LMFDB - Embedded newform 58.3.f.a.39.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [58,3,Mod(3,58)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(58, base_ring=CyclotomicField(28)) chi = DirichletCharacter(H, H._module([5])) N = Newforms(chi, 3, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("58.3"); S:= CuspForms(chi, 3); N := Newforms(S);

Level:	$ N $	$=$	$ 58 = 2 \cdot 29 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	58.f (of order $28$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$1.58038553329$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$2$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			39.1
Character	$\chi$	$=$	58.39
Dual form			58.3.f.a.3.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.19745 + 0.752407i) q^{2} +(-3.29155 - 1.15176i) q^{3} +(0.867767 - 1.80194i) q^{4} +(6.81899 + 1.55639i) q^{5} +(4.80806 - 1.09741i) q^{6} +(9.87394 - 4.75504i) q^{7} +(0.316683 + 2.81064i) q^{8} +(2.47126 + 1.97076i) q^{9} +(-9.33644 + 3.26696i) q^{10} +(0.486138 - 4.31459i) q^{11} +(-4.93170 + 4.93170i) q^{12} +(-1.82714 + 1.45710i) q^{13} +(-8.24582 + 13.1231i) q^{14} +(-20.6525 - 12.9768i) q^{15} +(-2.49396 - 3.12733i) q^{16} +(18.0690 + 18.0690i) q^{17} +(-4.44202 - 0.500495i) q^{18} +(-7.50304 - 21.4425i) q^{19} +(8.72182 - 10.9368i) q^{20} +(-37.9773 + 4.27901i) q^{21} +(2.66421 + 5.53228i) q^{22} +(-1.89944 - 8.32198i) q^{23} +(2.19481 - 9.61611i) q^{24} +(21.5521 + 10.3789i) q^{25} +(1.09158 - 3.11955i) q^{26} +(10.8335 + 17.2414i) q^{27} -21.9185i q^{28} +(-11.0318 + 26.8198i) q^{29} +34.4941 q^{30} +(-40.6455 + 25.5392i) q^{31} +(5.33941 + 1.86834i) q^{32} +(-6.56954 + 13.6418i) q^{33} +(-35.2319 - 8.04145i) q^{34} +(74.7311 - 17.0569i) q^{35} +(5.69566 - 2.74289i) q^{36} +(-6.33152 - 56.1938i) q^{37} +(25.1180 + 20.0309i) q^{38} +(7.69236 - 2.69167i) q^{39} +(-2.21500 + 19.6586i) q^{40} +(14.8570 - 14.8570i) q^{41} +(42.2563 - 33.6982i) q^{42} +(-31.0191 + 49.3667i) q^{43} +(-7.35278 - 4.62006i) q^{44} +(13.7842 + 17.2848i) q^{45} +(8.53600 + 8.53600i) q^{46} +(23.6347 + 2.66299i) q^{47} +(4.60705 + 13.1662i) q^{48} +(44.3334 - 55.5923i) q^{49} +(-33.6167 + 3.78770i) q^{50} +(-38.6637 - 80.2861i) q^{51} +(1.04006 + 4.55682i) q^{52} +(-16.2908 + 71.3747i) q^{53} +(-25.9451 - 12.4945i) q^{54} +(10.0302 - 28.6646i) q^{55} +(16.4916 + 26.2463i) q^{56} +79.2207i q^{57} +(-6.96940 - 40.4157i) q^{58} -59.5978 q^{59} +(-41.3049 + 25.9536i) q^{60} +(-83.9615 - 29.3794i) q^{61} +(29.4550 - 61.1639i) q^{62} +(33.7721 + 7.70826i) q^{63} +(-7.79942 + 1.78017i) q^{64} +(-14.7271 + 7.09219i) q^{65} +(-2.39749 - 21.2783i) q^{66} +(16.1905 + 12.9115i) q^{67} +(48.2388 - 16.8795i) q^{68} +(-3.33286 + 29.5799i) q^{69} +(-76.6529 + 76.6529i) q^{70} +(-49.1796 + 39.2194i) q^{71} +(-4.75650 + 7.56992i) q^{72} +(43.1667 + 27.1235i) q^{73} +(49.8623 + 62.5253i) q^{74} +(-58.9857 - 58.9857i) q^{75} +(-45.1489 - 5.08706i) q^{76} +(-15.7160 - 44.9137i) q^{77} +(-7.18597 + 9.01092i) q^{78} +(121.926 - 13.7378i) q^{79} +(-12.1390 - 25.2068i) q^{80} +(-22.1312 - 96.9631i) q^{81} +(-6.61198 + 28.9690i) q^{82} +(-23.5680 - 11.3497i) q^{83} +(-25.2449 + 72.1458i) q^{84} +(95.0898 + 151.335i) q^{85} -82.4531i q^{86} +(67.2016 - 75.5726i) q^{87} +12.2807 q^{88} +(-23.3143 + 14.6493i) q^{89} +(-29.5111 - 10.3264i) q^{90} +(-11.1125 + 23.0754i) q^{91} +(-16.6440 - 3.79888i) q^{92} +(163.202 - 37.2497i) q^{93} +(-30.3049 + 14.5941i) q^{94} +(-17.7903 - 157.894i) q^{95} +(-15.4230 - 12.2995i) q^{96} +(63.9752 - 22.3859i) q^{97} +(-11.2589 + 99.9256i) q^{98} +(9.70440 - 9.70440i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} - 4 q^{3} + 28 q^{5} + 34 q^{7} + 8 q^{8} + 4 q^{10} - 44 q^{11} + 8 q^{12} - 36 q^{14} - 90 q^{15} + 16 q^{16} + 32 q^{17} - 16 q^{18} - 56 q^{19} + 36 q^{20} - 168 q^{21} - 84 q^{22} + 68 q^{23}+ \cdots + 132 q^{99}+O(q^{100}) $ 24 * q - 4 * q^2 - 4 * q^3 + 28 * q^5 + 34 * q^7 + 8 * q^8 + 4 * q^10 - 44 * q^11 + 8 * q^12 - 36 * q^14 - 90 * q^15 + 16 * q^16 + 32 * q^17 - 16 * q^18 - 56 * q^19 + 36 * q^20 - 168 * q^21 - 84 * q^22 + 68 * q^23 - 40 * q^24 - 84 * q^25 - 96 * q^26 - 28 * q^27 + 144 * q^29 - 40 * q^30 + 106 * q^31 + 16 * q^32 + 98 * q^33 + 84 * q^34 + 196 * q^35 + 80 * q^36 - 262 * q^37 + 280 * q^38 + 458 * q^39 + 8 * q^40 + 116 * q^41 + 308 * q^42 - 212 * q^43 - 24 * q^44 + 14 * q^45 - 16 * q^46 - 238 * q^47 + 16 * q^48 + 188 * q^49 - 196 * q^50 - 462 * q^51 + 32 * q^52 - 126 * q^53 - 56 * q^54 - 96 * q^55 + 72 * q^56 - 24 * q^58 - 48 * q^59 - 180 * q^60 + 268 * q^61 - 56 * q^62 + 28 * q^63 + 376 * q^65 - 108 * q^66 + 490 * q^67 - 64 * q^68 - 328 * q^69 - 72 * q^70 - 14 * q^71 - 88 * q^72 - 552 * q^73 - 188 * q^74 - 356 * q^75 - 420 * q^76 - 186 * q^77 - 316 * q^78 - 358 * q^79 - 20 * q^81 + 288 * q^82 - 448 * q^83 - 140 * q^84 - 420 * q^85 + 606 * q^87 - 48 * q^88 + 314 * q^89 + 308 * q^90 - 182 * q^91 + 112 * q^92 + 1428 * q^93 + 336 * q^94 + 510 * q^95 + 424 * q^97 + 244 * q^98 + 132 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/58\mathbb{Z}\right)^\times$.

$n$	$31$
$\chi(n)$	$e\left(\frac{23}{28}\right)$

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 $

$2$	−1.19745	+	0.752407i	−0.598724	+	0.376203i
$2$	−1.19745	+	0.752407i	−0.598724	+	0.376203i
$3$	−3.29155	−	1.15176i	−1.09718	−	0.383921i	−0.279825	−	0.960051i	$-0.590276\pi$
$3$	−3.29155	−	1.15176i	−1.09718	−	0.383921i	−0.817358	+	0.576130i	$0.804562\pi$
$4$	0.867767	−	1.80194i	0.216942	−	0.450484i
$5$	6.81899	+	1.55639i	1.36380	+	0.311278i	0.840934	−	0.541137i	$-0.182006\pi$
$5$	6.81899	+	1.55639i	1.36380	+	0.311278i	0.522865	+	0.852416i	$0.324863\pi$
$6$	4.80806	−	1.09741i	0.801343	−	0.182901i
$7$	9.87394	−	4.75504i	1.41056	−	0.679292i	0.435289	−	0.900291i	$-0.356646\pi$
$7$	9.87394	−	4.75504i	1.41056	−	0.679292i	0.975274	+	0.220999i	$0.0709318\pi$
$8$	0.316683	+	2.81064i	0.0395854	+	0.351330i
$9$	2.47126	+	1.97076i	0.274584	+	0.218973i
$10$	−9.33644	+	3.26696i	−0.933644	+	0.326696i
$11$	0.486138	−	4.31459i	0.0441944	−	0.392236i	−0.952070	−	0.305880i	$-0.901049\pi$
$11$	0.486138	−	4.31459i	0.0441944	−	0.392236i	0.996264	−	0.0863557i	$-0.0275221\pi$
$12$	−4.93170	+	4.93170i	−0.410975	+	0.410975i
$13$	−1.82714	+	1.45710i	−0.140549	+	0.112084i	−0.691241	−	0.722625i	$-0.742936\pi$
$13$	−1.82714	+	1.45710i	−0.140549	+	0.112084i	0.550691	+	0.834709i	$0.314364\pi$
$14$	−8.24582	+	13.1231i	−0.588987	+	0.937367i
$15$	−20.6525	−	12.9768i	−1.37683	−	0.865120i
$16$	−2.49396	−	3.12733i	−0.155872	−	0.195458i
$17$	18.0690	+	18.0690i	1.06288	+	1.06288i	0.997886	+	0.0649950i	$0.0207031\pi$
$17$	18.0690	+	18.0690i	1.06288	+	1.06288i	0.0649950	+	0.997886i	$0.479297\pi$
$18$	−4.44202	−	0.500495i	−0.246779	−	0.0278053i
$19$	−7.50304	−	21.4425i	−0.394897	−	1.12855i	−0.954092	−	0.299515i	$-0.903175\pi$
$19$	−7.50304	−	21.4425i	−0.394897	−	1.12855i	0.559195	−	0.829036i	$-0.311110\pi$
$20$	8.72182	−	10.9368i	0.436091	−	0.546841i
$21$	−37.9773	+	4.27901i	−1.80844	+	0.203762i
$22$	2.66421	+	5.53228i	0.121100	+	0.251467i
$23$	−1.89944	−	8.32198i	−0.0825843	−	0.361825i	0.916703	−	0.399569i	$-0.130840\pi$
$23$	−1.89944	−	8.32198i	−0.0825843	−	0.361825i	−0.999287	+	0.0377435i	$0.987983\pi$
$24$	2.19481	−	9.61611i	0.0914506	−	0.400671i
$25$	21.5521	+	10.3789i	0.862084	+	0.415158i
$26$	1.09158	−	3.11955i	0.0419838	−	0.119983i
$27$	10.8335	+	17.2414i	0.401241	+	0.638572i
$28$		−	21.9185i		−	0.782804i
$29$	−11.0318	+	26.8198i	−0.380406	+	0.924820i
$29$	−11.0318	+	26.8198i	−0.380406	+	0.924820i
$30$	34.4941			1.14980
$31$	−40.6455	+	25.5392i	−1.31114	+	0.823846i	−0.992288	−	0.123957i	$-0.960442\pi$
$31$	−40.6455	+	25.5392i	−1.31114	+	0.823846i	−0.318856	+	0.947803i	$0.603299\pi$
$32$	5.33941	+	1.86834i	0.166857	+	0.0583856i
$33$	−6.56954	+	13.6418i	−0.199077	+	0.413387i
$34$	−35.2319	−	8.04145i	−1.03623	−	0.236513i
$35$	74.7311	−	17.0569i	2.13517	−	0.487339i
$36$	5.69566	−	2.74289i	0.158213	−	0.0761913i
$37$	−6.33152	−	56.1938i	−0.171122	−	1.51875i	−0.726508	−	0.687158i	$-0.758858\pi$
$37$	−6.33152	−	56.1938i	−0.171122	−	1.51875i	0.555385	−	0.831593i	$-0.312571\pi$
$38$	25.1180	+	20.0309i	0.660999	+	0.527129i
$39$	7.69236	−	2.69167i	0.197240	−	0.0690172i
$40$	−2.21500	+	19.6586i	−0.0553749	+	0.491466i
$41$	14.8570	−	14.8570i	0.362366	−	0.362366i	−0.502318	−	0.864683i	$-0.667519\pi$
$41$	14.8570	−	14.8570i	0.362366	−	0.362366i	0.864683	+	0.502318i	$0.167519\pi$
$42$	42.2563	−	33.6982i	1.00610	−	0.802339i
$43$	−31.0191	+	49.3667i	−0.721375	+	1.14806i	0.261751	+	0.965135i	$0.415700\pi$
$43$	−31.0191	+	49.3667i	−0.721375	+	1.14806i	−0.983127	+	0.182927i	$0.941443\pi$
$44$	−7.35278	−	4.62006i	−0.167109	−	0.105001i
$45$	13.7842	+	17.2848i	0.306316	+	0.384108i
$46$	8.53600	+	8.53600i	0.185565	+	0.185565i
$47$	23.6347	+	2.66299i	0.502865	+	0.0566593i	0.359754	−	0.933047i	$-0.382861\pi$
$47$	23.6347	+	2.66299i	0.502865	+	0.0566593i	0.143111	+	0.989707i	$0.454289\pi$
$48$	4.60705	+	13.1662i	0.0959802	+	0.274296i
$49$	44.3334	−	55.5923i	0.904762	−	1.13454i
$50$	−33.6167	+	3.78770i	−0.672335	+	0.0757539i
$51$	−38.6637	−	80.2861i	−0.758112	−	1.57424i
$52$	1.04006	+	4.55682i	0.0200012	+	0.0876311i
$53$	−16.2908	+	71.3747i	−0.307374	+	1.34669i	0.551359	+	0.834268i	$0.314109\pi$
$53$	−16.2908	+	71.3747i	−0.307374	+	1.34669i	−0.858733	+	0.512424i	$0.828748\pi$
$54$	−25.9451	−	12.4945i	−0.480466	−	0.231380i
$55$	10.0302	−	28.6646i	0.182367	−	0.521174i
$56$	16.4916	+	26.2463i	0.294493	+	0.468684i
$57$			79.2207i			1.38984i
$58$	−6.96940	−	40.4157i	−0.120162	−	0.696822i
$59$	−59.5978			−1.01013			−0.505066	−	0.863081i	$-0.668532\pi$
$59$	−59.5978			−1.01013			−0.505066	+	0.863081i	$0.668532\pi$
$60$	−41.3049	+	25.9536i	−0.688415	+	0.432560i
$61$	−83.9615	−	29.3794i	−1.37642	−	0.481629i	−0.462172	−	0.886790i	$-0.652930\pi$
$61$	−83.9615	−	29.3794i	−1.37642	−	0.481629i	−0.914245	+	0.405161i	$0.867216\pi$
$62$	29.4550	−	61.1639i	0.475080	−	0.986514i
$63$	33.7721	+	7.70826i	0.536065	+	0.122353i
$64$	−7.79942	+	1.78017i	−0.121866	+	0.0278151i
$65$	−14.7271	+	7.09219i	−0.226570	+	0.109111i
$66$	−2.39749	−	21.2783i	−0.0363256	−	0.322399i
$67$	16.1905	+	12.9115i	0.241650	+	0.192709i	0.736824	−	0.676084i	$-0.236324\pi$
$67$	16.1905	+	12.9115i	0.241650	+	0.192709i	−0.495175	+	0.868794i	$0.664896\pi$
$68$	48.2388	−	16.8795i	0.709394	−	0.248228i
$69$	−3.33286	+	29.5799i	−0.0483023	+	0.428694i
$70$	−76.6529	+	76.6529i	−1.09504	+	1.09504i
$71$	−49.1796	+	39.2194i	−0.692671	+	0.552386i	−0.905314	−	0.424744i	$-0.860364\pi$
$71$	−49.1796	+	39.2194i	−0.692671	+	0.552386i	0.212643	+	0.977130i	$0.431793\pi$
$72$	−4.75650	+	7.56992i	−0.0660625	+	0.105138i
$73$	43.1667	+	27.1235i	0.591325	+	0.371554i	0.794206	−	0.607649i	$-0.207887\pi$
$73$	43.1667	+	27.1235i	0.591325	+	0.371554i	−0.202880	+	0.979204i	$0.565030\pi$
$74$	49.8623	+	62.5253i	0.673815	+	0.844937i
$75$	−58.9857	−	58.9857i	−0.786476	−	0.786476i
$76$	−45.1489	−	5.08706i	−0.594064	−	0.0669350i
$77$	−15.7160	−	44.9137i	−0.204104	−	0.583294i
$78$	−7.18597	+	9.01092i	−0.0921278	+	0.115525i
$79$	121.926	−	13.7378i	1.54337	−	0.173896i	0.701145	−	0.713019i	$-0.252673\pi$
$79$	121.926	−	13.7378i	1.54337	−	0.173896i	0.842227	+	0.539123i	$0.181244\pi$
$80$	−12.1390	−	25.2068i	−0.151737	−	0.315085i
$81$	−22.1312	−	96.9631i	−0.273225	−	1.19708i
$82$	−6.61198	+	28.9690i	−0.0806339	+	0.353280i
$83$	−23.5680	−	11.3497i	−0.283952	−	0.136744i	0.286487	−	0.958084i	$-0.407512\pi$
$83$	−23.5680	−	11.3497i	−0.283952	−	0.136744i	−0.570439	+	0.821340i	$0.693227\pi$
$84$	−25.2449	+	72.1458i	−0.300535	+	0.858879i
$85$	95.0898	+	151.335i	1.11870	+	1.78041i
$86$		−	82.4531i		−	0.958757i
$87$	67.2016	−	75.5726i	0.772433	−	0.868651i
$88$	12.2807			0.139554
$89$	−23.3143	+	14.6493i	−0.261958	+	0.164599i	−0.656607	−	0.754233i	$-0.728009\pi$
$89$	−23.3143	+	14.6493i	−0.261958	+	0.164599i	0.394649	+	0.918832i	$0.370866\pi$
$90$	−29.5111	−	10.3264i	−0.327901	−	0.114738i
$91$	−11.1125	+	23.0754i	−0.122116	+	0.253576i
$92$	−16.6440	−	3.79888i	−0.180913	−	0.0412921i
$93$	163.202	−	37.2497i	1.75486	−	0.400535i
$94$	−30.3049	+	14.5941i	−0.322393	+	0.155256i
$95$	−17.7903	−	157.894i	−0.187267	−	1.66204i
$96$	−15.4230	−	12.2995i	−0.160657	−	0.128119i
$97$	63.9752	−	22.3859i	0.659538	−	0.230782i	0.0203031	−	0.999794i	$-0.493537\pi$
$97$	63.9752	−	22.3859i	0.659538	−	0.230782i	0.639235	+	0.769012i	$0.279251\pi$
$98$	−11.2589	+	99.9256i	−0.114887	+	1.01965i
$99$	9.70440	−	9.70440i	0.0980243	−	0.0980243i
$100$	37.4044	−	29.8290i	0.374044	−	0.298290i
$101$	22.7942	−	36.2768i	0.225686	−	0.359176i	−0.714617	−	0.699516i	$-0.753399\pi$
$101$	22.7942	−	36.2768i	0.225686	−	0.359176i	0.940303	+	0.340339i	$0.110542\pi$
$102$	106.706	+	67.0476i	1.04613	+	0.657329i
$103$	30.8694	+	38.7089i	0.299702	+	0.375815i	0.908766	−	0.417307i	$-0.137026\pi$
$103$	30.8694	+	38.7089i	0.299702	+	0.375815i	−0.609063	+	0.793122i	$0.708454\pi$
$104$	−4.67400	−	4.67400i	−0.0449423	−	0.0449423i
$105$	−265.626	−	29.9289i	−2.52978	−	0.285037i
$106$	−34.1954	−	97.7248i	−0.322598	−	0.921932i
$107$	−94.9351	+	119.045i	−0.887244	+	1.11257i	0.105749	+	0.994393i	$0.466276\pi$
$107$	−94.9351	+	119.045i	−0.887244	+	1.11257i	−0.992993	+	0.118176i	$0.962295\pi$
$108$	40.4690	−	4.55976i	0.374713	−	0.0422200i
$109$	−8.15306	−	16.9300i	−0.0747988	−	0.155321i	0.860216	−	0.509929i	$-0.170329\pi$
$109$	−8.15306	−	16.9300i	−0.0747988	−	0.155321i	−0.935015	+	0.354608i	$0.884614\pi$
$110$	9.55681	+	41.8711i	0.0868801	+	0.380647i
$111$	−43.8814	+	192.257i	−0.395328	+	1.73205i
$112$	−39.4958	−	19.0202i	−0.352641	−	0.169823i
$113$	19.0709	−	54.5015i	0.168769	−	0.482314i	−0.828172	−	0.560474i	$-0.810619\pi$
$113$	19.0709	−	54.5015i	0.168769	−	0.482314i	0.996941	+	0.0781603i	$0.0249046\pi$
$114$	−59.6062	−	94.8627i	−0.522861	−	0.832129i
$115$		−	59.7038i		−	0.519164i
$116$	38.7545	+	43.1519i	0.334091	+	0.371999i
$117$	−7.38692			−0.0631361
$118$	71.3653	−	44.8418i	0.604791	−	0.380015i
$119$	264.331	+	92.4933i	2.22127	+	0.777255i
$120$	29.9329	−	62.1562i	0.249441	−	0.517969i
$121$	99.5869	+	22.7301i	0.823032	+	0.187852i
$122$	122.645	−	27.9929i	1.00529	−	0.229450i
$123$	−66.0142	+	31.7908i	−0.536701	+	0.258462i
$124$	10.7493	+	95.4027i	0.0866879	+	0.769377i
$125$	−5.90022	−	4.70527i	−0.0472018	−	0.0376422i
$126$	−46.2401	+	16.1801i	−0.366985	+	0.128414i
$127$	−11.9911	+	106.424i	−0.0944184	+	0.837987i	0.853850	+	0.520518i	$0.174261\pi$
$127$	−11.9911	+	106.424i	−0.0944184	+	0.837987i	−0.948269	+	0.317468i	$0.897167\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$	158.960	−	126.766i	1.23225	−	0.982683i
$130$	12.2987	−	19.5733i	0.0946055	−	0.150564i
$131$	−37.9512	−	23.8463i	−0.289704	−	0.182033i	0.379337	−	0.925259i	$-0.376152\pi$
$131$	−37.9512	−	23.8463i	−0.289704	−	0.182033i	−0.669041	+	0.743225i	$0.733295\pi$
$132$	18.8808	+	23.6758i	0.143036	+	0.179362i
$133$	−176.044	−	176.044i	−1.32364	−	1.32364i
$134$	−29.1021	−	3.27901i	−0.217180	−	0.0244703i
$135$	47.0392	+	134.430i	0.348439	+	0.995781i
$136$	−45.0633	+	56.5076i	−0.331348	+	0.415497i
$137$	−72.4527	+	8.16346i	−0.528852	+	0.0595873i	−0.372353	−	0.928091i	$-0.621449\pi$
$137$	−72.4527	+	8.16346i	−0.528852	+	0.0595873i	−0.156498	+	0.987678i	$0.550021\pi$
$138$	−18.2652	−	37.9281i	−0.132357	−	0.274841i
$139$	−21.1084	−	92.4820i	−0.151859	−	0.665338i	−0.992344	−	0.123503i	$-0.960587\pi$
$139$	−21.1084	−	92.4820i	−0.151859	−	0.665338i	0.840485	−	0.541835i	$-0.182270\pi$
$140$	34.1138	−	149.462i	0.243670	−	1.06759i
$141$	−74.7275	−	35.9869i	−0.529982	−	0.255226i
$142$	29.3811	−	83.9663i	0.206909	−	0.591312i
$143$	5.39854	+	8.59173i	0.0377520	+	0.0600820i
$144$		−	12.6434i		−	0.0878015i
$145$	−116.968	+	165.714i	−0.806673	+	1.14286i
$146$	−72.0979			−0.493821
$147$	−209.955	+	131.923i	−1.42826	+	0.897437i
$148$	−106.752	−	37.3541i	−0.721297	−	0.252393i
$149$	−72.6389	+	150.836i	−0.487509	+	1.01232i	0.501594	+	0.865103i	$0.332747\pi$
$149$	−72.6389	+	150.836i	−0.487509	+	1.01232i	−0.989104	+	0.147221i	$0.952967\pi$
$150$	115.014	+	26.2511i	0.766758	+	0.175007i
$151$	−13.7774	+	3.14460i	−0.0912411	+	0.0208252i	−0.267898	−	0.963447i	$-0.586329\pi$
$151$	−13.7774	+	3.14460i	−0.0912411	+	0.0208252i	0.176657	+	0.984273i	$0.443472\pi$
$152$	57.8910	−	27.8788i	0.380862	−	0.183413i
$153$	9.04343	+	80.2626i	0.0591074	+	0.524592i
$154$	52.6124	+	41.9570i	0.341639	+	0.272448i
$155$	−316.910	+	110.892i	−2.04458	+	0.715430i
$156$	1.82495	−	16.1969i	0.0116984	−	0.103826i
$157$	33.9444	−	33.9444i	0.216206	−	0.216206i	−0.590691	−	0.806898i	$-0.701145\pi$
$157$	33.9444	−	33.9444i	0.216206	−	0.216206i	0.806898	+	0.590691i	$0.201145\pi$
$158$	−135.664	+	108.189i	−0.858634	+	0.684738i
$159$	135.829	−	216.170i	0.854268	−	1.35956i
$160$	33.5015	+	21.0504i	0.209385	+	0.131565i
$161$	−58.3263	−	73.1389i	−0.362275	−	0.454279i
$162$	99.4567	+	99.4567i	0.613930	+	0.613930i
$163$	−69.8378	−	7.86883i	−0.428453	−	0.0482750i	−0.104895	−	0.994483i	$-0.533451\pi$
$163$	−69.8378	−	7.86883i	−0.428453	−	0.0482750i	−0.323558	+	0.946208i	$0.604879\pi$
$164$	−13.8790	−	39.6638i	−0.0846278	−	0.241852i
$165$	−66.0296	+	82.7985i	−0.400179	+	0.501809i
$166$	36.7611	−	4.14198i	0.221452	−	0.0249517i
$167$	−69.3265	−	143.958i	−0.415129	−	0.862024i	−0.998749	−	0.0499974i	$-0.984079\pi$
$167$	−69.3265	−	143.958i	−0.415129	−	0.862024i	0.583621	−	0.812027i	$-0.301636\pi$
$168$	−24.0535	−	105.385i	−0.143176	−	0.627294i
$169$	−36.3907	+	159.438i	−0.215330	+	0.943421i
$170$	−227.730	−	109.669i	−1.33959	−	0.645113i
$171$	23.7160	−	67.7765i	0.138690	−	0.396354i
$172$	62.0383	+	98.7334i	0.360688	+	0.574031i
$173$		−	306.862i		−	1.77377i	−0.461992	−	0.886884i	$-0.652865\pi$
$173$		−	306.862i		−	1.77377i	0.461992	−	0.886884i	$-0.347135\pi$
$174$	−23.6092	+	141.057i	−0.135685	+	0.810674i
$175$	262.157			1.49804
$176$	−14.7056	+	9.24011i	−0.0835543	+	0.0525006i
$177$	196.169	+	68.6425i	1.10830	+	0.387811i
$178$	16.8954	−	35.0837i	0.0949180	−	0.197099i
$179$	247.236	+	56.4300i	1.38121	+	0.315251i	0.847669	−	0.530526i	$-0.178005\pi$
$179$	247.236	+	56.4300i	1.38121	+	0.315251i	0.533537	+	0.845777i	$0.320863\pi$
$180$	43.1077	−	9.83905i	0.239487	−	0.0546614i
$181$	57.3357	−	27.6114i	0.316772	−	0.152549i	−0.268741	−	0.963213i	$-0.586607\pi$
$181$	57.3357	−	27.6114i	0.316772	−	0.152549i	0.585513	+	0.810663i	$0.300893\pi$
$182$	−4.05541	−	35.9928i	−0.0222825	−	0.197763i
$183$	242.525	+	193.407i	1.32527	+	1.05687i
$184$	22.7886	−	7.97407i	0.123851	−	0.0433374i
$185$	44.2849	−	393.040i	0.239378	−	2.12454i
$186$	−167.399	+	167.399i	−0.899993	+	0.899993i
$187$	86.7443	−	69.1763i	0.463873	−	0.369927i
$188$	25.3079	−	40.2773i	0.134617	−	0.214241i
$189$	188.953	+	118.727i	0.999752	+	0.628186i
$190$	140.103	+	175.684i	0.737386	+	0.924653i
$191$	−47.6428	−	47.6428i	−0.249439	−	0.249439i	0.571301	−	0.820740i	$-0.306439\pi$
$191$	−47.6428	−	47.6428i	−0.249439	−	0.249439i	−0.820740	+	0.571301i	$0.806439\pi$
$192$	27.7225	+	3.12358i	0.144388	+	0.0162686i
$193$	−77.3978	−	221.190i	−0.401025	−	1.14606i	−0.950546	−	0.310583i	$-0.899476\pi$
$193$	−77.3978	−	221.190i	−0.401025	−	1.14606i	0.549521	−	0.835480i	$-0.314810\pi$
$194$	−59.7637	+	74.9413i	−0.308060	+	0.386296i
$195$	56.6434	−	6.38218i	0.290479	−	0.0327291i
$196$	−61.7028	−	128.127i	−0.314810	−	0.653710i
$197$	0.396399	+	1.73674i	0.00201218	+	0.00881592i	0.975924	−	0.218111i	$-0.0699894\pi$
$197$	0.396399	+	1.73674i	0.00201218	+	0.00881592i	−0.973912	+	0.226927i	$0.927132\pi$
$198$	−4.31887	+	18.9222i	−0.0218125	+	0.0955666i
$199$	139.072	+	66.9735i	0.698853	+	0.336550i	0.749350	−	0.662174i	$-0.230366\pi$
$199$	139.072	+	66.9735i	0.698853	+	0.336550i	−0.0504966	+	0.998724i	$0.516080\pi$
$200$	−22.3463	+	63.8621i	−0.111732	+	0.319311i
$201$	−38.4209	−	61.1466i	−0.191149	−	0.304212i
$202$			60.5902i			0.299951i
$203$	18.6020	+	317.273i	0.0916354	+	1.56292i
$204$	−178.222			−0.873635
$205$	124.433	−	78.1864i	0.606990	−	0.381397i
$206$	−66.0894	−	23.1257i	−0.320822	−	0.112261i
$207$	11.7066	−	24.3091i	0.0565538	−	0.117435i
$208$	9.11363	+	2.08013i	0.0438155	+	0.0100006i
$209$	−96.1631	+	21.9486i	−0.460110	+	0.105017i
$210$	340.593	−	164.021i	1.62187	−	0.781052i
$211$	−6.37200	−	56.5530i	−0.0301990	−	0.268024i	−0.999734	−	0.0230703i	$-0.992656\pi$
$211$	−6.37200	−	56.5530i	−0.0301990	−	0.268024i	0.969535	−	0.244954i	$-0.0787727\pi$
$212$	114.476	+	91.2916i	0.539982	+	0.430621i
$213$	207.049	−	72.4494i	0.972059	−	0.340138i
$214$	24.1098	−	213.980i	0.112662	−	0.999906i
$215$	−288.353	+	288.353i	−1.34118	+	1.34118i
$216$	−45.0287	+	35.9092i	−0.208466	+	0.166246i
$217$	−279.891	+	445.444i	−1.28982	+	2.05274i
$218$	22.5011	+	14.1384i	0.103216	+	0.0648551i
$219$	−110.846	−	138.996i	−0.506145	−	0.634685i
$220$	−42.9479	−	42.9479i	−0.195218	−	0.195218i
$221$	−59.3428	−	6.68633i	−0.268519	−	0.0302549i
$222$	−92.1098	−	263.235i	−0.414909	−	1.18574i
$223$	42.8782	−	53.7675i	0.192279	−	0.241110i	−0.676342	−	0.736588i	$-0.736436\pi$
$223$	42.8782	−	53.7675i	0.192279	−	0.241110i	0.868620	+	0.495478i	$0.165007\pi$
$224$	61.6051	−	6.94122i	0.275023	−	0.0309876i
$225$	32.8063	+	68.1231i	0.145806	+	0.302769i
$226$	18.1709	+	79.6118i	0.0804021	+	0.352265i
$227$	58.2395	−	255.164i	0.256562	−	1.12407i	−0.668338	−	0.743858i	$-0.732994\pi$
$227$	58.2395	−	255.164i	0.256562	−	1.12407i	0.924899	−	0.380212i	$-0.124149\pi$
$228$	142.751	+	68.7451i	0.626100	+	0.301514i
$229$	99.7341	−	285.024i	0.435520	−	1.24464i	−0.491909	−	0.870646i	$-0.663701\pi$
$229$	99.7341	−	285.024i	0.435520	−	1.24464i	0.927429	−	0.373998i	$-0.122013\pi$
$230$	44.9216	+	71.4923i	0.195311	+	0.310836i
$231$			165.937i			0.718340i
$232$	−78.8744	−	22.5130i	−0.339976	−	0.0970388i
$233$	95.0825			0.408080			0.204040	−	0.978963i	$-0.434593\pi$
$233$	95.0825			0.408080			0.204040	+	0.978963i	$0.434593\pi$
$234$	8.84546	−	5.55797i	0.0378011	−	0.0237520i
$235$	157.020	+	54.9436i	0.668170	+	0.233803i
$236$	−51.7170	+	107.391i	−0.219140	+	0.455049i
$237$	−417.149	−	95.2116i	−1.76012	−	0.401737i
$238$	−386.115	+	88.1282i	−1.62233	+	0.370287i
$239$	−236.272	+	113.782i	−0.988584	+	0.476077i	−0.857049	−	0.515235i	$-0.827705\pi$
$239$	−236.272	+	113.782i	−0.988584	+	0.476077i	−0.131535	+	0.991312i	$0.541991\pi$
$240$	10.9237	+	96.9506i	0.0455155	+	0.403961i
$241$	−245.324	−	195.639i	−1.01794	−	0.811782i	−0.0356928	−	0.999363i	$-0.511364\pi$
$241$	−245.324	−	195.639i	−1.01794	−	0.811782i	−0.982249	+	0.187581i	$0.939935\pi$
$242$	−136.352	+	47.7118i	−0.563440	+	0.197156i
$243$	−18.3137	+	162.538i	−0.0753649	+	0.668882i
$244$	−125.799	+	125.799i	−0.515569	+	0.515569i
$245$	388.832	−	310.083i	1.58707	−	1.26565i
$246$	55.1291	−	87.7374i	0.224102	−	0.356656i
$247$	44.9529	+	28.2458i	0.181995	+	0.114355i
$248$	−84.6534	−	106.152i	−0.341344	−	0.428032i
$249$	64.5030	+	64.5030i	0.259048	+	0.259048i
$250$	10.6055	+	1.19495i	0.0424220	+	0.00477981i
$251$	121.974	+	348.583i	0.485954	+	1.38878i	0.882305	+	0.470677i	$0.155990\pi$
$251$	121.974	+	348.583i	0.485954	+	1.38878i	−0.396351	+	0.918099i	$0.629724\pi$
$252$	43.1961	−	54.1662i	0.171413	−	0.214945i
$253$	−36.8294	+	4.14967i	−0.145571	+	0.0164019i
$254$	−65.7156	−	136.460i	−0.258723	−	0.537244i
$255$	−138.691	−	607.646i	−0.543887	−	2.38293i
$256$	−3.56033	+	15.5988i	−0.0139076	+	0.0609330i
$257$	86.6784	+	41.7421i	0.337270	+	0.162421i	0.594851	−	0.803836i	$-0.297211\pi$
$257$	86.6784	+	41.7421i	0.337270	+	0.162421i	−0.257581	+	0.966257i	$0.582925\pi$
$258$	−94.9664	+	271.398i	−0.368087	+	1.05193i
$259$	−329.721	−	524.748i	−1.27305	−	2.02605i
$260$			32.6917i			0.125737i
$261$	−80.1177	+	44.5375i	−0.306964	+	0.170642i
$262$	63.3868			0.241934
$263$	−236.506	+	148.607i	−0.899264	+	0.565045i	−0.900453	−	0.434954i	$-0.856765\pi$
$263$	−236.506	+	148.607i	−0.899264	+	0.565045i	0.00118852	+	0.999999i	$0.499622\pi$
$264$	−40.4226	−	14.1445i	−0.153116	−	0.0535776i
$265$	−222.174	+	461.349i	−0.838392	+	1.74094i
$266$	343.261	+	78.3471i	1.29046	+	0.294538i
$267$	93.6127	−	21.3665i	0.350609	−	0.0800243i
$268$	37.3154	−	17.9701i	0.139236	−	0.0670528i
$269$	36.4730	+	323.707i	0.135587	+	1.20337i	0.858640	+	0.512579i	$0.171310\pi$
$269$	36.4730	+	323.707i	0.135587	+	1.20337i	−0.723053	+	0.690793i	$0.757262\pi$
$270$	−157.473	−	125.581i	−0.583235	−	0.465114i
$271$	370.224	−	129.547i	1.36614	−	0.478033i	0.455133	−	0.890423i	$-0.349592\pi$
$271$	370.224	−	129.547i	1.36614	−	0.478033i	0.911007	+	0.412390i	$0.135306\pi$
$272$	11.4443	−	101.571i	0.0420746	−	0.373422i
$273$	63.1549	−	63.1549i	0.231337	−	0.231337i
$274$	80.6161	−	64.2892i	0.294219	−	0.234632i
$275$	55.2583	−	87.9430i	0.200939	−	0.319793i
$276$	50.4090	+	31.6741i	0.182641	+	0.114761i
$277$	281.328	+	352.775i	1.01563	+	1.27355i	0.961437	+	0.275024i	$0.0886856\pi$
$277$	281.328	+	352.775i	1.01563	+	1.27355i	0.0541881	+	0.998531i	$0.482743\pi$
$278$	94.8603	+	94.8603i	0.341224	+	0.341224i
$279$	−150.777	−	16.9885i	−0.540419	−	0.0608906i
$280$	71.6069	+	204.641i	0.255739	+	0.730860i
$281$	90.7393	−	113.783i	0.322916	−	0.404923i	−0.593704	−	0.804683i	$-0.702335\pi$
$281$	90.7393	−	113.783i	0.322916	−	0.404923i	0.916620	+	0.399760i	$0.130907\pi$
$282$	116.559	−	13.1331i	0.413330	−	0.0465711i
$283$	−114.731	−	238.242i	−0.405411	−	0.841844i	−0.999304	−	0.0373001i	$-0.988124\pi$
$283$	−114.731	−	238.242i	−0.405411	−	0.841844i	0.593894	−	0.804544i	$-0.297590\pi$
$284$	27.9945	+	122.652i	0.0985722	+	0.431873i
$285$	−123.298	+	540.205i	−0.432626	+	1.89546i
$286$	−12.9289	−	6.22625i	−0.0452061	−	0.0217701i
$287$	76.0515	−	217.343i	0.264988	−	0.757291i
$288$	9.51299	+	15.1398i	0.0330312	+	0.0525689i
$289$			363.975i			1.25943i
$290$	15.3783	−	286.441i	0.0530287	−	0.987729i
$291$	−236.361			−0.812236
$292$	86.3335	−	54.2469i	0.295663	−	0.185777i
$293$	196.687	+	68.8236i	0.671286	+	0.234893i	0.644334	−	0.764744i	$-0.277134\pi$
$293$	196.687	+	68.8236i	0.671286	+	0.234893i	0.0269510	+	0.999637i	$0.491420\pi$
$294$	152.150	−	315.942i	0.517517	−	1.07463i
$295$	−406.397	−	92.7574i	−1.37762	−	0.314432i
$296$	155.936	−	35.5913i	0.526809	−	0.120241i
$297$	79.6564	−	38.3605i	0.268203	−	0.129160i
$298$	−26.5089	−	235.273i	−0.0889559	−	0.789506i
$299$	15.5965	+	12.4378i	0.0521621	+	0.0415979i
$300$	−157.475	+	55.1027i	−0.524915	+	0.183676i
$301$	−71.5407	+	634.941i	−0.237677	+	2.10944i
$302$	14.1317	−	14.1317i	0.0467938	−	0.0467938i
$303$	−116.811	+	93.1534i	−0.385514	+	0.307437i
$304$	−48.3453	+	76.9411i	−0.159031	+	0.253096i
$305$	−526.807	−	331.015i	−1.72724	−	1.08529i
$306$	−71.2192	−	89.3061i	−0.232743	−	0.291850i
$307$	−140.888	−	140.888i	−0.458919	−	0.458919i	0.439382	−	0.898301i	$-0.355198\pi$
$307$	−140.888	−	140.888i	−0.458919	−	0.458919i	−0.898301	+	0.439382i	$0.855198\pi$
$308$	−94.5694	−	10.6554i	−0.307044	−	0.0345955i
$309$	−57.0245	−	162.967i	−0.184545	−	0.527400i
$310$	296.048	−	371.233i	0.954994	−	1.19752i
$311$	101.771	−	11.4669i	0.327239	−	0.0368709i	0.0531830	−	0.998585i	$-0.483063\pi$
$311$	101.771	−	11.4669i	0.327239	−	0.0368709i	0.274056	+	0.961714i	$0.411635\pi$
$312$	10.0014	+	20.7681i	0.0320557	+	0.0665643i
$313$	0.174066	+	0.762631i	0.000556120	+	0.00243652i	0.975205	−	0.221302i	$-0.0710308\pi$
$313$	0.174066	+	0.762631i	0.000556120	+	0.00243652i	−0.974649	+	0.223739i	$0.928174\pi$
$314$	−15.1067	+	66.1867i	−0.0481105	+	0.210786i
$315$	218.295	+	105.125i	0.692999	+	0.333731i
$316$	81.0491	−	231.625i	0.256484	−	0.732990i
$317$	231.247	+	368.028i	0.729487	+	1.16097i	0.981167	+	0.193162i	$0.0618742\pi$
$317$	231.247	+	368.028i	0.729487	+	1.16097i	−0.251680	+	0.967811i	$0.580983\pi$
$318$			361.051i			1.13538i
$319$	110.353	+	60.6357i	0.345936	+	0.190081i
$320$	−55.9549			−0.174859
$321$	449.595	−	282.499i	1.40061	−	0.880060i
$322$	124.873	+	43.6949i	0.387804	+	0.135699i
$323$	251.871	−	523.016i	0.779786	−	1.61924i
$324$	−193.926	−	44.2624i	−0.598538	−	0.136612i
$325$	−54.5019	+	12.4397i	−0.167698	+	0.0382760i
$326$	89.5477	−	43.1239i	0.274686	−	0.132282i
$327$	7.33685	+	65.1164i	0.0224369	+	0.199133i
$328$	46.4626	+	37.0527i	0.141654	+	0.112966i
$329$	246.030	−	86.0896i	0.747811	−	0.261670i
$330$	16.7689	−	148.828i	0.0508148	−	0.450994i
$331$	175.607	−	175.607i	0.530535	−	0.530535i	−0.390196	−	0.920732i	$-0.627593\pi$
$331$	175.607	−	175.607i	0.530535	−	0.530535i	0.920732	+	0.390196i	$0.127593\pi$
$332$	−40.9031	+	32.6191i	−0.123202	+	0.0982503i
$333$	95.0977	−	151.347i	0.285579	−	0.454496i
$334$	191.330	+	120.221i	0.572844	+	0.359942i
$335$	90.3078	+	113.242i	0.269575	+	0.338037i
$336$	108.096	+	108.096i	0.321713	+	0.321713i
$337$	457.979	+	51.6019i	1.35899	+	0.153121i	0.761192	−	0.648526i	$-0.224614\pi$
$337$	457.979	+	51.6019i	1.35899	+	0.153121i	0.597797	+	0.801647i	$0.296043\pi$
$338$	−76.3864	−	218.300i	−0.225995	−	0.645857i
$339$	−125.546	+	157.429i	−0.370341	+	0.464393i
$340$	355.211	−	40.0227i	1.04474	−	0.117714i
$341$	90.4321	+	187.784i	0.265197	+	0.550687i
$342$	22.5968	+	99.0030i	0.0660725	+	0.289482i
$343$	53.9071	−	236.182i	0.157163	−	0.688578i
$344$	−148.575	−	71.5501i	−0.431905	−	0.207995i
$345$	−68.7646	+	196.518i	−0.199318	+	0.569617i
$346$	230.885	+	367.452i	0.667298	+	1.06200i
$347$			3.47983i			0.0100283i	0.999987	+	0.00501416i	$0.00159606\pi$
$347$			3.47983i			0.0100283i	−0.999987	+	0.00501416i	$0.998404\pi$
$348$	−77.8617	−	186.673i	−0.223741	−	0.536416i
$349$	−313.072			−0.897055			−0.448528	−	0.893769i	$-0.648051\pi$
$349$	−313.072			−0.897055			−0.448528	+	0.893769i	$0.648051\pi$
$350$	−313.919	+	197.248i	−0.896912	+	0.563567i
$351$	−44.9168	−	15.7171i	−0.127968	−	0.0447780i
$352$	10.6568	−	22.1291i	0.0302751	−	0.0628668i
$353$	24.9449	+	5.69351i	0.0706654	+	0.0161289i	0.257707	−	0.966223i	$-0.417033\pi$
$353$	24.9449	+	5.69351i	0.0706654	+	0.0161289i	−0.187042	+	0.982352i	$0.559890\pi$
$354$	−286.549	+	65.4030i	−0.809462	+	0.184754i
$355$	−396.396	+	190.894i	−1.11661	+	0.537731i
$356$	6.16581	+	54.7231i	0.0173197	+	0.153717i
$357$	−763.527	−	608.893i	−2.13873	−	1.70558i
$358$	−338.511	+	118.450i	−0.945560	+	0.330866i
$359$	38.1983	−	339.019i	0.106402	−	0.944344i	−0.821166	−	0.570689i	$-0.806676\pi$
$359$	38.1983	−	339.019i	0.106402	−	0.944344i	0.927568	−	0.373654i	$-0.121895\pi$
$360$	−44.2163	+	44.2163i	−0.122823	+	0.122823i
$361$	−121.243	+	96.6877i	−0.335852	+	0.267833i
$362$	−47.8816	+	76.2031i	−0.132270	+	0.210506i
$363$	−301.615	−	189.518i	−0.830897	−	0.522087i
$364$	31.9374	+	40.0482i	0.0877401	+	0.110023i
$365$	252.139	+	252.139i	0.690792	+	0.690792i
$366$	−435.933	−	49.1178i	−1.19107	−	0.134202i
$367$	0.200501	+	0.572999i	0.000546325	+	0.00156131i	0.944156	−	0.329498i	$-0.106880\pi$
$367$	0.200501	+	0.572999i	0.000546325	+	0.00156131i	−0.943610	+	0.331060i	$0.892594\pi$
$368$	−21.2884	+	26.6948i	−0.0578490	+	0.0725403i
$369$	65.9950	−	7.43585i	0.178848	−	0.0201513i
$370$	242.697	+	503.965i	0.655937	+	1.36207i
$371$	178.535	+	782.213i	0.481226	+	2.10839i
$372$	74.4994	−	326.403i	0.200267	−	0.877428i
$373$	−63.6077	−	30.6319i	−0.170530	−	0.0821229i	0.346671	−	0.937987i	$-0.387312\pi$
$373$	−63.6077	−	30.6319i	−0.170530	−	0.0821229i	−0.517201	+	0.855864i	$0.673026\pi$
$374$	−51.8231	+	148.102i	−0.138565	+	0.395995i
$375$	14.0015	+	22.2833i	0.0373374	+	0.0594221i
$376$			67.2719i			0.178915i
$377$	−18.9224	−	65.0779i	−0.0501920	−	0.172620i
$378$	−315.593			−0.834902
$379$	−195.030	+	122.546i	−0.514591	+	0.323339i	−0.764170	−	0.645015i	$-0.776851\pi$
$379$	−195.030	+	122.546i	−0.514591	+	0.323339i	0.249578	+	0.968355i	$0.419708\pi$
$380$	−299.953	−	104.958i	−0.789349	−	0.276205i
$381$	162.045	−	336.490i	0.425315	−	0.883176i
$382$	92.8966	+	21.2031i	0.243185	+	0.0555054i
$383$	230.021	−	52.5009i	0.600578	−	0.137078i	0.0885864	−	0.996069i	$-0.471765\pi$
$383$	230.021	−	52.5009i	0.600578	−	0.137078i	0.511991	+	0.858991i	$0.328908\pi$
$384$	−35.5465	+	17.1183i	−0.0925690	+	0.0445789i
$385$	−37.2639	−	330.726i	−0.0967894	−	0.859029i
$386$	259.105	+	206.629i	0.671256	+	0.535309i
$387$	−173.946	+	60.8664i	−0.449473	+	0.157277i
$388$	15.1776	−	134.705i	0.0391176	−	0.347178i
$389$	177.953	−	177.953i	0.457463	−	0.457463i	−0.440359	−	0.897822i	$-0.645149\pi$
$389$	177.953	−	177.953i	0.457463	−	0.457463i	0.897822	+	0.440359i	$0.145149\pi$
$390$	−63.0256	+	50.2612i	−0.161604	+	0.128875i
$391$	116.049	−	184.691i	0.296800	−	0.472354i
$392$	170.290	+	107.000i	0.434412	+	0.272959i
$393$	97.4530	+	122.202i	0.247972	+	0.310947i
$394$	−1.78140	−	1.78140i	−0.00452132	−	0.00452132i
$395$	852.797	+	96.0871i	2.15898	+	0.243259i
$396$	−9.06556	−	25.9079i	−0.0228928	−	0.0654240i
$397$	4.80752	−	6.02844i	0.0121096	−	0.0151850i	−0.775740	−	0.631053i	$-0.782623\pi$
$397$	4.80752	−	6.02844i	0.0121096	−	0.0151850i	0.787849	+	0.615868i	$0.211195\pi$
$398$	−216.923	+	24.4413i	−0.545032	+	0.0614103i
$399$	376.697	+	782.220i	0.944104	+	1.96045i
$400$	−21.2917	−	93.2851i	−0.0532293	−	0.233213i
$401$	92.0482	−	403.290i	0.229547	−	1.00571i	−0.720464	−	0.693492i	$-0.756071\pi$
$401$	92.0482	−	403.290i	0.229547	−	1.00571i	0.950011	−	0.312218i	$-0.101072\pi$
$402$	92.0142	+	44.3117i	0.228891	+	0.110228i
$403$	37.0519	−	105.888i	0.0919401	−	0.262750i
$404$	−45.5885	−	72.5536i	−0.112843	−	0.179588i
$405$		−	695.636i		−	1.71762i
$406$	−260.994	−	365.922i	−0.642842	−	0.901287i
$407$	−245.531			−0.603271
$408$	213.411	−	134.095i	0.523067	−	0.328665i
$409$	−749.188	−	262.152i	−1.83176	−	0.640959i	−0.995735	−	0.0922622i	$-0.970590\pi$
$409$	−749.188	−	262.152i	−1.83176	−	0.640959i	−0.836021	−	0.548697i	$-0.815124\pi$
$410$	−90.1741	+	187.249i	−0.219937	+	0.456704i
$411$	247.884	+	56.5779i	0.603124	+	0.137659i
$412$	96.5385	−	22.0343i	0.234317	−	0.0534813i
$413$	−588.465	+	283.390i	−1.42486	+	0.686174i
$414$	4.27222	+	37.9170i	0.0103194	+	0.0915870i
$415$	−143.045	−	114.075i	−0.344687	−	0.274879i
$416$	−12.4782	+	4.36632i	−0.0299957	+	0.0104960i
$417$	−37.0380	+	328.721i	−0.0888200	+	0.788300i
$418$	98.6361	−	98.6361i	0.235971	−	0.235971i
$419$	−91.2090	+	72.7367i	−0.217682	+	0.173596i	−0.726260	−	0.687420i	$-0.758743\pi$
$419$	−91.2090	+	72.7367i	−0.217682	+	0.173596i	0.508577	+	0.861016i	$0.330172\pi$
$420$	−284.432	+	452.671i	−0.677219	+	1.07779i
$421$	−100.969	−	63.4430i	−0.239831	−	0.150696i	0.406754	−	0.913538i	$-0.366661\pi$
$421$	−100.969	−	63.4430i	−0.239831	−	0.150696i	−0.646585	+	0.762842i	$0.723803\pi$
$422$	50.1810	+	62.9250i	0.118912	+	0.149111i
$423$	53.1591	+	53.1591i	0.125672	+	0.125672i
$424$	−205.768	−	23.1845i	−0.485301	−	0.0546803i
$425$	201.887	+	576.961i	0.475029	+	1.35756i
$426$	−193.419	+	242.539i	−0.454034	+	0.569341i
$427$	−968.731	+	109.150i	−2.26869	+	0.255620i
$428$	132.130	+	274.370i	0.308715	+	0.641052i
$429$	−7.87393	−	34.4979i	−0.0183541	−	0.0804147i
$430$	128.329	−	562.247i	0.298440	−	1.30755i
$431$	−173.697	−	83.6480i	−0.403009	−	0.194079i	0.221388	−	0.975186i	$-0.428941\pi$
$431$	−173.697	−	83.6480i	−0.403009	−	0.194079i	−0.624398	+	0.781107i	$0.714655\pi$
$432$	26.9012	−	76.8793i	0.0622714	−	0.177961i
$433$	86.1211	+	137.061i	0.198894	+	0.316538i	0.931248	−	0.364386i	$-0.118721\pi$
$433$	86.1211	+	137.061i	0.198894	+	0.316538i	−0.732354	+	0.680924i	$0.761578\pi$
$434$		−	743.988i		−	1.71426i
$435$	575.868	−	410.737i	1.32383	−	0.944223i
$436$	−37.5818			−0.0861968
$437$	−164.192	+	103.169i	−0.375726	+	0.236084i
$438$	237.314	+	83.0396i	0.541812	+	0.189588i
$439$	194.417	−	403.710i	0.442862	−	0.919613i	−0.553374	−	0.832933i	$-0.686660\pi$
$439$	194.417	−	403.710i	0.442862	−	0.919613i	0.996236	−	0.0866801i	$-0.0276258\pi$
$440$	83.7423	+	19.1136i	0.190323	+	0.0434401i
$441$	219.118	−	50.0123i	0.496866	−	0.113407i
$442$	76.0908	−	36.6434i	0.172151	−	0.0829036i
$443$	7.62376	+	67.6627i	0.0172094	+	0.152737i	0.999378	−	0.0352646i	$-0.0112274\pi$
$443$	7.62376	+	67.6627i	0.0172094	+	0.152737i	−0.982169	+	0.188002i	$0.939799\pi$
$444$	308.356	+	245.906i	0.694496	+	0.553842i
$445$	−181.780	+	63.6076i	−0.408495	+	0.142938i
$446$	−10.8894	+	96.6457i	−0.0244156	+	0.216694i
$447$	412.822	−	412.822i	0.923539	−	0.923539i
$448$	−68.5463	+	54.6638i	−0.153005	+	0.122018i
$449$	−147.707	+	235.074i	−0.328969	+	0.523551i	−0.969727	−	0.244192i	$-0.921477\pi$
$449$	−147.707	+	235.074i	−0.328969	+	0.523551i	0.640758	+	0.767743i	$0.278620\pi$
$450$	−90.5402	−	56.8902i	−0.201200	−	0.126423i
$451$	−56.8793	−	71.3244i	−0.126118	−	0.158147i
$452$	−81.6592	−	81.6592i	−0.180662	−	0.180662i
$453$	48.9709	+	5.51769i	0.108103	+	0.0121803i
$454$	122.248	+	349.366i	0.269269	+	0.769528i
$455$	−111.691	+	140.056i	−0.245474	+	0.307815i
$456$	−222.661	+	25.0879i	−0.488292	+	0.0550172i
$457$	−140.306	−	291.348i	−0.307015	−	0.637523i	0.689188	−	0.724582i	$-0.257967\pi$
$457$	−140.306	−	291.348i	−0.307015	−	0.637523i	−0.996203	+	0.0870596i	$0.972253\pi$
$458$	95.0273	+	416.342i	0.207483	+	0.909043i
$459$	−115.785	+	507.285i	−0.252254	+	1.10520i
$460$	−107.583	−	51.8090i	−0.233875	−	0.112628i
$461$	182.662	−	522.017i	0.396229	−	1.13236i	−0.557106	−	0.830442i	$-0.688088\pi$
$461$	182.662	−	522.017i	0.396229	−	1.13236i	0.953335	−	0.301916i	$-0.0976261\pi$
$462$	−124.852	−	198.701i	−0.270242	−	0.430088i
$463$			530.379i			1.14553i	0.819721	+	0.572763i	$0.194129\pi$
$463$			530.379i			1.14553i	−0.819721	+	0.572763i	$0.805871\pi$
$464$	111.387	−	32.3875i	0.240058	−	0.0698006i
$465$	1170.85			2.51795
$466$	−113.856	+	71.5408i	−0.244327	+	0.153521i
$467$	244.347	+	85.5005i	0.523226	+	0.183085i	0.578952	−	0.815361i	$-0.303462\pi$
$467$	244.347	+	85.5005i	0.523226	+	0.183085i	−0.0557264	+	0.998446i	$0.517747\pi$
$468$	−6.41013	+	13.3108i	−0.0136969	+	0.0284418i
$469$	221.259	+	50.5010i	0.471768	+	0.107678i
$470$	−229.363	+	52.3507i	−0.488007	+	0.111384i
$471$	−150.826	+	72.6338i	−0.320224	+	0.154212i
$472$	−18.8736	−	167.508i	−0.0399865	−	0.354890i
$473$	197.918	+	157.834i	0.418431	+	0.333687i
$474$	571.153	−	199.855i	1.20496	−	0.421635i
$475$	60.8438	−	540.004i	0.128092	−	1.13685i
$476$	396.045	−	396.045i	0.832027	−	0.832027i
$477$	−180.921	+	144.280i	−0.379290	+	0.302473i
$478$	197.312	−	314.021i	0.412788	−	0.656948i
$479$	−492.713	−	309.592i	−1.02863	−	0.646331i	−0.0916773	−	0.995789i	$-0.529223\pi$
$479$	−492.713	−	309.592i	−1.02863	−	0.646331i	−0.936952	+	0.349458i	$0.886366\pi$
$480$	−86.0269	−	107.874i	−0.179223	−	0.224738i
$481$	93.4484	+	93.4484i	0.194279	+	0.194279i
$482$	440.963	+	49.6846i	0.914862	+	0.103080i
$483$	107.745	+	307.918i	0.223075	+	0.637512i
$484$	127.376	−	159.725i	0.263174	−	0.330010i
$485$	471.088	−	53.0788i	0.971315	−	0.109441i
$486$	−100.365	−	208.411i	−0.206513	−	0.428829i
$487$	49.1298	+	215.252i	0.100883	+	0.441995i	0.999991	+	0.00426924i	$0.00135895\pi$
$487$	49.1298	+	215.252i	0.100883	+	0.441995i	−0.899108	+	0.437726i	$0.855784\pi$
$488$	55.9858	−	245.290i	0.114725	−	0.502643i
$489$	220.811	+	106.337i	0.451557	+	0.217459i
$490$	−232.298	+	663.869i	−0.474077	+	1.35483i
$491$	−190.681	−	303.466i	−0.388351	−	0.618058i	0.594141	−	0.804361i	$-0.297492\pi$
$491$	−190.681	−	303.466i	−0.388351	−	0.618058i	−0.982492	+	0.186303i	$0.940349\pi$
$492$			146.541i			0.297847i
$493$	−683.938	+	285.273i	−1.38730	+	0.578647i
$494$	−75.0811			−0.151986
$495$	81.2781	−	51.0704i	0.164198	−	0.103173i
$496$	181.238	+	63.4178i	0.365398	+	0.127858i
$497$	−299.107	+	621.101i	−0.601824	+	1.24970i
$498$	−125.771	−	28.7065i	−0.252553	−	0.0576436i
$499$	382.895	−	87.3933i	0.767325	−	0.175137i	0.179096	−	0.983832i	$-0.442683\pi$
$499$	382.895	−	87.3933i	0.767325	−	0.175137i	0.588229	+	0.808695i	$0.299825\pi$
$500$	−13.5986	+	6.54875i	−0.0271973	+	0.0130975i
$501$	62.3862	+	553.693i	0.124523	+	1.10517i
$502$	−408.334	−	325.636i	−0.813415	−	0.648677i
$503$	−54.0856	+	18.9254i	−0.107526	+	0.0376250i	−0.383506	−	0.923538i	$-0.625283\pi$
$503$	−54.0856	+	18.9254i	−0.107526	+	0.0376250i	0.275980	+	0.961163i	$0.410998\pi$
$504$	−10.9701	+	97.3623i	−0.0217661	+	0.193179i
$505$	211.895	−	211.895i	0.419593	−	0.419593i
$506$	40.9790	−	32.6797i	0.0809862	−	0.0645844i
$507$	303.417	−	482.885i	0.598455	−	0.952436i
$508$	181.364	+	113.959i	0.357017	+	0.224328i
$509$	−544.158	−	682.353i	−1.06907	−	1.34057i	−0.936998	−	0.349335i	$-0.886408\pi$
$509$	−544.158	−	682.353i	−1.06907	−	1.34057i	−0.132075	−	0.991240i	$-0.542164\pi$
$510$	623.273	+	623.273i	1.22210	+	1.22210i
$511$	555.199	+	62.5559i	1.08650	+	0.122419i
$512$	−7.47336	−	21.3576i	−0.0145964	−	0.0417141i
$513$	288.415	−	361.660i	0.562212	−	0.704991i
$514$	−135.200	+	15.2334i	−0.263035	+	0.0296369i
$515$	150.252	+	312.001i	0.291751	+	0.605827i
$516$	−90.4846	−	396.439i	−0.175358	−	0.768293i
$517$	22.9794	−	100.679i	0.0444476	−	0.194738i
$518$	789.648	+	380.274i	1.52442	+	0.734120i
$519$	−353.432	+	1010.05i	−0.680987	+	1.94615i
$520$	−24.5974	−	39.1466i	−0.0473027	−	0.0752819i
$521$		−	88.6758i		−	0.170203i	−0.996372	−	0.0851015i	$-0.972879\pi$
$521$		−	88.6758i		−	0.170203i	0.996372	−	0.0851015i	$-0.0271215\pi$
$522$	62.4265	−	113.612i	0.119591	−	0.217648i
$523$	623.415			1.19200			0.596000	−	0.802985i	$-0.296756\pi$
$523$	623.415			1.19200			0.596000	+	0.802985i	$0.296756\pi$
$524$	−75.9025	+	47.6927i	−0.144852	+	0.0910166i
$525$	−862.901	−	301.942i	−1.64362	−	0.575128i
$526$	171.392	−	355.898i	0.325839	−	0.676613i
$527$	−1195.89	−	272.954i	−2.26924	−	0.517939i
$528$	59.0465	−	13.4770i	0.111830	−	0.0255246i
$529$	410.965	−	197.910i	0.776872	−	0.374122i
$530$	−81.0802	−	719.606i	−0.152981	−	1.35775i
$531$	−147.281	−	117.453i	−0.277366	−	0.221192i
$532$	−469.987	+	164.455i	−0.883434	+	0.309127i
$533$	−5.49775	+	48.7939i	−0.0103147	+	0.0915458i
$534$	−96.0201	+	96.0201i	−0.179813	+	0.179813i
$535$	−832.642	+	664.010i	−1.55634	+	1.24114i
$536$	−31.1624	+	49.5947i	−0.0581388	+	0.0925274i
$537$	−748.795	−	470.499i	−1.39440	−	0.876162i
$538$	−287.234	−	360.180i	−0.533892	−	0.669479i
$539$	−218.306	−	218.306i	−0.405020	−	0.405020i
$540$	283.054	+	31.8926i	0.524175	+	0.0590603i
$541$	303.637	+	867.743i	0.561251	+	1.60396i	0.778362	+	0.627815i	$0.216051\pi$
$541$	303.637	+	867.743i	0.561251	+	1.60396i	−0.217112	+	0.976147i	$0.569664\pi$
$542$	−345.852	+	433.685i	−0.638104	+	0.800157i
$543$	−220.525	+	24.8472i	−0.406124	+	0.0457592i
$544$	62.7187	+	130.237i	0.115292	+	0.239406i
$545$	−29.2460	−	128.135i	−0.0536624	−	0.235110i
$546$	−28.1066	+	123.143i	−0.0514772	+	0.225536i
$547$	−634.138	−	305.385i	−1.15930	−	0.558290i	−0.247486	−	0.968891i	$-0.579605\pi$
$547$	−634.138	−	305.385i	−1.15930	−	0.558290i	−0.911815	+	0.410601i	$0.865319\pi$
$548$	−48.1620	+	137.639i	−0.0878869	+	0.251166i
$549$	−149.591	−	238.072i	−0.272478	−	0.433647i
$550$			146.884i			0.267062i
$551$	657.854	+	35.3185i	1.19393	+	0.0640989i
$552$	−84.1940			−0.152525
$553$	1138.57	−	715.411i	2.05890	−	1.29369i
$554$	−602.306	−	210.756i	−1.08720	−	0.380426i
$555$	−598.454	+	1242.70i	−1.07830	+	2.23910i
$556$	−184.964	−	42.2168i	−0.332669	−	0.0759295i
$557$	−768.058	+	175.304i	−1.37892	+	0.314729i	−0.846787	−	0.531932i	$-0.821466\pi$
$557$	−768.058	+	175.304i	−1.37892	+	0.314729i	−0.532133	+	0.846661i	$0.678609\pi$
$558$	193.330	−	93.1028i	0.346470	−	0.166851i
$559$	−15.2557	−	135.398i	−0.0272910	−	0.242214i
$560$	−239.719	−	191.169i	−0.428069	−	0.341374i
$561$	−365.198	+	127.788i	−0.650976	+	0.227786i
$562$	−23.0442	+	204.523i	−0.0410039	+	0.363919i
$563$	−242.660	+	242.660i	−0.431012	+	0.431012i	−0.888973	−	0.457960i	$-0.848580\pi$
$563$	−242.660	+	242.660i	−0.431012	+	0.431012i	0.457960	+	0.888973i	$0.348580\pi$
$564$	−129.692	+	103.426i	−0.229951	+	0.183380i
$565$	214.870	−	341.963i	0.380301	−	0.605245i
$566$	316.639	+	198.958i	0.559434	+	0.351516i
$567$	−679.586	−	852.173i	−1.19856	−	1.50295i
$568$	−125.806	−	125.806i	−0.221490	−	0.221490i
$569$	−114.840	−	12.9394i	−0.201828	−	0.0227405i	0.0104717	−	0.999945i	$-0.496667\pi$
$569$	−114.840	−	12.9394i	−0.201828	−	0.0227405i	−0.212300	+	0.977205i	$0.568095\pi$
$570$	−258.811	−	739.639i	−0.454054	−	1.29761i
$571$	135.645	−	170.093i	0.237557	−	0.297887i	−0.648735	−	0.761015i	$-0.724701\pi$
$571$	135.645	−	170.093i	0.237557	−	0.297887i	0.886291	+	0.463128i	$0.153273\pi$
$572$	20.1664	−	2.27221i	0.0352560	−	0.00397240i
$573$	101.945	+	211.692i	0.177915	+	0.369445i
$574$	72.4624	+	317.478i	0.126241	+	0.553098i
$575$	45.4365	−	199.070i	0.0790200	−	0.346209i
$576$	−22.7826	−	10.9715i	−0.0395532	−	0.0190478i
$577$	−175.226	+	500.768i	−0.303685	+	0.867883i	0.686376	+	0.727247i	$0.259200\pi$
$577$	−175.226	+	500.768i	−0.303685	+	0.867883i	−0.990061	+	0.140636i	$0.955085\pi$
$578$	−273.858	−	435.842i	−0.473802	−	0.754052i
$579$			817.202i			1.41140i
$580$	197.106	+	354.570i	0.339838	+	0.611327i
$581$	−286.677			−0.493421
$582$	283.030	−	177.839i	0.486306	−	0.305566i
$583$	300.033	+	104.986i	0.514637	+	0.180079i
$584$	−62.5642	+	129.916i	−0.107130	+	0.222459i
$585$	−50.3714	−	11.4969i	−0.0861049	−	0.0196529i
$586$	−287.306	+	65.5756i	−0.490283	+	0.111904i
$587$	733.992	−	353.472i	1.25041	−	0.602167i	0.312790	−	0.949822i	$-0.398736\pi$
$587$	733.992	−	353.472i	1.25041	−	0.602167i	0.937623	+	0.347655i	$0.113022\pi$
$588$	55.5256	+	492.804i	0.0944313	+	0.838101i
$589$	852.589	+	679.917i	1.44752	+	1.15436i
$590$	556.431	−	194.704i	0.943103	−	0.330006i
$591$	0.695542	−	6.17311i	0.00117689	−	0.0104452i
$592$	−159.946	+	159.946i	−0.270179	+	0.270179i
$593$	−647.491	+	516.357i	−1.09189	+	0.870753i	−0.992248	−	0.124270i	$-0.960341\pi$
$593$	−647.491	+	516.357i	−1.09189	+	0.870753i	−0.0996414	+	0.995023i	$0.531770\pi$
$594$	−66.5217	+	105.869i	−0.111989	+	0.178230i
$595$	1658.51	+	1042.11i	2.78742	+	1.75145i
$596$	208.764	+	261.782i	0.350275	+	0.439231i
$597$	−380.624	−	380.624i	−0.637561	−	0.637561i
$598$	−28.0342	−	3.15870i	−0.0468800	−	0.00528211i
$599$	−369.153	−	1054.98i	−0.616282	−	1.76123i	−0.647893	−	0.761732i	$-0.724349\pi$
$599$	−369.153	−	1054.98i	−0.616282	−	1.76123i	0.0316109	−	0.999500i	$-0.489936\pi$
$600$	147.108	−	184.468i	0.245180	−	0.307446i
$601$	−751.080	+	84.6264i	−1.24972	+	0.140809i	−0.711917	−	0.702263i	$-0.752173\pi$
$601$	−751.080	+	84.6264i	−1.24972	+	0.140809i	−0.537800	+	0.843073i	$0.680744\pi$
$602$	−392.068	−	814.137i	−0.651275	−	1.35239i
$603$	14.5654	+	63.8153i	0.0241549	+	0.105830i
$604$	−6.28921	+	27.5548i	−0.0104126	+	0.0456206i
$605$	643.706	+	309.992i	1.06398	+	0.512384i
$606$	69.7855	−	199.436i	0.115158	−	0.329102i
$607$	142.469	+	226.738i	0.234709	+	0.373538i	0.943223	−	0.332159i	$-0.107777\pi$
$607$	142.469	+	226.738i	0.234709	+	0.373538i	−0.708514	+	0.705697i	$0.750634\pi$
$608$		−	128.508i		−	0.211362i
$609$	304.194	−	1065.75i	0.499498	−	1.74999i
$610$	879.882			1.44243
$611$	−47.0641	+	29.5723i	−0.0770280	+	0.0483999i
$612$	152.476	+	53.3536i	0.249144	+	0.0871791i
$613$	314.322	−	652.697i	0.512761	−	1.06476i	−0.470474	−	0.882414i	$-0.655917\pi$
$613$	314.322	−	652.697i	0.512761	−	1.06476i	0.983235	−	0.182345i	$-0.0583686\pi$
$614$	274.712	+	62.7011i	0.447413	+	0.102119i
$615$	−499.630	+	114.037i	−0.812406	+	0.185426i
$616$	121.259	−	58.3954i	0.196849	−	0.0947977i
$617$	−5.18215	−	45.9928i	−0.00839894	−	0.0745427i	0.988814	−	0.149157i	$-0.0476560\pi$
$617$	−5.18215	−	45.9928i	−0.00839894	−	0.0745427i	−0.997212	+	0.0746143i	$0.976227\pi$
$618$	190.901	+	152.239i	0.308901	+	0.246341i
$619$	924.880	−	323.629i	1.49415	−	0.522826i	0.545216	−	0.838296i	$-0.316448\pi$
$619$	924.880	−	323.629i	1.49415	−	0.522826i	0.948936	+	0.315469i	$0.102162\pi$
$620$	−75.1845	+	667.281i	−0.121265	+	1.07626i
$621$	122.905	−	122.905i	0.197915	−	0.197915i
$622$	−113.238	+	90.3044i	−0.182055	+	0.145184i
$623$	−160.546	+	255.507i	−0.257698	+	0.410124i
$624$	−27.6022	−	17.3436i	−0.0442342	−	0.0277942i
$625$	−405.773	−	508.824i	−0.649237	−	0.814118i
$626$	−0.782244	−	0.782244i	−0.00124959	−	0.00124959i
$627$	341.805	+	38.5122i	0.545144	+	0.0614229i
$628$	−31.7099	−	90.6216i	−0.0504934	−	0.144302i
$629$	900.960	−	1129.77i	1.43237	−	1.79613i
$630$	−340.493	+	38.3644i	−0.540466	+	0.0608959i
$631$	−44.5341	−	92.4760i	−0.0705770	−	0.146555i	0.862696	−	0.505724i	$-0.168774\pi$
$631$	−44.5341	−	92.4760i	−0.0705770	−	0.146555i	−0.933273	+	0.359169i	$0.883060\pi$
$632$	77.2241	+	338.341i	0.122190	+	0.535350i
$633$	−44.1619	+	193.486i	−0.0697661	+	0.305665i
$634$	−553.814	−	266.703i	−0.873524	−	0.420667i
$635$	−247.405	+	707.044i	−0.389615	+	1.11346i
$636$	−271.657	−	432.340i	−0.427134	−	0.679780i
$637$			166.173i			0.260868i
$638$	−177.765	+	10.4225i	−0.278629	+	0.0163362i
$639$	−198.827			−0.311154
$640$	67.0031	−	42.1008i	0.104692	−	0.0657825i
$641$	124.128	+	43.4341i	0.193647	+	0.0677600i	0.425360	−	0.905024i	$-0.360147\pi$
$641$	124.128	+	43.4341i	0.193647	+	0.0677600i	−0.231713	+	0.972784i	$0.574433\pi$
$642$	−325.813	+	676.557i	−0.507496	+	1.05383i
$643$	−2.98596	−	0.681526i	−0.00464379	−	0.00105992i	0.220198	−	0.975455i	$-0.429330\pi$
$643$	−2.98596	−	0.681526i	−0.00464379	−	0.00105992i	−0.224842	+	0.974395i	$0.572187\pi$
$644$	−182.405	+	41.6328i	−0.283238	+	0.0646473i
$645$	1281.24	−	617.014i	1.98642	−	0.956611i
$646$	91.9179	+	815.794i	0.142288	+	1.26284i
$647$	673.584	+	537.166i	1.04109	+	0.830241i	0.985748	−	0.168227i	$-0.0538042\pi$
$647$	673.584	+	537.166i	1.04109	+	0.830241i	0.0553404	+	0.998468i	$0.482376\pi$
$648$	265.520	−	92.9095i	0.409753	−	0.143379i
$649$	−28.9727	+	257.140i	−0.0446421	+	0.396210i
$650$	55.9035	−	55.9035i	0.0860054	−	0.0860054i
$651$	1434.32	−	1143.83i	2.20326	−	1.75704i
$652$	−74.7821	+	119.015i	−0.114696	+	0.182538i
$653$	−312.775	−	196.530i	−0.478982	−	0.300964i	0.270816	−	0.962631i	$-0.412706\pi$
$653$	−312.775	−	196.530i	−0.478982	−	0.300964i	−0.749798	+	0.661667i	$0.769849\pi$
$654$	−57.7795	−	72.4532i	−0.0883479	−	0.110785i
$655$	−221.675	−	221.675i	−0.338435	−	0.338435i
$656$	−83.5154	−	9.40992i	−0.127310	−	0.0143444i
$657$	53.2222	+	152.100i	0.0810079	+	0.231507i
$658$	−229.834	+	288.202i	−0.349291	+	0.437998i
$659$	191.449	−	21.5711i	0.290515	−	0.0327331i	0.0344955	−	0.999405i	$-0.489018\pi$
$659$	191.449	−	21.5711i	0.290515	−	0.0327331i	0.256019	+	0.966672i	$0.417589\pi$
$660$	91.8994	+	190.831i	0.139241	+	0.289138i
$661$	159.518	+	698.895i	0.241329	+	1.05733i	0.939809	+	0.341700i	$0.111003\pi$
$661$	159.518	+	698.895i	0.241329	+	1.05733i	−0.698480	+	0.715629i	$0.746140\pi$
$662$	−78.1526	+	342.409i	−0.118055	+	0.517234i
$663$	187.629	+	90.3572i	0.283000	+	0.136285i
$664$	24.4365	−	69.8354i	0.0368019	−	0.105174i
$665$	−926.452	−	1474.44i	−1.39316	−	2.21720i
$666$			252.783i			0.379554i
$667$	244.148	+	40.8637i	0.366039	+	0.0612649i
$668$	−319.563			−0.478387
$669$	−203.063	+	127.593i	−0.303532	+	0.190722i
$670$	−193.343	−	67.6538i	−0.288572	−	0.100976i
$671$	−167.577	+	347.977i	−0.249742	+	0.518595i
$672$	−210.771	−	48.1071i	−0.313647	−	0.0715879i
$673$	−1140.39	+	260.285i	−1.69448	+	0.386754i	−0.957335	−	0.288980i	$-0.906684\pi$
$673$	−1140.39	+	260.285i	−1.69448	+	0.386754i	−0.737145	+	0.675734i	$0.763827\pi$
$674$	−587.233	+	282.796i	−0.871265	+	0.419579i
$675$	54.5370	+	484.030i	0.0807956	+	0.717081i
$676$	255.719	+	203.929i	0.378283	+	0.301670i
$677$	691.122	−	241.834i	1.02086	−	0.357214i	0.232610	−	0.972570i	$-0.425273\pi$
$677$	691.122	−	241.834i	1.02086	−	0.357214i	0.788250	+	0.615356i	$0.210988\pi$
$678$	31.8836	−	282.975i	0.0470259	−	0.417367i
$679$	525.242	−	525.242i	0.773552	−	0.773552i
$680$	−395.234	+	315.189i	−0.581227	+	0.463513i
$681$	−485.587	+	772.807i	−0.713049	+	1.13481i
$682$	−249.578	−	156.820i	−0.365950	−	0.229942i
$683$	17.2569	+	21.6395i	0.0252663	+	0.0316830i	0.794304	−	0.607520i	$-0.207836\pi$
$683$	17.2569	+	21.6395i	0.0252663	+	0.0316830i	−0.769038	+	0.639203i	$0.779264\pi$
$684$	−101.549	−	101.549i	−0.148464	−	0.148464i
$685$	−506.760	−	57.0981i	−0.739795	−	0.0833549i
$686$	113.154	+	323.376i	0.164948	+	0.471394i
$687$	−656.559	+	823.299i	−0.955690	+	1.19840i
$688$	231.746	−	26.1115i	0.336840	−	0.0379528i
$689$	−74.2342	−	154.149i	−0.107742	−	0.223728i
$690$	−65.5194	−	287.059i	−0.0949557	−	0.416028i
$691$	259.239	−	1135.80i	0.375165	−	1.64370i	−0.336864	−	0.941553i	$-0.609366\pi$
$691$	259.239	−	1135.80i	0.375165	−	1.64370i	0.712029	−	0.702150i	$-0.247776\pi$
$692$	−552.946	−	266.285i	−0.799055	−	0.384805i
$693$	49.6759	−	141.966i	0.0716824	−	0.204857i
$694$	−2.61825	−	4.16691i	−0.00377269	−	0.00600420i
$695$		−	663.487i		−	0.954658i
$696$	233.689	+	164.947i	0.335760	+	0.236993i
$697$	536.901			0.770303
$698$	374.888	−	235.558i	0.537089	−	0.337475i
$699$	−312.969	−	109.513i	−0.447738	−	0.156670i
$700$	227.491	−	472.390i	0.324987	−	0.674843i
$701$	697.791	+	159.266i	0.995422	+	0.227199i	0.689051	−	0.724713i	$-0.258028\pi$
$701$	697.791	+	159.266i	0.995422	+	0.227199i	0.306372	+	0.951912i	$0.400885\pi$
$702$	65.6112	−	14.9753i	0.0934632	−	0.0213324i
$703$	−1157.43	+	557.388i	−1.64641	+	0.792870i
$704$	3.88910	+	34.5168i	0.00552430	+	0.0490295i
$705$	−453.557	−	361.699i	−0.643343	−	0.513049i
$706$	−34.1541	+	11.9510i	−0.0483769	+	0.0169278i
$707$	52.5713	−	466.583i	0.0743582	−	0.659947i
$708$	293.919	−	293.919i	0.415139	−	0.415139i
$709$	−577.108	+	460.228i	−0.813974	+	0.649123i	−0.939340	−	0.342988i	$-0.888561\pi$
$709$	−577.108	+	460.228i	−0.813974	+	0.649123i	0.125365	+	0.992111i	$0.459990\pi$
$710$	331.034	−	526.838i	0.466245	−	0.742025i
$711$	328.385	+	206.338i	0.461864	+	0.290208i
$712$	−48.5573	−	60.8889i	−0.0681984	−	0.0855181i
$713$	289.741	+	289.741i	0.406368	+	0.406368i
$714$	1372.42	+	154.635i	1.92216	+	0.216575i
$715$	23.4405	+	66.9892i	0.0327839	+	0.0936911i
$716$	316.227	−	396.536i	0.441657	−	0.553821i
$717$	908.750	−	102.392i	1.26743	−	0.142805i
$718$	209.340	+	434.699i	0.291560	+	0.605430i
$719$	−46.6530	−	204.400i	−0.0648860	−	0.284284i	0.932067	−	0.362285i	$-0.118003\pi$
$719$	−46.6530	−	204.400i	−0.0648860	−	0.284284i	−0.996953	+	0.0780012i	$0.975146\pi$
$720$	19.6781	−	86.2154i	0.0273307	−	0.119744i
$721$	488.865	+	235.425i	0.678037	+	0.326526i
$722$	72.4332	−	207.002i	0.100323	−	0.286707i
$723$	582.166	+	926.512i	0.805209	+	1.28148i
$724$		−	127.276i		−	0.175795i
$725$	−516.119	+	463.524i	−0.711888	+	0.639344i
$726$	503.763			0.693889
$727$	691.485	−	434.489i	0.951148	−	0.597646i	0.0353890	−	0.999374i	$-0.488733\pi$
$727$	691.485	−	434.489i	0.951148	−	0.597646i	0.915759	+	0.401728i	$0.131590\pi$
$728$	−68.3759	−	23.9258i	−0.0939230	−	0.0328651i
$729$	−140.888	+	292.556i	−0.193262	+	0.401312i
$730$	−491.635	−	112.212i	−0.673472	−	0.153716i
$731$	−1452.49	+	331.521i	−1.98699	+	0.453517i
$732$	558.964	−	269.183i	0.763612	−	0.367736i
$733$	−84.9207	−	753.692i	−0.115854	−	1.02823i	−0.908309	−	0.418300i	$-0.862626\pi$
$733$	−84.9207	−	753.692i	−0.115854	−	1.02823i	0.792455	−	0.609930i	$-0.208802\pi$
$734$	−0.671219	−	0.535279i	−0.000914467	−	0.000729263i
$735$	−1637.00	+	572.812i	−2.22721	+	0.779336i
$736$	5.40642	−	47.9833i	0.00734567	−	0.0651947i
$737$	63.5788	−	63.5788i	0.0862670	−	0.0862670i
$738$	−73.4308	+	58.5591i	−0.0994998	+	0.0793484i
$739$	−42.7748	+	68.0757i	−0.0578820	+	0.0921187i	−0.874412	−	0.485185i	$-0.838752\pi$
$739$	−42.7748	+	68.0757i	−0.0578820	+	0.0921187i	0.816530	+	0.577304i	$0.195895\pi$
$740$	−669.804	−	420.866i	−0.905140	−	0.568737i
$741$	−115.432	−	144.747i	−0.155779	−	0.195341i
$742$	−802.329	−	802.329i	−1.08131	−	1.08131i
$743$	−273.663	−	30.8344i	−0.368322	−	0.0414999i	−0.0741360	−	0.997248i	$-0.523620\pi$
$743$	−273.663	−	30.8344i	−0.368322	−	0.0414999i	−0.294186	+	0.955748i	$0.595048\pi$
$744$	156.379	+	446.905i	0.210187	+	0.600679i
$745$	−730.084	+	915.497i	−0.979979	+	1.22885i
$746$	99.2146	−	11.1788i	0.132995	−	0.0149850i
$747$	−35.8749	−	74.4950i	−0.0480253	−	0.0997255i
$748$	−49.3774	−	216.337i	−0.0660126	−	0.289220i
$749$	−371.321	+	1626.86i	−0.495755	+	2.17205i
$750$	−33.5322	−	16.1483i	−0.0447096	−	0.0215310i
$751$	63.0400	−	180.158i	0.0839414	−	0.239891i	−0.894260	−	0.447547i	$-0.852298\pi$
$751$	63.0400	−	180.158i	0.0839414	−	0.239891i	0.978202	+	0.207656i	$0.0665835\pi$
$752$	−50.6158	−	80.5546i	−0.0673083	−	0.107121i
$753$		−	1287.86i		−	1.71031i
$754$	71.6236	+	63.6901i	0.0949916	+	0.0844696i
$755$	−98.8423			−0.130917
$756$	377.906	−	237.454i	0.499876	−	0.314093i
$757$	1313.09	+	459.471i	1.73460	+	0.606963i	0.997620	−	0.0689502i	$-0.0219650\pi$
$757$	1313.09	+	459.471i	1.73460	+	0.606963i	0.736981	+	0.675913i	$0.236251\pi$
$758$	141.334	−	293.484i	0.186457	−	0.387182i
$759$	126.005	+	28.7598i	0.166015	+	0.0378918i
$760$	438.149	−	100.005i	0.576512	−	0.131585i
$761$	−1092.61	+	526.172i	−1.43575	+	0.691422i	−0.980058	−	0.198713i	$-0.936324\pi$
$761$	−1092.61	+	526.172i	−1.43575	+	0.691422i	−0.455696	+	0.890136i	$0.650609\pi$
$762$	59.1368	+	524.853i	0.0776073	+	0.688784i
$763$	−161.006	−	128.398i	−0.211017	−	0.168280i
$764$	−127.192	+	44.5065i	−0.166482	+	0.0582546i
$765$	−63.2530	+	561.386i	−0.0826836	+	0.733837i
$766$	−235.937	+	235.937i	−0.308011	+	0.308011i
$767$	108.894	−	86.8397i	0.141973	−	0.113220i
$768$	29.6852	−	47.2437i	0.0386526	−	0.0615152i
$769$	−551.817	−	346.729i	−0.717577	−	0.450884i	0.123118	−	0.992392i	$-0.460711\pi$
$769$	−551.817	−	346.729i	−0.717577	−	0.450884i	−0.840695	+	0.541508i	$0.817853\pi$
$770$	293.462	+	367.990i	0.381120	+	0.477909i
$771$	−237.229	−	237.229i	−0.307690	−	0.307690i
$772$	−465.734	−	52.4756i	−0.603283	−	0.0679736i
$773$	−249.976	−	714.390i	−0.323384	−	0.924179i	−0.984729	−	0.174097i	$-0.944300\pi$
$773$	−249.976	−	714.390i	−0.323384	−	0.924179i	0.661344	−	0.750082i	$-0.269986\pi$
$774$	162.495	−	203.763i	0.209942	−	0.263259i
$775$	−1141.07	+	128.567i	−1.47234	+	0.165893i
$776$	83.1786	+	172.722i	0.107189	+	0.222580i
$777$	480.908	+	2106.99i	0.618929	+	2.71170i
$778$	−79.1965	+	346.983i	−0.101795	+	0.445993i
$779$	−430.043	−	207.098i	−0.552045	−	0.265851i
$780$	37.6530	−	107.606i	0.0482731	−	0.137957i
$781$	145.308	+	231.256i	0.186054	+	0.296103i
$782$			308.473i			0.394467i
$783$	−581.924	+	100.349i	−0.743198	+	0.128159i
$784$	−284.421			−0.362782
$785$	284.298	−	178.636i	0.362163	−	0.227562i
$786$	−208.641	−	73.0066i	−0.265446	−	0.0928837i
$787$	−21.0666	+	43.7452i	−0.0267682	+	0.0555848i	−0.913924	−	0.405885i	$-0.866963\pi$
$787$	−21.0666	+	43.7452i	−0.0267682	+	0.0555848i	0.887156	+	0.461470i	$0.152678\pi$
$788$	3.47347	+	0.792797i	0.00440796	+	0.00100609i
$789$	949.632	−	216.747i	1.20359	−	0.274712i
$790$	−1093.48	+	526.591i	−1.38415	+	0.666571i
$791$	−70.8518	−	628.827i	−0.0895725	−	0.794978i
$792$	30.3488	+	24.2024i	0.0383192	+	0.0305586i
$793$	196.218	−	68.6597i	0.247438	−	0.0865822i
$794$	−1.22092	+	10.8360i	−0.00153768	+	0.0136473i
$795$	1262.66	−	1262.66i	1.58825	−	1.58825i
$796$	241.364	−	192.481i	0.303221	−	0.241811i
$797$	91.9404	−	146.322i	0.115358	−	0.183591i	−0.784055	−	0.620692i	$-0.786852\pi$
$797$	91.9404	−	146.322i	0.115358	−	0.183591i	0.899413	+	0.437101i	$0.143995\pi$
$798$	−1039.62	−	653.239i	−1.30279	−	0.818595i
$799$	378.936	+	475.171i	0.474263	+	0.594707i
$800$	95.6841	+	95.6841i	0.119605	+	0.119605i
$801$	−86.4859	−	9.74462i	−0.107972	−	0.0121656i
$802$	193.215	+	552.177i	0.240916	+	0.688499i
$803$	138.012	−	173.061i	0.171870	−	0.215518i
$804$	−143.523	+	16.1711i	−0.178511	+	0.0201133i
$805$	−283.894	−	589.512i	−0.352663	−	0.732313i
$806$	35.3033	+	154.674i	0.0438006	+	0.191903i
$807$	252.781	−	1107.51i	0.313235	−	1.37237i
$808$	109.180	+	52.5782i	0.135123	+	0.0650720i
$809$	−119.206	+	340.671i	−0.147350	+	0.421101i	−0.993775	−	0.111406i	$-0.964464\pi$
$809$	−119.206	+	340.671i	−0.147350	+	0.421101i	0.846425	+	0.532508i	$0.178750\pi$
$810$	523.401	+	832.988i	0.646174	+	1.02838i
$811$			858.719i			1.05884i	0.848360	+	0.529420i	$0.177590\pi$
$811$			858.719i			1.05884i	−0.848360	+	0.529420i	$0.822410\pi$
$812$	587.849	+	241.800i	0.723952	+	0.297783i
$813$	−1367.82			−1.68243
$814$	294.011	−	184.740i	0.361193	−	0.226953i
$815$	−463.976	−	162.352i	−0.569296	−	0.199205i
$816$	−154.655	+	321.144i	−0.189528	+	0.393559i
$817$	1291.28	+	294.727i	1.58052	+	0.360742i
$818$	1094.36	−	249.780i	1.33785	−	0.305355i
$819$	−72.9381	+	35.1251i	−0.0890575	+	0.0428878i
$820$	−32.9082	−	292.068i	−0.0401319	−	0.356181i
$821$	342.107	+	272.821i	0.416696	+	0.332304i	0.809291	−	0.587407i	$-0.199851\pi$
$821$	342.107	+	272.821i	0.416696	+	0.332304i	−0.392596	+	0.919711i	$0.628423\pi$
$822$	−339.398	+	118.760i	−0.412893	+	0.144477i
$823$	77.1796	−	684.988i	0.0937784	−	0.832306i	−0.855486	−	0.517826i	$-0.826741\pi$
$823$	77.1796	−	684.988i	0.0937784	−	0.832306i	0.949264	−	0.314480i	$-0.101830\pi$
$824$	−99.0212	+	99.0212i	−0.120171	+	0.120171i
$825$	−283.175	+	225.824i	−0.343242	+	0.273726i
$826$	491.432	−	782.110i	0.594954	−	0.946865i
$827$	679.775	+	427.131i	0.821977	+	0.516482i	0.876144	−	0.482050i	$-0.160107\pi$
$827$	679.775	+	427.131i	0.821977	+	0.516482i	−0.0541671	+	0.998532i	$0.517250\pi$
$828$	−33.6448	−	42.1893i	−0.0406338	−	0.0509532i
$829$	595.519	+	595.519i	0.718358	+	0.718358i	0.968269	−	0.249911i	$-0.0804013\pi$
$829$	595.519	+	595.519i	0.718358	+	0.718358i	−0.249911	+	0.968269i	$0.580401\pi$
$830$	257.120	+	28.9705i	0.309783	+	0.0349042i
$831$	−519.693	−	1485.20i	−0.625383	−	1.78724i
$832$	11.6568	−	14.6171i	0.0140105	−	0.0175687i
$833$	1805.55	−	203.437i	2.16753	−	0.244222i
$834$	−202.981	−	421.494i	−0.243382	−	0.505389i
$835$	−248.682	−	1089.55i	−0.297823	−	1.30485i
$836$	−43.8972	+	192.326i	−0.0525086	+	0.230055i
$837$	−880.666	−	424.106i	−1.05217	−	0.506698i
$838$	54.4904	−	155.725i	0.0650244	−	0.185829i
$839$	101.099	+	160.898i	0.120499	+	0.191774i	0.901527	−	0.432723i	$-0.142447\pi$
$839$	101.099	+	160.898i	0.120499	+	0.191774i	−0.781028	+	0.624496i	$0.785304\pi$
$840$		−	756.059i		−	0.900070i
$841$	−597.600	−	591.739i	−0.710583	−	0.703614i
$842$	168.640			0.200285
$843$	−429.724	+	270.014i	−0.509756	+	0.320301i
$844$	−107.434	−	37.5929i	−0.127292	−	0.0445414i
$845$	−496.296	+	1030.57i	−0.587333	+	1.21961i
$846$	−103.653	−	23.6580i	−0.122521	−	0.0279646i
$847$	1091.40	−	249.104i	1.28854	−	0.294102i
$848$	263.840	−	127.059i	0.311133	−	0.149834i
$849$	103.245	+	916.328i	0.121608	+	1.07930i
$850$	−675.860	−	538.980i	−0.795129	−	0.634094i
$851$	−455.617	+	159.427i	−0.535391	+	0.187341i
$852$	49.1207	−	435.958i	0.0576534	−	0.511688i
$853$	−686.296	+	686.296i	−0.804567	+	0.804567i	−0.983806	−	0.179239i	$-0.942637\pi$
$853$	−686.296	+	686.296i	−0.804567	+	0.804567i	0.179239	+	0.983806i	$0.442637\pi$
$854$	1077.88	−	859.581i	1.26216	−	1.00654i
$855$	267.206	−	425.256i	0.312522	−	0.497376i
$856$	−364.657	−	229.129i	−0.426001	−	0.267674i
$857$	580.676	+	728.144i	0.677568	+	0.849643i	0.995128	−	0.0985948i	$-0.0314348\pi$
$857$	580.676	+	728.144i	0.677568	+	0.849643i	−0.317560	+	0.948238i	$0.602863\pi$
$858$	35.3851	+	35.3851i	0.0412414	+	0.0412414i
$859$	−979.107	−	110.319i	−1.13982	−	0.128427i	−0.478190	−	0.878256i	$-0.658707\pi$
$859$	−979.107	−	110.319i	−1.13982	−	0.128427i	−0.661631	+	0.749829i	$0.730136\pi$
$860$	269.371	+	769.818i	0.313222	+	0.895137i
$861$	−500.654	+	627.801i	−0.581480	+	0.729153i
$862$	270.931	−	30.5265i	0.314305	−	0.0354136i
$863$	720.630	+	1496.40i	0.835029	+	1.73396i	0.662656	+	0.748924i	$0.269429\pi$
$863$	720.630	+	1496.40i	0.835029	+	1.73396i	0.172373	+	0.985032i	$0.444856\pi$
$864$	25.6317	+	112.300i	0.0296663	+	0.129977i
$865$	477.597	−	2092.49i	0.552135	−	2.41906i
$866$	−206.251	−	99.3253i	−0.238165	−	0.114694i
$867$	419.213	−	1198.04i	0.483522	−	1.38183i
$868$	559.782	+	890.888i	0.644910	+	1.02637i
$869$		−	532.741i		−	0.613051i
$870$	−380.531	+	925.124i	−0.437392	+	1.06336i
$871$	−48.3957			−0.0555634
$872$	45.0023	−	28.2768i	0.0516081	−	0.0324275i
$873$	202.216	+	70.7585i	0.231634	+	0.0810521i
$874$	118.987	−	247.079i	0.136141	−	0.282699i
$875$	−80.6322	−	18.4038i	−0.0921511	−	0.0210329i
$876$	−346.651	+	79.1207i	−0.395720	+	0.0903205i
$877$	1250.71	−	602.309i	1.42612	−	0.686783i	0.447848	−	0.894110i	$-0.352190\pi$
$877$	1250.71	−	602.309i	1.42612	−	0.686783i	0.978272	+	0.207326i	$0.0664762\pi$
$878$	70.9504	+	629.703i	0.0808092	+	0.717201i
$879$	−568.135	−	453.073i	−0.646343	−	0.515441i
$880$	−114.658	+	40.1207i	−0.130294	+	0.0455917i
$881$	−34.8258	+	309.088i	−0.0395299	+	0.350837i	0.958342	+	0.285625i	$0.0922011\pi$
$881$	−34.8258	+	309.088i	−0.0395299	+	0.350837i	−0.997871	+	0.0652125i	$0.979227\pi$
$882$	−224.753	+	224.753i	−0.254822	+	0.254822i
$883$	−386.022	+	307.842i	−0.437171	+	0.348632i	−0.817212	−	0.576338i	$-0.804481\pi$
$883$	−386.022	+	307.842i	−0.437171	+	0.348632i	0.380041	+	0.924970i	$0.375910\pi$
$884$	−63.5441	+	101.130i	−0.0718825	+	0.114400i
$885$	1230.84	+	773.389i	1.39078	+	0.873885i
$886$	−60.0389	−	75.2865i	−0.0677640	−	0.0849734i
$887$	807.923	+	807.923i	0.910849	+	0.910849i	0.996339	−	0.0854900i	$-0.0272456\pi$
$887$	807.923	+	807.923i	0.910849	+	0.910849i	−0.0854900	+	0.996339i	$0.527246\pi$
$888$	−554.262	−	62.4504i	−0.624169	−	0.0703270i
$889$	387.652	+	1107.85i	0.436054	+	1.24617i
$890$	169.814	−	212.939i	0.190802	−	0.239258i
$891$	−429.115	+	48.3497i	−0.481611	+	0.0542645i
$892$	−59.6774	−	123.921i	−0.0669030	−	0.138925i
$893$	−120.231	−	526.766i	−0.134637	−	0.589883i
$894$	−183.723	+	804.943i	−0.205507	+	0.900384i
$895$	1598.07	+	769.591i	1.78556	+	0.859879i
$896$	40.9512	−	117.032i	0.0457045	−	0.130616i
$897$	−37.0112	−	58.9030i	−0.0412611	−	0.0656667i
$898$		−	392.625i		−	0.437222i
$899$	−236.565	−	1371.84i	−0.263142	−	1.52597i
$900$	151.222			0.168024
$901$	−1584.02	+	995.309i	−1.75807	+	1.10467i
$902$	121.775	+	42.6109i	0.135006	+	0.0472405i
$903$	966.781	−	2007.54i	1.07063	−	2.22319i
$904$	159.224	+	36.3417i	0.176132	+	0.0402010i
$905$	433.946	−	99.0454i	0.479499	−	0.109442i
$906$	−62.7917	+	30.2389i	−0.0693065	+	0.0333762i
$907$	66.9962	+	594.608i	0.0738657	+	0.655576i	0.975026	+	0.222091i	$0.0712880\pi$
$907$	66.9962	+	594.608i	0.0738657	+	0.655576i	−0.901160	+	0.433486i	$0.857283\pi$
$908$	−409.251	−	326.367i	−0.450717	−	0.359435i
$909$	127.823	−	44.7273i	0.140620	−	0.0492050i
$910$	28.3650	−	251.746i	0.0311703	−	0.276644i
$911$	−350.898	+	350.898i	−0.385179	+	0.385179i	−0.872964	−	0.487785i	$-0.837805\pi$
$911$	−350.898	+	350.898i	−0.385179	+	0.385179i	0.487785	+	0.872964i	$0.337805\pi$
$912$	247.749	−	197.573i	0.271654	−	0.216637i
$913$	−60.4268	+	96.1687i	−0.0661849	+	0.105333i
$914$	387.221	+	243.307i	0.423655	+	0.266200i
$915$	1352.76	+	1696.31i	1.47843	+	1.85389i
$916$	−427.049	−	427.049i	−0.466211	−	0.466211i
$917$	−488.119	−	54.9978i	−0.532299	−	0.0599757i
$918$	−243.039	−	694.565i	−0.264748	−	0.756607i
$919$	−363.128	+	455.348i	−0.395134	+	0.495482i	−0.939109	−	0.343619i	$-0.888347\pi$
$919$	−363.128	+	455.348i	−0.395134	+	0.495482i	0.543975	+	0.839101i	$0.316919\pi$
$920$	167.806	−	18.9072i	0.182398	−	0.0205513i
$921$	301.471	+	626.010i	0.327330	+	0.679707i
$922$	174.041	+	762.524i	0.188765	+	0.827033i
$923$	32.7116	−	143.319i	0.0354405	−	0.155275i
$924$	299.007	+	143.994i	0.323601	+	0.155838i
$925$	446.775	−	1276.81i	0.483000	−	1.38033i
$926$	−399.061	−	635.102i	−0.430951	−	0.685855i
$927$			156.496i			0.168820i
$928$	−109.012	+	122.591i	−0.117469	+	0.132102i
$929$	−1217.42			−1.31046			−0.655229	−	0.755430i	$-0.727428\pi$
$929$	−1217.42			−1.31046			−0.655229	+	0.755430i	$0.727428\pi$
$930$	−1402.03	+	880.953i	−1.50756	+	0.947261i
$931$	−1524.67	−	533.505i	−1.63767	−	0.573045i
$932$	82.5095	−	171.333i	0.0885295	−	0.183833i
$933$	−348.192	−	79.4726i	−0.373196	−	0.0851796i
$934$	−356.924	+	81.4655i	−0.382145	+	0.0872222i
$935$	699.174	−	336.705i	0.747780	−	0.360112i
$936$	−2.33932	−	20.7620i	−0.00249927	−	0.0221816i
$937$	−818.205	−	652.496i	−0.873217	−	0.696368i	0.0806026	−	0.996746i	$-0.474316\pi$
$937$	−818.205	−	652.496i	−0.873217	−	0.696368i	−0.953820	+	0.300379i	$0.902887\pi$
$938$	−302.944	+	106.005i	−0.322968	+	0.113011i
$939$	0.305425	−	2.71072i	0.000325266	−	0.00288682i
$940$	235.262	−	235.262i	0.250278	−	0.250278i
$941$	582.593	−	464.602i	0.619121	−	0.493732i	−0.262975	−	0.964803i	$-0.584704\pi$
$941$	582.593	−	464.602i	0.619121	−	0.493732i	0.882096	+	0.471070i	$0.156132\pi$
$942$	125.956	−	200.458i	0.133711	−	0.212800i
$943$	−151.859	−	95.4196i	−0.161039	−	0.101187i
$944$	148.634	+	186.382i	0.157452	+	0.197438i
$945$	1103.68	+	1103.68i	1.16792	+	1.16792i
$946$	−355.752	−	40.0836i	−0.376059	−	0.0423717i
$947$	142.543	+	407.364i	0.150521	+	0.430163i	0.994312	−	0.106509i	$-0.0339671\pi$
$947$	142.543	+	407.364i	0.150521	+	0.430163i	−0.843791	+	0.536672i	$0.819681\pi$
$948$	−533.554	+	669.056i	−0.562821	+	0.705755i
$949$	−118.393	+	13.3397i	−0.124756	+	0.0140566i
$950$	333.445	+	692.407i	0.350995	+	0.728849i
$951$	−337.281	−	1477.73i	−0.354660	−	1.55386i
$952$	−176.256	+	772.230i	−0.185143	+	0.811166i
$953$	434.453	+	209.221i	0.455879	+	0.219540i	0.647708	−	0.761889i	$-0.275728\pi$
$953$	434.453	+	209.221i	0.455879	+	0.219540i	−0.191829	+	0.981428i	$0.561442\pi$
$954$	108.087	−	308.894i	0.113298	−	0.323788i
$955$	−250.725	−	399.027i	−0.262540	−	0.417829i
$956$			524.483i			0.548623i
$957$	−293.396	−	326.687i	−0.306579	−	0.341365i
$958$	822.939			0.859017
$959$	−676.576	+	425.121i	−0.705502	+	0.443296i
$960$	184.178	+	64.4467i	0.191852	+	0.0671320i
$961$	582.839	−	1210.28i	0.606492	−	1.25939i
$962$	−182.211	−	41.5884i	−0.189408	−	0.0432312i
$963$	−469.218	+	107.096i	−0.487246	+	0.111211i
$964$	−565.414	+	272.289i	−0.586529	+	0.282458i
$965$	−183.517	−	1628.76i	−0.190173	−	1.68783i
$966$	−360.699	−	287.648i	−0.373395	−	0.297772i
$967$	−548.500	+	191.928i	−0.567218	+	0.198478i	−0.598626	−	0.801028i	$-0.704287\pi$
$967$	−548.500	+	191.928i	−0.567218	+	0.198478i	0.0314082	+	0.999507i	$0.490001\pi$
$968$	−32.3486	+	287.101i	−0.0334179	+	0.296592i
$969$	−1431.44	+	1431.44i	−1.47723	+	1.47723i
$970$	−524.166	+	418.009i	−0.540378	+	0.430937i
$971$	−331.079	+	526.910i	−0.340967	+	0.542646i	−0.972559	−	0.232654i	$-0.925259\pi$
$971$	−331.079	+	526.910i	−0.340967	+	0.542646i	0.631592	+	0.775301i	$0.282402\pi$
$972$	276.992	+	174.046i	0.284971	+	0.179059i
$973$	−648.179	−	812.791i	−0.666165	−	0.835345i
$974$	−220.787	−	220.787i	−0.226681	−	0.226681i
$975$	193.723	+	21.8274i	0.198690	+	0.0223870i
$976$	117.518	+	335.846i	0.120407	+	0.344104i
$977$	907.738	−	1138.27i	0.929107	−	1.16506i	−0.0569033	−	0.998380i	$-0.518123\pi$
$977$	907.738	−	1138.27i	0.929107	−	1.16506i	0.986010	−	0.166684i	$-0.0533059\pi$
$978$	−344.419	+	38.8067i	−0.352167	+	0.0396797i
$979$	51.8720	+	107.713i	0.0529847	+	0.110024i
$980$	−221.335	−	969.732i	−0.225852	−	0.989522i
$981$	13.2167	−	57.9061i	0.0134727	−	0.0590276i
$982$	456.660	+	219.916i	0.465031	+	0.223947i
$983$	−577.944	+	1651.67i	−0.587939	+	1.68023i	0.136287	+	0.990669i	$0.456483\pi$
$983$	−577.944	+	1651.67i	−0.587939	+	1.68023i	−0.724225	+	0.689563i	$0.757803\pi$
$984$	−110.258	−	175.475i	−0.112051	−	0.178328i
$985$			12.4597i			0.0126495i
$986$	604.340	−	856.200i	0.612921	−	0.868357i
$987$	−908.974			−0.920946
$988$	89.9057	−	56.4915i	0.0909977	−	0.0571777i
$989$	469.748	+	164.372i	0.474972	+	0.166200i
$990$	−58.9006	+	122.308i	−0.0594956	+	0.123544i
$991$	796.873	+	181.881i	0.804110	+	0.183533i	0.604773	−	0.796398i	$-0.293264\pi$
$991$	796.873	+	181.881i	0.804110	+	0.183533i	0.199337	+	0.979931i	$0.436121\pi$
$992$	−264.739	+	60.4249i	−0.266874	+	0.0609122i
$993$	−780.278	+	375.762i	−0.785778	+	0.378411i
$994$	−109.156	−	968.787i	−0.109815	−	0.974635i
$995$	844.093	+	673.142i	0.848335	+	0.676524i
$996$	172.204	−	60.2567i	0.172895	−	0.0604987i
$997$	−79.1025	+	702.054i	−0.0793405	+	0.704167i	0.889577	+	0.456784i	$0.150999\pi$
$997$	−79.1025	+	702.054i	−0.0793405	+	0.704167i	−0.968918	+	0.247382i	$0.920430\pi$
$998$	−392.742	+	392.742i	−0.393529	+	0.393529i
$999$	900.269	−	717.941i	0.901170	−	0.718659i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	58.3.f.a.39.1	yes	24
29.3	odd	28	inner	58.3.f.a.3.1	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
58.3.f.a.3.1	✓	24	29.3	odd	28	inner
58.3.f.a.39.1	yes	24	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 58 = 2 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	58.f (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.19745 + 0.752407i) q^{2} +(-3.29155 - 1.15176i) q^{3} +(0.867767 - 1.80194i) q^{4} +(6.81899 + 1.55639i) q^{5} +(4.80806 - 1.09741i) q^{6} +(9.87394 - 4.75504i) q^{7} +(0.316683 + 2.81064i) q^{8} +(2.47126 + 1.97076i) q^{9} +(-9.33644 + 3.26696i) q^{10} +(0.486138 - 4.31459i) q^{11} +(-4.93170 + 4.93170i) q^{12} +(-1.82714 + 1.45710i) q^{13} +(-8.24582 + 13.1231i) q^{14} +(-20.6525 - 12.9768i) q^{15} +(-2.49396 - 3.12733i) q^{16} +(18.0690 + 18.0690i) q^{17} +(-4.44202 - 0.500495i) q^{18} +(-7.50304 - 21.4425i) q^{19} +(8.72182 - 10.9368i) q^{20} +(-37.9773 + 4.27901i) q^{21} +(2.66421 + 5.53228i) q^{22} +(-1.89944 - 8.32198i) q^{23} +(2.19481 - 9.61611i) q^{24} +(21.5521 + 10.3789i) q^{25} +(1.09158 - 3.11955i) q^{26} +(10.8335 + 17.2414i) q^{27} -21.9185i q^{28} +(-11.0318 + 26.8198i) q^{29} +34.4941 q^{30} +(-40.6455 + 25.5392i) q^{31} +(5.33941 + 1.86834i) q^{32} +(-6.56954 + 13.6418i) q^{33} +(-35.2319 - 8.04145i) q^{34} +(74.7311 - 17.0569i) q^{35} +(5.69566 - 2.74289i) q^{36} +(-6.33152 - 56.1938i) q^{37} +(25.1180 + 20.0309i) q^{38} +(7.69236 - 2.69167i) q^{39} +(-2.21500 + 19.6586i) q^{40} +(14.8570 - 14.8570i) q^{41} +(42.2563 - 33.6982i) q^{42} +(-31.0191 + 49.3667i) q^{43} +(-7.35278 - 4.62006i) q^{44} +(13.7842 + 17.2848i) q^{45} +(8.53600 + 8.53600i) q^{46} +(23.6347 + 2.66299i) q^{47} +(4.60705 + 13.1662i) q^{48} +(44.3334 - 55.5923i) q^{49} +(-33.6167 + 3.78770i) q^{50} +(-38.6637 - 80.2861i) q^{51} +(1.04006 + 4.55682i) q^{52} +(-16.2908 + 71.3747i) q^{53} +(-25.9451 - 12.4945i) q^{54} +(10.0302 - 28.6646i) q^{55} +(16.4916 + 26.2463i) q^{56} +79.2207i q^{57} +(-6.96940 - 40.4157i) q^{58} -59.5978 q^{59} +(-41.3049 + 25.9536i) q^{60} +(-83.9615 - 29.3794i) q^{61} +(29.4550 - 61.1639i) q^{62} +(33.7721 + 7.70826i) q^{63} +(-7.79942 + 1.78017i) q^{64} +(-14.7271 + 7.09219i) q^{65} +(-2.39749 - 21.2783i) q^{66} +(16.1905 + 12.9115i) q^{67} +(48.2388 - 16.8795i) q^{68} +(-3.33286 + 29.5799i) q^{69} +(-76.6529 + 76.6529i) q^{70} +(-49.1796 + 39.2194i) q^{71} +(-4.75650 + 7.56992i) q^{72} +(43.1667 + 27.1235i) q^{73} +(49.8623 + 62.5253i) q^{74} +(-58.9857 - 58.9857i) q^{75} +(-45.1489 - 5.08706i) q^{76} +(-15.7160 - 44.9137i) q^{77} +(-7.18597 + 9.01092i) q^{78} +(121.926 - 13.7378i) q^{79} +(-12.1390 - 25.2068i) q^{80} +(-22.1312 - 96.9631i) q^{81} +(-6.61198 + 28.9690i) q^{82} +(-23.5680 - 11.3497i) q^{83} +(-25.2449 + 72.1458i) q^{84} +(95.0898 + 151.335i) q^{85} -82.4531i q^{86} +(67.2016 - 75.5726i) q^{87} +12.2807 q^{88} +(-23.3143 + 14.6493i) q^{89} +(-29.5111 - 10.3264i) q^{90} +(-11.1125 + 23.0754i) q^{91} +(-16.6440 - 3.79888i) q^{92} +(163.202 - 37.2497i) q^{93} +(-30.3049 + 14.5941i) q^{94} +(-17.7903 - 157.894i) q^{95} +(-15.4230 - 12.2995i) q^{96} +(63.9752 - 22.3859i) q^{97} +(-11.2589 + 99.9256i) q^{98} +(9.70440 - 9.70440i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} - 4 q^{3} + 28 q^{5} + 34 q^{7} + 8 q^{8} + 4 q^{10} - 44 q^{11} + 8 q^{12} - 36 q^{14} - 90 q^{15} + 16 q^{16} + 32 q^{17} - 16 q^{18} - 56 q^{19} + 36 q^{20} - 168 q^{21} - 84 q^{22} + 68 q^{23}+ \cdots + 132 q^{99}+O(q^{100}) \) 24 * q - 4 * q^2 - 4 * q^3 + 28 * q^5 + 34 * q^7 + 8 * q^8 + 4 * q^10 - 44 * q^11 + 8 * q^12 - 36 * q^14 - 90 * q^15 + 16 * q^16 + 32 * q^17 - 16 * q^18 - 56 * q^19 + 36 * q^20 - 168 * q^21 - 84 * q^22 + 68 * q^23 - 40 * q^24 - 84 * q^25 - 96 * q^26 - 28 * q^27 + 144 * q^29 - 40 * q^30 + 106 * q^31 + 16 * q^32 + 98 * q^33 + 84 * q^34 + 196 * q^35 + 80 * q^36 - 262 * q^37 + 280 * q^38 + 458 * q^39 + 8 * q^40 + 116 * q^41 + 308 * q^42 - 212 * q^43 - 24 * q^44 + 14 * q^45 - 16 * q^46 - 238 * q^47 + 16 * q^48 + 188 * q^49 - 196 * q^50 - 462 * q^51 + 32 * q^52 - 126 * q^53 - 56 * q^54 - 96 * q^55 + 72 * q^56 - 24 * q^58 - 48 * q^59 - 180 * q^60 + 268 * q^61 - 56 * q^62 + 28 * q^63 + 376 * q^65 - 108 * q^66 + 490 * q^67 - 64 * q^68 - 328 * q^69 - 72 * q^70 - 14 * q^71 - 88 * q^72 - 552 * q^73 - 188 * q^74 - 356 * q^75 - 420 * q^76 - 186 * q^77 - 316 * q^78 - 358 * q^79 - 20 * q^81 + 288 * q^82 - 448 * q^83 - 140 * q^84 - 420 * q^85 + 606 * q^87 - 48 * q^88 + 314 * q^89 + 308 * q^90 - 182 * q^91 + 112 * q^92 + 1428 * q^93 + 336 * q^94 + 510 * q^95 + 424 * q^97 + 244 * q^98 + 132 * q^99

Introduction

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