LMFDB - Embedded newform 117.2.z.b.5.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,2,Mod(5,117)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([10, 9]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("117.5");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.z (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$11$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			5.11
Character	$\chi$	$=$	117.5
Dual form			117.2.z.b.47.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.685712 - 2.55911i) q^{2} +(-1.63413 + 0.574122i) q^{3} +(-4.34680 - 2.50963i) q^{4} +(-1.47168 + 0.394337i) q^{5} +(0.348700 + 4.57561i) q^{6} +(0.901137 - 3.36309i) q^{7} +(-5.65626 + 5.65626i) q^{8} +(2.34077 - 1.87638i) q^{9} +4.03661i q^{10} +(-1.45498 - 0.389861i) q^{11} +(8.54407 + 1.60546i) q^{12} +(3.37994 - 1.25539i) q^{13} +(-7.98860 - 4.61222i) q^{14} +(2.17853 - 1.48932i) q^{15} +(5.57719 + 9.65998i) q^{16} +2.59775 q^{17} +(-3.19678 - 7.27694i) q^{18} +(2.70795 - 2.70795i) q^{19} +(7.38675 + 1.97927i) q^{20} +(0.458249 + 6.01309i) q^{21} +(-1.99539 + 3.45613i) q^{22} +(0.905093 - 1.56767i) q^{23} +(5.99569 - 12.4905i) q^{24} +(-2.31977 + 1.33932i) q^{25} +(-0.895016 - 9.51048i) q^{26} +(-2.74785 + 4.41014i) q^{27} +(-12.3571 + 12.3571i) q^{28} +(-6.78705 + 3.91851i) q^{29} +(-2.31751 - 6.59634i) q^{30} +(-0.677098 - 2.52697i) q^{31} +(13.0921 - 3.50802i) q^{32} +(2.60146 - 0.198253i) q^{33} +(1.78131 - 6.64794i) q^{34} +5.30475i q^{35} +(-14.8839 + 2.28181i) q^{36} +(4.52449 + 4.52449i) q^{37} +(-5.07307 - 8.78681i) q^{38} +(-4.80252 + 3.99197i) q^{39} +(6.09376 - 10.5547i) q^{40} +(10.4949 - 2.81210i) q^{41} +(15.7024 + 2.95054i) q^{42} +(3.63308 - 2.09756i) q^{43} +(5.34610 + 5.34610i) q^{44} +(-2.70494 + 3.68449i) q^{45} +(-3.39120 - 3.39120i) q^{46} +(1.79215 + 0.480206i) q^{47} +(-14.6599 - 12.5837i) q^{48} +(-4.43613 - 2.56120i) q^{49} +(1.83678 + 6.85495i) q^{50} +(-4.24507 + 1.49143i) q^{51} +(-17.8425 - 3.02546i) q^{52} +0.406662i q^{53} +(9.40181 + 10.0561i) q^{54} +2.29501 q^{55} +(13.9254 + 24.1196i) q^{56} +(-2.87045 + 5.97984i) q^{57} +(5.37393 + 20.0558i) q^{58} +(-0.450677 - 1.68195i) q^{59} +(-13.2073 + 1.00651i) q^{60} +(1.91165 + 3.31107i) q^{61} -6.93108 q^{62} +(-4.20109 - 9.56308i) q^{63} -13.6009i q^{64} +(-4.47916 + 3.18037i) q^{65} +(1.27650 - 6.79336i) q^{66} +(-0.615801 - 2.29820i) q^{67} +(-11.2919 - 6.51938i) q^{68} +(-0.579007 + 3.08141i) q^{69} +(13.5755 + 3.63753i) q^{70} +(-8.23276 - 8.23276i) q^{71} +(-2.62668 + 23.8533i) q^{72} +(8.55641 + 8.55641i) q^{73} +(14.6812 - 8.47619i) q^{74} +(3.02188 - 3.52046i) q^{75} +(-18.5668 + 4.97497i) q^{76} +(-2.62227 + 4.54191i) q^{77} +(6.92275 + 15.0275i) q^{78} +(-5.66639 - 9.81447i) q^{79} +(-12.0171 - 12.0171i) q^{80} +(1.95838 - 8.78435i) q^{81} -28.7859i q^{82} +(-1.64831 + 6.15156i) q^{83} +(13.0987 - 27.2877i) q^{84} +(-3.82307 + 1.02439i) q^{85} +(-2.87664 - 10.7358i) q^{86} +(8.84123 - 10.2999i) q^{87} +(10.4349 - 6.02460i) q^{88} +(2.83751 - 2.83751i) q^{89} +(7.57421 + 9.44875i) q^{90} +(-1.17620 - 12.4983i) q^{91} +(-7.86851 + 4.54289i) q^{92} +(2.55725 + 3.74065i) q^{93} +(2.45780 - 4.25704i) q^{94} +(-2.91740 + 5.05309i) q^{95} +(-19.3802 + 13.2490i) q^{96} +(-1.28483 - 0.344269i) q^{97} +(-9.59631 + 9.59631i) q^{98} +(-4.13730 + 1.81753i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 2 q^{3} - 14 q^{6} - 14 q^{9} - 6 q^{11} + 4 q^{13} - 36 q^{14} + 4 q^{15} + 4 q^{18} + 12 q^{19} - 18 q^{20} + 22 q^{21} - 28 q^{22} - 24 q^{24} + 4 q^{27} - 16 q^{28} + 8 q^{31} + 6 q^{32} - 14 q^{33}+ \cdots - 68 q^{99}+O(q^{100}) $ 44 * q - 2 * q^3 - 14 * q^6 - 14 * q^9 - 6 * q^11 + 4 * q^13 - 36 * q^14 + 4 * q^15 + 4 * q^18 + 12 * q^19 - 18 * q^20 + 22 * q^21 - 28 * q^22 - 24 * q^24 + 4 * q^27 - 16 * q^28 + 8 * q^31 + 6 * q^32 - 14 * q^33 - 12 * q^34 - 16 * q^37 + 16 * q^39 + 36 * q^40 + 36 * q^41 + 20 * q^42 - 56 * q^45 - 12 * q^46 - 18 * q^47 - 8 * q^48 + 120 * q^50 - 8 * q^52 + 52 * q^54 - 64 * q^55 - 8 * q^57 - 40 * q^58 - 24 * q^59 + 8 * q^60 + 2 * q^61 + 64 * q^63 - 42 * q^65 - 4 * q^66 - 36 * q^68 + 20 * q^70 + 18 * q^72 + 48 * q^73 + 216 * q^74 - 26 * q^76 + 22 * q^78 - 22 * q^79 + 10 * q^81 + 30 * q^83 + 94 * q^84 - 18 * q^85 - 120 * q^86 + 68 * q^87 - 72 * q^92 - 62 * q^93 + 32 * q^94 + 16 * q^96 - 4 * q^97 - 68 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	0.685712	−	2.55911i	0.484871	−	1.80956i	−0.0957675	−	0.995404i	$-0.530531\pi$
$2$	0.685712	−	2.55911i	0.484871	−	1.80956i	0.580639	−	0.814161i	$-0.302803\pi$
$3$	−1.63413	+	0.574122i	−0.943466	+	0.331470i
$3$	−1.63413	+	0.574122i	−0.943466	+	0.331470i
$4$	−4.34680	−	2.50963i	−2.17340	−	1.25481i
$5$	−1.47168	+	0.394337i	−0.658157	+	0.176353i	−0.572414	−	0.819965i	$-0.693993\pi$
$5$	−1.47168	+	0.394337i	−0.658157	+	0.176353i	−0.0857430	+	0.996317i	$0.527326\pi$
$6$	0.348700	+	4.57561i	0.142356	+	1.86798i
$7$	0.901137	−	3.36309i	0.340598	−	1.27113i	−0.557074	−	0.830463i	$-0.688076\pi$
$7$	0.901137	−	3.36309i	0.340598	−	1.27113i	0.897672	−	0.440665i	$-0.145257\pi$
$8$	−5.65626	+	5.65626i	−1.99979	+	1.99979i
$9$	2.34077	−	1.87638i	0.780256	−	0.625461i
$10$			4.03661i			1.27649i
$11$	−1.45498	−	0.389861i	−0.438693	−	0.117547i	0.0327108	−	0.999465i	$-0.489586\pi$
$11$	−1.45498	−	0.389861i	−0.438693	−	0.117547i	−0.471404	+	0.881917i	$0.656253\pi$
$12$	8.54407	+	1.60546i	2.46646	+	0.463457i
$13$	3.37994	−	1.25539i	0.937427	−	0.348182i
$13$	3.37994	−	1.25539i	0.937427	−	0.348182i
$14$	−7.98860	−	4.61222i	−2.13504	−	1.23267i
$15$	2.17853	−	1.48932i	0.562493	−	0.384542i
$16$	5.57719	+	9.65998i	1.39430	+	2.41499i
$17$	2.59775			0.630047			0.315024	−	0.949084i	$-0.397988\pi$
$17$	2.59775			0.630047			0.315024	+	0.949084i	$0.397988\pi$
$18$	−3.19678	−	7.27694i	−0.753488	−	1.71519i
$19$	2.70795	−	2.70795i	0.621246	−	0.621246i	−0.324604	−	0.945850i	$-0.605231\pi$
$19$	2.70795	−	2.70795i	0.621246	−	0.621246i	0.945850	+	0.324604i	$0.105231\pi$
$20$	7.38675	+	1.97927i	1.65173	+	0.442579i
$21$	0.458249	+	6.01309i	0.0999981	+	1.31216i
$22$	−1.99539	+	3.45613i	−0.425420	+	0.736848i
$23$	0.905093	−	1.56767i	0.188725	−	0.326881i	−0.756100	−	0.654456i	$-0.772898\pi$
$23$	0.905093	−	1.56767i	0.188725	−	0.326881i	0.944825	+	0.327574i	$0.106231\pi$
$24$	5.99569	−	12.4905i	1.22386	−	2.54960i
$25$	−2.31977	+	1.33932i	−0.463955	+	0.267864i
$26$	−0.895016	−	9.51048i	−0.175527	−	1.86516i
$27$	−2.74785	+	4.41014i	−0.528823	+	0.848732i
$28$	−12.3571	+	12.3571i	−2.33528	+	2.33528i
$29$	−6.78705	+	3.91851i	−1.26032	+	0.727648i	−0.973137	−	0.230226i	$-0.926053\pi$
$29$	−6.78705	+	3.91851i	−1.26032	+	0.727648i	−0.287187	+	0.957875i	$0.592720\pi$
$30$	−2.31751	−	6.59634i	−0.423117	−	1.20432i
$31$	−0.677098	−	2.52697i	−0.121610	−	0.453856i	0.878086	−	0.478503i	$-0.158821\pi$
$31$	−0.677098	−	2.52697i	−0.121610	−	0.453856i	−0.999696	+	0.0246469i	$0.992154\pi$
$32$	13.0921	−	3.50802i	2.31438	−	0.620136i
$33$	2.60146	−	0.198253i	0.452855	−	0.0345115i
$34$	1.78131	−	6.64794i	0.305492	−	1.14011i
$35$			5.30475i			0.896667i
$36$	−14.8839	+	2.28181i	−2.48064	+	0.380301i
$37$	4.52449	+	4.52449i	0.743822	+	0.743822i	0.973311	−	0.229489i	$-0.0737055\pi$
$37$	4.52449	+	4.52449i	0.743822	+	0.743822i	−0.229489	+	0.973311i	$0.573705\pi$
$38$	−5.07307	−	8.78681i	−0.822960	−	1.42541i
$39$	−4.80252	+	3.99197i	−0.769018	+	0.639227i
$40$	6.09376	−	10.5547i	0.963508	−	1.66885i
$41$	10.4949	−	2.81210i	1.63903	−	0.439177i	0.682518	−	0.730869i	$-0.260885\pi$
$41$	10.4949	−	2.81210i	1.63903	−	0.439177i	0.956512	+	0.291692i	$0.0942182\pi$
$42$	15.7024	+	2.95054i	2.42293	+	0.455278i
$43$	3.63308	−	2.09756i	0.554040	−	0.319875i	−0.196710	−	0.980462i	$-0.563026\pi$
$43$	3.63308	−	2.09756i	0.554040	−	0.319875i	0.750750	+	0.660587i	$0.229692\pi$
$44$	5.34610	+	5.34610i	0.805955	+	0.805955i
$45$	−2.70494	+	3.68449i	−0.403229	+	0.549252i
$46$	−3.39120	−	3.39120i	−0.500005	−	0.500005i
$47$	1.79215	+	0.480206i	0.261413	+	0.0700453i	0.387145	−	0.922019i	$-0.373461\pi$
$47$	1.79215	+	0.480206i	0.261413	+	0.0700453i	−0.125732	+	0.992064i	$0.540128\pi$
$48$	−14.6599	−	12.5837i	−2.11597	−	1.81630i
$49$	−4.43613	−	2.56120i	−0.633733	−	0.365886i
$50$	1.83678	+	6.85495i	0.259760	+	0.969436i
$51$	−4.24507	+	1.49143i	−0.594428	+	0.208842i
$52$	−17.8425	−	3.02546i	−2.47431	−	0.419556i
$53$			0.406662i			0.0558593i	0.999610	+	0.0279297i	$0.00889145\pi$
$53$			0.406662i			0.0558593i	−0.999610	+	0.0279297i	$0.991109\pi$
$54$	9.40181	+	10.0561i	1.27942	+	1.36847i
$55$	2.29501			0.309459
$56$	13.9254	+	24.1196i	1.86087	+	3.22311i
$57$	−2.87045	+	5.97984i	−0.380200	+	0.792049i
$58$	5.37393	+	20.0558i	0.705632	+	2.63345i
$59$	−0.450677	−	1.68195i	−0.0586732	−	0.218971i	0.930364	−	0.366637i	$-0.119491\pi$
$59$	−0.450677	−	1.68195i	−0.0586732	−	0.218971i	−0.989037	+	0.147665i	$0.952824\pi$
$60$	−13.2073	+	1.00651i	−1.70505	+	0.129939i
$61$	1.91165	+	3.31107i	0.244762	+	0.423940i	0.962065	−	0.272822i	$-0.0879570\pi$
$61$	1.91165	+	3.31107i	0.244762	+	0.423940i	−0.717303	+	0.696761i	$0.754624\pi$
$62$	−6.93108			−0.880248
$63$	−4.20109	−	9.56308i	−0.529287	−	1.20483i
$64$		−	13.6009i		−	1.70011i
$65$	−4.47916	+	3.18037i	−0.555571	+	0.394476i
$66$	1.27650	−	6.79336i	0.157126	−	0.836205i
$67$	−0.615801	−	2.29820i	−0.0752321	−	0.280770i	0.918054	−	0.396456i	$-0.129760\pi$
$67$	−0.615801	−	2.29820i	−0.0752321	−	0.280770i	−0.993286	+	0.115686i	$0.963093\pi$
$68$	−11.2919	−	6.51938i	−1.36934	−	0.790591i
$69$	−0.579007	+	3.08141i	−0.0697043	+	0.370958i
$70$	13.5755	+	3.63753i	1.62258	+	0.434768i
$71$	−8.23276	−	8.23276i	−0.977049	−	0.977049i	0.0226938	−	0.999742i	$-0.492776\pi$
$71$	−8.23276	−	8.23276i	−0.977049	−	0.977049i	−0.999742	+	0.0226938i	$0.992776\pi$
$72$	−2.62668	+	23.8533i	−0.309558	+	2.81114i
$73$	8.55641	+	8.55641i	1.00145	+	1.00145i	0.999999	+	0.00145288i	$0.000462465\pi$
$73$	8.55641	+	8.55641i	1.00145	+	1.00145i	0.00145288	+	0.999999i	$0.499538\pi$
$74$	14.6812	−	8.47619i	1.70665	−	0.985337i
$75$	3.02188	−	3.52046i	0.348937	−	0.406508i
$76$	−18.5668	+	4.97497i	−2.12976	+	0.570668i
$77$	−2.62227	+	4.54191i	−0.298836	+	0.517599i
$78$	6.92275	+	15.0275i	0.783847	+	1.70153i
$79$	−5.66639	−	9.81447i	−0.637519	−	1.10421i	−0.985976	−	0.166890i	$-0.946628\pi$
$79$	−5.66639	−	9.81447i	−0.637519	−	1.10421i	0.348457	−	0.937325i	$-0.386706\pi$
$80$	−12.0171	−	12.0171i	−1.34356	−	1.34356i
$81$	1.95838	−	8.78435i	0.217598	−	0.976039i
$82$		−	28.7859i		−	3.17888i
$83$	−1.64831	+	6.15156i	−0.180925	+	0.675222i	0.814541	+	0.580106i	$0.196989\pi$
$83$	−1.64831	+	6.15156i	−0.180925	+	0.675222i	−0.995466	+	0.0951160i	$0.969678\pi$
$84$	13.0987	−	27.2877i	1.42918	−	2.97733i
$85$	−3.82307	+	1.02439i	−0.414670	+	0.111111i
$86$	−2.87664	−	10.7358i	−0.310196	−	1.15767i
$87$	8.84123	−	10.2999i	0.947879	−	1.10427i
$88$	10.4349	−	6.02460i	1.11237	−	0.642224i
$89$	2.83751	−	2.83751i	0.300775	−	0.300775i	−0.540542	−	0.841317i	$-0.681781\pi$
$89$	2.83751	−	2.83751i	0.300775	−	0.300775i	0.841317	+	0.540542i	$0.181781\pi$
$90$	7.57421	+	9.44875i	0.798392	+	0.995986i
$91$	−1.17620	−	12.4983i	−0.123299	−	1.31018i
$92$	−7.86851	+	4.54289i	−0.820349	+	0.473629i
$93$	2.55725	+	3.74065i	0.265175	+	0.387888i
$94$	2.45780	−	4.25704i	0.253503	−	0.439080i
$95$	−2.91740	+	5.05309i	−0.299319	+	0.518436i
$96$	−19.3802	+	13.2490i	−1.97798	+	1.35222i
$97$	−1.28483	−	0.344269i	−0.130455	−	0.0349552i	0.193001	−	0.981199i	$-0.438178\pi$
$97$	−1.28483	−	0.344269i	−0.130455	−	0.0349552i	−0.323456	+	0.946243i	$0.604845\pi$
$98$	−9.59631	+	9.59631i	−0.969374	+	0.969374i
$99$	−4.13730	+	1.81753i	−0.415814	+	0.182668i
$100$	13.4448			1.34448
$101$	−0.742738	−	1.28646i	−0.0739051	−	0.128007i	0.826704	−	0.562636i	$-0.190213\pi$
$101$	−0.742738	−	1.28646i	−0.0739051	−	0.128007i	−0.900610	+	0.434629i	$0.856880\pi$
$102$	0.905837	+	11.8863i	0.0896912	+	1.17692i
$103$	7.82136	+	4.51566i	0.770661	+	0.444941i	0.833110	−	0.553107i	$-0.186558\pi$
$103$	7.82136	+	4.51566i	0.770661	+	0.444941i	−0.0624492	+	0.998048i	$0.519891\pi$
$104$	−12.0170	+	26.2186i	−1.17837	+	2.57095i
$105$	−3.04558	−	8.66866i	−0.297218	−	0.845975i
$106$	1.04069	+	0.278853i	0.101081	+	0.0270846i
$107$			10.4763i			1.01278i	0.862303	+	0.506392i	$0.169021\pi$
$107$			10.4763i			1.01278i	−0.862303	+	0.506392i	$0.830979\pi$
$108$	23.0121	−	12.2739i	2.21434	−	1.18106i
$109$	−9.73483	+	9.73483i	−0.932427	+	0.932427i	−0.997857	−	0.0654300i	$-0.979158\pi$
$109$	−9.73483	+	9.73483i	−0.932427	+	0.932427i	0.0654300	+	0.997857i	$0.479158\pi$
$110$	1.57371	−	5.87318i	0.150048	−	0.559986i
$111$	−9.99123	−	4.79600i	−0.948326	−	0.455216i
$112$	37.5132	−	10.0516i	3.54466	−	0.949789i
$113$	−0.217607	−	0.125635i	−0.0204707	−	0.0118188i	0.489730	−	0.871874i	$-0.337095\pi$
$113$	−0.217607	−	0.125635i	−0.0204707	−	0.0118188i	−0.510200	+	0.860056i	$0.670429\pi$
$114$	13.3348	+	11.4462i	1.24892	+	1.07204i
$115$	−0.713822	+	2.66402i	−0.0665643	+	0.248421i
$116$	39.3359			3.65225
$117$	5.55606	−	9.28063i	0.513658	−	0.857995i
$118$	−4.61333			−0.424692
$119$	2.34093	−	8.73647i	0.214593	−	0.800871i
$120$	−3.89831	+	20.7463i	−0.355866	+	1.89387i
$121$	−7.56130	−	4.36552i	−0.687391	−	0.396865i
$122$	9.78425	−	2.62168i	0.885824	−	0.237356i
$123$	−15.5356	+	10.6207i	−1.40080	+	0.957637i
$124$	−3.39853	+	12.6835i	−0.305197	+	1.13901i
$125$	8.27257	−	8.27257i	0.739921	−	0.739921i
$126$	−27.3537	+	4.19353i	−2.43686	+	0.373589i
$127$		−	7.23973i		−	0.642422i	−0.947008	−	0.321211i	$-0.895910\pi$
$127$		−	7.23973i		−	0.642422i	0.947008	−	0.321211i	$-0.104090\pi$
$128$	−8.62194	−	2.31024i	−0.762079	−	0.204198i
$129$	−4.73267	+	5.51352i	−0.416689	+	0.485438i
$130$	5.06751	+	13.6435i	0.444450	+	1.19661i
$131$	−0.716979	−	0.413948i	−0.0626427	−	0.0361668i	0.468352	−	0.883542i	$-0.344848\pi$
$131$	−0.716979	−	0.413948i	−0.0626427	−	0.0361668i	−0.530994	+	0.847375i	$0.678181\pi$
$132$	−11.8055	−	5.66691i	−1.02754	−	0.493242i
$133$	−6.66684	−	11.5473i	−0.578088	−	1.00128i
$134$	−6.30362			−0.544550
$135$	2.30488	−	7.57391i	0.198373	−	0.651858i
$136$	−14.6936	+	14.6936i	−1.25996	+	1.25996i
$137$	16.7313	+	4.48314i	1.42945	+	0.383020i	0.888827	−	0.458244i	$-0.151521\pi$
$137$	16.7313	+	4.48314i	1.42945	+	0.383020i	0.540625	+	0.841264i	$0.318188\pi$
$138$	7.48863	+	3.59470i	0.637474	+	0.306001i
$139$	−6.15846	+	10.6668i	−0.522354	+	0.904743i	0.477308	+	0.878736i	$0.341613\pi$
$139$	−6.15846	+	10.6668i	−0.522354	+	0.904743i	−0.999662	+	0.0260070i	$0.991721\pi$
$140$	13.3129	−	23.0587i	1.12515	−	1.94882i
$141$	−3.20431	+	0.244196i	−0.269852	+	0.0205650i
$142$	−26.7138	+	15.4232i	−2.24178	+	1.29429i
$143$	−5.40718	+	0.508860i	−0.452171	+	0.0425530i
$144$	31.1807	+	12.1468i	2.59839	+	1.01223i
$145$	8.44319	−	8.44319i	0.701168	−	0.701168i
$146$	27.7640	−	16.0296i	2.29777	−	1.32662i
$147$	8.71966	+	1.63846i	0.719186	+	0.135138i
$148$	−8.31228	−	31.0219i	−0.683265	−	2.54998i
$149$	14.5351	−	3.89466i	1.19076	−	0.319063i	0.391574	−	0.920147i	$-0.371931\pi$
$149$	14.5351	−	3.89466i	1.19076	−	0.319063i	0.799186	+	0.601083i	$0.205264\pi$
$150$	−6.93711	−	10.1473i	−0.566413	−	0.828527i
$151$	−0.773087	+	2.88520i	−0.0629130	+	0.234794i	−0.990222	−	0.139503i	$-0.955449\pi$
$151$	−0.773087	+	2.88520i	−0.0629130	+	0.234794i	0.927309	+	0.374298i	$0.122116\pi$
$152$			30.6337i			2.48472i
$153$	6.08073	−	4.87437i	0.491598	−	0.394070i
$154$	9.82513	+	9.82513i	0.791731	+	0.791731i
$155$	1.99295	+	3.45189i	0.160078	+	0.277263i
$156$	30.8939	−	5.29977i	2.47349	−	0.424321i
$157$	−7.17679	+	12.4306i	−0.572770	+	0.992067i	0.423510	+	0.905891i	$0.360798\pi$
$157$	−7.17679	+	12.4306i	−0.572770	+	0.992067i	−0.996280	+	0.0861753i	$0.972535\pi$
$158$	−29.0018	+	7.77102i	−2.30726	+	0.618229i
$159$	−0.233474	−	0.664539i	−0.0185157	−	0.0527014i
$160$	−17.8841	+	10.3254i	−1.41386	+	0.816294i
$161$	−4.45659	−	4.45659i	−0.351228	−	0.351228i
$162$	−21.1372	−	11.0352i	−1.66070	−	0.867011i
$163$	7.58297	+	7.58297i	0.593944	+	0.593944i	0.938694	−	0.344750i	$-0.112036\pi$
$163$	7.58297	+	7.58297i	0.593944	+	0.593944i	−0.344750	+	0.938694i	$0.612036\pi$
$164$	−52.6766	−	14.1147i	−4.11335	−	1.10217i
$165$	−3.75034	+	1.31762i	−0.291964	+	0.102576i
$166$	14.6123	+	8.43640i	1.13413	+	0.654792i
$167$	2.46928	+	9.21548i	0.191079	+	0.713115i	0.993247	+	0.116018i	$0.0370129\pi$
$167$	2.46928	+	9.21548i	0.191079	+	0.713115i	−0.802169	+	0.597098i	$0.796320\pi$
$168$	−36.6036	−	31.4196i	−2.82403	−	2.42408i
$169$	9.84800	−	8.48628i	0.757538	−	0.652791i
$170$			10.4861i			0.804247i
$171$	1.25753	−	11.4198i	0.0961657	−	0.873296i
$172$	−21.0564			−1.60553
$173$	−4.25787	−	7.37485i	−0.323720	−	0.560700i	0.657532	−	0.753426i	$-0.271600\pi$
$173$	−4.25787	−	7.37485i	−0.323720	−	0.560700i	−0.981252	+	0.192727i	$0.938267\pi$
$174$	−20.2962	−	29.6885i	−1.53865	−	2.25068i
$175$	2.41382	+	9.00851i	0.182468	+	0.680980i
$176$	−4.34866	−	16.2294i	−0.327792	−	1.22334i
$177$	1.70211	+	2.48978i	0.127938	+	0.187143i
$178$	−5.31578	−	9.20721i	−0.398435	−	0.690109i
$179$	18.3712			1.37312			0.686562	−	0.727071i	$-0.259119\pi$
$179$	18.3712			1.37312			0.686562	+	0.727071i	$0.259119\pi$
$180$	21.0045	−	9.22735i	1.56559	−	0.687766i
$181$		−	17.5314i		−	1.30310i	−0.758606	−	0.651550i	$-0.774119\pi$
$181$		−	17.5314i		−	1.30310i	0.758606	−	0.651550i	$-0.225881\pi$
$182$	−32.7911	−	5.56022i	−2.43064	−	0.412151i
$183$	−5.02485	−	4.31321i	−0.371447	−	0.318841i
$184$	3.74769	+	13.9866i	0.276284	+	1.03110i
$185$	−8.44280	−	4.87445i	−0.620727	−	0.358377i
$186$	11.3263	−	3.97929i	0.830484	−	0.291776i
$187$	−3.77968	−	1.01276i	−0.276397	−	0.0740605i
$188$	−6.58500	−	6.58500i	−0.480260	−	0.480260i
$189$	12.3555	+	13.2154i	0.898731	+	0.961278i
$190$	10.9309	+	10.9309i	0.793012	+	0.793012i
$191$	−1.43051	+	0.825903i	−0.103508	+	0.0597602i	−0.550860	−	0.834597i	$-0.685700\pi$
$191$	−1.43051	+	0.825903i	−0.103508	+	0.0597602i	0.447352	+	0.894358i	$0.352367\pi$
$192$	7.80856	+	22.2256i	0.563535	+	1.60399i
$193$	−16.7712	+	4.49382i	−1.20722	+	0.323472i	−0.805669	−	0.592366i	$-0.798194\pi$
$193$	−16.7712	+	4.49382i	−1.20722	+	0.323472i	−0.401547	+	0.915839i	$0.631527\pi$
$194$	−1.76204	+	3.05195i	−0.126507	+	0.219117i
$195$	5.49361	−	7.76873i	0.393406	−	0.556330i
$196$	12.8553	+	22.2661i	0.918237	+	1.59043i
$197$	0.00937350	+	0.00937350i	0.000667834	+	0.000667834i	0.707441	−	0.706773i	$-0.249850\pi$
$197$	0.00937350	+	0.00937350i	0.000667834	+	0.000667834i	−0.706773	+	0.707441i	$0.749850\pi$
$198$	1.81426	+	11.8341i	0.128934	+	0.841013i
$199$			25.9833i			1.84191i	0.389674	+	0.920953i	$0.372588\pi$
$199$			25.9833i			1.84191i	−0.389674	+	0.920953i	$0.627412\pi$
$200$	5.54569	−	20.6968i	0.392140	−	1.46349i
$201$	2.32575	+	3.40202i	0.164046	+	0.239960i
$202$	−3.80150	+	1.01861i	−0.267472	+	0.0716690i
$203$	7.06222	+	26.3566i	0.495670	+	1.84987i
$204$	22.1954	+	4.17059i	1.55399	+	0.292000i
$205$	−14.3363	+	8.27706i	−1.00129	+	0.578095i
$206$	16.9193	−	16.9193i	1.17882	−	1.17882i
$207$	−0.822930	−	5.36784i	−0.0571976	−	0.373091i
$208$	30.9776	+	25.6486i	2.14791	+	1.77841i
$209$	−4.99574	+	2.88429i	−0.345562	+	0.199510i
$210$	−24.2725	+	1.84977i	−1.67496	+	0.127646i
$211$	0.0840989	−	0.145664i	0.00578960	−	0.0100279i	−0.863116	−	0.505006i	$-0.831490\pi$
$211$	0.0840989	−	0.145664i	0.00578960	−	0.0100279i	0.868906	+	0.494978i	$0.164824\pi$
$212$	1.02057	−	1.76768i	0.0700930	−	0.121405i
$213$	18.1800	+	8.72679i	1.24567	+	0.597950i
$214$	26.8101	+	7.18374i	1.83270	+	0.491070i
$215$	−4.51960	+	4.51960i	−0.308234	+	0.308234i
$216$	−9.40237	−	40.4875i	−0.639750	−	2.75482i
$217$	−9.10856			−0.618330
$218$	18.2372	+	31.5878i	1.23518	+	2.13939i
$219$	−18.8947	−	9.06986i	−1.27679	−	0.612885i
$220$	−9.97594	−	5.75961i	−0.672578	−	0.388313i
$221$	8.78025	−	3.26119i	0.590623	−	0.219371i
$222$	−19.1246	+	22.2800i	−1.28356	+	1.49534i
$223$	12.4141	+	3.32636i	0.831312	+	0.222749i	0.649286	−	0.760544i	$-0.275068\pi$
$223$	12.4141	+	3.32636i	0.831312	+	0.222749i	0.182026	+	0.983294i	$0.441734\pi$
$224$		−	47.1911i		−	3.15309i
$225$	−2.91697	+	7.48782i	−0.194465	+	0.499188i
$226$	−0.470730	+	0.470730i	−0.0313125	+	0.0313125i
$227$	−0.279501	+	1.04311i	−0.0185511	+	0.0692337i	−0.974581	−	0.224036i	$-0.928077\pi$
$227$	−0.279501	+	1.04311i	−0.0185511	+	0.0692337i	0.956030	+	0.293270i	$0.0947434\pi$
$228$	27.4844	−	18.7894i	1.82020	−	1.24436i
$229$	−0.302939	+	0.0811723i	−0.0200188	+	0.00536402i	−0.268815	−	0.963192i	$-0.586632\pi$
$229$	−0.302939	+	0.0811723i	−0.0200188	+	0.00536402i	0.248796	+	0.968556i	$0.419965\pi$
$230$	6.32805	+	3.65350i	0.417259	+	0.240905i
$231$	1.67752	−	8.92758i	0.110373	−	0.587392i
$232$	16.2252	−	60.5534i	1.06524	−	3.97553i
$233$	−22.2388			−1.45691			−0.728456	−	0.685092i	$-0.759762\pi$
$233$	−22.2388			−1.45691			−0.728456	+	0.685092i	$0.759762\pi$
$234$	−19.9403	−	20.5824i	−1.30354	−	1.34552i
$235$	−2.82685			−0.184403
$236$	−2.26206	+	8.44213i	−0.147248	+	0.549536i
$237$	14.8943	+	12.7849i	0.967491	+	0.830471i
$238$	−20.7524	−	11.9814i	−1.34518	−	0.776639i
$239$	6.85098	−	1.83572i	0.443153	−	0.118743i	−0.0303407	−	0.999540i	$-0.509659\pi$
$239$	6.85098	−	1.83572i	0.443153	−	0.118743i	0.473494	+	0.880797i	$0.342993\pi$
$240$	26.5369	+	12.7383i	1.71295	+	0.822252i
$241$	−7.33687	+	27.3816i	−0.472609	+	1.76380i	0.157730	+	0.987482i	$0.449582\pi$
$241$	−7.33687	+	27.3816i	−0.472609	+	1.76380i	−0.630339	+	0.776320i	$0.717084\pi$
$242$	−16.3567	+	16.3567i	−1.05145	+	1.05145i
$243$	1.84304	+	15.4791i	0.118231	+	0.992986i
$244$		−	19.1901i		−	1.22852i
$245$	7.53856	+	2.01995i	0.481621	+	0.129050i
$246$	16.5267	+	47.0400i	1.05370	+	2.99916i
$247$	5.75318	−	12.5522i	0.366066	−	0.798680i
$248$	18.1230	+	10.4633i	1.15081	+	0.664422i
$249$	−0.838202	−	10.9988i	−0.0531189	−	0.697020i
$250$	−15.4978	−	26.8430i	−0.980169	−	1.69770i
$251$	−8.19840			−0.517478			−0.258739	−	0.965947i	$-0.583307\pi$
$251$	−8.19840			−0.517478			−0.258739	+	0.965947i	$0.583307\pi$
$252$	−5.73847	+	52.1119i	−0.361490	+	3.28274i
$253$	−1.92806	+	1.92806i	−0.121216	+	0.121216i
$254$	−18.5273	−	4.96437i	−1.16250	−	0.311492i
$255$	5.65927	−	3.86890i	0.354397	−	0.242280i
$256$	1.77654	−	3.07706i	0.111034	−	0.192316i
$257$	6.91036	−	11.9691i	0.431056	−	0.746612i	−0.565908	−	0.824468i	$-0.691474\pi$
$257$	6.91036	−	11.9691i	0.431056	−	0.746612i	0.996965	+	0.0778567i	$0.0248077\pi$
$258$	10.8645	+	15.8921i	0.676392	+	0.989400i
$259$	19.2935	−	11.1391i	1.19884	−	0.692149i
$260$	27.4515	−	2.58342i	1.70247	−	0.160217i
$261$	−8.53429	+	21.9074i	−0.528259	+	1.35603i
$262$	−1.55098	+	1.55098i	−0.0958198	+	0.0958198i
$263$	−14.6369	+	8.45062i	−0.902550	+	0.521088i	−0.878027	−	0.478611i	$-0.841140\pi$
$263$	−14.6369	+	8.45062i	−0.902550	+	0.521088i	−0.0245237	+	0.999699i	$0.507807\pi$
$264$	−13.5932	+	15.8359i	−0.836601	+	0.974632i
$265$	−0.160362	−	0.598478i	−0.00985094	−	0.0367642i
$266$	−34.1224	+	9.14306i	−2.09218	+	0.560597i
$267$	−3.00778	+	6.26593i	−0.184073	+	0.383469i
$268$	−3.09086	+	11.5353i	−0.188804	+	0.704628i
$269$		−	9.83504i		−	0.599653i	−0.953994	−	0.299826i	$-0.903071\pi$
$269$		−	9.83504i		−	0.599653i	0.953994	−	0.299826i	$-0.0969287\pi$
$270$	−17.8020	−	11.0920i	−1.08339	−	0.675036i
$271$	−3.22322	−	3.22322i	−0.195797	−	0.195797i	0.602399	−	0.798195i	$-0.294212\pi$
$271$	−3.22322	−	3.22322i	−0.195797	−	0.195797i	−0.798195	+	0.602399i	$0.794212\pi$
$272$	14.4882	+	25.0942i	0.878473	+	1.52156i
$273$	9.09762	+	19.7486i	0.550613	+	1.19524i
$274$	22.9457	−	39.7431i	1.38620	−	2.40097i
$275$	3.89738	−	1.04430i	0.235021	−	0.0629736i
$276$	10.2500	−	11.9412i	0.616978	−	0.718773i
$277$	12.7572	−	7.36536i	0.766505	−	0.442542i	−0.0651216	−	0.997877i	$-0.520744\pi$
$277$	12.7572	−	7.36536i	0.766505	−	0.442542i	0.831626	+	0.555336i	$0.187410\pi$
$278$	23.0745	+	23.0745i	1.38392	+	1.38392i
$279$	−6.32648	−	4.64454i	−0.378757	−	0.278061i
$280$	−30.0051	−	30.0051i	−1.79315	−	1.79315i
$281$	2.64741	+	0.709373i	0.157932	+	0.0423176i	0.336918	−	0.941534i	$-0.390615\pi$
$281$	2.64741	+	0.709373i	0.157932	+	0.0423176i	−0.178987	+	0.983851i	$0.557282\pi$
$282$	−1.57231	+	8.36764i	−0.0936297	+	0.498286i
$283$	8.85528	+	5.11260i	0.526392	+	0.303912i	0.739546	−	0.673106i	$-0.235040\pi$
$283$	8.85528	+	5.11260i	0.526392	+	0.303912i	−0.213154	+	0.977019i	$0.568374\pi$
$284$	15.1250	+	56.4473i	0.897504	+	3.34953i
$285$	1.86633	−	9.93235i	0.110552	−	0.588342i
$286$	−2.40553	+	14.1865i	−0.142242	+	0.838865i
$287$		−	37.8294i		−	2.23300i
$288$	24.0632	−	32.7772i	1.41794	−	1.93142i
$289$	−10.2517			−0.603040
$290$	−15.8175	−	27.3966i	−0.928833	−	1.60879i
$291$	2.29723	−	0.175069i	0.134666	−	0.0102627i
$292$	−15.7196	−	58.6664i	−0.919920	−	3.43319i
$293$	−6.73463	−	25.1340i	−0.393441	−	1.46834i	−0.824419	−	0.565980i	$-0.808498\pi$
$293$	−6.73463	−	25.1340i	−0.393441	−	1.46834i	0.430978	−	0.902363i	$-0.358169\pi$
$294$	10.1722	−	21.1911i	0.593253	−	1.23589i
$295$	1.32651	+	2.29758i	0.0772323	+	0.133770i
$296$	−51.1835			−2.97498
$297$	5.71740	−	5.34539i	0.331757	−	0.310171i
$298$		−	39.8675i		−	2.30946i
$299$	1.09113	−	6.43486i	0.0631015	−	0.372138i
$300$	−21.9705	+	7.71895i	−1.26847	+	0.445654i
$301$	−3.78038	−	14.1086i	−0.217897	−	0.813204i
$302$	6.85344	+	3.95683i	0.394371	+	0.227690i
$303$	1.95232	+	1.67582i	0.112158	+	0.0962734i
$304$	41.2615	+	11.0560i	2.36651	+	0.634104i
$305$	−4.11902	−	4.11902i	−0.235854	−	0.235854i
$306$	−8.30444	−	18.9037i	−0.474733	−	1.08065i
$307$	−3.60824	−	3.60824i	−0.205933	−	0.205933i	0.596603	−	0.802536i	$-0.296517\pi$
$307$	−3.60824	−	3.60824i	−0.205933	−	0.205933i	−0.802536	+	0.596603i	$0.796517\pi$
$308$	22.7970	−	13.1618i	1.29898	−	0.749966i
$309$	−15.3737	−	2.88877i	−0.874577	−	0.164336i
$310$	10.2004	−	2.73318i	0.579342	−	0.155234i
$311$	−11.8420	+	20.5109i	−0.671498	+	1.16307i	0.305981	+	0.952038i	$0.401016\pi$
$311$	−11.8420	+	20.5109i	−0.671498	+	1.16307i	−0.977479	+	0.211031i	$0.932318\pi$
$312$	4.58467	−	49.7439i	0.259556	−	2.81620i
$313$	7.69408	+	13.3265i	0.434895	+	0.753261i	0.997287	−	0.0736102i	$-0.0234521\pi$
$313$	7.69408	+	13.3265i	0.434895	+	0.753261i	−0.562392	+	0.826871i	$0.690119\pi$
$314$	26.8900	+	26.8900i	1.51749	+	1.51749i
$315$	9.95375	+	12.4172i	0.560830	+	0.699630i
$316$			56.8821i			3.19987i
$317$	−0.337466	+	1.25944i	−0.0189540	+	0.0707372i	−0.974755	−	0.223277i	$-0.928325\pi$
$317$	−0.337466	+	1.25944i	−0.0189540	+	0.0707372i	0.955801	+	0.294014i	$0.0949913\pi$
$318$	−1.86073	+	0.141803i	−0.104344	+	0.00795193i
$319$	11.4027	−	3.05534i	0.638429	−	0.171066i
$320$	5.36332	+	20.0162i	0.299819	+	1.11894i
$321$	−6.01469	−	17.1197i	−0.335707	−	0.955527i
$322$	−14.4608	+	8.34897i	−0.805871	+	0.465270i
$323$	7.03458	−	7.03458i	0.391414	−	0.391414i
$324$	−30.5581	+	33.2690i	−1.69767	+	1.84828i
$325$	−6.15933	+	7.43905i	−0.341658	+	0.412644i
$326$	24.6054	−	14.2059i	1.36277	−	0.786794i
$327$	10.3190	−	21.4970i	0.570642	−	1.18878i
$328$	−43.4560	+	75.2680i	−2.39946	+	4.15598i
$329$	3.22995	−	5.59444i	0.178073	−	0.308431i
$330$	0.800270	+	10.5011i	0.0440534	+	0.578064i
$331$	5.35508	+	1.43489i	0.294342	+	0.0788687i	0.402968	−	0.915214i	$-0.367979\pi$
$331$	5.35508	+	1.43489i	0.294342	+	0.0788687i	−0.108626	+	0.994083i	$0.534645\pi$
$332$	22.6030	−	22.6030i	1.24050	−	1.24050i
$333$	19.0805	+	2.10111i	1.04560	+	0.115140i
$334$	25.2767			1.38308
$335$	1.81253	+	3.13939i	0.0990291	+	0.171523i
$336$	−55.5305	+	37.9628i	−3.02944	+	2.07104i
$337$	14.8804	+	8.59121i	0.810588	+	0.467993i	0.847160	−	0.531338i	$-0.178311\pi$
$337$	14.8804	+	8.59121i	0.810588	+	0.467993i	−0.0365723	+	0.999331i	$0.511644\pi$
$338$	−14.9645	−	31.0213i	−0.813959	−	1.68733i
$339$	0.427728	+	0.0803717i	0.0232310	+	0.00436519i
$340$	19.1889	+	5.14166i	1.04067	+	0.278846i
$341$			3.94066i			0.213399i
$342$	−28.3623	−	11.0489i	−1.53366	−	0.597454i
$343$	4.62255	−	4.62255i	0.249594	−	0.249594i
$344$	−8.68531	+	32.4140i	−0.468280	+	1.74765i
$345$	−0.362995	−	4.76318i	−0.0195430	−	0.256441i
$346$	−21.7927	+	5.83935i	−1.17159	+	0.313925i
$347$	−20.6639	−	11.9303i	−1.10930	−	0.640454i	−0.170651	−	0.985332i	$-0.554587\pi$
$347$	−20.6639	−	11.9303i	−1.10930	−	0.640454i	−0.938648	+	0.344878i	$0.887920\pi$
$348$	−64.2801	+	22.5836i	−3.44577	+	1.21061i
$349$	−3.27980	+	12.2404i	−0.175564	+	0.655213i	0.820891	+	0.571085i	$0.193477\pi$
$349$	−3.27980	+	12.2404i	−0.175564	+	0.655213i	−0.996455	+	0.0841282i	$0.973189\pi$
$350$	24.7090			1.32075
$351$	−3.75111	+	18.3556i	−0.200220	+	0.979751i
$352$	−20.4164			−1.08820
$353$	−7.78873	+	29.0679i	−0.414552	+	1.54713i	0.371179	+	0.928561i	$0.378954\pi$
$353$	−7.78873	+	29.0679i	−0.414552	+	1.54713i	−0.785731	+	0.618568i	$0.787713\pi$
$354$	7.53879	−	2.64862i	0.400682	−	0.140772i
$355$	15.3625	+	8.86954i	0.815357	+	0.470746i
$356$	−19.4551	+	5.21299i	−1.03112	+	0.276288i
$357$	1.19042	+	15.6205i	0.0630035	+	0.826725i
$358$	12.5973	−	47.0138i	0.665789	−	2.48476i
$359$	−0.225715	+	0.225715i	−0.0119128	+	0.0119128i	−0.713038	−	0.701125i	$-0.752681\pi$
$359$	−0.225715	+	0.225715i	−0.0119128	+	0.0119128i	0.701125	+	0.713038i	$0.252681\pi$
$360$	−5.54058	−	36.1403i	−0.292014	−	1.90476i
$361$			4.33403i			0.228107i
$362$	−44.8649	−	12.0215i	−2.35804	−	0.631836i
$363$	14.8625	+	2.79272i	0.780079	+	0.146580i
$364$	−26.2534	+	57.2795i	−1.37605	+	3.00226i
$365$	−15.9664	−	9.21823i	−0.835721	−	0.482504i
$366$	−14.4836	+	9.90152i	−0.757068	+	0.517561i
$367$	−16.2690	−	28.1787i	−0.849234	−	1.47092i	−0.881893	−	0.471450i	$-0.843731\pi$
$367$	−16.2690	−	28.1787i	−0.849234	−	1.47092i	0.0326586	−	0.999467i	$-0.489603\pi$
$368$	20.1915			1.05255
$369$	19.2896	−	26.2750i	1.00417	−	1.36782i
$370$	−18.2636	+	18.2636i	−0.949479	+	0.949479i
$371$	1.36764	+	0.366458i	0.0710043	+	0.0190256i
$372$	−1.72823	−	22.6776i	−0.0896045	−	1.17578i
$373$	11.7674	−	20.3817i	0.609293	−	1.05533i	−0.382064	−	0.924136i	$-0.624787\pi$
$373$	11.7674	−	20.3817i	0.609293	−	1.05533i	0.991357	−	0.131191i	$-0.0418801\pi$
$374$	−5.18354	+	8.97815i	−0.268034	+	0.464249i
$375$	−8.76899	+	18.2679i	−0.452829	+	0.943352i
$376$	−12.8531	+	7.42072i	−0.662846	+	0.382695i
$377$	−18.0206	+	21.7647i	−0.928107	+	1.12094i
$378$	42.2920	−	22.5572i	2.17526	−	1.16022i
$379$	−18.0218	+	18.0218i	−0.925715	+	0.925715i	−0.997426	−	0.0717103i	$-0.977154\pi$
$379$	−18.0218	+	18.0218i	−0.925715	+	0.925715i	0.0717103	+	0.997426i	$0.477154\pi$
$380$	25.3627	−	14.6432i	1.30108	−	0.751179i
$381$	4.15649	+	11.8307i	0.212944	+	0.606104i
$382$	1.13266	+	4.22715i	0.0579521	+	0.216280i
$383$	13.3659	−	3.58139i	0.682967	−	0.183001i	0.0993783	−	0.995050i	$-0.468315\pi$
$383$	13.3659	−	3.58139i	0.682967	−	0.183001i	0.583589	+	0.812049i	$0.301648\pi$
$384$	15.4157	−	1.17481i	0.786681	−	0.0599518i
$385$	2.06812	−	7.71831i	0.105401	−	0.393362i
$386$			46.0008i			2.34138i
$387$	4.56837	−	11.7269i	0.232223	−	0.596114i
$388$	4.72091	+	4.72091i	0.239668	+	0.239668i
$389$	−12.3693	−	21.4243i	−0.627150	−	1.08626i	−0.988121	−	0.153679i	$-0.950888\pi$
$389$	−12.3693	−	21.4243i	−0.627150	−	1.08626i	0.360971	−	0.932577i	$-0.382445\pi$
$390$	−16.1140	−	19.3859i	−0.815964	−	0.981642i
$391$	2.35121	−	4.07241i	0.118906	−	0.205951i
$392$	39.5788	−	10.6051i	1.99903	−	0.535638i
$393$	1.40929	+	0.264811i	0.0710895	+	0.0133580i
$394$	0.0304154	−	0.0175603i	0.00153230	−	0.000884676i
$395$	12.2093	+	12.2093i	0.614319	+	0.614319i
$396$	22.5453	+	2.48265i	1.13294	+	0.124758i
$397$	4.42850	+	4.42850i	0.222260	+	0.222260i	0.809450	−	0.587189i	$-0.199766\pi$
$397$	4.42850	+	4.42850i	0.222260	+	0.222260i	−0.587189	+	0.809450i	$0.699766\pi$
$398$	66.4941	+	17.8170i	3.33305	+	0.893088i
$399$	17.5240	+	15.0422i	0.877300	+	0.753053i
$400$	−25.8756	−	14.9393i	−1.29378	−	0.746965i
$401$	−8.01423	−	29.9095i	−0.400212	−	1.49361i	−0.812719	−	0.582656i	$-0.802014\pi$
$401$	−8.01423	−	29.9095i	−0.400212	−	1.49361i	0.412507	−	0.910954i	$-0.364653\pi$
$402$	10.3009	−	3.61905i	0.513764	−	0.180502i
$403$	−5.46088	−	7.69097i	−0.272026	−	0.383115i
$404$			7.45597i			0.370949i
$405$	0.581872	+	13.7000i	0.0289135	+	0.680761i
$406$	72.2920			3.58779
$407$	−4.81913	−	8.34698i	−0.238875	−	0.413744i
$408$	15.5753	−	32.4471i	0.771093	−	1.60637i
$409$	−4.56541	−	17.0383i	−0.225745	−	0.842491i	−0.982105	−	0.188335i	$-0.939691\pi$
$409$	−4.56541	−	17.0383i	−0.225745	−	0.842491i	0.756360	−	0.654156i	$-0.226976\pi$
$410$	11.3514	+	42.3638i	0.560603	+	2.09220i
$411$	−29.9150	+	2.27978i	−1.47560	+	0.112453i
$412$	−22.6652	−	39.2574i	−1.11664	−	1.93407i
$413$	−6.06267			−0.298324
$414$	−14.3012	−	1.57482i	−0.702866	−	0.0773983i
$415$		−	9.70315i		−	0.476309i
$416$	39.8466	−	28.2926i	1.95364	−	1.38716i
$417$	3.93970	−	20.9666i	0.192928	−	1.02674i
$418$	3.95558	+	14.7624i	0.193474	+	0.722054i
$419$	8.59709	+	4.96353i	0.419996	+	0.242485i	0.695075	−	0.718937i	$-0.255371\pi$
$419$	8.59709	+	4.96353i	0.419996	+	0.242485i	−0.275080	+	0.961421i	$0.588704\pi$
$420$	−8.51658	+	45.3242i	−0.415567	+	2.21159i
$421$	−31.9538	−	8.56199i	−1.55733	−	0.417286i	−0.625514	−	0.780213i	$-0.715111\pi$
$421$	−31.9538	−	8.56199i	−1.55733	−	0.417286i	−0.931818	+	0.362927i	$0.881777\pi$
$422$	−0.315102	−	0.315102i	−0.0153389	−	0.0153389i
$423$	5.09607	−	2.23871i	0.247779	−	0.108850i
$424$	−2.30019	−	2.30019i	−0.111707	−	0.111707i
$425$	−6.02620	+	3.47923i	−0.292313	+	0.168767i
$426$	34.7991	−	40.5406i	1.68602	−	1.96420i
$427$	12.8581	−	3.44531i	0.622246	−	0.166730i
$428$	26.2916	−	45.5385i	1.27085	−	2.20118i
$429$	8.54388	−	3.93592i	0.412503	−	0.190028i
$430$	8.46702	+	14.6653i	0.408316	+	0.707224i
$431$	−18.0095	−	18.0095i	−0.867485	−	0.867485i	0.124708	−	0.992193i	$-0.460200\pi$
$431$	−18.0095	−	18.0095i	−0.867485	−	0.867485i	−0.992193	+	0.124708i	$0.960200\pi$
$432$	−57.9271	−	1.94794i	−2.78702	−	0.0937203i
$433$		−	18.6308i		−	0.895339i	−0.894199	−	0.447670i	$-0.852254\pi$
$433$		−	18.6308i		−	0.895339i	0.894199	−	0.447670i	$-0.147746\pi$
$434$	−6.24585	+	23.3098i	−0.299810	+	1.11891i
$435$	−8.94985	+	18.6447i	−0.429112	+	0.893945i
$436$	66.7461	−	17.8846i	3.19656	−	0.856515i
$437$	−1.79422	−	6.69610i	−0.0858290	−	0.320318i
$438$	−36.1671	+	42.1344i	−1.72813	+	2.01326i
$439$	−36.0215	+	20.7970i	−1.71921	+	0.992588i	−0.798843	+	0.601539i	$0.794554\pi$
$439$	−36.0215	+	20.7970i	−1.71921	+	0.992588i	−0.920370	+	0.391049i	$0.872112\pi$
$440$	−12.9812	+	12.9812i	−0.618853	+	0.618853i
$441$	−15.1897	+	2.32870i	−0.723321	+	0.110891i
$442$	−2.32503	−	24.7059i	−0.110590	−	1.17514i
$443$	−6.74756	+	3.89571i	−0.320586	+	0.185091i	−0.651654	−	0.758516i	$-0.725925\pi$
$443$	−6.74756	+	3.89571i	−0.320586	+	0.185091i	0.331068	+	0.943607i	$0.392591\pi$
$444$	31.3937	+	45.9215i	1.48988	+	2.17934i
$445$	−3.05698	+	5.29485i	−0.144915	+	0.251000i
$446$	17.0250	−	29.4882i	0.806159	−	1.39631i
$447$	−21.5162	+	14.7093i	−1.01768	+	0.695726i
$448$	−45.7409	−	12.2562i	−2.16105	−	0.579053i
$449$	11.7413	−	11.7413i	0.554107	−	0.554107i	−0.373517	−	0.927623i	$-0.621848\pi$
$449$	11.7413	−	11.7413i	0.554107	−	0.554107i	0.927623	+	0.373517i	$0.121848\pi$
$450$	17.1620	+	12.5993i	0.809023	+	0.593939i
$451$	−16.3662			−0.770656
$452$	0.630595	+	1.09222i	0.0296607	+	0.0513739i
$453$	−0.393133	−	5.15864i	−0.0184710	−	0.242374i
$454$	2.47778	+	1.43055i	0.116288	+	0.0671389i
$455$	6.65953	+	17.9298i	0.312204	+	0.840560i
$456$	−17.5875	−	50.0595i	−0.823611	−	2.34425i
$457$	29.4761	+	7.89809i	1.37883	+	0.369457i	0.870697	−	0.491820i	$-0.163668\pi$
$457$	29.4761	+	7.89809i	1.37883	+	0.369457i	0.508135	+	0.861277i	$0.330335\pi$
$458$			0.830916i			0.0388262i
$459$	−7.13822	+	11.4564i	−0.333184	+	0.534741i
$460$	9.78854	−	9.78854i	0.456393	−	0.456393i
$461$	10.3723	−	38.7099i	0.483086	−	1.80290i	−0.105443	−	0.994425i	$-0.533626\pi$
$461$	10.3723	−	38.7099i	0.483086	−	1.80290i	0.588529	−	0.808476i	$-0.299707\pi$
$462$	−21.6964	−	10.4147i	−1.00941	−	0.484537i
$463$	−1.21548	+	0.325687i	−0.0564881	+	0.0151359i	−0.286952	−	0.957945i	$-0.592642\pi$
$463$	−1.21548	+	0.325687i	−0.0564881	+	0.0151359i	0.230464	+	0.973081i	$0.425976\pi$
$464$	−75.7053	−	43.7085i	−3.51453	−	2.02912i
$465$	−5.23855	−	4.49664i	−0.242932	−	0.208527i
$466$	−15.2494	+	56.9116i	−0.706416	+	2.63638i
$467$	14.8110			0.685372			0.342686	−	0.939450i	$-0.388663\pi$
$467$	14.8110			0.685372			0.342686	+	0.939450i	$0.388663\pi$
$468$	−47.4420	+	26.3974i	−2.19301	+	1.22022i
$469$	−8.28398			−0.382518
$470$	−1.93840	+	7.23422i	−0.0894119	+	0.333690i
$471$	4.59115	−	24.4335i	0.211549	−	1.12584i
$472$	12.0627	+	6.96440i	0.555231	+	0.320563i
$473$	−6.10382	+	1.63551i	−0.280654	+	0.0752010i
$474$	42.9313	−	29.3495i	1.97190	−	1.34807i
$475$	−2.65501	+	9.90864i	−0.121820	+	0.454640i
$476$	−32.1008	+	32.1008i	−1.47134	+	1.47134i
$477$	0.763053	+	0.951901i	0.0349378	+	0.0435846i
$478$		−	18.7912i		−	0.859490i
$479$	29.8830	+	8.00712i	1.36539	+	0.365855i	0.865792	−	0.500403i	$-0.166815\pi$
$479$	29.8830	+	8.00712i	1.36539	+	0.365855i	0.499597	+	0.866258i	$0.333482\pi$
$480$	23.2969	−	27.1407i	1.06335	−	1.23880i
$481$	20.9725	+	9.61252i	0.956265	+	0.438293i
$482$	65.0415	+	37.5517i	2.96256	+	1.71043i
$483$	9.84127	+	4.72402i	0.447793	+	0.214950i
$484$	21.9116	+	37.9521i	0.995984	+	1.72509i
$485$	2.02662			0.0920241
$486$	40.8766	+	5.89767i	1.85420	+	0.267524i
$487$	12.6165	−	12.6165i	0.571707	−	0.571707i	−0.360898	−	0.932605i	$-0.617530\pi$
$487$	12.6165	−	12.6165i	0.571707	−	0.571707i	0.932605	+	0.360898i	$0.117530\pi$
$488$	−29.5411	−	7.91551i	−1.33726	−	0.358318i
$489$	−16.7451	−	8.03801i	−0.757240	−	0.363491i
$490$	10.3386	−	17.9069i	0.467049	−	0.808952i
$491$	−20.4459	+	35.4134i	−0.922711	+	1.59818i	−0.127510	+	0.991837i	$0.540698\pi$
$491$	−20.4459	+	35.4134i	−0.922711	+	1.59818i	−0.795201	+	0.606346i	$0.792635\pi$
$492$	94.1840	−	7.17763i	4.24614	−	0.323592i
$493$	−17.6311	+	10.1793i	−0.794064	+	0.458453i
$494$	−28.1775	−	23.3302i	−1.26777	−	1.04968i
$495$	5.37208	−	4.30631i	0.241457	−	0.193554i
$496$	20.6341	−	20.6341i	0.926499	−	0.926499i
$497$	−35.1063	+	20.2686i	−1.57473	+	0.909173i
$498$	−28.7219	−	5.39695i	−1.28706	−	0.241843i
$499$	−0.601764	−	2.24581i	−0.0269387	−	0.100536i	0.951148	−	0.308737i	$-0.0999061\pi$
$499$	−0.601764	−	2.24581i	−0.0269387	−	0.100536i	−0.978086	+	0.208200i	$0.933239\pi$
$500$	−56.7202	+	15.1981i	−2.53661	+	0.679682i
$501$	−9.32594	−	13.6416i	−0.416652	−	0.609463i
$502$	−5.62174	+	20.9806i	−0.250911	+	0.936411i
$503$		−	8.35857i		−	0.372690i	−0.982484	−	0.186345i	$-0.940336\pi$
$503$		−	8.35857i		−	0.372690i	0.982484	−	0.186345i	$-0.0596642\pi$
$504$	77.8538	+	30.3289i	3.46788	+	1.35095i
$505$	1.60037	+	1.60037i	0.0712157	+	0.0712157i
$506$	3.61203	+	6.25623i	0.160575	+	0.278123i
$507$	−11.2207	+	19.5216i	−0.498331	+	0.866987i
$508$	−18.1690	+	31.4697i	−0.806120	+	1.39624i
$509$	−15.0368	+	4.02911i	−0.666496	+	0.178587i	−0.576176	−	0.817326i	$-0.695456\pi$
$509$	−15.0368	+	4.02911i	−0.666496	+	0.178587i	−0.0903201	+	0.995913i	$0.528789\pi$
$510$	−6.02030	−	17.1357i	−0.266584	−	0.758780i
$511$	36.4864	−	21.0655i	1.61407	−	0.931881i
$512$	−19.2797	−	19.2797i	−0.852052	−	0.852052i
$513$	4.50141	+	19.3835i	0.198742	+	0.855801i
$514$	−25.8917	−	25.8917i	−1.14204	−	1.14204i
$515$	−13.2913	−	3.56138i	−0.585683	−	0.156933i
$516$	34.4088	−	12.0889i	1.51477	−	0.532185i
$517$	−2.42034	−	1.39738i	−0.106446	−	0.0614568i
$518$	−15.2764	−	57.0123i	−0.671207	−	2.50498i
$519$	11.1920	+	9.60693i	0.491274	+	0.421698i
$520$	7.34629	−	43.3243i	0.322156	−	1.89990i
$521$			38.0816i			1.66839i	0.551472	+	0.834193i	$0.314066\pi$
$521$			38.0816i			1.66839i	−0.551472	+	0.834193i	$0.685934\pi$
$522$	50.2114	+	36.8624i	2.19769	+	1.61342i
$523$	−13.1520			−0.575099			−0.287549	−	0.957766i	$-0.592841\pi$
$523$	−13.1520			−0.575099			−0.287549	+	0.957766i	$0.592841\pi$
$524$	2.07771	+	3.59870i	0.0907651	+	0.157210i
$525$	−9.11649	−	13.3353i	−0.397876	−	0.581998i
$526$	11.5894	+	43.2522i	0.505321	+	1.88588i
$527$	−1.75893	−	6.56443i	−0.0766203	−	0.285951i
$528$	16.4239	+	24.0243i	0.714760	+	1.04552i
$529$	9.86161	+	17.0808i	0.428766	+	0.742644i
$530$	−1.64153			−0.0713037
$531$	−4.21091	−	3.09141i	−0.182738	−	0.134156i
$532$			66.9250i			2.90157i
$533$	31.9419	−	22.6799i	1.38356	−	0.982378i
$534$	13.9727	+	11.9939i	0.604660	+	0.519025i
$535$	−4.13120	−	15.4178i	−0.178607	−	0.666571i
$536$	16.4824	+	9.51610i	0.711930	+	0.411033i
$537$	−30.0209	+	10.5473i	−1.29550	+	0.455149i
$538$	−25.1689	−	6.74400i	−1.08511	−	0.290754i
$539$	5.45597	+	5.45597i	0.235005	+	0.235005i
$540$	−29.0265	+	27.1379i	−1.24910	+	1.16783i
$541$	−15.8564	−	15.8564i	−0.681722	−	0.681722i	0.278666	−	0.960388i	$-0.410108\pi$
$541$	−15.8564	−	15.8564i	−0.681722	−	0.681722i	−0.960388	+	0.278666i	$0.910108\pi$
$542$	−10.4588	+	6.03838i	−0.449243	+	0.259371i
$543$	10.0652	+	28.6486i	0.431938	+	1.22943i
$544$	34.0100	−	9.11296i	1.45817	−	0.390715i
$545$	10.4878	−	18.1654i	0.449248	−	0.778120i
$546$	56.7772	−	9.73997i	2.42984	−	0.416832i
$547$	21.7059	+	37.5957i	0.928077	+	1.60748i	0.786536	+	0.617545i	$0.211873\pi$
$547$	21.7059	+	37.5957i	0.928077	+	1.60748i	0.141541	+	0.989932i	$0.454794\pi$
$548$	−61.4766	−	61.4766i	−2.62615	−	2.62615i
$549$	10.6876	+	4.16347i	0.456134	+	0.177692i
$550$		−	10.6899i		−	0.455819i
$551$	−7.76787	+	28.9901i	−0.330922	+	1.23502i
$552$	−14.1542	−	20.7043i	−0.602444	−	0.881232i
$553$	−38.1131	+	10.2124i	−1.62073	+	0.434275i
$554$	−10.1010	−	37.6976i	−0.429152	−	1.60162i
$555$	16.5952	+	3.11829i	0.704426	+	0.132364i
$556$	53.5392	−	30.9108i	2.27057	−	1.31091i
$557$	−4.28113	+	4.28113i	−0.181397	+	0.181397i	−0.791965	−	0.610567i	$-0.790942\pi$
$557$	−4.28113	+	4.28113i	−0.181397	+	0.181397i	0.610567	+	0.791965i	$0.290942\pi$
$558$	−16.2240	+	13.0054i	−0.686819	+	0.550561i
$559$	9.64634	−	11.6506i	0.407997	−	0.492766i
$560$	−51.2438	+	29.5856i	−2.16545	+	1.25022i
$561$	6.75794	−	0.515013i	0.285320	−	0.0217439i
$562$	3.63073	−	6.28860i	0.153153	−	0.265269i
$563$	−14.8023	+	25.6383i	−0.623841	+	1.08052i	0.364923	+	0.931038i	$0.381095\pi$
$563$	−14.8023	+	25.6383i	−0.623841	+	1.08052i	−0.988764	+	0.149486i	$0.952238\pi$
$564$	14.5413	+	6.98015i	0.612301	+	0.293917i
$565$	0.369791	+	0.0990852i	0.0155572	+	0.00416855i
$566$	19.1559	−	19.1559i	0.805182	−	0.805182i
$567$	−27.7778	−	14.5021i	−1.16656	−	0.609031i
$568$	93.1333			3.90779
$569$	11.1751	+	19.3559i	0.468485	+	0.811441i	0.999351	−	0.0360153i	$-0.0114665\pi$
$569$	11.1751	+	19.3559i	0.468485	+	0.811441i	−0.530866	+	0.847456i	$0.678133\pi$
$570$	−24.1382	−	11.5869i	−1.01104	−	0.485320i
$571$	20.6827	+	11.9412i	0.865545	+	0.499722i	0.865865	−	0.500278i	$-0.166769\pi$
$571$	20.6827	+	11.9412i	0.865545	+	0.499722i	−0.000320542		1.00000i	$0.500102\pi$
$572$	24.7810	+	11.3581i	1.03614	+	0.474905i
$573$	1.86346	−	2.17092i	0.0778473	−	0.0906914i
$574$	−96.8097	−	25.9401i	−4.04076	−	1.08272i
$575$			4.84884i			0.202211i
$576$	−25.5204	−	31.8365i	−1.06335	−	1.32652i
$577$	12.4224	−	12.4224i	0.517153	−	0.517153i	−0.399556	−	0.916709i	$-0.630836\pi$
$577$	12.4224	−	12.4224i	0.517153	−	0.517153i	0.916709	+	0.399556i	$0.130836\pi$
$578$	−7.02970	+	26.2352i	−0.292397	+	1.09124i
$579$	24.8263	−	16.9722i	1.03175	−	0.705341i
$580$	−57.8901	+	15.5116i	−2.40375	+	0.644084i
$581$	19.2029	+	11.0868i	0.796671	+	0.459958i
$582$	1.12722	−	5.99891i	0.0467247	−	0.248663i
$583$	0.158542	−	0.591685i	0.00656612	−	0.0245051i
$584$	−96.7946			−4.00539
$585$	−4.51708	+	15.8491i	−0.186758	+	0.655281i
$586$	−68.9387			−2.84783
$587$	9.92311	−	37.0336i	0.409571	−	1.52854i	−0.385897	−	0.922542i	$-0.626108\pi$
$587$	9.92311	−	37.0336i	0.409571	−	1.52854i	0.795467	−	0.605997i	$-0.207225\pi$
$588$	−33.7907	−	29.0051i	−1.39351	−	1.19615i
$589$	−8.67644	−	5.00934i	−0.357506	−	0.206406i
$590$	6.78937	−	1.81921i	0.279514	−	0.0748955i
$591$	−0.0206991	−	0.00993599i	−0.000851446	−	0.000408712i
$592$	−18.4725	+	68.9405i	−0.759217	+	2.83344i
$593$	16.6426	−	16.6426i	0.683430	−	0.683430i	−0.277342	−	0.960771i	$-0.589453\pi$
$593$	16.6426	−	16.6426i	0.683430	−	0.683430i	0.960771	+	0.277342i	$0.0894534\pi$
$594$	−9.75896	−	18.2969i	−0.400415	−	0.750730i
$595$			13.7804i			0.564943i
$596$	−72.9552	−	19.5483i	−2.98836	−	0.800729i
$597$	−14.9176	−	42.4601i	−0.610536	−	1.73778i
$598$	−15.7193	−	7.20478i	−0.642811	−	0.294625i
$599$	32.4992	+	18.7634i	1.32788	+	0.766653i	0.984972	−	0.172716i	$-0.0552542\pi$
$599$	32.4992	+	18.7634i	1.32788	+	0.766653i	0.342910	+	0.939368i	$0.388587\pi$
$600$	2.82011	+	37.0052i	0.115131	+	1.51073i
$601$	4.29929	+	7.44659i	0.175372	+	0.303753i	0.940290	−	0.340375i	$-0.110554\pi$
$601$	4.29929	+	7.44659i	0.175372	+	0.303753i	−0.764918	+	0.644127i	$0.777221\pi$
$602$	−38.6976			−1.57720
$603$	−5.75375	−	4.22408i	−0.234311	−	0.172018i
$604$	10.6012	−	10.6012i	0.431358	−	0.431358i
$605$	12.8493	+	3.44297i	0.522400	+	0.139977i
$606$	5.62734	−	3.84706i	0.228595	−	0.156276i
$607$	−1.38843	+	2.40483i	−0.0563546	+	0.0976090i	−0.892826	−	0.450401i	$-0.851281\pi$
$607$	−1.38843	+	2.40483i	−0.0563546	+	0.0976090i	0.836472	+	0.548010i	$0.184614\pi$
$608$	25.9532	−	44.9523i	1.05254	−	1.82305i
$609$	−26.6725	−	39.0155i	−1.08082	−	1.58099i
$610$	−13.3655	+	7.71657i	−0.541153	+	0.312435i
$611$	6.66022	−	0.626782i	0.269444	−	0.0253569i
$612$	−38.6646	+	5.92757i	−1.56292	+	0.239608i
$613$	−4.35760	+	4.35760i	−0.176002	+	0.176002i	−0.789610	−	0.613609i	$-0.789717\pi$
$613$	−4.35760	+	4.35760i	−0.176002	+	0.176002i	0.613609	+	0.789610i	$0.289717\pi$
$614$	−11.7081	+	6.75968i	−0.472501	+	0.272798i
$615$	18.6753	−	21.7566i	0.753062	−	0.877310i
$616$	−10.8580	−	40.5225i	−0.437480	−	1.63270i
$617$	−2.91939	+	0.782248i	−0.117530	+	0.0314921i	−0.317105	−	0.948391i	$-0.602711\pi$
$617$	−2.91939	+	0.782248i	−0.117530	+	0.0314921i	0.199575	+	0.979883i	$0.436044\pi$
$618$	−17.9346	+	37.3621i	−0.721435	+	1.50292i
$619$	−2.83071	+	10.5643i	−0.113776	+	0.424617i	−0.999192	−	0.0401814i	$-0.987206\pi$
$619$	−2.83071	+	10.5643i	−0.113776	+	0.424617i	0.885417	+	0.464798i	$0.153873\pi$
$620$		−	20.0062i		−	0.803470i
$621$	4.42657	+	8.29929i	0.177632	+	0.333039i
$622$	44.3696	+	44.3696i	1.77906	+	1.77906i
$623$	−6.98580	−	12.0998i	−0.279880	−	0.484767i
$624$	−65.3469	−	24.1282i	−2.61597	−	0.965902i
$625$	−2.21582	+	3.83792i	−0.0886329	+	0.153517i
$626$	39.3800	−	10.5518i	1.57394	−	0.421737i
$627$	6.50775	−	7.58147i	0.259895	−	0.302775i
$628$	62.3921	−	36.0221i	2.48972	−	1.43744i
$629$	11.7535	+	11.7535i	0.468643	+	0.468643i
$630$	38.6024	−	16.9581i	1.53796	−	0.675628i
$631$	−0.613522	−	0.613522i	−0.0244239	−	0.0244239i	0.694789	−	0.719213i	$-0.255498\pi$
$631$	−0.613522	−	0.613522i	−0.0244239	−	0.0244239i	−0.719213	+	0.694789i	$0.755498\pi$
$632$	87.5638	+	23.4627i	3.48310	+	0.933294i
$633$	−0.0537999	+	0.286316i	−0.00213835	+	0.0113801i
$634$	2.99164	+	1.72723i	0.118813	+	0.0685969i
$635$	2.85489	+	10.6546i	0.113293	+	0.422815i
$636$	−0.652881	+	3.47455i	−0.0258884	+	0.137775i
$637$	−18.2092	−	3.08764i	−0.721474	−	0.122337i
$638$		−	31.2759i		−	1.23822i
$639$	−34.7188	−	3.82317i	−1.37345	−	0.151242i
$640$	13.5998			0.537579
$641$	4.38829	+	7.60073i	0.173327	+	0.300211i	0.939581	−	0.342327i	$-0.111215\pi$
$641$	4.38829	+	7.60073i	0.173327	+	0.300211i	−0.766254	+	0.642538i	$0.777882\pi$
$642$	−47.9355	+	3.65310i	−1.89186	+	0.144176i
$643$	−4.74157	−	17.6958i	−0.186989	−	0.697853i	−0.994196	−	0.107584i	$-0.965688\pi$
$643$	−4.74157	−	17.6958i	−0.186989	−	0.697853i	0.807207	−	0.590269i	$-0.200978\pi$
$644$	8.18752	+	30.5563i	0.322634	+	1.20409i
$645$	4.79082	−	9.98043i	0.188638	−	0.392979i
$646$	−13.1786	−	22.8260i	−0.518504	−	0.898075i
$647$	35.0174			1.37667			0.688337	−	0.725391i	$-0.258341\pi$
$647$	35.0174			1.37667			0.688337	+	0.725391i	$0.258341\pi$
$648$	38.6095	+	60.7637i	1.51672	+	2.38702i
$649$			2.62291i			0.102958i
$650$	14.8138	+	20.8634i	0.581046	+	0.818332i
$651$	14.8846	−	5.22943i	0.583373	−	0.204958i
$652$	−13.9312	−	51.9921i	−0.545589	−	2.03617i
$653$	15.9682	+	9.21926i	0.624885	+	0.360778i	0.778768	−	0.627311i	$-0.215845\pi$
$653$	15.9682	+	9.21926i	0.624885	+	0.360778i	−0.153883	+	0.988089i	$0.549178\pi$
$654$	−47.9373	−	41.1482i	−1.87450	−	1.60902i
$655$	1.21840	+	0.326470i	0.0476069	+	0.0127562i
$656$	85.6970	+	85.6970i	3.34591	+	3.34591i
$657$	36.0836	+	3.97347i	1.40776	+	0.155020i
$658$	−12.1020	−	12.1020i	−0.471784	−	0.471784i
$659$	−33.3339	+	19.2453i	−1.29850	+	0.749691i	−0.980146	−	0.198279i	$-0.936465\pi$
$659$	−33.3339	+	19.2453i	−1.29850	+	0.749691i	−0.318358	+	0.947971i	$0.603131\pi$
$660$	19.6087	+	3.68455i	0.763268	+	0.143421i
$661$	−0.546150	+	0.146341i	−0.0212428	+	0.00569199i	−0.269425	−	0.963021i	$-0.586834\pi$
$661$	−0.546150	+	0.146341i	−0.0212428	+	0.00569199i	0.248182	+	0.968713i	$0.420167\pi$
$662$	7.34409	−	12.7203i	0.285436	−	0.494390i
$663$	−12.4757	+	10.3701i	−0.484518	+	0.402743i
$664$	−25.4716	−	44.1181i	−0.988490	−	1.71212i
$665$	14.3650	+	14.3650i	0.557051	+	0.557051i
$666$	18.4607	−	47.3883i	0.715336	−	1.83626i
$667$			14.1864i			0.549301i
$668$	12.3939	−	46.2548i	0.479536	−	1.78965i
$669$	−22.1961	+	1.69153i	−0.858150	+	0.0653983i
$670$	9.27693	−	2.48575i	0.358399	−	0.0960328i
$671$	−1.49055	−	5.56283i	−0.0575422	−	0.214750i
$672$	27.0935	+	77.1164i	1.04515	+	2.97483i
$673$	7.10954	−	4.10470i	0.274053	−	0.158224i	−0.356675	−	0.934228i	$-0.616090\pi$
$673$	7.10954	−	4.10470i	0.274053	−	0.158224i	0.630728	+	0.776004i	$0.282756\pi$
$674$	32.1895	−	32.1895i	1.23989	−	1.23989i
$675$	0.467784	−	13.9108i	0.0180050	−	0.535426i
$676$	−64.1046	+	12.1734i	−2.46556	+	0.468207i
$677$	30.2227	−	17.4491i	1.16155	−	0.670622i	0.209877	−	0.977728i	$-0.432694\pi$
$677$	30.2227	−	17.4491i	1.16155	−	0.670622i	0.951675	+	0.307105i	$0.0993604\pi$
$678$	0.498978	−	1.03949i	0.0191631	−	0.0399215i
$679$	−2.31561	+	4.01076i	−0.0888650	+	0.153919i
$680$	15.8301	−	27.4185i	0.607056	−	1.05145i
$681$	−0.142132	−	1.86505i	−0.00544653	−	0.0714687i
$682$	10.0846	+	2.70216i	0.386159	+	0.103471i
$683$	−14.2401	+	14.2401i	−0.544884	+	0.544884i	−0.924957	−	0.380073i	$-0.875899\pi$
$683$	−14.2401	+	14.2401i	−0.544884	+	0.544884i	0.380073	+	0.924957i	$0.375899\pi$
$684$	−34.1257	+	46.4837i	−1.30483	+	1.77735i
$685$	−26.3911			−1.00835
$686$	−8.65988	−	14.9993i	−0.330636	−	0.572678i
$687$	0.448440	−	0.306570i	0.0171090	−	0.0116964i
$688$	40.5248	+	23.3970i	1.54499	+	0.892002i
$689$	0.510519	+	1.37449i	0.0194492	+	0.0523640i
$690$	−12.4384	−	2.33722i	−0.473523	−	0.0889766i
$691$	−10.2939	−	2.75823i	−0.391597	−	0.104928i	0.0576473	−	0.998337i	$-0.481640\pi$
$691$	−10.2939	−	2.75823i	−0.391597	−	0.104928i	−0.449244	+	0.893409i	$0.648307\pi$
$692$			42.7427i			1.62483i
$693$	2.38423	+	15.5519i	0.0905693	+	0.590769i
$694$	−44.7006	+	44.7006i	−1.69681	+	1.69681i
$695$	4.85701	−	18.1266i	0.184237	−	0.687582i
$696$	8.25091	+	108.268i	0.312750	+	4.10387i
$697$	27.2632	−	7.30515i	1.03267	−	0.276702i
$698$	29.0755	+	16.7868i	1.10052	+	0.635388i
$699$	36.3411	−	12.7678i	1.37455	−	0.482923i
$700$	12.1156	−	45.2160i	0.457926	−	1.70900i
$701$	−38.5917			−1.45759			−0.728795	−	0.684732i	$-0.759919\pi$
$701$	−38.5917			−1.45759			−0.728795	+	0.684732i	$0.759919\pi$
$702$	44.4019	+	22.1862i	1.67584	+	0.837364i
$703$	24.5042			0.924193
$704$	−5.30245	+	19.7890i	−0.199843	+	0.745826i
$705$	4.61944	−	1.62296i	0.173978	−	0.0611241i
$706$	69.0472	+	39.8644i	2.59863	+	1.50032i
$707$	−4.99578	+	1.33862i	−0.187886	+	0.0503438i
$708$	−1.15031	−	15.0942i	−0.0432313	−	0.567276i
$709$	10.1793	−	37.9898i	0.382293	−	1.42674i	−0.460098	−	0.887868i	$-0.652186\pi$
$709$	10.1793	−	37.9898i	0.382293	−	1.42674i	0.842390	−	0.538868i	$-0.181148\pi$
$710$	33.2324	−	33.2324i	1.24719	−	1.24719i
$711$	−31.6794	−	12.3411i	−1.18807	−	0.462827i
$712$			32.0994i			1.20297i
$713$	−4.57428	−	1.22567i	−0.171308	−	0.0459018i
$714$	40.7909	+	7.66476i	1.52656	+	0.286846i
$715$	7.75699	−	2.88113i	0.290095	−	0.107748i
$716$	−79.8557	−	46.1047i	−2.98435	−	1.72301i
$717$	−10.1415	+	6.93310i	−0.378740	+	0.258921i
$718$	0.422854	+	0.732405i	0.0157808	+	0.0273331i
$719$	22.3551			0.833706			0.416853	−	0.908974i	$-0.363133\pi$
$719$	22.3551			0.833706			0.416853	+	0.908974i	$0.363133\pi$
$720$	−50.6781	−	5.58058i	−1.88866	−	0.207976i
$721$	22.2347	−	22.2347i	0.828063	−	0.828063i
$722$	11.0913	+	2.97190i	0.412774	+	0.110603i
$723$	−3.73097	−	48.9573i	−0.138756	−	1.82074i
$724$	−43.9973	+	76.2056i	−1.63515	+	2.83216i
$725$	10.4963	−	18.1801i	0.389822	−	0.675192i
$726$	17.3383	−	36.1198i	0.643483	−	1.34053i
$727$	1.62673	−	0.939194i	0.0603321	−	0.0348328i	−0.469531	−	0.882916i	$-0.655577\pi$
$727$	1.62673	−	0.939194i	0.0603321	−	0.0348328i	0.529863	+	0.848083i	$0.322243\pi$
$728$	77.3466	+	64.0409i	2.86666	+	2.37351i
$729$	−11.8987	−	24.2368i	−0.440692	−	0.897658i
$730$	−34.5388	+	34.5388i	−1.27834	+	1.27834i
$731$	9.43784	−	5.44894i	0.349071	−	0.201536i
$732$	11.0175	+	31.3591i	0.407217	+	1.15907i
$733$	4.44175	+	16.5768i	0.164060	+	0.612280i	0.998158	+	0.0606639i	$0.0193218\pi$
$733$	4.44175	+	16.5768i	0.164060	+	0.612280i	−0.834098	+	0.551616i	$0.814012\pi$
$734$	−83.2683	+	22.3117i	−3.07349	+	0.823539i
$735$	−13.4787	+	1.02719i	−0.497169	+	0.0378885i
$736$	6.35016	−	23.6991i	0.234070	−	0.873561i
$737$			3.58392i			0.132015i
$738$	−54.0134	−	67.3812i	−1.98826	−	2.48034i
$739$	2.86775	+	2.86775i	0.105492	+	0.105492i	0.757883	−	0.652391i	$-0.226234\pi$
$739$	2.86775	+	2.86775i	0.105492	+	0.105492i	−0.652391	+	0.757883i	$0.726234\pi$
$740$	24.4661	+	42.3765i	0.899392	+	1.55779i
$741$	−2.19492	+	23.8150i	−0.0806325	+	0.874867i
$742$	1.87561	−	3.24866i	0.0688560	−	0.119262i
$743$	−17.3205	+	4.64102i	−0.635429	+	0.170263i	−0.562132	−	0.827048i	$-0.690019\pi$
$743$	−17.3205	+	4.64102i	−0.635429	+	0.170263i	−0.0732967	+	0.997310i	$0.523352\pi$
$744$	−35.6226	−	6.69362i	−1.30599	−	0.245400i
$745$	−19.8552	+	11.4634i	−0.727440	+	0.419988i
$746$	−44.0901	−	44.0901i	−1.61425	−	1.61425i
$747$	7.68438	+	17.4922i	0.281157	+	0.640007i
$748$	13.8878	+	13.8878i	0.507790	+	0.507790i
$749$	35.2328	+	9.44060i	1.28738	+	0.344952i
$750$	40.7367	+	34.9674i	1.48749	+	1.27683i
$751$	−44.2134	−	25.5266i	−1.61337	−	0.931480i	−0.988581	−	0.150687i	$-0.951851\pi$
$751$	−44.2134	−	25.5266i	−1.61337	−	0.931480i	−0.624790	−	0.780793i	$-0.714815\pi$
$752$	5.35640	+	19.9904i	0.195328	+	0.728974i
$753$	13.3973	−	4.70688i	0.488223	−	0.171528i
$754$	43.3414	+	61.0410i	1.57840	+	2.22298i
$755$		−	4.55096i		−	0.165626i
$756$	−20.5412	−	88.4523i	−0.747077	−	3.21698i
$757$	−2.83386			−0.102999			−0.0514993	−	0.998673i	$-0.516400\pi$
$757$	−2.83386			−0.102999			−0.0514993	+	0.998673i	$0.516400\pi$
$758$	33.7619	+	58.4774i	1.22629	+	2.12399i
$759$	2.04376	−	4.25765i	0.0741839	−	0.154543i
$760$	−12.0800	−	45.0832i	−0.438188	−	1.63534i
$761$	3.59413	+	13.4135i	0.130287	+	0.486239i	0.999973	−	0.00736746i	$-0.00234516\pi$
$761$	3.59413	+	13.4135i	0.130287	+	0.486239i	−0.869686	+	0.493606i	$0.835678\pi$
$762$	33.1262	−	2.52450i	1.20003	−	0.0914529i
$763$	23.9667	+	41.5115i	0.867651	+	1.50282i
$764$	8.29083			0.299952
$765$	−7.02677	+	9.57140i	−0.254053	+	0.346055i
$766$		−	36.6607i		−	1.32461i
$767$	−3.63476	−	5.11911i	−0.131244	−	0.184841i
$768$	−1.13649	+	6.04827i	−0.0410096	+	0.218248i
$769$	5.06534	+	18.9041i	0.182661	+	0.681699i	0.995119	+	0.0986801i	$0.0314621\pi$
$769$	5.06534	+	18.9041i	0.182661	+	0.681699i	−0.812458	+	0.583019i	$0.801871\pi$
$770$	−18.3339	−	10.5851i	−0.660708	−	0.381460i
$771$	−4.42071	+	23.5265i	−0.159208	+	0.847285i
$772$	84.1787	+	22.5556i	3.02966	+	0.811795i
$773$	−1.22713	−	1.22713i	−0.0441368	−	0.0441368i	0.684694	−	0.728831i	$-0.259936\pi$
$773$	−1.22713	−	1.22713i	−0.0441368	−	0.0441368i	−0.728831	+	0.684694i	$0.759936\pi$
$774$	−26.8780	−	19.7323i	−0.966109	−	0.709262i
$775$	4.95514	+	4.95514i	0.177994	+	0.177994i
$776$	9.21460	−	5.32005i	0.330785	−	0.190979i
$777$	−25.1328	+	29.2795i	−0.901636	+	1.05040i
$778$	−63.3090	+	16.9636i	−2.26974	+	0.608174i
$779$	20.8047	−	36.0347i	0.745404	−	1.29108i
$780$	−43.3762	+	19.9822i	−1.55312	+	0.715477i
$781$	8.76887	+	15.1881i	0.313775	+	0.543474i
$782$	−8.80950	−	8.80950i	−0.315027	−	0.315027i
$783$	1.36861	−	40.6993i	0.0489103	−	1.45447i
$784$		−	57.1372i		−	2.04062i
$785$	5.66014	−	21.1239i	0.202019	−	0.753945i
$786$	1.64405	−	3.42495i	0.0586414	−	0.122164i
$787$	−32.9331	+	8.82439i	−1.17394	+	0.314555i	−0.792519	−	0.609847i	$-0.791231\pi$
$787$	−32.9331	+	8.82439i	−1.17394	+	0.314555i	−0.381418	+	0.924403i	$0.624564\pi$
$788$	−0.0172207	−	0.0642687i	−0.000613464	−	0.00228948i
$789$	19.0669	−	22.2128i	0.678801	−	0.790797i
$790$	39.6172	−	22.8730i	1.40951	−	0.813784i
$791$	−0.618616	+	0.618616i	−0.0219955	+	0.0219955i
$792$	13.1212	−	33.6821i	0.466243	−	1.19684i
$793$	10.6179	+	8.79137i	0.377054	+	0.312191i
$794$	14.3697	−	8.29636i	0.509962	−	0.294427i
$795$	0.605652	+	0.885924i	0.0214803	+	0.0314205i
$796$	65.2083	−	112.944i	2.31125	−	4.00320i
$797$	1.38190	−	2.39353i	0.0489495	−	0.0847830i	−0.840513	−	0.541792i	$-0.817746\pi$
$797$	1.38190	−	2.39353i	0.0489495	−	0.0847830i	0.889462	+	0.457009i	$0.151079\pi$
$798$	50.5112	−	34.5314i	1.78808	−	1.22240i
$799$	4.65557	+	1.24746i	0.164702	+	0.0441318i
$800$	−25.6723	+	25.6723i	−0.907654	+	0.907654i
$801$	1.31770	−	11.9662i	0.0465585	−	0.422804i
$802$	−82.0372			−2.89684
$803$	−9.11360	−	15.7852i	−0.321612	−	0.557048i
$804$	−1.57177	−	20.6246i	−0.0554322	−	0.727375i
$805$	8.31609	+	4.80129i	0.293104	+	0.169223i
$806$	−23.4266	+	8.70120i	−0.825168	+	0.306487i
$807$	5.64651	+	16.0717i	0.198767	+	0.565752i
$808$	11.4777	+	3.07543i	0.403783	+	0.108193i
$809$			14.2958i			0.502614i	0.967907	+	0.251307i	$0.0808603\pi$
$809$			14.2958i			0.502614i	−0.967907	+	0.251307i	$0.919140\pi$
$810$	35.4589	+	7.90521i	1.24590	+	0.277761i
$811$	20.9499	−	20.9499i	0.735649	−	0.735649i	−0.236084	−	0.971733i	$-0.575864\pi$
$811$	20.9499	−	20.9499i	0.735649	−	0.735649i	0.971733	+	0.236084i	$0.0758639\pi$
$812$	35.4470	−	132.290i	1.24395	−	4.64247i
$813$	7.11769	+	3.41664i	0.249628	+	0.119827i
$814$	−24.6654	+	6.60907i	−0.864521	+	0.231648i
$815$	−14.1500	−	8.16949i	−0.495652	−	0.286165i
$816$	−38.0827	−	32.6893i	−1.33316	−	1.14435i
$817$	4.15811	−	15.5183i	0.145474	−	0.542916i
$818$	−46.7335			−1.63400
$819$	−26.2048	−	27.0486i	−0.915670	−	0.945156i
$820$	83.0893			2.90160
$821$	−9.30358	+	34.7214i	−0.324697	+	1.21179i	0.589919	+	0.807463i	$0.299160\pi$
$821$	−9.30358	+	34.7214i	−0.324697	+	1.21179i	−0.914616	+	0.404324i	$0.867507\pi$
$822$	−14.6789	+	78.1191i	−0.511984	+	2.72472i
$823$	−31.3343	−	18.0909i	−1.09224	−	0.630608i	−0.158072	−	0.987428i	$-0.550528\pi$
$823$	−31.3343	−	18.0909i	−1.09224	−	0.630608i	−0.934173	+	0.356820i	$0.883861\pi$
$824$	−69.7814	+	18.6979i	−2.43095	+	0.651371i
$825$	−5.76927	+	3.94409i	−0.200860	+	0.137316i
$826$	−4.15724	+	15.5150i	−0.144649	+	0.539837i
$827$	−26.7110	+	26.7110i	−0.928832	+	0.928832i	−0.997631	−	0.0687984i	$-0.978083\pi$
$827$	−26.7110	+	26.7110i	−0.928832	+	0.928832i	0.0687984	+	0.997631i	$0.478083\pi$
$828$	−9.89416	+	25.3982i	−0.343846	+	0.882648i
$829$			14.7734i			0.513100i	0.966531	+	0.256550i	$0.0825858\pi$
$829$			14.7734i			0.513100i	−0.966531	+	0.256550i	$0.917414\pi$
$830$	−24.8314	−	6.65356i	−0.861912	−	0.230949i
$831$	−16.6183	+	19.3601i	−0.576482	+	0.671596i
$832$	−17.0744	−	45.9701i	−0.591948	−	1.59373i
$833$	−11.5240	−	6.65337i	−0.399282	−	0.230526i
$834$	−50.9543	−	24.4592i	−1.76440	−	0.846952i
$835$	−7.26800	−	12.5885i	−0.251520	−	0.435645i
$836$	28.9539			1.00139
$837$	13.0048	+	3.95761i	0.449513	+	0.136795i
$838$	18.5974	−	18.5974i	0.642435	−	0.642435i
$839$	−24.8036	−	6.64609i	−0.856314	−	0.229449i	−0.196153	−	0.980573i	$-0.562845\pi$
$839$	−24.8036	−	6.64609i	−0.856314	−	0.229449i	−0.660160	+	0.751125i	$0.729512\pi$
$840$	66.2588	+	31.8056i	2.28615	+	1.09740i
$841$	16.2094	−	28.0755i	0.558944	−	0.968119i
$842$	−43.8222	+	75.9022i	−1.51021	+	2.61576i
$843$	−4.73349	+	0.360732i	−0.163030	+	0.0124243i
$844$	−0.731122	+	0.422113i	−0.0251662	+	0.0145297i
$845$	−11.1467	+	16.3726i	−0.383458	+	0.563233i
$846$	−2.23469	−	14.5765i	−0.0768302	−	0.501151i
$847$	−21.4954	+	21.4954i	−0.738590	+	0.738590i
$848$	−3.92835	+	2.26803i	−0.134900	+	0.0778845i
$849$	−17.4059	−	3.27064i	−0.597370	−	0.112248i
$850$	4.77149	+	17.8075i	0.163661	+	0.610791i
$851$	11.1880	−	2.99781i	0.383519	−	0.102764i
$852$	−57.1239	−	83.5586i	−1.95703	−	2.86267i
$853$	11.9723	−	44.6812i	0.409924	−	1.52986i	−0.384867	−	0.922972i	$-0.625753\pi$
$853$	11.9723	−	44.6812i	0.409924	−	1.52986i	0.794790	−	0.606884i	$-0.207581\pi$
$854$		−	35.2678i		−	1.20684i
$855$	2.65257	+	17.3023i	0.0907159	+	0.591725i
$856$	−59.2568	−	59.2568i	−2.02536	−	2.02536i
$857$	28.2912	+	49.0018i	0.966409	+	1.67387i	0.705782	+	0.708429i	$0.250596\pi$
$857$	28.2912	+	49.0018i	0.966409	+	1.67387i	0.260627	+	0.965440i	$0.416071\pi$
$858$	−4.21383	−	24.5637i	−0.143858	−	0.838589i
$859$	10.2918	−	17.8258i	0.351150	−	0.608210i	−0.635301	−	0.772265i	$-0.719124\pi$
$859$	10.2918	−	17.8258i	0.351150	−	0.608210i	0.986451	+	0.164055i	$0.0524573\pi$
$860$	30.9883	−	8.30329i	1.05669	−	0.283140i
$861$	21.7187	+	61.8182i	0.740172	+	2.10676i
$862$	−58.4375	+	33.7389i	−1.99039	+	1.14915i
$863$	33.1684	+	33.1684i	1.12907	+	1.12907i	0.990329	+	0.138737i	$0.0443042\pi$
$863$	33.1684	+	33.1684i	1.12907	+	1.12907i	0.138737	+	0.990329i	$0.455696\pi$
$864$	−20.5042	+	67.3775i	−0.697568	+	2.29223i
$865$	9.17442	+	9.17442i	0.311940	+	0.311940i
$866$	−47.6783	−	12.7754i	−1.62017	−	0.434125i
$867$	16.7526	−	5.88572i	0.568948	−	0.199890i
$868$	39.5931	+	22.8591i	1.34388	+	0.775888i
$869$	4.41821	+	16.4890i	0.149877	+	0.559350i
$870$	41.5768	+	35.6885i	1.40959	+	1.20995i
$871$	−4.96651	−	6.99472i	−0.168284	−	0.237007i
$872$		−	110.125i		−	3.72932i
$873$	−3.65346	+	1.60498i	−0.123651	+	0.0543202i
$874$	−18.3664			−0.621252
$875$	−20.3667	−	35.2761i	−0.688519	−	1.19255i
$876$	59.3696	+	86.8435i	2.00591	+	2.93417i
$877$	1.16577	+	4.35070i	0.0393651	+	0.146913i	0.982811	−	0.184613i	$-0.0591032\pi$
$877$	1.16577	+	4.35070i	0.0393651	+	0.146913i	−0.943446	+	0.331526i	$0.892437\pi$
$878$	28.5215	+	106.444i	0.962555	+	3.59231i
$879$	25.4352	+	37.2057i	0.857910	+	1.25492i
$880$	12.7997	+	22.1697i	0.431478	+	0.747341i
$881$	4.76109			0.160405			0.0802026	−	0.996779i	$-0.474443\pi$
$881$	4.76109			0.160405			0.0802026	+	0.996779i	$0.474443\pi$
$882$	−4.45638	+	40.4691i	−0.150054	+	1.36266i
$883$		−	26.0791i		−	0.877630i	−0.898577	−	0.438815i	$-0.855398\pi$
$883$		−	26.0791i		−	0.877630i	0.898577	−	0.438815i	$-0.144602\pi$
$884$	−46.3503	−	7.85939i	−1.55893	−	0.264340i
$885$	−3.48678	−	2.99297i	−0.117207	−	0.100608i
$886$	5.34266	+	19.9391i	0.179490	+	0.669867i
$887$	−12.5140	−	7.22495i	−0.420178	−	0.242590i	0.274975	−	0.961451i	$-0.411330\pi$
$887$	−12.5140	−	7.22495i	−0.420178	−	0.242590i	−0.695154	+	0.718861i	$0.744664\pi$
$888$	83.6405	−	29.3856i	2.80679	−	0.986115i
$889$	−24.3479	−	6.52399i	−0.816601	−	0.218808i
$890$	11.4539	+	11.4539i	0.383935	+	0.383935i
$891$	−6.27408	+	12.0176i	−0.210190	+	0.402603i
$892$	−45.6139	−	45.6139i	−1.52726	−	1.52726i
$893$	6.15343	−	3.55269i	0.205917	−	0.118886i
$894$	22.8888	+	65.1487i	0.765517	+	2.17890i
$895$	−27.0365	+	7.24442i	−0.903732	+	0.242154i
$896$	−15.5391	+	26.9145i	−0.519124	+	0.899150i
$897$	1.91135	+	11.1418i	0.0638182	+	0.372016i
$898$	−21.9962	−	38.0985i	−0.734021	−	1.27136i
$899$	14.4974	+	14.4974i	0.483516	+	0.483516i
$900$	31.4711	−	25.2276i	1.04904	−	0.840919i
$901$			1.05641i			0.0351940i
$902$	−11.2225	+	41.8830i	−0.373669	+	1.39455i
$903$	14.2777	+	20.8848i	0.475131	+	0.695004i
$904$	1.94147	−	0.520215i	0.0645723	−	0.0173021i
$905$	6.91328	+	25.8007i	0.229805	+	0.857645i
$906$	−13.4711	−	2.53127i	−0.447548	−	0.0840959i
$907$	−12.2300	+	7.06100i	−0.406091	+	0.234457i	−0.689109	−	0.724658i	$-0.741998\pi$
$907$	−12.2300	+	7.06100i	−0.406091	+	0.234457i	0.283018	+	0.959115i	$0.408664\pi$
$908$	3.83275	−	3.83275i	0.127194	−	0.127194i
$909$	−4.15246	−	1.61764i	−0.137729	−	0.0536538i
$910$	50.4508	−	4.74784i	1.67243	−	0.157389i
$911$	−18.8292	+	10.8711i	−0.623840	+	0.360174i	−0.778363	−	0.627815i	$-0.783950\pi$
$911$	−18.8292	+	10.8711i	−0.623840	+	0.360174i	0.154522	+	0.987989i	$0.450616\pi$
$912$	−73.7741	+	5.62222i	−2.44290	+	0.186170i
$913$	4.79651	−	8.30780i	0.158741	−	0.274948i
$914$	40.4242	−	70.0167i	1.33711	−	2.31595i
$915$	9.09584	+	4.36620i	0.300699	+	0.144342i
$916$	1.52053	+	0.407424i	0.0502397	+	0.0134617i
$917$	−2.03824	+	2.03824i	−0.0673086	+	0.0673086i
$918$	24.4236	+	26.1233i	0.806098	+	0.862198i
$919$	−8.36301			−0.275870			−0.137935	−	0.990441i	$-0.544047\pi$
$919$	−8.36301			−0.275870			−0.137935	+	0.990441i	$0.544047\pi$
$920$	−11.0308	−	19.1060i	−0.363676	−	0.629905i
$921$	7.96791	+	3.82477i	0.262552	+	0.126030i
$922$	−91.9506	−	53.0877i	−3.02823	−	1.74835i
$923$	−38.1615	−	17.4909i	−1.25610	−	0.575721i
$924$	−29.6967	+	34.5964i	−0.976951	+	1.13814i
$925$	−16.5556	−	4.43605i	−0.544343	−	0.145856i
$926$			3.33387i			0.109558i
$927$	26.7811	−	4.10574i	0.879606	−	0.134850i
$928$	−75.1106	+	75.1106i	−2.46562	+	2.46562i
$929$	−5.79268	+	21.6186i	−0.190052	+	0.709282i	0.803441	+	0.595385i	$0.203000\pi$
$929$	−5.79268	+	21.6186i	−0.190052	+	0.709282i	−0.993492	+	0.113898i	$0.963666\pi$
$930$	−15.0995	+	10.3226i	−0.495134	+	0.338492i
$931$	−18.9484	+	5.07721i	−0.621009	+	0.166399i
$932$	96.6676	+	55.8111i	3.16645	+	1.82815i
$933$	7.57558	−	40.3163i	0.248013	−	1.31990i
$934$	10.1561	−	37.9030i	0.332317	−	1.24022i
$935$	5.96186			0.194974
$936$	21.0672	+	83.9203i	0.688601	+	2.74302i
$937$	45.3172			1.48045			0.740224	−	0.672361i	$-0.234720\pi$
$937$	45.3172			1.48045			0.740224	+	0.672361i	$0.234720\pi$
$938$	−5.68042	+	21.1996i	−0.185472	+	0.692192i
$939$	−20.2242	−	17.3600i	−0.659992	−	0.566521i
$940$	12.2877	+	7.09433i	0.400782	+	0.231392i
$941$	−4.09768	+	1.09797i	−0.133581	+	0.0357928i	−0.324990	−	0.945717i	$-0.605361\pi$
$941$	−4.09768	+	1.09797i	−0.133581	+	0.0357928i	0.191409	+	0.981510i	$0.438694\pi$
$942$	−59.3799	−	28.5036i	−1.93470	−	0.928698i
$943$	5.09043	−	18.9977i	0.165767	−	0.618652i
$944$	13.7341	−	13.7341i	0.447006	−	0.447006i
$945$	−23.3947	−	14.5767i	−0.761030	−	0.474178i
$946$			16.7418i			0.544324i
$947$	43.1659	+	11.5663i	1.40270	+	0.375853i	0.879315	−	0.476241i	$-0.158001\pi$
$947$	43.1659	+	11.5663i	1.40270	+	0.375853i	0.523389	+	0.852094i	$0.324668\pi$
$948$	−32.6573	−	92.9527i	−1.06066	−	3.01896i
$949$	39.6618	+	18.1785i	1.28748	+	0.590100i
$950$	23.5367	+	13.5889i	0.763633	+	0.440884i
$951$	−0.171609	−	2.25184i	−0.00556481	−	0.0730208i
$952$	36.1748	+	62.6567i	1.17243	+	2.03071i
$953$	−59.2801			−1.92027			−0.960135	−	0.279536i	$-0.909819\pi$
$953$	−59.2801			−1.92027			−0.960135	+	0.279536i	$0.909819\pi$
$954$	2.95926	−	1.30001i	0.0958094	−	0.0420893i
$955$	1.77957	−	1.77957i	0.0575855	−	0.0575855i
$956$	−34.3868	−	9.21392i	−1.11215	−	0.297999i
$957$	−16.8794	+	11.5394i	−0.545632	+	0.373015i
$958$	40.9822	−	70.9833i	1.32408	−	2.29337i
$959$	30.1544	−	52.2289i	0.973735	−	1.68656i
$960$	−20.2561	−	29.6299i	−0.653763	−	0.956300i
$961$	20.9197	−	12.0780i	0.674829	−	0.389613i
$962$	38.9806	−	47.0796i	1.25679	−	1.51791i
$963$	19.6576	+	24.5226i	0.633457	+	0.790231i
$964$	100.609	−	100.609i	3.24041	−	3.24041i
$965$	22.9098	−	13.2270i	0.737492	−	0.425791i
$966$	18.8376	−	21.9456i	0.606089	−	0.706088i
$967$	10.3693	+	38.6988i	0.333454	+	1.24447i	0.905535	+	0.424271i	$0.139470\pi$
$967$	10.3693	+	38.6988i	0.333454	+	1.24447i	−0.572081	+	0.820197i	$0.693864\pi$
$968$	67.4612	−	18.0762i	2.16829	−	0.580991i
$969$	−7.45671	+	15.5341i	−0.239544	+	0.499028i
$970$	1.38968	−	5.18635i	0.0446198	−	0.166524i
$971$		−	20.8436i		−	0.668904i	−0.942413	−	0.334452i	$-0.891449\pi$
$971$		−	20.8436i		−	0.668904i	0.942413	−	0.334452i	$-0.108551\pi$
$972$	30.8355	−	71.9100i	0.989048	−	2.30651i
$973$	30.3236	+	30.3236i	0.972131	+	0.972131i
$974$	−23.6357	−	40.9382i	−0.757337	−	1.31175i
$975$	5.79422	−	15.6926i	0.185564	−	0.502565i
$976$	−21.3233	+	36.9330i	−0.682541	+	1.18220i
$977$	−28.0073	+	7.50453i	−0.896033	+	0.240091i	−0.677312	−	0.735696i	$-0.736855\pi$
$977$	−28.0073	+	7.50453i	−0.896033	+	0.240091i	−0.218721	+	0.975787i	$0.570188\pi$
$978$	−32.0525	+	37.3409i	−1.02493	+	1.19403i
$979$	−5.23475	+	3.02228i	−0.167303	+	0.0965926i
$980$	−27.6993	−	27.6993i	−0.884821	−	0.884821i
$981$	−4.52071	+	41.0532i	−0.144335	+	1.31073i
$982$	76.6067	+	76.6067i	2.44462	+	2.44462i
$983$	−43.7487	−	11.7224i	−1.39537	−	0.373888i	−0.518689	−	0.854963i	$-0.673580\pi$
$983$	−43.7487	−	11.7224i	−1.39537	−	0.373888i	−0.876679	+	0.481075i	$0.840246\pi$
$984$	27.7997	−	147.947i	0.886224	−	4.71637i
$985$	−0.0174911	−	0.0100985i	−0.000557314	−	0.000321766i
$986$	13.9601	+	52.0999i	0.444581	+	1.65920i
$987$	−2.06627	+	10.9964i	−0.0657701	+	0.350020i
$988$	−56.5093	+	40.1237i	−1.79780	+	1.27651i
$989$		−	7.59395i		−	0.241473i
$990$	−7.33664	−	16.7006i	−0.233174	−	0.530781i
$991$	22.6104			0.718243			0.359122	−	0.933291i	$-0.383076\pi$
$991$	22.6104			0.718243			0.359122	+	0.933291i	$0.383076\pi$
$992$	−17.7293	−	30.7080i	−0.562905	−	0.974980i
$993$	−9.57471	+	0.729675i	−0.303844	+	0.0231555i
$994$	27.7969	+	103.739i	0.881664	+	3.29042i
$995$	−10.2462	−	38.2392i	−0.324825	−	1.21226i
$996$	−23.9594	+	49.9131i	−0.759181	+	1.58156i
$997$	−2.91264	−	5.04484i	−0.0922442	−	0.159772i	0.816211	−	0.577754i	$-0.196071\pi$
$997$	−2.91264	−	5.04484i	−0.0922442	−	0.159772i	−0.908455	+	0.417982i	$0.862737\pi$
$998$	−6.15993			−0.194989
$999$	−32.3863	+	7.52104i	−1.02466	+	0.237955i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.z.b.5.11	✓	44
3.2	odd	2		351.2.bc.b.44.1		44
9.2	odd	6	inner	117.2.z.b.83.11	yes	44
9.7	even	3		351.2.bc.b.278.1		44
13.8	odd	4	inner	117.2.z.b.86.11	yes	44
39.8	even	4		351.2.bc.b.125.1		44
117.34	odd	12		351.2.bc.b.8.1		44
117.47	even	12	inner	117.2.z.b.47.11	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.z.b.5.11	✓	44	1.1	even	1	trivial
117.2.z.b.47.11	yes	44	117.47	even	12	inner
117.2.z.b.83.11	yes	44	9.2	odd	6	inner
117.2.z.b.86.11	yes	44	13.8	odd	4	inner
351.2.bc.b.8.1		44	117.34	odd	12
351.2.bc.b.44.1		44	3.2	odd	2
351.2.bc.b.125.1		44	39.8	even	4
351.2.bc.b.278.1		44	9.7	even	3

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.z (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.685712 - 2.55911i) q^{2} +(-1.63413 + 0.574122i) q^{3} +(-4.34680 - 2.50963i) q^{4} +(-1.47168 + 0.394337i) q^{5} +(0.348700 + 4.57561i) q^{6} +(0.901137 - 3.36309i) q^{7} +(-5.65626 + 5.65626i) q^{8} +(2.34077 - 1.87638i) q^{9} +4.03661i q^{10} +(-1.45498 - 0.389861i) q^{11} +(8.54407 + 1.60546i) q^{12} +(3.37994 - 1.25539i) q^{13} +(-7.98860 - 4.61222i) q^{14} +(2.17853 - 1.48932i) q^{15} +(5.57719 + 9.65998i) q^{16} +2.59775 q^{17} +(-3.19678 - 7.27694i) q^{18} +(2.70795 - 2.70795i) q^{19} +(7.38675 + 1.97927i) q^{20} +(0.458249 + 6.01309i) q^{21} +(-1.99539 + 3.45613i) q^{22} +(0.905093 - 1.56767i) q^{23} +(5.99569 - 12.4905i) q^{24} +(-2.31977 + 1.33932i) q^{25} +(-0.895016 - 9.51048i) q^{26} +(-2.74785 + 4.41014i) q^{27} +(-12.3571 + 12.3571i) q^{28} +(-6.78705 + 3.91851i) q^{29} +(-2.31751 - 6.59634i) q^{30} +(-0.677098 - 2.52697i) q^{31} +(13.0921 - 3.50802i) q^{32} +(2.60146 - 0.198253i) q^{33} +(1.78131 - 6.64794i) q^{34} +5.30475i q^{35} +(-14.8839 + 2.28181i) q^{36} +(4.52449 + 4.52449i) q^{37} +(-5.07307 - 8.78681i) q^{38} +(-4.80252 + 3.99197i) q^{39} +(6.09376 - 10.5547i) q^{40} +(10.4949 - 2.81210i) q^{41} +(15.7024 + 2.95054i) q^{42} +(3.63308 - 2.09756i) q^{43} +(5.34610 + 5.34610i) q^{44} +(-2.70494 + 3.68449i) q^{45} +(-3.39120 - 3.39120i) q^{46} +(1.79215 + 0.480206i) q^{47} +(-14.6599 - 12.5837i) q^{48} +(-4.43613 - 2.56120i) q^{49} +(1.83678 + 6.85495i) q^{50} +(-4.24507 + 1.49143i) q^{51} +(-17.8425 - 3.02546i) q^{52} +0.406662i q^{53} +(9.40181 + 10.0561i) q^{54} +2.29501 q^{55} +(13.9254 + 24.1196i) q^{56} +(-2.87045 + 5.97984i) q^{57} +(5.37393 + 20.0558i) q^{58} +(-0.450677 - 1.68195i) q^{59} +(-13.2073 + 1.00651i) q^{60} +(1.91165 + 3.31107i) q^{61} -6.93108 q^{62} +(-4.20109 - 9.56308i) q^{63} -13.6009i q^{64} +(-4.47916 + 3.18037i) q^{65} +(1.27650 - 6.79336i) q^{66} +(-0.615801 - 2.29820i) q^{67} +(-11.2919 - 6.51938i) q^{68} +(-0.579007 + 3.08141i) q^{69} +(13.5755 + 3.63753i) q^{70} +(-8.23276 - 8.23276i) q^{71} +(-2.62668 + 23.8533i) q^{72} +(8.55641 + 8.55641i) q^{73} +(14.6812 - 8.47619i) q^{74} +(3.02188 - 3.52046i) q^{75} +(-18.5668 + 4.97497i) q^{76} +(-2.62227 + 4.54191i) q^{77} +(6.92275 + 15.0275i) q^{78} +(-5.66639 - 9.81447i) q^{79} +(-12.0171 - 12.0171i) q^{80} +(1.95838 - 8.78435i) q^{81} -28.7859i q^{82} +(-1.64831 + 6.15156i) q^{83} +(13.0987 - 27.2877i) q^{84} +(-3.82307 + 1.02439i) q^{85} +(-2.87664 - 10.7358i) q^{86} +(8.84123 - 10.2999i) q^{87} +(10.4349 - 6.02460i) q^{88} +(2.83751 - 2.83751i) q^{89} +(7.57421 + 9.44875i) q^{90} +(-1.17620 - 12.4983i) q^{91} +(-7.86851 + 4.54289i) q^{92} +(2.55725 + 3.74065i) q^{93} +(2.45780 - 4.25704i) q^{94} +(-2.91740 + 5.05309i) q^{95} +(-19.3802 + 13.2490i) q^{96} +(-1.28483 - 0.344269i) q^{97} +(-9.59631 + 9.59631i) q^{98} +(-4.13730 + 1.81753i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 2 q^{3} - 14 q^{6} - 14 q^{9} - 6 q^{11} + 4 q^{13} - 36 q^{14} + 4 q^{15} + 4 q^{18} + 12 q^{19} - 18 q^{20} + 22 q^{21} - 28 q^{22} - 24 q^{24} + 4 q^{27} - 16 q^{28} + 8 q^{31} + 6 q^{32} - 14 q^{33}+ \cdots - 68 q^{99}+O(q^{100}) \) 44 * q - 2 * q^3 - 14 * q^6 - 14 * q^9 - 6 * q^11 + 4 * q^13 - 36 * q^14 + 4 * q^15 + 4 * q^18 + 12 * q^19 - 18 * q^20 + 22 * q^21 - 28 * q^22 - 24 * q^24 + 4 * q^27 - 16 * q^28 + 8 * q^31 + 6 * q^32 - 14 * q^33 - 12 * q^34 - 16 * q^37 + 16 * q^39 + 36 * q^40 + 36 * q^41 + 20 * q^42 - 56 * q^45 - 12 * q^46 - 18 * q^47 - 8 * q^48 + 120 * q^50 - 8 * q^52 + 52 * q^54 - 64 * q^55 - 8 * q^57 - 40 * q^58 - 24 * q^59 + 8 * q^60 + 2 * q^61 + 64 * q^63 - 42 * q^65 - 4 * q^66 - 36 * q^68 + 20 * q^70 + 18 * q^72 + 48 * q^73 + 216 * q^74 - 26 * q^76 + 22 * q^78 - 22 * q^79 + 10 * q^81 + 30 * q^83 + 94 * q^84 - 18 * q^85 - 120 * q^86 + 68 * q^87 - 72 * q^92 - 62 * q^93 + 32 * q^94 + 16 * q^96 - 4 * q^97 - 68 * q^99

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