787$	−857.112	+	1282.76i	−1.08909	+	1.62994i	−0.379713	+	0.925104i	$0.623977\pi$
$787$	−857.112	+	1282.76i	−1.08909	+	1.62994i	−0.709375	+	0.704831i	$0.751023\pi$
$788$	248.802	+	49.4897i	0.315738	+	0.0628042i
$789$	655.319	+	980.754i	0.830569	+	1.24303i
$790$	−112.201	−	270.877i	−0.142026	−	0.342882i
$791$	707.924	−	293.232i	0.894973	−	0.370710i
$792$	−366.967	+	245.199i	−0.463342	+	0.309595i
$793$	−46.4220	+	233.379i	−0.0585397	+	0.294299i
$794$	−52.0749	−	34.7954i	−0.0655856	−	0.0438229i
$795$	680.496	−	680.496i	0.855970	−	0.855970i
$796$	−15.7874	−	79.3688i	−0.0198335	−	0.0997095i
$797$	−430.853	+	1040.17i	−0.540593	+	1.30511i	0.383712	+	0.923453i	$0.374645\pi$
$797$	−430.853	+	1040.17i	−0.540593	+	1.30511i	−0.924305	+	0.381654i	$0.875355\pi$
$798$			720.593i			0.902998i
$799$		0			0
$800$	−483.288			−0.604110
$801$	−272.996	−	113.079i	−0.340819	−	0.141172i
$802$	−258.963	+	51.5110i	−0.322897	+	0.0642281i
$803$	459.675	+	459.675i	0.572448	+	0.572448i
$804$	−56.7776	+	84.9737i	−0.0706189	+	0.105689i
$805$	357.793	+	71.1694i	0.444463	+	0.0884092i
$806$	124.581	+	186.449i	0.154567	+	0.231326i
$807$	157.796	+	380.953i	0.195534	+	0.472061i
$808$	991.179	−	410.560i	1.22671	−	0.508119i
$809$	273.249	−	182.579i	0.337761	−	0.225685i	−0.375109	−	0.926981i	$-0.622395\pi$
$809$	273.249	−	182.579i	0.337761	−	0.225685i	0.712870	+	0.701296i	$0.247395\pi$
$810$	247.785	−	1245.70i	0.305907	−	1.53790i
$811$	242.645	+	162.131i	0.299193	+	0.199914i	0.696101	−	0.717944i	$-0.254917\pi$
$811$	242.645	+	162.131i	0.299193	+	0.199914i	−0.396908	+	0.917859i	$0.629917\pi$
$812$	−30.7091	+	30.7091i	−0.0378191	+	0.0378191i
$813$	300.846	+	1512.45i	0.370044	+	1.86034i
$814$	151.285	−	365.235i	0.185854	−	0.448692i
$815$			300.260i			0.368417i
$816$		0			0
$817$	85.7829			0.104997
$818$	650.588	+	269.482i	0.795340	+	0.329441i
$819$	99.4124	−	19.7743i	0.121383	−	0.0241445i
$820$	163.457	+	163.457i	0.199337	+	0.199337i
$821$	600.209	−	898.276i	0.731070	−	1.09412i	−0.260616	−	0.965443i	$-0.583926\pi$
$821$	600.209	−	898.276i	0.731070	−	1.09412i	0.991686	−	0.128681i	$-0.0410744\pi$
$822$	370.216	+	73.6406i	0.450385	+	0.0895871i
$823$	−50.4221	−	75.4620i	−0.0612662	−	0.0916914i	0.799572	−	0.600571i	$-0.205060\pi$
$823$	−50.4221	−	75.4620i	−0.0612662	−	0.0916914i	−0.860838	+	0.508879i	$0.830060\pi$
$824$	577.631	+	1394.52i	0.701008	+	1.69238i
$825$	−905.033	+	374.877i	−1.09701	+	0.454396i
$826$	−70.5539	+	47.1426i	−0.0854163	+	0.0570733i
$827$	94.8310	−	476.748i	0.114669	−	0.576479i	−0.880140	−	0.474715i	$-0.842551\pi$
$827$	94.8310	−	476.748i	0.114669	−	0.576479i	0.994809	−	0.101764i	$-0.0324487\pi$
$828$	−62.4255	−	41.7114i	−0.0753931	−	0.0503760i
$829$	743.445	−	743.445i	0.896797	−	0.896797i	−0.0983544	−	0.995151i	$-0.531358\pi$
$829$	743.445	−	743.445i	0.896797	−	0.896797i	0.995151	+	0.0983544i	$0.0313579\pi$
$830$	302.613	+	1521.34i	0.364594	+	1.83294i
$831$	−104.095	+	251.307i	−0.125264	+	0.302415i
$832$			239.065i			0.287338i
$833$		0			0
$834$	374.896			0.449516
$835$	−257.571	−	106.690i	−0.308469	−	0.127772i
$836$	148.212	−	29.4812i	0.177287	−	0.0352646i
$837$	−175.711	−	175.711i	−0.209930	−	0.209930i
$838$	36.6811	−	54.8971i	0.0437722	−	0.0655097i
$839$	449.855	+	89.4817i	0.536180	+	0.106653i	0.455751	−	0.890108i	$-0.349371\pi$
$839$	449.855	+	89.4817i	0.536180	+	0.106653i	0.0804292	+	0.996760i	$0.474371\pi$
$840$	−613.807	−	918.627i	−0.730723	−	1.09360i
$841$	−266.619	−	643.676i	−0.317027	−	0.765370i
$842$	−721.276	+	298.762i	−0.856622	+	0.354824i
$843$	1268.73	−	847.739i	1.50502	−	1.00562i
$844$	−6.23235	+	31.3321i	−0.00738430	+	0.0371234i
$845$	1014.84	+	678.093i	1.20099	+	0.802477i
$846$	−41.2482	+	41.2482i	−0.0487568	+	0.0487568i
$847$	58.1534	+	292.357i	0.0686581	+	0.345167i
$848$	−137.426	+	331.775i	−0.162059	+	0.391244i
$849$		−	1201.22i		−	1.41486i
$850$		0			0
$851$	371.728			0.436813
$852$	113.516	+	47.0197i	0.133234	+	0.0551875i
$853$	−7.38457	+	1.46888i	−0.00865717	+	0.00172202i	−0.199417	−	0.979915i	$-0.563905\pi$
$853$	−7.38457	+	1.46888i	−0.00865717	+	0.00172202i	0.190760	+	0.981637i	$0.438905\pi$
$854$	362.035	+	362.035i	0.423929	+	0.423929i
$855$	781.680	−	1169.87i	0.914246	−	1.36827i
$856$	−337.089	−	67.0512i	−0.393796	−	0.0783309i
$857$	28.1682	+	42.1566i	0.0328683	+	0.0491910i	0.847540	−	0.530732i	$-0.178083\pi$
$857$	28.1682	+	42.1566i	0.0328683	+	0.0491910i	−0.814672	+	0.579923i	$0.803083\pi$
$858$	63.7026	+	153.792i	0.0742455	+	0.179244i
$859$	−464.849	+	192.547i	−0.541151	+	0.224152i	−0.636479	−	0.771294i	$-0.719610\pi$
$859$	−464.849	+	192.547i	−0.541151	+	0.224152i	0.0953281	+	0.995446i	$0.469610\pi$
$860$	−19.7842	+	13.2194i	−0.0230048	+	0.0153713i
$861$	−109.243	+	549.204i	−0.126880	+	0.637867i
$862$	−509.190	−	340.230i	−0.590708	−	0.394698i
$863$	−98.9573	+	98.9573i	−0.114667	+	0.114667i	−0.762112	−	0.647445i	$-0.775837\pi$
$863$	−98.9573	+	98.9573i	−0.114667	+	0.114667i	0.647445	+	0.762112i	$0.275837\pi$
$864$	−17.7546	−	89.2585i	−0.0205493	−	0.103309i
$865$	571.580	−	1379.92i	0.660786	−	1.59528i
$866$			94.8830i			0.109565i
$867$		0			0
$868$	−136.778			−0.157579
$869$	−137.605	−	56.9977i	−0.158348	−	0.0655900i
$870$	−651.310	+	129.554i	−0.748632	+	0.148912i
$871$	67.8634	+	67.8634i	0.0779143	+	0.0779143i
$872$	−219.498	+	328.502i	−0.251718	+	0.376722i
$873$	1203.50	+	239.390i	1.37858	+	0.274216i
$874$	−278.477	−	416.771i	−0.318624	−	0.476855i
$875$	−119.746	−	289.092i	−0.136853	−	0.330391i
$876$	309.423	−	128.167i	0.353222	−	0.146309i
$877$	−789.554	+	527.563i	−0.900289	+	0.601554i	−0.917254	−	0.398302i	$-0.869600\pi$
$877$	−789.554	+	527.563i	−0.900289	+	0.601554i	0.0169652	+	0.999856i	$0.494600\pi$
$878$	−83.7792	+	421.187i	−0.0954205	+	0.479711i
$879$	−475.131	−	317.472i	−0.540536	−	0.361174i
$880$	443.732	−	443.732i	0.504241	−	0.504241i
$881$	−204.085	−	1026.00i	−0.231651	−	1.16459i	−0.905049	−	0.425308i	$-0.860166\pi$
$881$	−204.085	−	1026.00i	−0.231651	−	1.16459i	0.673398	−	0.739280i	$-0.264834\pi$
$882$	−160.738	+	388.057i	−0.182243	+	0.439974i
$883$		−	1264.99i		−	1.43261i	−0.697789	−	0.716303i	$-0.745833\pi$
$883$		−	1264.99i		−	1.43261i	0.697789	−	0.716303i	$-0.254167\pi$
$884$		0			0
$885$	367.818			0.415613
$886$	186.898	+	77.4157i	0.210946	+	0.0873766i
$887$	−766.671	+	152.500i	−0.864341	+	0.171928i	−0.607300	−	0.794472i	$-0.707747\pi$
$887$	−766.671	+	152.500i	−0.864341	+	0.171928i	−0.257041	+	0.966401i	$0.582747\pi$
$888$	−796.059	−	796.059i	−0.896463	−	0.896463i
$889$	93.3794	−	139.752i	0.105039	−	0.157201i
$890$	536.687	+	106.754i	0.603019	+	0.119948i
$891$	−358.459	−	536.472i	−0.402311	−	0.602101i
$892$	−136.286	−	329.023i	−0.152787	−	0.368860i
$893$	102.000	−	42.2496i	0.114221	−	0.0473120i
$894$	307.441	−	205.425i	0.343894	−	0.229782i
$895$	365.941	−	1839.71i	0.408872	−	2.05554i
$896$	239.124	+	159.777i	0.266879	+	0.178323i
$897$	−110.680	+	110.680i	−0.123389	+	0.123389i
$898$	−187.081	−	940.519i	−0.208331	−	1.04735i
$899$	−173.904	+	419.842i	−0.193442	+	0.467010i
$900$			227.333i			0.252592i
$901$		0			0
$902$	−414.241			−0.459247
$903$	−53.2511	−	22.0573i	−0.0589713	−	0.0244267i
$904$	1583.22	−	314.922i	1.75135	−	0.348365i
$905$	−746.999	−	746.999i	−0.825413	−	0.825413i
$906$	−953.854	+	1427.54i	−1.05282	+	1.57566i
$907$	366.570	+	72.9154i	0.404157	+	0.0803918i	0.392983	−	0.919546i	$-0.371443\pi$
$907$	366.570	+	72.9154i	0.404157	+	0.0803918i	0.0111739	+	0.999938i	$0.496443\pi$
$908$	61.9644	+	92.7363i	0.0682428	+	0.102133i
$909$	−351.306	−	848.129i	−0.386476	−	0.933035i
$910$	−173.416	+	71.8311i	−0.190567	+	0.0789352i
$911$	101.362	−	67.7280i	0.111265	−	0.0743447i	−0.498693	−	0.866779i	$-0.666186\pi$
$911$	101.362	−	67.7280i	0.111265	−	0.0743447i	0.609958	+	0.792434i	$0.291186\pi$
$912$	−227.390	+	1143.17i	−0.249331	+	1.25347i
$913$	655.180	+	437.777i	0.717612	+	0.479493i
$914$	280.276	−	280.276i	0.306647	−	0.306647i
$915$	−432.972	−	2176.70i	−0.473193	−	2.37890i
$916$	−41.5657	+	100.349i	−0.0453774	+	0.109551i
$917$		−	787.702i		−	0.858999i
$918$		0			0
$919$	1592.00			1.73232			0.866158	−	0.499770i	$-0.166582\pi$
$919$	1592.00			1.73232			0.866158	+	0.499770i	$0.166582\pi$
$920$	710.018	+	294.099i	0.771759	+	0.319673i
$921$	1030.53	−	204.986i	1.11893	−	0.222569i
$922$	314.913	+	314.913i	0.341555	+	0.341555i
$923$	64.1050	−	95.9399i	0.0694528	−	0.103944i
$924$	−99.5855	−	19.8088i	−0.107777	−	0.0214381i
$925$	−625.331	−	935.874i	−0.676033	−	1.01176i
$926$	−84.6976	−	204.478i	−0.0914661	−	0.220819i
$927$	1193.26	−	494.265i	1.28723	−	0.533188i
$928$	−138.382	+	92.4638i	−0.149118	+	0.0996377i
$929$	132.478	−	666.010i	0.142602	−	0.716910i	−0.841633	−	0.540049i	$-0.818406\pi$
$929$	132.478	−	666.010i	0.142602	−	0.716910i	0.984236	−	0.176861i	$-0.0565944\pi$
$930$	−1738.98	−	1161.95i	−1.86987	−	1.24941i
$931$	562.118	−	562.118i	0.603778	−	0.603778i
$932$	10.3662	+	52.1145i	0.0111226	+	0.0559169i
$933$	873.641	−	2109.16i	0.936378	−	2.26062i
$934$		−	1223.18i		−	1.30961i
$935$		0			0
$936$	213.532			0.228133
$937$	271.967	+	112.652i	0.290253	+	0.120227i	0.523059	−	0.852296i	$-0.324791\pi$
$937$	271.967	+	112.652i	0.290253	+	0.120227i	−0.232806	+	0.972523i	$0.574791\pi$
$938$	202.536	−	40.2869i	0.215923	−	0.0429498i
$939$	−1304.18	−	1304.18i	−1.38890	−	1.38890i
$940$	−17.0134	+	25.4624i	−0.0180994	+	0.0270877i
$941$	−819.035	−	162.916i	−0.870388	−	0.173131i	−0.260361	−	0.965511i	$-0.583841\pi$
$941$	−819.035	−	162.916i	−0.870388	−	0.173131i	−0.610027	+	0.792381i	$0.708841\pi$
$942$	−1067.35	−	1597.41i	−1.13307	−	1.69576i
$943$	−149.060	−	359.862i	−0.158070	−	0.381614i
$944$	−126.805	+	52.5243i	−0.134327	+	0.0556402i
$945$	172.950	−	115.561i	0.183016	−	0.122287i
$946$	8.31845	−	41.8196i	0.00879328	−	0.0442068i
$947$	−517.880	−	346.036i	−0.546864	−	0.365403i	0.251238	−	0.967925i	$-0.419162\pi$
$947$	−517.880	−	346.036i	−0.546864	−	0.365403i	−0.798102	+	0.602523i	$0.794162\pi$
$948$	−54.2592	+	54.2592i	−0.0572355	+	0.0572355i
$949$	−61.3599	−	308.477i	−0.0646575	−	0.325055i
$950$	−580.814	+	1402.21i	−0.611383	+	1.47601i
$951$			1343.30i			1.41252i
$952$		0			0
$953$	−373.214			−0.391620			−0.195810	−	0.980642i	$-0.562734\pi$
$953$	−373.214			−0.391620			−0.195810	+	0.980642i	$0.562734\pi$
$954$	369.746	+	153.154i	0.387575	+	0.160539i
$955$	1322.81	−	263.124i	1.38514	−	0.275522i
$956$	178.619	+	178.619i	0.186840	+	0.186840i
$957$	−187.419	+	280.493i	−0.195841	+	0.293096i
$958$	828.832	+	164.865i	0.865169	+	0.172093i
$959$	120.126	+	179.781i	0.125262	+	0.187468i
$960$	−853.280	−	2060.00i	−0.888833	−	2.14583i
$961$	−434.426	+	179.945i	−0.452056	+	0.187248i
$962$	−159.033	+	106.262i	−0.165315	+	0.110460i
$963$	−57.3741	+	288.439i	−0.0595786	+	0.299522i
$964$	91.3352	+	61.0282i	0.0947460	+	0.0633073i
$965$	1026.89	−	1026.89i	1.06414	−	1.06414i
$966$	65.7051	+	330.322i	0.0680177	+	0.341948i
$967$	−392.472	+	947.512i	−0.405866	+	0.979847i	0.580348	+	0.814369i	$0.302917\pi$
$967$	−392.472	+	947.512i	−0.405866	+	0.979847i	−0.986213	+	0.165478i	$0.947083\pi$
$968$			627.966i			0.648725i
$969$		0			0
$970$	−2272.36			−2.34264
$971$	909.171	+	376.591i	0.936325	+	0.387838i	0.798074	−	0.602559i	$-0.205852\pi$
$971$	909.171	+	376.591i	0.936325	+	0.387838i	0.138250	+	0.990397i	$0.455852\pi$
$972$	−274.797	+	54.6605i	−0.282713	+	0.0562351i
$973$	151.849	+	151.849i	0.156063	+	0.156063i
$974$	397.869	−	595.453i	0.408490	−	0.611348i
$975$	464.842	+	92.4629i	0.476761	+	0.0948337i
$976$	460.099	+	688.586i	0.471413	+	0.705519i
$977$	217.809	+	525.837i	0.222936	+	0.538216i	0.995286	−	0.0969814i	$-0.0309187\pi$
$977$	217.809	+	525.837i	0.222936	+	0.538216i	−0.772350	+	0.635197i	$0.780919\pi$
$978$	−256.105	+	106.082i	−0.261866	+	0.108469i
$979$	231.129	−	154.436i	0.236087	−	0.157748i
$980$	−43.0178	+	216.265i	−0.0438957	+	0.220679i
$981$	281.091	+	187.819i	0.286535	+	0.191457i
$982$	77.4444	−	77.4444i	0.0788639	−	0.0788639i
$983$	280.516	+	1410.25i	0.285368	+	1.43464i	0.811558	+	0.584272i	$0.198620\pi$
$983$	280.516	+	1410.25i	0.285368	+	1.43464i	−0.526190	+	0.850367i	$0.676380\pi$
$984$	−451.436	+	1089.86i	−0.458776	+	1.10758i
$985$			2221.92i			2.25575i
$986$		0			0
$987$	−74.1814			−0.0751585
$988$	−67.5473	−	27.9790i	−0.0683677	−	0.0283188i
$989$	39.3231	−	7.82186i	0.0397605	−	0.00790886i
$990$	−494.517	−	494.517i	−0.499512	−	0.499512i
$991$	−46.6472	+	69.8125i	−0.0470709	+	0.0704465i	−0.854259	−	0.519848i	$-0.825988\pi$
$991$	−46.6472	+	69.8125i	−0.0470709	+	0.0704465i	0.807188	+	0.590295i	$0.200988\pi$
$992$	−514.093	−	102.259i	−0.518239	−	0.103084i
$993$	−1325.39	−	1983.58i	−1.33473	−	1.99757i
$994$	−95.0102	−	229.375i	−0.0955837	−	0.230759i
$995$	654.847	−	271.246i	0.658137	−	0.272609i
$996$	337.545	−	225.540i	0.338900	−	0.226446i
$997$	146.965	−	738.843i	0.147407	−	0.741066i	−0.834396	−	0.551165i	$-0.814183\pi$
$997$	146.965	−	738.843i	0.147407	−	0.741066i	0.981803	−	0.189901i	$-0.0608167\pi$
$998$	−753.360	−	503.379i	−0.754870	−	0.504388i
$999$	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.g.40.1		8
17.2	even	8		289.3.e.j.75.1		8
17.3	odd	16	inner	289.3.e.g.224.1		8
17.4	even	4		289.3.e.f.249.1		8
17.5	odd	16		289.3.e.f.65.1		8
17.6	odd	16		289.3.e.a.131.1		8
17.7	odd	16		289.3.e.n.158.1		8
17.8	even	8		289.3.e.e.214.1		8
17.9	even	8		289.3.e.a.214.1		8
17.10	odd	16		289.3.e.j.158.1		8
17.11	odd	16		289.3.e.e.131.1		8
17.12	odd	16		289.3.e.h.65.1		8
17.13	even	4		289.3.e.h.249.1		8
17.14	odd	16		17.3.e.b.3.1	✓	8
17.15	even	8		289.3.e.n.75.1		8
17.16	even	2		17.3.e.b.6.1	yes	8
51.14	even	16		153.3.p.a.37.1		8
51.50	odd	2		153.3.p.a.91.1		8
68.31	even	16		272.3.bh.b.241.1		8
68.67	odd	2		272.3.bh.b.193.1		8
85.14	odd	16		425.3.u.a.326.1		8
85.33	odd	4		425.3.t.b.74.1		8
85.48	even	16		425.3.t.d.224.1		8
85.67	odd	4		425.3.t.d.74.1		8
85.82	even	16		425.3.t.b.224.1		8
85.84	even	2		425.3.u.a.176.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
17.3.e.b.3.1	✓	8	17.14	odd	16
17.3.e.b.6.1	yes	8	17.16	even	2
153.3.p.a.37.1		8	51.14	even	16
153.3.p.a.91.1		8	51.50	odd	2
272.3.bh.b.193.1		8	68.67	odd	2
272.3.bh.b.241.1		8	68.31	even	16
289.3.e.a.131.1		8	17.6	odd	16
289.3.e.a.214.1		8	17.9	even	8
289.3.e.e.131.1		8	17.11	odd	16
289.3.e.e.214.1		8	17.8	even	8
289.3.e.f.65.1		8	17.5	odd	16
289.3.e.f.249.1		8	17.4	even	4
289.3.e.g.40.1		8	1.1	even	1	trivial
289.3.e.g.224.1		8	17.3	odd	16	inner
289.3.e.h.65.1		8	17.12	odd	16
289.3.e.h.249.1		8	17.13	even	4
289.3.e.j.75.1		8	17.2	even	8
289.3.e.j.158.1		8	17.10	odd	16
289.3.e.n.75.1		8	17.15	even	8
289.3.e.n.158.1		8	17.7	odd	16
425.3.t.b.74.1		8	85.33	odd	4
425.3.t.b.224.1		8	85.82	even	16
425.3.t.d.74.1		8	85.67	odd	4
425.3.t.d.224.1		8	85.48	even	16
425.3.u.a.176.1		8	85.84	even	2
425.3.u.a.326.1		8	85.14	odd	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

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

\(f(q)\)	\(=\)	\(q+(-1.63099 - 0.675577i) q^{2} +(-3.96908 + 0.789499i) q^{3} +(-0.624715 - 0.624715i) q^{4} +(4.29916 - 6.43416i) q^{5} +(7.00688 + 1.39376i) q^{6} +(2.27356 + 3.40262i) q^{7} +(3.29916 + 7.96489i) q^{8} +(6.81537 - 2.82302i) q^{9} +(-11.3586 + 7.58960i) q^{10} +(-1.35387 + 6.80638i) q^{11} +(2.97275 + 1.98633i) q^{12} +(2.37416 - 2.37416i) q^{13} +(-1.40941 - 7.08560i) q^{14} +(-11.9840 + 28.9319i) q^{15} -11.6855i q^{16} -13.0229 q^{18} +(22.7712 + 9.43215i) q^{19} +(-6.70526 + 1.33376i) q^{20} +(-11.7103 - 11.7103i) q^{21} +(6.80638 - 10.1865i) q^{22} +(11.2984 + 2.24740i) q^{23} +(-19.3829 - 29.0086i) q^{24} +(-13.3484 - 32.2260i) q^{25} +(-5.47615 + 2.26829i) q^{26} +(5.46144 - 3.64922i) q^{27} +(0.705343 - 3.54600i) q^{28} +(-9.98767 - 6.67355i) q^{29} +(39.0914 - 39.0914i) q^{30} +(-7.38055 - 37.1045i) q^{31} +(5.30218 - 12.8006i) q^{32} -28.0839i q^{33} +31.6674 q^{35} +(-6.02124 - 2.49408i) q^{36} +(31.6486 - 6.29529i) q^{37} +(-30.7674 - 30.7674i) q^{38} +(-7.54883 + 11.2976i) q^{39} +(65.4310 + 13.0150i) q^{40} +(-18.7852 - 28.1140i) q^{41} +(11.1881 + 27.0106i) q^{42} +(3.21547 - 1.33189i) q^{43} +(5.09783 - 3.40626i) q^{44} +(11.1367 - 55.9877i) q^{45} +(-16.9093 - 11.2984i) q^{46} +(3.16735 - 3.16735i) q^{47} +(9.22573 + 46.3809i) q^{48} +(12.3427 - 29.7979i) q^{49} +61.5781i q^{50} -2.96634 q^{52} +(-28.3919 - 11.7603i) q^{53} +(-11.3729 + 2.26220i) q^{54} +(37.9728 + 37.9728i) q^{55} +(-19.6007 + 29.3345i) q^{56} +(-97.8275 - 19.4591i) q^{57} +(11.7813 + 17.6319i) q^{58} +(-4.49481 - 10.8514i) q^{59} +(25.5607 - 10.5876i) q^{60} +(-58.9263 + 39.3733i) q^{61} +(-13.0294 + 65.5031i) q^{62} +(25.1008 + 16.7718i) q^{63} +(-50.3473 + 50.3473i) q^{64} +(-5.06881 - 25.4826i) q^{65} +(-18.9728 + 45.8045i) q^{66} +28.5842i q^{67} -46.6187 q^{69} +(-51.6491 - 21.3938i) q^{70} +(33.7056 - 6.70446i) q^{71} +(44.9700 + 44.9700i) q^{72} +(52.0431 - 77.8880i) q^{73} +(-55.8713 - 11.1135i) q^{74} +(78.4234 + 117.369i) q^{75} +(-8.33312 - 20.1179i) q^{76} +(-26.2377 + 10.8680i) q^{77} +(19.9444 - 13.3265i) q^{78} +(-4.18708 + 21.0499i) q^{79} +(-75.1866 - 50.2381i) q^{80} +(-65.7422 + 65.7422i) q^{81} +(11.6452 + 58.5443i) q^{82} +(43.4522 - 104.903i) q^{83} +14.6312i q^{84} -6.14419 q^{86} +(44.9106 + 18.6026i) q^{87} +(-58.6787 + 11.6719i) q^{88} +(-28.3238 - 28.3238i) q^{89} +(-55.9877 + 83.7916i) q^{90} +(13.4762 + 2.68058i) q^{91} +(-5.65432 - 8.46229i) q^{92} +(58.5880 + 141.444i) q^{93} +(-7.30570 + 3.02612i) q^{94} +(158.585 - 105.963i) q^{95} +(-10.9387 + 54.9926i) q^{96} +(138.307 + 92.4136i) q^{97} +(-40.2616 + 40.2616i) q^{98} +(9.98738 + 50.2100i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4} + 24 q^{5} + 16 q^{7} + 16 q^{8} + 8 q^{9} - 40 q^{11} - 40 q^{12} - 16 q^{14} + 32 q^{15} - 136 q^{18} - 32 q^{19} + 40 q^{20} - 64 q^{21} + 8 q^{23} - 24 q^{24} + 16 q^{25} - 96 q^{27} - 80 q^{28}+ \cdots - 136 q^{99}+O(q^{100}) \) 8 * q - 8 * q^4 + 24 * q^5 + 16 * q^7 + 16 * q^8 + 8 * q^9 - 40 * q^11 - 40 * q^12 - 16 * q^14 + 32 * q^15 - 136 * q^18 - 32 * q^19 + 40 * q^20 - 64 * q^21 + 8 * q^23 - 24 * q^24 + 16 * q^25 - 96 * q^27 - 80 * q^28 - 24 * q^29 + 168 * q^30 - 32 * q^31 - 24 * q^32 + 80 * q^35 - 104 * q^36 + 168 * q^37 + 8 * q^38 + 72 * q^39 + 200 * q^40 - 72 * q^42 + 96 * q^43 + 96 * q^44 + 88 * q^45 - 80 * q^47 - 88 * q^48 + 8 * q^49 + 240 * q^52 + 96 * q^53 - 208 * q^54 - 8 * q^55 - 72 * q^56 - 248 * q^57 + 8 * q^59 + 16 * q^60 - 264 * q^61 + 136 * q^62 - 8 * q^63 - 120 * q^64 + 32 * q^65 + 8 * q^66 - 208 * q^69 - 80 * q^70 - 32 * q^71 + 24 * q^72 - 24 * q^73 - 176 * q^74 + 192 * q^75 - 80 * q^76 - 216 * q^77 + 368 * q^78 + 96 * q^79 - 24 * q^80 - 224 * q^81 + 408 * q^82 - 88 * q^83 + 288 * q^86 + 312 * q^87 - 176 * q^88 + 288 * q^89 - 256 * q^90 + 24 * q^91 - 336 * q^92 + 280 * q^93 - 8 * q^94 + 152 * q^95 - 328 * q^96 + 344 * q^97 + 16 * q^98 - 136 * q^99

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