LMFDB - Embedded newform 117.2.l.b.4.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [117,2,Mod(4,117)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("117.4"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(117, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	117.l (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [22] 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:	$0.934249703649$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			4.7
Character	$\chi$	$=$	117.4
Dual form			117.2.l.b.88.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.571953i q^{2} +(-0.656000 + 1.60302i) q^{3} +1.67287 q^{4} +(0.796103 + 0.459630i) q^{5} +(-0.916851 - 0.375201i) q^{6} +(-1.67386 - 0.966405i) q^{7} +2.10071i q^{8} +(-2.13933 - 2.10316i) q^{9} +(-0.262887 + 0.455333i) q^{10} +4.20402i q^{11} +(-1.09740 + 2.68164i) q^{12} +(2.21656 - 2.84374i) q^{13} +(0.552738 - 0.957371i) q^{14} +(-1.25904 + 0.974649i) q^{15} +2.14423 q^{16} +(-1.20321 - 2.08402i) q^{17} +(1.20291 - 1.22360i) q^{18} +(1.60854 - 0.928692i) q^{19} +(1.33178 + 0.768901i) q^{20} +(2.64722 - 2.04927i) q^{21} -2.40450 q^{22} +(-4.11198 - 7.12216i) q^{23} +(-3.36747 - 1.37807i) q^{24} +(-2.07748 - 3.59830i) q^{25} +(1.62649 + 1.26777i) q^{26} +(4.77480 - 2.04971i) q^{27} +(-2.80015 - 1.61667i) q^{28} +4.73399 q^{29} +(-0.557453 - 0.720111i) q^{30} +(4.29178 + 2.47786i) q^{31} +5.42782i q^{32} +(-6.73911 - 2.75784i) q^{33} +(1.19196 - 0.688181i) q^{34} +(-0.888377 - 1.53871i) q^{35} +(-3.57882 - 3.51831i) q^{36} +(-0.959703 - 0.554085i) q^{37} +(0.531168 + 0.920010i) q^{38} +(3.10451 + 5.41867i) q^{39} +(-0.965549 + 1.67238i) q^{40} +(-0.490992 + 0.283475i) q^{41} +(1.17209 + 1.51408i) q^{42} +(-4.79362 + 8.30280i) q^{43} +7.03277i q^{44} +(-0.736449 - 2.65763i) q^{45} +(4.07354 - 2.35186i) q^{46} +(1.35155 - 0.780318i) q^{47} +(-1.40662 + 3.43724i) q^{48} +(-1.63212 - 2.82692i) q^{49} +(2.05806 - 1.18822i) q^{50} +(4.13003 - 0.561649i) q^{51} +(3.70801 - 4.75721i) q^{52} -4.09727 q^{53} +(1.17234 + 2.73096i) q^{54} +(-1.93229 + 3.34683i) q^{55} +(2.03014 - 3.51630i) q^{56} +(0.433505 + 3.18774i) q^{57} +2.70762i q^{58} -6.11841i q^{59} +(-2.10621 + 1.63046i) q^{60} +(-0.669384 + 1.15941i) q^{61} +(-1.41722 + 2.45470i) q^{62} +(1.54844 + 5.58785i) q^{63} +1.18401 q^{64} +(3.07168 - 1.24512i) q^{65} +(1.57735 - 3.85446i) q^{66} +(-14.1282 + 8.15690i) q^{67} +(-2.01282 - 3.48630i) q^{68} +(14.1144 - 1.91944i) q^{69} +(0.880073 - 0.508110i) q^{70} +(-10.6135 + 6.12771i) q^{71} +(4.41813 - 4.49411i) q^{72} +8.77557i q^{73} +(0.316911 - 0.548905i) q^{74} +(7.13097 - 0.969750i) q^{75} +(2.69088 - 1.55358i) q^{76} +(4.06278 - 7.03695i) q^{77} +(-3.09923 + 1.77563i) q^{78} +(4.09875 + 7.09924i) q^{79} +(1.70703 + 0.985554i) q^{80} +(0.153446 + 8.99869i) q^{81} +(-0.162134 - 0.280825i) q^{82} +(2.31396 - 1.33597i) q^{83} +(4.42845 - 3.42816i) q^{84} -2.21213i q^{85} +(-4.74881 - 2.74173i) q^{86} +(-3.10550 + 7.58867i) q^{87} -8.83142 q^{88} +(-11.4616 - 6.61737i) q^{89} +(1.52004 - 0.421215i) q^{90} +(-6.45842 + 2.61794i) q^{91} +(-6.87881 - 11.9144i) q^{92} +(-6.78746 + 5.25432i) q^{93} +(0.446305 + 0.773023i) q^{94} +1.70742 q^{95} +(-8.70089 - 3.56065i) q^{96} +(12.0294 + 6.94519i) q^{97} +(1.61687 - 0.933498i) q^{98} +(8.84172 - 8.99377i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q - q^{3} - 20 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} + 7 q^{9} - 7 q^{10} - 11 q^{12} - 9 q^{14} - 6 q^{15} + 24 q^{16} + 9 q^{17} + 30 q^{18} - 6 q^{19} - 24 q^{20} - 12 q^{21} + 26 q^{22} + 6 q^{23}+ \cdots + 18 q^{99}+O(q^{100}) $ 22 * q - q^3 - 20 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 + 7 * q^9 - 7 * q^10 - 11 * q^12 - 9 * q^14 - 6 * q^15 + 24 * q^16 + 9 * q^17 + 30 * q^18 - 6 * q^19 - 24 * q^20 - 12 * q^21 + 26 * q^22 + 6 * q^23 + 24 * q^24 + 4 * q^25 - 12 * q^26 + 14 * q^27 + 3 * q^28 + 48 * q^29 + 9 * q^30 - 27 * q^31 - 3 * q^33 + 15 * q^34 - 27 * q^35 - 34 * q^36 + 6 * q^37 + 21 * q^38 + 19 * q^39 + 13 * q^40 + 6 * q^41 - 30 * q^42 - 4 * q^43 + 6 * q^45 - 15 * q^46 - 6 * q^47 - 13 * q^48 + 7 * q^49 + 18 * q^50 + 12 * q^51 - 22 * q^52 - 24 * q^53 + 21 * q^54 - 13 * q^55 - 9 * q^56 - 42 * q^57 + 6 * q^60 + 3 * q^61 - 54 * q^63 - 24 * q^64 - 57 * q^65 + 30 * q^66 - 45 * q^67 - 69 * q^68 + 42 * q^69 - 24 * q^70 + 9 * q^71 - 24 * q^72 - 6 * q^74 - 8 * q^75 + 18 * q^76 + 42 * q^77 + 6 * q^78 - 6 * q^79 + 105 * q^80 + 19 * q^81 - 16 * q^82 + 42 * q^83 + 66 * q^84 + 45 * q^86 - 6 * q^87 + 22 * q^88 - 30 * q^89 + 30 * q^90 + 15 * q^91 - 3 * q^92 + 39 * q^93 + 44 * q^94 + 6 * q^95 - 9 * q^96 - 27 * q^97 + 117 * q^98 + 18 * q^99

Character values

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

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$			0.571953i			0.404432i	0.979341	+	0.202216i	$0.0648143\pi$
$2$			0.571953i			0.404432i	−0.979341	+	0.202216i	$0.935186\pi$
$3$	−0.656000	+	1.60302i	−0.378742	+	0.925502i
$3$	−0.656000	+	1.60302i	−0.378742	+	0.925502i
$4$	1.67287			0.836435
$5$	0.796103	+	0.459630i	0.356028	+	0.205553i	0.667337	−	0.744756i	$-0.267434\pi$
$5$	0.796103	+	0.459630i	0.356028	+	0.205553i	−0.311309	+	0.950309i	$0.600767\pi$
$6$	−0.916851	−	0.375201i	−0.374303	−	0.153175i
$7$	−1.67386	−	0.966405i	−0.632660	−	0.365267i	0.149121	−	0.988819i	$-0.452356\pi$
$7$	−1.67386	−	0.966405i	−0.632660	−	0.365267i	−0.781782	+	0.623552i	$0.785689\pi$
$8$			2.10071i			0.742713i
$9$	−2.13933	−	2.10316i	−0.713109	−	0.701053i
$10$	−0.262887	+	0.455333i	−0.0831321	+	0.143989i
$11$			4.20402i			1.26756i	0.773514	+	0.633780i	$0.218497\pi$
$11$			4.20402i			1.26756i	−0.773514	+	0.633780i	$0.781503\pi$
$12$	−1.09740	+	2.68164i	−0.316793	+	0.774122i
$13$	2.21656	−	2.84374i	0.614762	−	0.788713i
$13$	2.21656	−	2.84374i	0.614762	−	0.788713i
$14$	0.552738	−	0.957371i	0.147725	−	0.255868i
$15$	−1.25904	+	0.974649i	−0.325082	+	0.251653i
$16$	2.14423			0.536058
$17$	−1.20321	−	2.08402i	−0.291822	−	0.505450i	0.682419	−	0.730961i	$-0.260928\pi$
$17$	−1.20321	−	2.08402i	−0.291822	−	0.505450i	−0.974241	+	0.225511i	$0.927595\pi$
$18$	1.20291	−	1.22360i	0.283528	−	0.288404i
$19$	1.60854	−	0.928692i	0.369025	−	0.213056i	−0.304008	−	0.952670i	$-0.598325\pi$
$19$	1.60854	−	0.928692i	0.369025	−	0.213056i	0.673032	+	0.739613i	$0.264991\pi$
$20$	1.33178	+	0.768901i	0.297794	+	0.171932i
$21$	2.64722	−	2.04927i	0.577670	−	0.447187i
$22$	−2.40450			−0.512641
$23$	−4.11198	−	7.12216i	−0.857407	−	1.48507i	−0.874394	−	0.485217i	$-0.838741\pi$
$23$	−4.11198	−	7.12216i	−0.857407	−	1.48507i	0.0169865	−	0.999856i	$-0.494593\pi$
$24$	−3.36747	−	1.37807i	−0.687382	−	0.281296i
$25$	−2.07748	−	3.59830i	−0.415496	−	0.719660i
$26$	1.62649	+	1.26777i	0.318981	+	0.248629i
$27$	4.77480	−	2.04971i	0.918910	−	0.394466i
$28$	−2.80015	−	1.61667i	−0.529179	−	0.305522i
$29$	4.73399			0.879080			0.439540	−	0.898223i	$-0.355142\pi$
$29$	4.73399			0.879080			0.439540	+	0.898223i	$0.355142\pi$
$30$	−0.557453	−	0.720111i	−0.101777	−	0.131474i
$31$	4.29178	+	2.47786i	0.770826	+	0.445037i	0.833169	−	0.553018i	$-0.186524\pi$
$31$	4.29178	+	2.47786i	0.770826	+	0.445037i	−0.0623429	+	0.998055i	$0.519857\pi$
$32$			5.42782i			0.959512i
$33$	−6.73911	−	2.75784i	−1.17313	−	0.480078i
$34$	1.19196	−	0.688181i	0.204420	−	0.118022i
$35$	−0.888377	−	1.53871i	−0.150163	−	0.260090i
$36$	−3.57882	−	3.51831i	−0.596469	−	0.586385i
$37$	−0.959703	−	0.554085i	−0.157774	−	0.0910910i	0.419034	−	0.907970i	$-0.362369\pi$
$37$	−0.959703	−	0.554085i	−0.157774	−	0.0910910i	−0.576808	+	0.816879i	$0.695702\pi$
$38$	0.531168	+	0.920010i	0.0861668	+	0.149245i
$39$	3.10451	+	5.41867i	0.497119	+	0.867682i
$40$	−0.965549	+	1.67238i	−0.152667	+	0.264427i
$41$	−0.490992	+	0.283475i	−0.0766801	+	0.0442713i	−0.537850	−	0.843041i	$-0.680763\pi$
$41$	−0.490992	+	0.283475i	−0.0766801	+	0.0442713i	0.461170	+	0.887312i	$0.347430\pi$
$42$	1.17209	+	1.51408i	0.180857	+	0.233628i
$43$	−4.79362	+	8.30280i	−0.731021	+	1.26616i	0.225427	+	0.974260i	$0.427622\pi$
$43$	−4.79362	+	8.30280i	−0.731021	+	1.26616i	−0.956447	+	0.291905i	$0.905711\pi$
$44$			7.03277i			1.06023i
$45$	−0.736449	−	2.65763i	−0.109783	−	0.396176i
$46$	4.07354	−	2.35186i	0.600611	−	0.346763i
$47$	1.35155	−	0.780318i	0.197144	−	0.113821i	−0.398179	−	0.917308i	$-0.630358\pi$
$47$	1.35155	−	0.780318i	0.197144	−	0.113821i	0.595323	+	0.803487i	$0.297024\pi$
$48$	−1.40662	+	3.43724i	−0.203028	+	0.496123i
$49$	−1.63212	−	2.82692i	−0.233161	−	0.403846i
$50$	2.05806	−	1.18822i	0.291054	−	0.168040i
$51$	4.13003	−	0.561649i	0.578320	−	0.0786466i
$52$	3.70801	−	4.75721i	0.514208	−	0.659707i
$53$	−4.09727			−0.562804			−0.281402	−	0.959590i	$-0.590799\pi$
$53$	−4.09727			−0.562804			−0.281402	+	0.959590i	$0.590799\pi$
$54$	1.17234	+	2.73096i	0.159535	+	0.371637i
$55$	−1.93229	+	3.34683i	−0.260550	+	0.451287i
$56$	2.03014	−	3.51630i	0.271288	−	0.469885i
$57$	0.433505	+	3.18774i	0.0574192	+	0.422227i
$58$			2.70762i			0.355528i
$59$		−	6.11841i		−	0.796549i	−0.917266	−	0.398274i	$-0.869609\pi$
$59$		−	6.11841i		−	0.796549i	0.917266	−	0.398274i	$-0.130391\pi$
$60$	−2.10621	+	1.63046i	−0.271910	+	0.210492i
$61$	−0.669384	+	1.15941i	−0.0857059	+	0.148447i	−0.905692	−	0.423937i	$-0.860648\pi$
$61$	−0.669384	+	1.15941i	−0.0857059	+	0.148447i	0.819986	+	0.572384i	$0.193981\pi$
$62$	−1.41722	+	2.45470i	−0.179987	+	0.311747i
$63$	1.54844	+	5.58785i	0.195085	+	0.704003i
$64$	1.18401			0.148001
$65$	3.07168	−	1.24512i	0.380995	−	0.154438i
$66$	1.57735	−	3.85446i	0.194159	−	0.474451i
$67$	−14.1282	+	8.15690i	−1.72603	+	0.996524i	−0.821360	+	0.570410i	$0.806784\pi$
$67$	−14.1282	+	8.15690i	−1.72603	+	0.996524i	−0.904670	+	0.426113i	$0.859882\pi$
$68$	−2.01282	−	3.48630i	−0.244090	−	0.422776i
$69$	14.1144	−	1.91944i	1.69917	−	0.231073i
$70$	0.880073	−	0.508110i	0.105189	−	0.0607308i
$71$	−10.6135	+	6.12771i	−1.25959	+	0.727225i	−0.972995	−	0.230827i	$-0.925857\pi$
$71$	−10.6135	+	6.12771i	−1.25959	+	0.727225i	−0.286596	+	0.958052i	$0.592524\pi$
$72$	4.41813	−	4.49411i	0.520681	−	0.529635i
$73$			8.77557i			1.02710i	0.858059	+	0.513551i	$0.171670\pi$
$73$			8.77557i			1.02710i	−0.858059	+	0.513551i	$0.828330\pi$
$74$	0.316911	−	0.548905i	0.0368401	−	0.0638089i
$75$	7.13097	−	0.969750i	0.823413	−	0.111977i
$76$	2.69088	−	1.55358i	0.308665	−	0.178208i
$77$	4.06278	−	7.03695i	0.462997	−	0.801935i
$78$	−3.09923	+	1.77563i	−0.350918	+	0.201051i
$79$	4.09875	+	7.09924i	0.461145	+	0.798727i	0.999018	−	0.0442988i	$-0.0141054\pi$
$79$	4.09875	+	7.09924i	0.461145	+	0.798727i	−0.537873	+	0.843026i	$0.680772\pi$
$80$	1.70703	+	0.985554i	0.190852	+	0.110188i
$81$	0.153446	+	8.99869i	0.0170495	+	0.999855i
$82$	−0.162134	−	0.280825i	−0.0179047	−	0.0310119i
$83$	2.31396	−	1.33597i	0.253991	−	0.146642i	−0.367600	−	0.929984i	$-0.619820\pi$
$83$	2.31396	−	1.33597i	0.253991	−	0.146642i	0.621590	+	0.783343i	$0.286487\pi$
$84$	4.42845	−	3.42816i	0.483183	−	0.374043i
$85$		−	2.21213i		−	0.239939i
$86$	−4.74881	−	2.74173i	−0.512077	−	0.295648i
$87$	−3.10550	+	7.58867i	−0.332944	+	0.813590i
$88$	−8.83142			−0.941433
$89$	−11.4616	−	6.61737i	−1.21493	−	0.701440i	−0.251101	−	0.967961i	$-0.580793\pi$
$89$	−11.4616	−	6.61737i	−1.21493	−	0.701440i	−0.963829	+	0.266521i	$0.914126\pi$
$90$	1.52004	−	0.421215i	0.160226	−	0.0443999i
$91$	−6.45842	+	2.61794i	−0.677026	+	0.274435i
$92$	−6.87881	−	11.9144i	−0.717165	−	1.24217i
$93$	−6.78746	+	5.25432i	−0.703827	+	0.544848i
$94$	0.446305	+	0.773023i	0.0460329	+	0.0797313i
$95$	1.70742			0.175177
$96$	−8.70089	−	3.56065i	−0.888030	−	0.363407i
$97$	12.0294	+	6.94519i	1.22140	+	0.705177i	0.965217	−	0.261451i	$-0.0842009\pi$
$97$	12.0294	+	6.94519i	1.22140	+	0.705177i	0.256186	+	0.966628i	$0.417534\pi$
$98$	1.61687	−	0.933498i	0.163328	−	0.0942976i
$99$	8.84172	−	8.99377i	0.888626	−	0.903908i
$100$	−3.47535	−	6.01949i	−0.347535	−	0.601949i
$101$	2.20750			0.219655			0.109827	−	0.993951i	$-0.464970\pi$
$101$	2.20750			0.219655			0.109827	+	0.993951i	$0.464970\pi$
$102$	0.321237	+	2.36219i	0.0318072	+	0.233891i
$103$	3.00242	−	5.20034i	0.295837	−	0.512405i	−0.679342	−	0.733822i	$-0.737735\pi$
$103$	3.00242	−	5.20034i	0.295837	−	0.512405i	0.975179	+	0.221417i	$0.0710682\pi$
$104$	5.97388	+	4.65634i	0.585787	+	0.456592i
$105$	3.04936	−	0.414687i	0.297587	−	0.0404693i
$106$		−	2.34345i		−	0.227616i
$107$	4.84922	−	8.39910i	0.468792	−	0.811972i	−0.530572	−	0.847640i	$-0.678023\pi$
$107$	4.84922	−	8.39910i	0.468792	−	0.811972i	0.999364	+	0.0356684i	$0.0113560\pi$
$108$	7.98762	−	3.42889i	0.768609	−	0.329945i
$109$		−	11.2437i		−	1.07695i	−0.842641	−	0.538476i	$-0.819000\pi$
$109$		−	11.2437i		−	1.07695i	0.842641	−	0.538476i	$-0.181000\pi$
$110$	−1.91423	−	1.10518i	−0.182515	−	0.105375i
$111$	1.51777	−	1.17494i	0.144061	−	0.111520i
$112$	−3.58915	−	2.07220i	−0.339143	−	0.195804i
$113$	1.45567			0.136938			0.0684690	−	0.997653i	$-0.478189\pi$
$113$	1.45567			0.136938			0.0684690	+	0.997653i	$0.478189\pi$
$114$	−1.82324	+	0.247945i	−0.170762	+	0.0232222i
$115$		−	7.55996i		−	0.704970i
$116$	7.91935			0.735293
$117$	−10.7228	+	1.42193i	−0.991322	+	0.131458i
$118$	3.49944			0.322150
$119$			4.65116i			0.426371i
$120$	−2.04745	−	2.64487i	−0.186906	−	0.241443i
$121$	−6.67377			−0.606706
$122$	−0.663127	−	0.382856i	−0.0600367	−	0.0346622i
$123$	−0.132324	−	0.973029i	−0.0119312	−	0.0877350i
$124$	7.17959	+	4.14514i	0.644746	+	0.372244i
$125$		−	8.41579i		−	0.752731i
$126$	−3.19599	+	0.885633i	−0.284721	+	0.0788985i
$127$	−0.170609	+	0.295504i	−0.0151391	+	0.0262217i	−0.873496	−	0.486832i	$-0.838152\pi$
$127$	−0.170609	+	0.295504i	−0.0151391	+	0.0262217i	0.858357	+	0.513054i	$0.171486\pi$
$128$			11.5328i			1.01937i
$129$	−10.1649	−	13.1309i	−0.894970	−	1.15611i
$130$	0.712148	+	1.75686i	0.0624595	+	0.154086i
$131$	−7.50010	+	12.9906i	−0.655287	+	1.13499i	0.326535	+	0.945185i	$0.394119\pi$
$131$	−7.50010	+	12.9906i	−0.655287	+	1.13499i	−0.981822	+	0.189805i	$0.939214\pi$
$132$	−11.2737	−	4.61350i	−0.981246	−	0.401554i
$133$	−3.58997			−0.311290
$134$	−4.66536	−	8.08065i	−0.403026	−	0.698061i
$135$	4.74334	+	0.562865i	0.408241	+	0.0484437i
$136$	4.37793	−	2.52760i	0.375404	−	0.216740i
$137$	−4.75390	−	2.74466i	−0.406153	−	0.234492i	0.282983	−	0.959125i	$-0.408676\pi$
$137$	−4.75390	−	2.74466i	−0.406153	−	0.234492i	−0.689135	+	0.724633i	$0.742009\pi$
$138$	1.09783	+	8.07278i	0.0934534	+	0.687200i
$139$	13.1219			1.11298			0.556492	−	0.830853i	$-0.312147\pi$
$139$	13.1219			1.11298			0.556492	+	0.830853i	$0.312147\pi$
$140$	−1.48614	−	2.57407i	−0.125602	−	0.217549i
$141$	0.364246	+	2.67845i	0.0306750	+	0.225566i
$142$	−3.50476	−	6.07042i	−0.294113	−	0.509419i
$143$	11.9552	+	9.31844i	0.999740	+	0.779247i
$144$	−4.58722	−	4.50966i	−0.382268	−	0.375805i
$145$	3.76874	+	2.17588i	0.312977	+	0.180697i
$146$	−5.01921			−0.415393
$147$	5.60228	−	0.761862i	0.462068	−	0.0628373i
$148$	−1.60546	−	0.926912i	−0.131968	−	0.0761917i
$149$			18.8973i			1.54813i	0.633106	+	0.774065i	$0.281780\pi$
$149$			18.8973i			1.54813i	−0.633106	+	0.774065i	$0.718220\pi$
$150$	0.554652	+	4.07858i	0.0452871	+	0.333015i
$151$	−9.20639	+	5.31531i	−0.749205	+	0.432554i	−0.825407	−	0.564539i	$-0.809054\pi$
$151$	−9.20639	+	5.31531i	−0.749205	+	0.432554i	0.0762014	+	0.997092i	$0.475721\pi$
$152$	1.95091	+	3.37908i	0.158240	+	0.274079i
$153$	−1.80897	+	6.98896i	−0.146247	+	0.565024i
$154$	4.02480	+	2.32372i	0.324328	+	0.187251i
$155$	2.27780	+	3.94526i	0.182957	+	0.316891i
$156$	5.19344	+	9.06473i	0.415808	+	0.725760i
$157$	5.60693	−	9.71149i	0.447482	−	0.775061i	−0.550740	−	0.834677i	$-0.685654\pi$
$157$	5.60693	−	9.71149i	0.447482	−	0.775061i	0.998221	+	0.0596160i	$0.0189876\pi$
$158$	−4.06043	+	2.34429i	−0.323031	+	0.186502i
$159$	2.68781	−	6.56800i	0.213157	−	0.520876i
$160$	−2.49479	+	4.32110i	−0.197230	+	0.341613i
$161$			15.8953i			1.25273i
$162$	−5.14683	+	0.0877638i	−0.404373	+	0.00689538i
$163$	−7.31577	+	4.22376i	−0.573015	+	0.330830i	−0.758353	−	0.651845i	$-0.773995\pi$
$163$	−7.31577	+	4.22376i	−0.573015	+	0.330830i	0.185338	+	0.982675i	$0.440662\pi$
$164$	−0.821366	+	0.474216i	−0.0641379	+	0.0370301i
$165$	−4.09744	−	5.29302i	−0.318985	−	0.412061i
$166$	0.764111	+	1.32348i	0.0593065	+	0.102722i
$167$	22.3640	−	12.9119i	1.73058	−	0.999151i	0.844685	−	0.535263i	$-0.179788\pi$
$167$	22.3640	−	12.9119i	1.73058	−	0.999151i	0.885894	−	0.463887i	$-0.153546\pi$
$168$	4.30492	+	5.56103i	0.332131	+	0.429043i
$169$	−3.17376	−	12.6066i	−0.244135	−	0.969741i
$170$	1.26523			0.0970391
$171$	−5.39438	−	1.39624i	−0.412519	−	0.106773i
$172$	−8.01911	+	13.8895i	−0.611451	+	1.05906i
$173$	−6.03034	+	10.4448i	−0.458478	+	0.794107i	−0.998881	−	0.0472993i	$-0.984939\pi$
$173$	−6.03034	+	10.4448i	−0.458478	+	0.794107i	0.540403	+	0.841406i	$0.318272\pi$
$174$	−4.34036	−	1.77620i	−0.329042	−	0.134653i
$175$			8.03075i			0.607067i
$176$			9.01439i			0.679485i
$177$	9.80791	+	4.01368i	0.737208	+	0.301686i
$178$	3.78483	−	6.55551i	0.283685	−	0.491356i
$179$	11.5169	−	19.9478i	0.860812	−	1.49097i	−0.0103340	−	0.999947i	$-0.503289\pi$
$179$	11.5169	−	19.9478i	0.860812	−	1.49097i	0.871146	−	0.491024i	$-0.163377\pi$
$180$	−1.23198	−	4.44587i	−0.0918267	−	0.331375i
$181$	0.758558			0.0563832			0.0281916	−	0.999603i	$-0.491025\pi$
$181$	0.758558			0.0563832			0.0281916	+	0.999603i	$0.491025\pi$
$182$	−1.49734	−	3.69391i	−0.110990	−	0.273811i
$183$	−1.41943	−	1.83361i	−0.104928	−	0.135544i
$184$	14.9616	−	8.63808i	1.10298	−	0.636807i
$185$	−0.509348	−	0.882217i	−0.0374480	−	0.0648619i
$186$	−3.00522	−	3.88211i	−0.220354	−	0.284650i
$187$	8.76128	−	5.05833i	0.640688	−	0.369901i
$188$	2.26097	−	1.30537i	0.164898	−	0.0952039i
$189$	−9.97320	−	1.18346i	−0.725444	−	0.0860842i
$190$			0.976563i			0.0708474i
$191$	−8.57804	+	14.8576i	−0.620685	+	1.07506i	0.368674	+	0.929559i	$0.379812\pi$
$191$	−8.57804	+	14.8576i	−0.620685	+	1.07506i	−0.989358	+	0.145499i	$0.953521\pi$
$192$	−0.776709	+	1.89798i	−0.0560541	+	0.136975i
$193$	−2.96462	+	1.71162i	−0.213398	+	0.123205i	−0.602890	−	0.797825i	$-0.705984\pi$
$193$	−2.96462	+	1.71162i	−0.213398	+	0.123205i	0.389492	+	0.921030i	$0.372651\pi$
$194$	−3.97232	+	6.88026i	−0.285196	+	0.493974i
$195$	−0.0190775	+	5.74075i	−0.00136617	+	0.411103i
$196$	−2.73033	−	4.72907i	−0.195024	−	0.337791i
$197$	22.8976	+	13.2200i	1.63139	+	0.941882i	0.983665	+	0.180006i	$0.0576118\pi$
$197$	22.8976	+	13.2200i	1.63139	+	0.941882i	0.647723	+	0.761876i	$0.275721\pi$
$198$	5.14402	+	5.05705i	0.365569	+	0.359389i
$199$	8.06121	+	13.9624i	0.571444	+	0.989770i	0.996418	+	0.0845645i	$0.0269499\pi$
$199$	8.06121	+	13.9624i	0.571444	+	0.989770i	−0.424974	+	0.905206i	$0.639717\pi$
$200$	7.55898	−	4.36418i	0.534501	−	0.308594i
$201$	−3.80757	−	27.9986i	−0.268565	−	1.97487i
$202$			1.26259i			0.0888353i
$203$	−7.92405	−	4.57495i	−0.556159	−	0.321099i
$204$	6.90901	−	0.939566i	0.483727	−	0.0657828i
$205$	−0.521174			−0.0364004
$206$	2.97435	+	1.71724i	0.207233	+	0.119646i
$207$	−6.18216	+	23.8848i	−0.429690	+	1.66011i
$208$	4.75281	−	6.09765i	0.329548	−	0.422796i
$209$	3.90424	+	6.76234i	0.270062	+	0.467761i
$210$	0.237182	+	1.74409i	0.0163671	+	0.120354i
$211$	−2.98674	−	5.17318i	−0.205616	−	0.356137i	0.744713	−	0.667385i	$-0.232586\pi$
$211$	−2.98674	−	5.17318i	−0.205616	−	0.356137i	−0.950329	+	0.311248i	$0.899253\pi$
$212$	−6.85420			−0.470749
$213$	−2.86036	−	21.0334i	−0.195989	−	1.44118i
$214$	4.80389	+	2.77353i	0.328387	+	0.189594i
$215$	−7.63243	+	4.40659i	−0.520528	+	0.300527i
$216$	4.30584	+	10.0305i	0.292975	+	0.682487i
$217$	−4.78923	−	8.29519i	−0.325114	−	0.563114i
$218$	6.43087			0.435553
$219$	−14.0674	−	5.75677i	−0.950586	−	0.389007i
$220$	−3.23248	+	5.59881i	−0.217933	+	0.377472i
$221$	−8.59342	−	1.19773i	−0.578056	−	0.0805680i
$222$	0.672011	+	0.868095i	0.0451024	+	0.0582627i
$223$		−	15.3827i		−	1.03010i	−0.857160	−	0.515050i	$-0.827773\pi$
$223$		−	15.3827i		−	1.03010i	0.857160	−	0.515050i	$-0.172227\pi$
$224$	5.24547	−	9.08542i	0.350478	−	0.607045i
$225$	−3.12339	+	12.0672i	−0.208226	+	0.804481i
$226$			0.832575i			0.0553821i
$227$	−21.5086	−	12.4180i	−1.42757	−	0.824210i	−0.430645	−	0.902521i	$-0.641714\pi$
$227$	−21.5086	−	12.4180i	−1.42757	−	0.824210i	−0.996929	+	0.0783109i	$0.975047\pi$
$228$	0.725198	+	5.33267i	0.0480274	+	0.353165i
$229$	−1.33179	−	0.768908i	−0.0880071	−	0.0508109i	0.455351	−	0.890312i	$-0.349514\pi$
$229$	−1.33179	−	0.768908i	−0.0880071	−	0.0508109i	−0.543358	+	0.839501i	$0.682847\pi$
$230$	4.32394			0.285112
$231$	8.61516	+	11.1289i	0.566836	+	0.732231i
$232$			9.94474i			0.652904i
$233$	−12.3941			−0.811967			−0.405983	−	0.913880i	$-0.633071\pi$
$233$	−12.3941			−0.811967			−0.405983	+	0.913880i	$0.633071\pi$
$234$	−0.813278	−	6.13293i	−0.0531656	−	0.400922i
$235$	1.43463			0.0935850
$236$		−	10.2353i		−	0.666261i
$237$	−14.0690	+	1.91326i	−0.913879	+	0.124280i
$238$	−2.66024			−0.172438
$239$	1.80901	+	1.04443i	0.117015	+	0.0675589i	0.557365	−	0.830267i	$-0.311812\pi$
$239$	1.80901	+	1.04443i	0.117015	+	0.0675589i	−0.440350	+	0.897826i	$0.645146\pi$
$240$	−2.69967	+	2.08987i	−0.174263	+	0.134901i
$241$	1.22552	+	0.707554i	0.0789426	+	0.0455775i	0.538952	−	0.842337i	$-0.318821\pi$
$241$	1.22552	+	0.707554i	0.0789426	+	0.0455775i	−0.460009	+	0.887914i	$0.652154\pi$
$242$		−	3.81708i		−	0.245371i
$243$	−14.5257	−	5.65717i	−0.931825	−	0.362907i
$244$	−1.11979	+	1.93954i	−0.0716874	+	0.124166i
$245$		−	3.00069i		−	0.191707i
$246$	0.556527	−	0.0756829i	0.0354828	−	0.00482536i
$247$	0.924460	−	6.63278i	0.0588220	−	0.422033i
$248$	−5.20526	+	9.01578i	−0.330535	+	0.572503i
$249$	0.623619	+	4.58572i	0.0395202	+	0.290608i
$250$	4.81344			0.304429
$251$	−12.6610	−	21.9295i	−0.799155	−	1.38418i	−0.920167	−	0.391526i	$-0.871947\pi$
$251$	−12.6610	−	21.9295i	−0.799155	−	1.38418i	0.121012	−	0.992651i	$-0.461386\pi$
$252$	2.59033	+	9.34775i	0.163176	+	0.588853i
$253$	29.9417	−	17.2868i	1.88242	−	1.08681i
$254$	−0.169014	−	0.0975805i	−0.0106049	−	0.00612274i
$255$	3.54608	+	1.45116i	0.222064	+	0.0908750i
$256$	−4.22823			−0.264264
$257$	8.17386	+	14.1575i	0.509871	+	0.883123i	0.999935	+	0.0114360i	$0.00364026\pi$
$257$	8.17386	+	14.1575i	0.509871	+	0.883123i	−0.490063	+	0.871687i	$0.663026\pi$
$258$	7.51026	−	5.81385i	0.467568	−	0.361955i
$259$	1.07094	+	1.85492i	0.0665450	+	0.115259i
$260$	5.13851	−	2.08292i	0.318677	−	0.129177i
$261$	−10.1276	−	9.95633i	−0.626880	−	0.616281i
$262$	−7.42999	−	4.28971i	−0.459026	−	0.265019i
$263$	0.494129			0.0304693			0.0152347	−	0.999884i	$-0.495150\pi$
$263$	0.494129			0.0304693			0.0152347	+	0.999884i	$0.495150\pi$
$264$	5.79341	−	14.1569i	0.356560	−	0.871298i
$265$	−3.26185	−	1.88323i	−0.200374	−	0.115686i
$266$		−	2.05329i		−	0.125895i
$267$	18.1266	−	14.0322i	1.10933	−	0.858756i
$268$	−23.6346	+	13.6454i	−1.44371	+	0.833527i
$269$	2.76326	+	4.78611i	0.168479	+	0.291814i	0.937885	−	0.346945i	$-0.112781\pi$
$269$	2.76326	+	4.78611i	0.168479	+	0.291814i	−0.769406	+	0.638760i	$0.779448\pi$
$270$	−0.321932	+	2.71297i	−0.0195922	+	0.165106i
$271$	−17.8220	−	10.2895i	−1.08261	−	0.625045i	−0.151011	−	0.988532i	$-0.548253\pi$
$271$	−17.8220	−	10.2895i	−1.08261	−	0.625045i	−0.931599	+	0.363487i	$0.881586\pi$
$272$	−2.57997	−	4.46863i	−0.156433	−	0.270951i
$273$	0.0401118	−	12.0703i	0.00242768	−	0.730529i
$274$	1.56982	−	2.71901i	0.0948362	−	0.164261i
$275$	15.1273	−	8.73377i	0.912212	−	0.526666i
$276$	23.6116	−	3.21097i	1.42125	−	0.193278i
$277$	−1.86984	+	3.23867i	−0.112348	+	0.194593i	−0.916717	−	0.399538i	$-0.869171\pi$
$277$	−1.86984	+	3.23867i	−0.112348	+	0.194593i	0.804368	+	0.594131i	$0.202504\pi$
$278$			7.50510i			0.450126i
$279$	−3.97019	−	14.3272i	−0.237689	−	0.857750i
$280$	3.23239	−	1.86622i	0.193172	−	0.111528i
$281$	22.6500	−	13.0770i	1.35119	−	0.780107i	0.362770	−	0.931879i	$-0.381831\pi$
$281$	22.6500	−	13.0770i	1.35119	−	0.780107i	0.988416	+	0.151772i	$0.0484978\pi$
$282$	−1.53195	+	0.208332i	−0.0912261	+	0.0124060i
$283$	2.72770	+	4.72451i	0.162145	+	0.280843i	0.935638	−	0.352962i	$-0.114825\pi$
$283$	2.72770	+	4.72451i	0.162145	+	0.280843i	−0.773493	+	0.633805i	$0.781492\pi$
$284$	−17.7550	+	10.2509i	−1.05357	+	0.608276i
$285$	−1.12007	+	2.73702i	−0.0663470	+	0.162127i
$286$	−5.32971	+	6.83779i	−0.315152	+	0.404327i
$287$	1.09580			0.0646833
$288$	11.4156	−	11.6119i	0.672669	−	0.684237i
$289$	5.60456	−	9.70739i	0.329680	−	0.571023i
$290$	−1.24450	+	2.15554i	−0.0730798	+	0.126578i
$291$	−19.0246	+	14.7273i	−1.11524	+	0.863331i
$292$			14.6804i			0.859104i
$293$			10.8117i			0.631628i	0.948821	+	0.315814i	$0.102278\pi$
$293$			10.8117i			0.631628i	−0.948821	+	0.315814i	$0.897722\pi$
$294$	0.435749	+	3.20424i	0.0254134	+	0.186875i
$295$	2.81220	−	4.87088i	0.163733	−	0.283594i
$296$	1.16397	−	2.01606i	0.0676544	−	0.117181i
$297$	8.61700	+	20.0733i	0.500009	+	1.16477i
$298$	−10.8084			−0.626113
$299$	−29.3680	−	4.09325i	−1.69840	−	0.236719i
$300$	11.9292	−	1.62227i	0.688731	−	0.0936616i
$301$	16.0477	−	9.26516i	0.924976	−	0.534035i
$302$	−3.04011	−	5.26562i	−0.174939	−	0.303003i
$303$	−1.44812	+	3.53866i	−0.0831924	+	0.203291i
$304$	3.44909	−	1.99133i	0.197819	−	0.114211i
$305$	−1.06580	+	0.615338i	−0.0610274	+	0.0352342i
$306$	−3.99736	−	1.03465i	−0.228514	−	0.0591468i
$307$		−	15.9285i		−	0.909086i	−0.890725	−	0.454543i	$-0.849803\pi$
$307$		−	15.9285i		−	0.909086i	0.890725	−	0.454543i	$-0.150197\pi$
$308$	6.79651	−	11.7719i	0.387267	−	0.670766i
$309$	6.36665	+	8.22435i	0.362186	+	0.467867i
$310$	−2.25651	+	1.30279i	−0.128161	+	0.0739937i
$311$	11.1816	−	19.3671i	0.634051	−	1.09821i	−0.352665	−	0.935750i	$-0.614724\pi$
$311$	11.1816	−	19.3671i	0.634051	−	1.09821i	0.986715	−	0.162458i	$-0.0519422\pi$
$312$	−11.3831	+	6.52167i	−0.644439	+	0.369217i
$313$	16.8654	+	29.2118i	0.953290	+	1.65115i	0.738233	+	0.674546i	$0.235661\pi$
$313$	16.8654	+	29.2118i	0.953290	+	1.65115i	0.215058	+	0.976601i	$0.431006\pi$
$314$	5.55452	+	3.20690i	0.313459	+	0.180976i
$315$	−1.33563	+	5.16021i	−0.0752543	+	0.290745i
$316$	6.85667	+	11.8761i	0.385718	+	0.668083i
$317$	5.66544	−	3.27094i	0.318203	−	0.183715i	−0.332388	−	0.943143i	$-0.607854\pi$
$317$	5.66544	−	3.27094i	0.318203	−	0.183715i	0.650591	+	0.759428i	$0.274521\pi$
$318$	3.75659	+	1.53730i	0.210659	+	0.0862076i
$319$			19.9018i			1.11429i
$320$	0.942591	+	0.544205i	0.0526924	+	0.0304220i
$321$	10.2828	+	13.2832i	0.573931	+	0.741396i
$322$	−9.09139			−0.506644
$323$	−3.87083	−	2.23483i	−0.215379	−	0.124349i
$324$	0.256695	+	15.0536i	0.0142608	+	0.836313i
$325$	−14.8375	−	2.06801i	−0.823036	−	0.114713i
$326$	−2.41579	−	4.18427i	−0.133798	−	0.231746i
$327$	18.0238	+	7.37587i	0.996721	+	0.407886i
$328$	−0.595498	−	1.03143i	−0.0328809	−	0.0569513i
$329$	−3.01641			−0.166300
$330$	3.02736	−	2.34354i	0.166651	−	0.129008i
$331$	−5.69415	−	3.28752i	−0.312979	−	0.180698i	0.335280	−	0.942119i	$-0.391169\pi$
$331$	−5.69415	−	3.28752i	−0.312979	−	0.180698i	−0.648259	+	0.761420i	$0.724502\pi$
$332$	3.87096	−	2.23490i	0.212447	−	0.122656i
$333$	0.887791	+	3.20378i	0.0486506	+	0.175566i
$334$	7.38498	+	12.7912i	0.404088	+	0.699902i
$335$	−14.9966			−0.819353
$336$	5.67625	−	4.39411i	0.309665	−	0.239718i
$337$	−11.9883	+	20.7644i	−0.653046	+	1.13111i	0.329333	+	0.944214i	$0.393176\pi$
$337$	−11.9883	+	20.7644i	−0.653046	+	1.13111i	−0.982380	+	0.186896i	$0.940157\pi$
$338$	7.21040	−	1.81524i	0.392194	−	0.0987361i
$339$	−0.954920	+	2.33346i	−0.0518641	+	0.126736i
$340$		−	3.70061i		−	0.200693i
$341$	−10.4170	+	18.0427i	−0.564111	+	0.977068i
$342$	0.798585	−	3.08533i	0.0431825	−	0.166836i
$343$			19.8388i			1.07120i
$344$	−17.4418	−	10.0700i	−0.940397	−	0.542938i
$345$	12.1187	+	4.95934i	0.652451	+	0.267002i
$346$	−5.97396	−	3.44907i	−0.321162	−	0.185423i
$347$	17.0564			0.915635			0.457818	−	0.889046i	$-0.348631\pi$
$347$	17.0564			0.915635			0.457818	+	0.889046i	$0.348631\pi$
$348$	−5.19509	+	12.6948i	−0.278486	+	0.680515i
$349$		−	5.85292i		−	0.313300i	−0.987654	−	0.156650i	$-0.949931\pi$
$349$		−	5.85292i		−	0.313300i	0.987654	−	0.156650i	$-0.0500694\pi$
$350$	−4.59321			−0.245517
$351$	4.75477	−	18.1216i	0.253791	−	0.967259i
$352$	−22.8186			−1.21624
$353$		−	9.20680i		−	0.490028i	−0.969519	−	0.245014i	$-0.921207\pi$
$353$		−	9.20680i		−	0.490028i	0.969519	−	0.245014i	$-0.0787926\pi$
$354$	−2.29563	+	5.60967i	−0.122012	+	0.298150i
$355$	−11.2659			−0.597933
$356$	−19.1738	−	11.0700i	−1.01621	−	0.586709i
$357$	−7.45589	−	3.05116i	−0.394607	−	0.161485i
$358$	11.4092	+	6.58712i	0.602996	+	0.348140i
$359$		−	9.17346i		−	0.484157i	−0.970257	−	0.242078i	$-0.922171\pi$
$359$		−	9.17346i		−	0.484157i	0.970257	−	0.242078i	$-0.0778291\pi$
$360$	5.58291	−	1.54707i	0.294245	−	0.0815375i
$361$	−7.77506	+	13.4668i	−0.409214	+	0.708779i
$362$			0.433860i			0.0228032i
$363$	4.37799	−	10.6982i	0.229785	−	0.561508i
$364$	−10.8041	+	4.37948i	−0.566288	+	0.229547i
$365$	−4.03351	+	6.98625i	−0.211124	+	0.365677i
$366$	1.04874	−	0.811850i	0.0548183	−	0.0424361i
$367$	−21.1465			−1.10384			−0.551920	−	0.833897i	$-0.686105\pi$
$367$	−21.1465			−1.10384			−0.551920	+	0.833897i	$0.686105\pi$
$368$	−8.81704	−	15.2716i	−0.459620	−	0.796085i
$369$	1.64659	+	0.426190i	0.0857178	+	0.0221866i
$370$	0.504587	−	0.291323i	0.0262322	−	0.0151452i
$371$	6.85827	+	3.95962i	0.356064	+	0.205573i
$372$	−11.3545	+	8.78979i	−0.588705	+	0.455729i
$373$	16.5822			0.858595			0.429297	−	0.903163i	$-0.358761\pi$
$373$	16.5822			0.858595			0.429297	+	0.903163i	$0.358761\pi$
$374$	2.89312	+	5.01104i	0.149600	+	0.259115i
$375$	13.4907	+	5.52076i	0.696655	+	0.285091i
$376$	1.63922	+	2.83921i	0.0845364	+	0.146421i
$377$	10.4932	−	13.4623i	0.540425	−	0.693341i
$378$	0.676885	−	5.70420i	0.0348152	−	0.293393i
$379$	−1.56715	−	0.904793i	−0.0804990	−	0.0464761i	0.459210	−	0.888328i	$-0.348132\pi$
$379$	−1.56715	−	0.904793i	−0.0804990	−	0.0464761i	−0.539709	+	0.841852i	$0.681466\pi$
$380$	2.85629			0.146525
$381$	−0.361778	−	0.467340i	−0.0185345	−	0.0239426i
$382$	−8.49785	−	4.90623i	−0.434788	−	0.251025i
$383$			27.9946i			1.43046i	0.698889	+	0.715230i	$0.253678\pi$
$383$			27.9946i			1.43046i	−0.698889	+	0.715230i	$0.746322\pi$
$384$	−18.4873	−	7.56554i	−0.943428	−	0.386077i
$385$	6.46879	−	3.73476i	0.329680	−	0.190341i
$386$	−0.978968	−	1.69562i	−0.0498282	−	0.0863049i
$387$	27.7172	−	7.68066i	1.40895	−	0.390430i
$388$	20.1236	+	11.6184i	1.02162	+	0.589835i
$389$	15.9117	+	27.5599i	0.806755	+	1.39734i	0.915100	+	0.403227i	$0.132111\pi$
$389$	15.9117	+	27.5599i	0.806755	+	1.39734i	−0.108345	+	0.994113i	$0.534555\pi$
$390$	−3.28344	−	0.0109114i	−0.166263	−	0.000552522i
$391$	−9.89517	+	17.1389i	−0.500420	+	0.866753i
$392$	5.93854	−	3.42862i	0.299942	−	0.173171i
$393$	−15.9040	−	20.5446i	−0.802252	−	1.03634i
$394$	−7.56119	+	13.0964i	−0.380927	+	0.659785i
$395$			7.53563i			0.379159i
$396$	14.7910	−	15.0454i	0.743278	−	0.756060i
$397$	−0.359861	+	0.207766i	−0.0180609	+	0.0104275i	−0.509003	−	0.860765i	$-0.669986\pi$
$397$	−0.359861	+	0.207766i	−0.0180609	+	0.0104275i	0.490942	+	0.871192i	$0.336653\pi$
$398$	−7.98585	+	4.61063i	−0.400295	+	0.231110i
$399$	2.35502	−	5.75478i	0.117898	−	0.288099i
$400$	−4.45460	−	7.71559i	−0.222730	−	0.385780i
$401$	19.9369	−	11.5106i	0.995600	−	0.574810i	0.0886566	−	0.996062i	$-0.471743\pi$
$401$	19.9369	−	11.5106i	0.995600	−	0.574810i	0.906944	+	0.421252i	$0.138409\pi$
$402$	16.0139	−	2.17775i	0.798700	−	0.108616i
$403$	16.5594	−	6.71241i	0.824881	−	0.334369i
$404$	3.69286			0.183727
$405$	−4.01391	+	7.23441i	−0.199453	+	0.359481i
$406$	2.61666	−	4.53218i	0.129862	−	0.224928i
$407$	2.32938	−	4.03461i	0.115463	−	0.199988i
$408$	1.17986	+	8.67600i	0.0584119	+	0.429526i
$409$		−	17.9789i		−	0.888997i	−0.895780	−	0.444499i	$-0.853382\pi$
$409$		−	17.9789i		−	0.888997i	0.895780	−	0.444499i	$-0.146618\pi$
$410$		−	0.298087i		−	0.0147215i
$411$	7.51830	−	5.82008i	0.370850	−	0.287083i
$412$	5.02265	−	8.69949i	0.247448	−	0.428593i
$413$	−5.91286	+	10.2414i	−0.290953	+	0.503945i
$414$	−13.6610	−	3.53590i	−0.671400	−	0.173780i
$415$	2.45620			0.120570
$416$	15.4353	+	12.0311i	0.756779	+	0.589871i
$417$	−8.60796	+	21.0346i	−0.421534	+	1.03007i
$418$	−3.86774	+	2.23304i	−0.189177	+	0.109222i
$419$	−0.999021	−	1.73035i	−0.0488054	−	0.0845334i	0.840591	−	0.541671i	$-0.182208\pi$
$419$	−0.999021	−	1.73035i	−0.0488054	−	0.0845334i	−0.889396	+	0.457137i	$0.848875\pi$
$420$	5.10119	−	0.693717i	0.248912	−	0.0338499i
$421$	7.93701	−	4.58244i	0.386826	−	0.223334i	−0.293958	−	0.955818i	$-0.594973\pi$
$421$	7.93701	−	4.58244i	0.386826	−	0.223334i	0.680784	+	0.732484i	$0.261639\pi$
$422$	2.95882	−	1.70827i	0.144033	−	0.0831575i
$423$	−4.53254	−	1.17317i	−0.220380	−	0.0570414i
$424$		−	8.60718i		−	0.418002i
$425$	−4.99930	+	8.65904i	−0.242502	+	0.420025i
$426$	12.0301	−	1.63599i	0.582861	−	0.0792641i
$427$	2.24091	−	1.29379i	0.108445	−	0.0626110i
$428$	8.11212	−	14.0506i	0.392114	−	0.679161i
$429$	−22.7802	+	13.0514i	−1.09984	+	0.630128i
$430$	−2.52036	−	4.36539i	−0.121543	−	0.210518i
$431$	−7.81972	−	4.51472i	−0.376663	−	0.217466i	0.299702	−	0.954033i	$-0.403113\pi$
$431$	−7.81972	−	4.51472i	−0.376663	−	0.217466i	−0.676365	+	0.736566i	$0.736446\pi$
$432$	10.2383	−	4.39505i	0.492589	−	0.211457i
$433$	−9.48511	−	16.4287i	−0.455825	−	0.789512i	0.542910	−	0.839791i	$-0.317322\pi$
$433$	−9.48511	−	16.4287i	−0.455825	−	0.789512i	−0.998735	+	0.0502786i	$0.983989\pi$
$434$	4.74446	−	2.73922i	0.227741	−	0.131487i
$435$	−5.96027	+	4.61398i	−0.285773	+	0.221223i
$436$		−	18.8092i		−	0.900800i
$437$	−13.2286	−	7.63752i	−0.632809	−	0.365352i
$438$	3.29260	−	8.04588i	0.157327	−	0.384447i
$439$	10.4975			0.501017			0.250509	−	0.968114i	$-0.419402\pi$
$439$	10.4975			0.501017			0.250509	+	0.968114i	$0.419402\pi$
$440$	−7.03072	−	4.05919i	−0.335176	−	0.193514i
$441$	−2.45382	+	9.48033i	−0.116848	+	0.451444i
$442$	0.685045	−	4.91503i	0.0325843	−	0.233784i
$443$	−2.54044	−	4.40017i	−0.120700	−	0.209058i	0.799344	−	0.600874i	$-0.205181\pi$
$443$	−2.54044	−	4.40017i	−0.120700	−	0.209058i	−0.920044	+	0.391815i	$0.871847\pi$
$444$	2.53904	−	1.96552i	0.120497	−	0.0932796i
$445$	−6.08309	−	10.5362i	−0.288366	−	0.499465i
$446$	8.79817			0.416605
$447$	−30.2928	−	12.3967i	−1.43280	−	0.586342i
$448$	−1.98186	−	1.14423i	−0.0936343	−	0.0540598i
$449$	−12.9970	+	7.50384i	−0.613368	+	0.354128i	−0.774282	−	0.632840i	$-0.781889\pi$
$449$	−12.9970	+	7.50384i	−0.613368	+	0.354128i	0.160915	+	0.986968i	$0.448556\pi$
$450$	−6.90188	−	1.78643i	−0.325358	−	0.0842132i
$451$	−1.19173	−	2.06414i	−0.0561165	−	0.0971966i
$452$	2.43515			0.114540
$453$	−2.48114	−	18.2448i	−0.116574	−	0.857218i
$454$	7.10250	−	12.3019i	0.333337	−	0.577357i
$455$	−6.34485	−	0.884330i	−0.297451	−	0.0414580i
$456$	−6.69652	+	0.910669i	−0.313593	+	0.0426460i
$457$		−	7.57637i		−	0.354408i	−0.984174	−	0.177204i	$-0.943295\pi$
$457$		−	7.57637i		−	0.354408i	0.984174	−	0.177204i	$-0.0567052\pi$
$458$	0.439780	−	0.761721i	0.0205496	−	0.0355929i
$459$	−10.0167	−	7.48457i	−0.467541	−	0.349350i
$460$		−	12.6468i		−	0.589661i
$461$	19.9973	+	11.5454i	0.931365	+	0.537724i	0.887243	−	0.461302i	$-0.152618\pi$
$461$	19.9973	+	11.5454i	0.931365	+	0.537724i	0.0441221	+	0.999026i	$0.485951\pi$
$462$	−6.36524	+	4.92747i	−0.296138	+	0.229247i
$463$	22.2320	+	12.8357i	1.03321	+	0.596523i	0.917902	−	0.396807i	$-0.129882\pi$
$463$	22.2320	+	12.8357i	1.03321	+	0.596523i	0.115307	+	0.993330i	$0.463215\pi$
$464$	10.1508			0.471238
$465$	−7.81856	+	1.06326i	−0.362577	+	0.0493074i
$466$		−	7.08886i		−	0.328385i
$467$	−13.4856			−0.624041			−0.312021	−	0.950075i	$-0.601006\pi$
$467$	−13.4856			−0.624041			−0.312021	+	0.950075i	$0.601006\pi$
$468$	−17.9378	+	2.37870i	−0.829176	+	0.109956i
$469$	31.5315			1.45599
$470$			0.820542i			0.0378488i
$471$	11.8895	+	15.3587i	0.547841	+	0.707693i
$472$	12.8530			0.591607
$473$	−34.9051	−	20.1525i	−1.60494	−	0.926612i
$474$	−1.09430	−	8.04680i	−0.0502627	−	0.369602i
$475$	−6.68343	−	3.85868i	−0.306657	−	0.177048i
$476$			7.78078i			0.356632i
$477$	8.76541	+	8.61722i	0.401341	+	0.394555i
$478$	−0.597368	+	1.03467i	−0.0273230	+	0.0473247i
$479$			7.57835i			0.346263i	0.984899	+	0.173132i	$0.0553886\pi$
$479$			7.57835i			0.346263i	−0.984899	+	0.173132i	$0.944611\pi$
$480$	−5.29022	−	6.83383i	−0.241464	−	0.311920i
$481$	−3.70291	+	1.50099i	−0.168838	+	0.0684392i
$482$	−0.404688	+	0.700939i	−0.0184330	+	0.0319269i
$483$	−25.4805	−	10.4274i	−1.15940	−	0.474461i
$484$	−11.1643			−0.507470
$485$	6.38444	+	11.0582i	0.289902	+	0.502125i
$486$	3.23563	−	8.30803i	0.146771	−	0.376860i
$487$	−17.0654	+	9.85273i	−0.773308	+	0.446470i	−0.834053	−	0.551684i	$-0.813986\pi$
$487$	−17.0654	+	9.85273i	−0.773308	+	0.446470i	0.0607452	+	0.998153i	$0.480652\pi$
$488$	−2.43558	−	1.40618i	−0.110253	−	0.0636549i
$489$	−1.97162	−	14.4981i	−0.0891595	−	0.655626i
$490$	1.71626			0.0775325
$491$	4.42062	+	7.65674i	0.199500	+	0.345544i	0.948366	−	0.317177i	$-0.102735\pi$
$491$	4.42062	+	7.65674i	0.199500	+	0.345544i	−0.748867	+	0.662721i	$0.769402\pi$
$492$	−0.221360	−	1.62775i	−0.00997968	−	0.0733846i
$493$	−5.69599	−	9.86575i	−0.256535	−	0.444331i
$494$	3.79364	+	0.528748i	0.170684	+	0.0237895i
$495$	11.1727	−	3.09605i	0.502177	−	0.139157i
$496$	9.20257	+	5.31311i	0.413208	+	0.238566i
$497$	23.6874			1.06252
$498$	−2.62282	+	0.356681i	−0.117531	+	0.0159832i
$499$	−7.19943	−	4.15660i	−0.322291	−	0.186075i	0.330122	−	0.943938i	$-0.392910\pi$
$499$	−7.19943	−	4.15660i	−0.322291	−	0.186075i	−0.652413	+	0.757863i	$0.726243\pi$
$500$		−	14.0785i		−	0.629611i
$501$	6.02715	+	44.3201i	0.269273	+	1.98008i
$502$	12.5426	−	7.24150i	0.559805	−	0.323204i
$503$	−0.0196627	−	0.0340569i	−0.000876718	−	0.00151852i	0.865587	−	0.500759i	$-0.166946\pi$
$503$	−0.0196627	−	0.0340569i	−0.000876718	−	0.00151852i	−0.866463	+	0.499241i	$0.833612\pi$
$504$	−11.7385	+	3.25282i	−0.522872	+	0.144892i
$505$	1.75740	+	1.01463i	0.0782032	+	0.0451506i
$506$	9.88726	+	17.1252i	0.439542	+	0.761310i
$507$	22.2906	+	3.18237i	0.989962	+	0.141334i
$508$	−0.285407	+	0.494339i	−0.0126629	+	0.0219328i
$509$	−24.0747	+	13.8995i	−1.06709	+	0.616086i	−0.927386	−	0.374107i	$-0.877949\pi$
$509$	−24.0747	+	13.8995i	−1.06709	+	0.616086i	−0.139707	+	0.990193i	$0.544616\pi$
$510$	−0.829994	+	2.02819i	−0.0367528	+	0.0898099i
$511$	8.48075	−	14.6891i	0.375166	−	0.649807i
$512$			20.6473i			0.912491i
$513$	5.77692	−	7.73135i	0.255057	−	0.341348i
$514$	−8.09745	+	4.67506i	−0.357163	+	0.206208i
$515$	4.78047	−	2.76000i	0.210652	−	0.121620i
$516$	−17.0046	−	21.9663i	−0.748584	−	0.967011i
$517$	3.28047	+	5.68194i	0.144275	+	0.249892i
$518$	−1.06093	+	0.612528i	−0.0466145	+	0.0269129i
$519$	−12.7874	−	16.5186i	−0.561303	−	0.725084i
$520$	2.61563	+	6.45270i	0.114703	+	0.282970i
$521$	10.8017			0.473233			0.236616	−	0.971603i	$-0.423962\pi$
$521$	10.8017			0.473233			0.236616	+	0.971603i	$0.423962\pi$
$522$	5.69455	−	5.79249i	0.249244	−	0.253530i
$523$	8.02036	−	13.8917i	0.350706	−	0.607440i	−0.635668	−	0.771963i	$-0.719275\pi$
$523$	8.02036	−	13.8917i	0.350706	−	0.607440i	0.986373	+	0.164523i	$0.0526084\pi$
$524$	−12.5467	+	21.7315i	−0.548105	+	0.949346i
$525$	−12.8734	−	5.26817i	−0.561842	−	0.229922i
$526$			0.282619i			0.0123228i
$527$		−	11.9256i		−	0.519486i
$528$	−14.4502	−	5.91344i	−0.628865	−	0.257350i
$529$	−22.3168	+	38.6538i	−0.970294	+	1.68060i
$530$	1.07712	−	1.86563i	0.0467871	−	0.0810376i
$531$	−12.8680	+	13.0893i	−0.558423	+	0.568026i
$532$	−6.00555			−0.260374
$533$	−0.282183	+	2.02459i	−0.0122227	+	0.0876949i
$534$	8.02575	+	10.3676i	0.347308	+	0.448648i
$535$	7.72096	−	4.45770i	0.333806	−	0.192723i
$536$	−17.1353	−	29.6792i	−0.740131	−	1.28194i
$537$	24.4216	+	31.5475i	1.05387	+	1.36138i
$538$	−2.73743	+	1.58046i	−0.118019	+	0.0681383i
$539$	11.8844	−	6.86148i	0.511899	−	0.295545i
$540$	7.93499	+	0.941599i	0.341467	+	0.0405200i
$541$			34.1857i			1.46976i	0.678198	+	0.734879i	$0.262761\pi$
$541$			34.1857i			1.46976i	−0.678198	+	0.734879i	$0.737239\pi$
$542$	5.88514	−	10.1934i	0.252788	−	0.437842i
$543$	−0.497614	+	1.21598i	−0.0213547	+	0.0521828i
$544$	11.3117	−	6.53082i	0.484985	−	0.280006i
$545$	5.16794	−	8.95114i	0.221370	−	0.383425i
$546$	6.90366	+	0.0229421i	0.295449	+	0.000981830i
$547$	−7.57954	−	13.1281i	−0.324078	−	0.561319i	0.657248	−	0.753675i	$-0.271721\pi$
$547$	−7.57954	−	13.1281i	−0.324078	−	0.561319i	−0.981325	+	0.192356i	$0.938387\pi$
$548$	−7.95265	−	4.59146i	−0.339720	−	0.196138i
$549$	3.87045	−	1.07253i	0.165187	−	0.0457745i
$550$	4.99530	+	8.65212i	0.213000	+	0.368928i
$551$	7.61482	−	4.39642i	0.324402	−	0.187294i
$552$	4.03218	+	29.6503i	0.171621	+	1.26200i
$553$		−	15.8442i		−	0.673764i
$554$	−1.85237	−	1.06946i	−0.0786995	−	0.0454372i
$555$	1.74834	−	0.237759i	0.0742130	−	0.0100923i
$556$	21.9512			0.930938
$557$	20.4227	+	11.7911i	0.865338	+	0.499603i	0.865796	−	0.500397i	$-0.166813\pi$
$557$	20.4227	+	11.7911i	0.865338	+	0.499603i	−0.000458464		1.00000i	$0.500146\pi$
$558$	8.19451	−	2.27076i	0.346901	−	0.0961290i
$559$	12.9857	+	32.0355i	0.549236	+	1.35496i
$560$	−1.90489	−	3.29936i	−0.0804962	−	0.139423i
$561$	2.36118	+	17.3627i	0.0996893	+	0.733055i
$562$	7.47942	+	12.9547i	0.315500	+	0.546462i
$563$	2.36994			0.0998811			0.0499405	−	0.998752i	$-0.484097\pi$
$563$	2.36994			0.0998811			0.0499405	+	0.998752i	$0.484097\pi$
$564$	0.609336	+	4.48069i	0.0256577	+	0.188671i
$565$	1.15886	+	0.669070i	0.0487537	+	0.0281480i
$566$	−2.70220	+	1.56012i	−0.113582	+	0.0655766i
$567$	8.43953	−	15.2109i	0.354427	−	0.638796i
$568$	−12.8725	−	22.2959i	−0.540119	−	0.935514i
$569$	−10.4757			−0.439165			−0.219583	−	0.975594i	$-0.570470\pi$
$569$	−10.4757			−0.439165			−0.219583	+	0.975594i	$0.570470\pi$
$570$	−1.56545	−	0.640626i	−0.0655694	−	0.0268329i
$571$	18.4593	−	31.9724i	0.772497	−	1.33800i	−0.163694	−	0.986511i	$-0.552341\pi$
$571$	18.4593	−	31.9724i	0.772497	−	1.33800i	0.936191	−	0.351492i	$-0.114326\pi$
$572$	19.9994	+	15.5885i	0.836217	+	0.651790i
$573$	−18.1898	−	23.4973i	−0.759889	−	0.981615i
$574$			0.626749i			0.0261600i
$575$	−17.0851	+	29.5923i	−0.712499	+	1.23408i
$576$	−2.53298	−	2.49015i	−0.105541	−	0.103756i
$577$		−	12.5027i		−	0.520493i	−0.965542	−	0.260246i	$-0.916196\pi$
$577$		−	12.5027i		−	0.520493i	0.965542	−	0.260246i	$-0.0838038\pi$
$578$	5.55217	+	3.20555i	0.230940	+	0.133333i
$579$	−0.798971	−	5.87516i	−0.0332041	−	0.244163i
$580$	6.30461	+	3.63997i	0.261785	+	0.151142i
$581$	−5.16434			−0.214253
$582$	−8.42334	−	10.8812i	−0.349159	−	0.451038i
$583$		−	17.2250i		−	0.713387i
$584$	−18.4349			−0.762842
$585$	−9.19000	−	3.79651i	−0.379960	−	0.156966i
$586$	−6.18381			−0.255451
$587$		−	16.5606i		−	0.683530i	−0.939786	−	0.341765i	$-0.888975\pi$
$587$		−	16.5606i		−	0.683530i	0.939786	−	0.341765i	$-0.111025\pi$
$588$	9.37188	−	1.27450i	0.386490	−	0.0525593i
$589$	9.20467			0.379272
$590$	2.78592	+	1.60845i	0.114694	+	0.0662188i
$591$	−36.2127	+	28.0330i	−1.48959	+	1.15312i
$592$	−2.05783	−	1.18809i	−0.0845761	−	0.0488301i
$593$			36.4880i			1.49838i	0.662353	+	0.749192i	$0.269558\pi$
$593$			36.4880i			1.49838i	−0.662353	+	0.749192i	$0.730442\pi$
$594$	−11.4810	+	4.92852i	−0.471072	+	0.202220i
$595$	−2.13781	+	3.70280i	−0.0876418	+	0.151800i
$596$			31.6128i			1.29491i
$597$	−27.6702	+	3.76290i	−1.13246	+	0.154005i
$598$	2.34114	−	16.7971i	0.0957365	−	0.686886i
$599$	7.36202	−	12.7514i	0.300804	−	0.521008i	−0.675514	−	0.737347i	$-0.736078\pi$
$599$	7.36202	−	12.7514i	0.300804	−	0.521008i	0.976318	+	0.216339i	$0.0694117\pi$
$600$	2.03716	+	14.9801i	0.0831668	+	0.611559i
$601$	20.2481			0.825939			0.412969	−	0.910745i	$-0.364492\pi$
$601$	20.2481			0.825939			0.412969	+	0.910745i	$0.364492\pi$
$602$	5.29924	+	9.17855i	0.215981	+	0.374090i
$603$	47.3800	+	12.2635i	1.92946	+	0.499408i
$604$	−15.4011	+	8.89182i	−0.626661	+	0.361803i
$605$	−5.31301	−	3.06747i	−0.216004	−	0.124710i
$606$	−2.02395	−	0.828257i	−0.0822173	−	0.0336457i
$607$	−27.2317			−1.10530			−0.552650	−	0.833413i	$-0.686383\pi$
$607$	−27.2317			−1.10530			−0.552650	+	0.833413i	$0.686383\pi$
$608$	5.04077	+	8.73087i	0.204430	+	0.354084i
$609$	12.5319	−	9.70121i	0.507818	−	0.393113i
$610$	−0.351945	−	0.609586i	−0.0142498	−	0.0246814i
$611$	0.776763	−	5.57308i	0.0314245	−	0.225463i
$612$	−3.02617	+	11.6916i	−0.122326	+	0.472606i
$613$	3.30340	+	1.90722i	0.133423	+	0.0770319i	0.565226	−	0.824936i	$-0.308789\pi$
$613$	3.30340	+	1.90722i	0.133423	+	0.0770319i	−0.431803	+	0.901968i	$0.642122\pi$
$614$	9.11034			0.367663
$615$	0.341890	−	0.835451i	0.0137863	−	0.0336886i
$616$	14.7826	+	8.53473i	0.595607	+	0.343874i
$617$		−	16.0120i		−	0.644620i	−0.946634	−	0.322310i	$-0.895541\pi$
$617$		−	16.0120i		−	0.644620i	0.946634	−	0.322310i	$-0.104459\pi$
$618$	−4.70394	+	3.64142i	−0.189220	+	0.146480i
$619$	−10.4156	+	6.01344i	−0.418638	+	0.241701i	−0.694494	−	0.719498i	$-0.744372\pi$
$619$	−10.4156	+	6.01344i	−0.418638	+	0.241701i	0.275857	+	0.961199i	$0.411039\pi$
$620$	3.81046	+	6.59991i	0.153032	+	0.265059i
$621$	−34.2322	−	25.5785i	−1.37369	−	1.02643i
$622$	11.0771	+	6.39535i	0.444150	+	0.256430i
$623$	12.7901	+	22.1531i	0.512425	+	0.887547i
$624$	6.65679	+	11.6189i	0.266485	+	0.465128i
$625$	−6.51925	+	11.2917i	−0.260770	+	0.451667i
$626$	−16.7078	+	9.64623i	−0.667777	+	0.385541i
$627$	−13.4013	+	1.82246i	−0.535197	+	0.0727822i
$628$	9.37966	−	16.2461i	0.374289	−	0.648288i
$629$			2.66673i			0.106329i
$630$	−2.95140	−	0.763918i	−0.117587	−	0.0304352i
$631$	8.92097	−	5.15052i	0.355138	−	0.205039i	−0.311808	−	0.950145i	$-0.600935\pi$
$631$	8.92097	−	5.15052i	0.355138	−	0.205039i	0.666946	+	0.745106i	$0.267601\pi$
$632$	−14.9134	+	8.61028i	−0.593225	+	0.342498i
$633$	10.2520	−	1.39418i	0.407481	−	0.0554139i
$634$	1.87083	+	3.24037i	0.0743000	+	0.128691i
$635$	−0.271645	+	0.156834i	−0.0107799	+	0.00622378i
$636$	4.49636	−	10.9874i	0.178292	−	0.435679i
$637$	−11.6567	−	1.62469i	−0.461857	−	0.0643725i
$638$	−11.3829			−0.450653
$639$	35.5933	+	9.21270i	1.40805	+	0.364449i
$640$	−5.30084	+	9.18132i	−0.209534	+	0.362924i
$641$	12.9868	−	22.4938i	0.512947	−	0.888451i	−0.486940	−	0.873435i	$-0.661887\pi$
$641$	12.9868	−	22.4938i	0.512947	−	0.888451i	0.999887	−	0.0150152i	$-0.00477967\pi$
$642$	−7.59737	+	5.88129i	−0.299844	+	0.232116i
$643$			13.3862i			0.527899i	0.964537	+	0.263949i	$0.0850252\pi$
$643$			13.3862i			0.527899i	−0.964537	+	0.263949i	$0.914975\pi$
$644$			26.5908i			1.04783i
$645$	−2.05696	−	15.1256i	−0.0809926	−	0.595572i
$646$	1.27822	−	2.21393i	0.0502907	−	0.0871061i
$647$	20.3910	−	35.3182i	0.801653	−	1.38850i	−0.116875	−	0.993147i	$-0.537288\pi$
$647$	20.3910	−	35.3182i	0.801653	−	1.38850i	0.918528	−	0.395356i	$-0.129379\pi$
$648$	−18.9036	+	0.322345i	−0.742605	+	0.0126629i
$649$	25.7219			1.00967
$650$	1.18281	−	8.48635i	0.0463935	−	0.332862i
$651$	16.4391	−	2.23557i	0.644298	−	0.0876190i
$652$	−12.2383	+	7.06580i	−0.479290	+	0.276718i
$653$	0.672102	+	1.16411i	0.0263014	+	0.0455553i	0.878877	−	0.477049i	$-0.158294\pi$
$653$	0.672102	+	1.16411i	0.0263014	+	0.0455553i	−0.852575	+	0.522605i	$0.824960\pi$
$654$	−4.21865	+	10.3088i	−0.164962	+	0.403106i
$655$	−11.9417	+	6.89455i	−0.466601	+	0.269392i
$656$	−1.05280	+	0.607835i	−0.0411050	+	0.0237320i
$657$	18.4564	−	18.7738i	0.720053	−	0.732436i
$658$		−	1.72525i		−	0.0672571i
$659$	−7.41816	+	12.8486i	−0.288970	+	0.500511i	−0.973564	−	0.228413i	$-0.926646\pi$
$659$	−7.41816	+	12.8486i	−0.288970	+	0.500511i	0.684594	+	0.728925i	$0.259980\pi$
$660$	−6.85449	−	8.85453i	−0.266811	−	0.344662i
$661$	−32.4666	+	18.7446i	−1.26280	+	0.729080i	−0.973616	−	0.228193i	$-0.926718\pi$
$661$	−32.4666	+	18.7446i	−1.26280	+	0.729080i	−0.289187	+	0.957273i	$0.593385\pi$
$662$	1.88031	−	3.25679i	0.0730802	−	0.126579i
$663$	7.55727	−	12.9897i	0.293500	−	0.504478i
$664$	2.80648	+	4.86097i	0.108913	+	0.188642i
$665$	−2.85798	−	1.65006i	−0.110828	−	0.0639865i
$666$	−1.83241	+	0.507775i	−0.0710045	+	0.0196759i
$667$	−19.4661	−	33.7162i	−0.753729	−	1.30550i
$668$	37.4121	−	21.5999i	1.44752	−	0.835724i
$669$	24.6587	+	10.0910i	0.953360	+	0.390142i
$670$		−	8.57737i		−	0.331373i
$671$	−4.87417	−	2.81410i	−0.188165	−	0.108637i
$672$	11.1231	+	14.3686i	0.429081	+	0.554281i
$673$	0.444667			0.0171407			0.00857033	−	0.999963i	$-0.497272\pi$
$673$	0.444667			0.0171407			0.00857033	+	0.999963i	$0.497272\pi$
$674$	−11.8763	−	6.85677i	−0.457457	−	0.264113i
$675$	−17.2950	−	12.9229i	−0.665685	−	0.497404i
$676$	−5.30928	−	21.0893i	−0.204203	−	0.811125i
$677$	−2.02087	−	3.50025i	−0.0776683	−	0.134526i	0.824575	−	0.565752i	$-0.191414\pi$
$677$	−2.02087	−	3.50025i	−0.0776683	−	0.134526i	−0.902244	+	0.431227i	$0.858081\pi$
$678$	−1.33463	−	0.546169i	−0.0512562	−	0.0209755i
$679$	−13.4237	−	23.2506i	−0.515155	−	0.892275i
$680$	4.64704			0.178206
$681$	34.0159	−	26.3324i	1.30349	−	1.00906i
$682$	−10.3196	−	5.95802i	−0.395158	−	0.228144i
$683$	27.1773	−	15.6908i	1.03991	−	0.600393i	0.120103	−	0.992761i	$-0.461678\pi$
$683$	27.1773	−	15.6908i	1.03991	−	0.600393i	0.919808	+	0.392369i	$0.128344\pi$
$684$	−9.02410	−	2.33573i	−0.345045	−	0.0893089i
$685$	−2.52306	−	4.37007i	−0.0964011	−	0.166972i
$686$	−11.3469			−0.433226
$687$	2.10623	−	1.63048i	0.0803576	−	0.0622065i
$688$	−10.2786	+	17.8031i	−0.391869	+	0.678738i
$689$	−9.08184	+	11.6516i	−0.345990	+	0.443890i
$690$	−2.83651	+	6.93135i	−0.107984	+	0.263872i
$691$			39.4039i			1.49900i	0.662007	+	0.749498i	$0.269705\pi$
$691$			39.4039i			1.49900i	−0.662007	+	0.749498i	$0.730295\pi$
$692$	−10.0880	+	17.4729i	−0.383487	+	0.664219i
$693$	−23.4914	+	6.50966i	−0.892366	+	0.247281i
$694$			9.75546i			0.370312i
$695$	10.4464	+	6.03121i	0.396253	+	0.228777i
$696$	−15.9416	−	6.52375i	−0.604264	−	0.247282i
$697$	1.18154	+	0.682160i	0.0447539	+	0.0258387i
$698$	3.34759			0.126708
$699$	8.13055	−	19.8680i	0.307526	−	0.751477i
$700$			13.4344i			0.507772i
$701$	−35.7282			−1.34943			−0.674717	−	0.738077i	$-0.735734\pi$
$701$	−35.7282			−1.34943			−0.674717	+	0.738077i	$0.735734\pi$
$702$	10.3647	+	2.71950i	0.391190	+	0.102641i
$703$	−2.05830			−0.0776301
$704$			4.97759i			0.187600i
$705$	−0.941118	+	2.29974i	−0.0354446	+	0.0866131i
$706$	5.26586			0.198183
$707$	−3.69505	−	2.13334i	−0.138967	−	0.0802325i
$708$	16.4074	+	6.71436i	0.616626	+	0.252341i
$709$	−25.3060	−	14.6104i	−0.950386	−	0.548705i	−0.0571849	−	0.998364i	$-0.518212\pi$
$709$	−25.3060	−	14.6104i	−0.950386	−	0.548705i	−0.893201	+	0.449658i	$0.851546\pi$
$710$		−	6.44357i		−	0.241823i
$711$	6.16226	−	23.8079i	0.231103	−	0.892867i
$712$	13.9012	−	24.0775i	0.520969	−	0.902344i
$713$		−	40.7557i		−	1.52631i
$714$	1.74512	−	4.26442i	0.0653095	−	0.159592i
$715$	5.23449	+	12.9134i	0.195759	+	0.482933i
$716$	19.2662	−	33.3701i	0.720013	−	1.24710i
$717$	−2.86096	+	2.21473i	−0.106844	+	0.0827106i
$718$	5.24679			0.195808
$719$	−1.47825	−	2.56041i	−0.0551295	−	0.0954872i	0.837144	−	0.546983i	$-0.184224\pi$
$719$	−1.47825	−	2.56041i	−0.0551295	−	0.0954872i	−0.892273	+	0.451496i	$0.850891\pi$
$720$	−1.57912	−	5.69858i	−0.0588503	−	0.212373i
$721$	−10.0513	+	5.80310i	−0.374329	+	0.216119i
$722$	−7.70238	−	4.44697i	−0.286653	−	0.165499i
$723$	−1.93816	+	1.50037i	−0.0720810	+	0.0557995i
$724$	1.26897			0.0471609
$725$	−9.83477	−	17.0343i	−0.365254	−	0.632639i
$726$	6.11885	+	2.50401i	0.227092	+	0.0929324i
$727$	14.4954	+	25.1067i	0.537603	+	0.931156i	0.999032	+	0.0439788i	$0.0140034\pi$
$727$	14.4954	+	25.1067i	0.537603	+	0.931156i	−0.461429	+	0.887177i	$0.652663\pi$
$728$	−5.49954	−	13.5673i	−0.203827	−	0.502836i
$729$	18.5974	−	19.5739i	0.688793	−	0.724958i
$730$	−3.99581	−	2.30698i	−0.147892	−	0.0853852i
$731$	23.0710			0.853311
$732$	−2.37453	−	3.06738i	−0.0877651	−	0.113374i
$733$	29.5424	+	17.0563i	1.09117	+	0.629990i	0.933889	−	0.357563i	$-0.116392\pi$
$733$	29.5424	+	17.0563i	1.09117	+	0.629990i	0.157286	+	0.987553i	$0.449726\pi$
$734$		−	12.0948i		−	0.446428i
$735$	4.81016	+	1.96845i	0.177426	+	0.0726076i
$736$	38.6578	−	22.3191i	1.42494	−	0.822692i
$737$	−34.2917	−	59.3951i	−1.26315	−	2.18784i
$738$	−0.243761	+	0.941770i	−0.00897295	+	0.0346670i
$739$	−20.9816	−	12.1138i	−0.771822	−	0.445612i	0.0617021	−	0.998095i	$-0.480347\pi$
$739$	−20.9816	−	12.1138i	−0.771822	−	0.445612i	−0.833524	+	0.552483i	$0.813680\pi$
$740$	−0.852073	−	1.47583i	−0.0313228	−	0.0542527i
$741$	10.0260	+	5.83303i	0.368315	+	0.214282i
$742$	−2.26472	+	3.92261i	−0.0831405	+	0.144004i
$743$	−21.3091	+	12.3028i	−0.781754	+	0.451346i	−0.837052	−	0.547124i	$-0.815723\pi$
$743$	−21.3091	+	12.3028i	−0.781754	+	0.451346i	0.0552976	+	0.998470i	$0.482389\pi$
$744$	−11.0378	−	14.2585i	−0.404665	−	0.522741i
$745$	−8.68578	+	15.0442i	−0.318223	+	0.551178i
$746$			9.48425i			0.347243i
$747$	−7.76008	−	2.00856i	−0.283927	−	0.0734894i
$748$	14.6565	−	8.46192i	0.535894	−	0.309398i
$749$	−16.2339	+	9.37263i	−0.593172	+	0.342468i
$750$	−3.15762	+	7.71602i	−0.115300	+	0.281749i
$751$	−14.2551	−	24.6906i	−0.520176	−	0.900971i	−0.999725	−	0.0234561i	$-0.992533\pi$
$751$	−14.2551	−	24.6906i	−0.520176	−	0.900971i	0.479549	−	0.877515i	$-0.340800\pi$
$752$	2.89804	−	1.67318i	0.105681	−	0.0610147i
$753$	43.4590	−	5.91005i	1.58373	−	0.215374i
$754$	7.69978	+	6.00159i	0.280409	+	0.218565i
$755$	−9.77231			−0.355651
$756$	−16.6839	−	1.97978i	−0.606786	−	0.0720038i
$757$	−13.7952	+	23.8940i	−0.501395	+	0.868441i	0.498604	+	0.866830i	$0.333846\pi$
$757$	−13.7952	+	23.8940i	−0.501395	+	0.868441i	−0.999999	+	0.00161112i	$0.999487\pi$
$758$	0.517499	−	0.896335i	0.0187964	−	0.0325563i
$759$	8.06935	+	59.3372i	0.292899	+	2.15380i
$760$			3.58679i			0.130107i
$761$		−	30.7406i		−	1.11435i	−0.830396	−	0.557174i	$-0.811886\pi$
$761$		−	30.7406i		−	1.11435i	0.830396	−	0.557174i	$-0.188114\pi$
$762$	0.267297	−	0.206920i	0.00968313	−	0.00749592i
$763$	−10.8660	+	18.8204i	−0.393374	+	0.681344i
$764$	−14.3499	+	24.8548i	−0.519162	+	0.899216i
$765$	−4.65246	+	4.73247i	−0.168210	+	0.171103i
$766$	−16.0116			−0.578523
$767$	−17.3992	−	13.5618i	−0.628248	−	0.489688i
$768$	2.77372	−	6.77792i	0.100088	−	0.244577i
$769$	−42.3105	+	24.4280i	−1.52576	+	0.880896i	−0.526223	+	0.850347i	$0.676392\pi$
$769$	−42.3105	+	24.4280i	−1.52576	+	0.880896i	−0.999533	+	0.0305492i	$0.990274\pi$
$770$	2.13610	+	3.69984i	0.0769799	+	0.133333i
$771$	−28.0568	+	3.81549i	−1.01044	+	0.137411i
$772$	−4.95942	+	2.86332i	−0.178493	+	0.103053i
$773$	36.5290	−	21.0900i	1.31386	−	0.758555i	0.331124	−	0.943587i	$-0.392572\pi$
$773$	36.5290	−	21.0900i	1.31386	−	0.758555i	0.982732	+	0.185032i	$0.0592389\pi$
$774$	4.39297	+	15.8530i	0.157902	+	0.569823i
$775$		−	20.5908i		−	0.739644i
$776$	−14.5898	+	25.2703i	−0.523744	+	0.907151i
$777$	−3.67601	+	0.499906i	−0.131876	+	0.0179340i
$778$	−15.7629	+	9.10074i	−0.565129	+	0.326277i
$779$	−0.526521	+	0.911961i	−0.0188646	+	0.0326744i
$780$	−0.0319142	+	9.60352i	−0.00114271	+	0.343861i
$781$	−25.7610	−	44.6193i	−0.921801	−	1.59661i
$782$	−9.80267	−	5.65957i	−0.350543	−	0.202386i
$783$	22.6038	−	9.70329i	0.807796	−	0.346767i
$784$	−3.49965	−	6.06158i	−0.124988	−	0.216485i
$785$	8.92738	−	5.15423i	0.318632	−	0.183962i
$786$	11.7506	−	9.09636i	0.419128	−	0.324456i
$787$			18.1264i			0.646136i	0.946376	+	0.323068i	$0.104714\pi$
$787$			18.1264i			0.646136i	−0.946376	+	0.323068i	$0.895286\pi$
$788$	38.3047	+	22.1153i	1.36455	+	0.787823i
$789$	−0.324149	+	0.792098i	−0.0115400	+	0.0281994i
$790$	−4.31003			−0.153344
$791$	−2.43659	−	1.40677i	−0.0866352	−	0.0500189i
$792$	18.8933	+	18.5739i	0.671344	+	0.659994i
$793$	1.81333	+	4.47345i	0.0643933	+	0.158857i
$794$	−0.118832	−	0.205824i	−0.00421720	−	0.00730441i
$795$	5.15862	−	3.99340i	0.182958	−	0.141631i
$796$	13.4854	+	23.3573i	0.477976	+	0.827878i
$797$	44.0909			1.56178			0.780890	−	0.624668i	$-0.214766\pi$
$797$	44.0909			1.56178			0.780890	+	0.624668i	$0.214766\pi$
$798$	3.29146	+	1.34696i	0.116517	+	0.0476819i
$799$	−3.25240	−	1.87778i	−0.115062	−	0.0664309i
$800$	19.5309	−	11.2762i	0.690523	−	0.398673i
$801$	10.6028	+	38.2623i	0.374631	+	1.35193i
$802$	6.58350	+	11.4030i	0.232472	+	0.402652i
$803$	−36.8926			−1.30191
$804$	−6.36957	−	46.8380i	−0.224637	−	1.65185i
$805$	−7.30598	+	12.6543i	−0.257502	+	0.446007i
$806$	3.83918	+	9.47118i	0.135229	+	0.333608i
$807$	−9.48492	+	1.28987i	−0.333885	+	0.0454055i
$808$			4.63732i			0.163140i
$809$	−11.0906	+	19.2094i	−0.389924	+	0.675367i	−0.992439	−	0.122740i	$-0.960832\pi$
$809$	−11.0906	+	19.2094i	−0.389924	+	0.675367i	0.602515	+	0.798107i	$0.294165\pi$
$810$	−4.13774	−	2.29577i	−0.145386	−	0.0806651i
$811$			21.0778i			0.740140i	0.929004	+	0.370070i	$0.120666\pi$
$811$			21.0778i			0.740140i	−0.929004	+	0.370070i	$0.879334\pi$
$812$	−13.2559	−	7.65329i	−0.465191	−	0.268578i
$813$	28.1856	−	21.8191i	0.988511	−	0.765228i
$814$	2.30761	+	1.33230i	0.0808816	+	0.0466970i
$815$	−7.76547			−0.272012
$816$	8.85575	−	1.20431i	0.310013	−	0.0421592i
$817$			17.8072i			0.622995i
$818$	10.2831			0.359539
$819$	19.3226	+	7.98243i	0.675187	+	0.278929i
$820$	−0.871856			−0.0304465
$821$		−	28.7564i		−	1.00361i	−0.864982	−	0.501803i	$-0.832670\pi$
$821$		−	28.7564i		−	1.00361i	0.864982	−	0.501803i	$-0.167330\pi$
$822$	3.32881	+	4.30011i	0.116106	+	0.149984i
$823$	17.1498			0.597804			0.298902	−	0.954284i	$-0.403380\pi$
$823$	17.1498			0.597804			0.298902	+	0.954284i	$0.403380\pi$
$824$	10.9244	+	6.30721i	0.380570	+	0.219722i
$825$	4.07685	+	29.9787i	0.141938	+	1.04372i
$826$	−5.85758	−	3.38188i	−0.203811	−	0.117671i
$827$			2.18115i			0.0758460i	0.999281	+	0.0379230i	$0.0120742\pi$
$827$			2.18115i			0.0758460i	−0.999281	+	0.0379230i	$0.987926\pi$
$828$	−10.3419	+	39.9561i	−0.359407	+	1.38857i
$829$	−0.589756	+	1.02149i	−0.0204831	+	0.0354777i	−0.876085	−	0.482156i	$-0.839854\pi$
$829$	−0.589756	+	1.02149i	−0.0204831	+	0.0354777i	0.855602	+	0.517634i	$0.173187\pi$
$830$			1.40483i			0.0487625i
$831$	−3.96502	−	5.12196i	−0.137545	−	0.177679i
$832$	2.62442	−	3.36701i	0.0909853	−	0.116730i
$833$	−3.92758	+	6.80277i	−0.136083	+	0.235702i
$834$	−12.0308	−	4.92335i	−0.416593	−	0.170482i
$835$	23.7387			0.821513
$836$	6.53128	+	11.3125i	0.225889	+	0.391251i
$837$	25.5713	+	3.03440i	0.883872	+	0.104884i
$838$	0.989682	−	0.571393i	0.0341880	−	0.0197384i
$839$	−13.2618	−	7.65671i	−0.457848	−	0.264339i	0.253291	−	0.967390i	$-0.418487\pi$
$839$	−13.2618	−	7.65671i	−0.457848	−	0.264339i	−0.711139	+	0.703051i	$0.751820\pi$
$840$	0.871137	+	6.40582i	0.0300571	+	0.221022i
$841$	−6.58934			−0.227219
$842$	2.62094	+	4.53960i	0.0903235	+	0.156445i
$843$	6.10422	+	44.8868i	0.210241	+	1.54598i
$844$	−4.99642	−	8.65406i	−0.171984	−	0.297885i
$845$	3.26775	−	11.4949i	0.112414	−	0.395438i
$846$	0.670998	−	2.59240i	0.0230694	−	0.0891286i
$847$	11.1710	+	6.44956i	0.383839	+	0.221610i
$848$	−8.78551			−0.301695
$849$	−9.36285	+	1.27327i	−0.321332	+	0.0436984i
$850$	−4.95256	−	2.85936i	−0.169872	−	0.0980754i
$851$			9.11354i			0.312408i
$852$	−4.78501	−	35.1861i	−0.163932	−	1.20546i
$853$	12.7937	−	7.38645i	0.438048	−	0.252907i	−0.264721	−	0.964325i	$-0.585280\pi$
$853$	12.7937	−	7.38645i	0.438048	−	0.252907i	0.702769	+	0.711418i	$0.251947\pi$
$854$	0.739989	+	1.28170i	0.0253219	+	0.0438588i
$855$	−3.65273	−	3.59097i	−0.124921	−	0.122809i
$856$	17.6441	+	10.1868i	0.603062	+	0.348178i
$857$	−19.7286	−	34.1710i	−0.673917	−	1.16726i	−0.976784	−	0.214225i	$-0.931277\pi$
$857$	−19.7286	−	34.1710i	−0.673917	−	1.16726i	0.302868	−	0.953033i	$-0.402056\pi$
$858$	−7.46480	−	13.0292i	−0.254844	−	0.444810i
$859$	16.7988	−	29.0963i	0.573166	−	0.992753i	−0.423072	−	0.906096i	$-0.639048\pi$
$859$	16.7988	−	29.0963i	0.573166	−	0.992753i	0.996238	−	0.0866569i	$-0.0276184\pi$
$860$	−12.7681	+	7.37165i	−0.435387	+	0.251371i
$861$	−0.718848	+	1.75659i	−0.0244983	+	0.0598646i
$862$	2.58221	−	4.47251i	0.0879503	−	0.152334i
$863$		−	10.2293i		−	0.348210i	−0.984727	−	0.174105i	$-0.944297\pi$
$863$		−	10.2293i		−	0.348210i	0.984727	−	0.174105i	$-0.0557032\pi$
$864$	11.1254	+	25.9167i	0.378495	+	0.881705i
$865$	−9.60153	+	5.54345i	−0.326462	+	0.188483i
$866$	9.39644	−	5.42504i	0.319304	−	0.184350i
$867$	11.8845	+	15.3523i	0.403619	+	0.521390i
$868$	−8.01176	−	13.8768i	−0.271937	−	0.471008i
$869$	−29.8453	+	17.2312i	−1.01243	+	0.584529i
$870$	−2.63898	−	3.40900i	−0.0894698	−	0.115576i
$871$	−8.11973	+	58.2571i	−0.275127	+	1.97397i
$872$	23.6197			0.799865
$873$	−11.1280	−	40.1578i	−0.376627	−	1.35914i
$874$	4.36831	−	7.56613i	0.147760	−	0.255928i
$875$	−8.13306	+	14.0869i	−0.274948	+	0.476223i
$876$	−23.5329	−	9.63033i	−0.795103	−	0.325379i
$877$		−	50.8430i		−	1.71685i	−0.512942	−	0.858423i	$-0.671444\pi$
$877$		−	50.8430i		−	1.71685i	0.512942	−	0.858423i	$-0.328556\pi$
$878$			6.00407i			0.202627i
$879$	−17.3314	−	7.09250i	−0.584574	−	0.239224i
$880$	−4.14329	+	7.17638i	−0.139670	+	0.241916i
$881$	−12.1321	+	21.0133i	−0.408739	+	0.707958i	−0.994749	−	0.102347i	$-0.967365\pi$
$881$	−12.1321	+	21.0133i	−0.408739	+	0.707958i	0.586009	+	0.810304i	$0.300698\pi$
$882$	−5.42230	−	1.40347i	−0.182578	−	0.0472572i
$883$	31.1390			1.04791			0.523956	−	0.851746i	$-0.324456\pi$
$883$	31.1390			1.04791			0.523956	+	0.851746i	$0.324456\pi$
$884$	−14.3757	−	2.00365i	−0.483506	−	0.0673899i
$885$	5.96330	+	7.70331i	0.200454	+	0.258944i
$886$	2.51669	−	1.45301i	0.0845498	−	0.0488149i
$887$	26.5333	+	45.9569i	0.890900	+	1.54308i	0.838799	+	0.544441i	$0.183258\pi$
$887$	26.5333	+	45.9569i	0.890900	+	1.54308i	0.0521007	+	0.998642i	$0.483408\pi$
$888$	2.46821	+	3.18840i	0.0828277	+	0.106996i
$889$	0.571153	−	0.329755i	0.0191558	−	0.0110596i
$890$	6.02622	−	3.47924i	0.201999	−	0.116624i
$891$	−37.8307	+	0.645089i	−1.26737	+	0.0216113i
$892$		−	25.7332i		−	0.861612i
$893$	1.44935	−	2.51035i	0.0485006	−	0.0840056i
$894$	7.09030	−	17.3260i	0.237135	−	0.579469i
$895$	18.3372	−	10.5870i	0.612946	−	0.353885i
$896$	11.1454	−	19.3044i	0.372341	−	0.644914i
$897$	25.8270	−	44.3923i	0.862338	−	1.48222i
$898$	−4.29184	−	7.43369i	−0.143221	−	0.248066i
$899$	20.3172	+	11.7302i	0.677618	+	0.391223i
$900$	−5.22502	+	20.1869i	−0.174167	+	0.672896i
$901$	4.92989	+	8.53882i	0.164238	+	0.284469i
$902$	1.18059	−	0.681615i	0.0393094	−	0.0226953i
$903$	4.32490	+	31.8027i	0.143924	+	1.05833i
$904$			3.05794i			0.101706i
$905$	0.603890	+	0.348656i	0.0200740	+	0.0115897i
$906$	10.4352	−	1.41910i	0.346686	−	0.0471463i
$907$	−0.360804			−0.0119803			−0.00599015	−	0.999982i	$-0.501907\pi$
$907$	−0.360804			−0.0119803			−0.00599015	+	0.999982i	$0.501907\pi$
$908$	−35.9810	−	20.7737i	−1.19407	−	0.689398i
$909$	−4.72257	−	4.64273i	−0.156638	−	0.153989i
$910$	0.505795	−	3.62896i	0.0167669	−	0.120299i
$911$	−2.42756	−	4.20466i	−0.0804287	−	0.139307i	0.823005	−	0.568033i	$-0.192296\pi$
$911$	−2.42756	−	4.20466i	−0.0804287	−	0.139307i	−0.903434	+	0.428727i	$0.858962\pi$
$912$	0.929536	+	6.83526i	0.0307800	+	0.226338i
$913$	5.61643	+	9.72795i	0.185877	+	0.321948i
$914$	4.33333			0.143334
$915$	−0.287235	−	2.11215i	−0.00949569	−	0.0698256i
$916$	−2.22791	−	1.28628i	−0.0736122	−	0.0425000i
$917$	25.1083	−	14.4963i	0.829149	−	0.478709i
$918$	4.28082	−	5.72910i	0.141288	−	0.189089i
$919$	13.4500	+	23.2961i	0.443675	+	0.768468i	0.997959	−	0.0638598i	$-0.0203410\pi$
$919$	13.4500	+	23.2961i	0.443675	+	0.768468i	−0.554284	+	0.832328i	$0.687008\pi$
$920$	15.8813			0.523590
$921$	25.5336	+	10.4491i	0.841361	+	0.344309i
$922$	−6.60344	+	11.4375i	−0.217473	+	0.376674i
$923$	−6.09979	+	43.7645i	−0.200777	+	1.44053i
$924$	14.4120	+	18.6173i	0.474121	+	0.612464i
$925$			4.60440i			0.151392i
$926$	−7.34139	+	12.7157i	−0.241253	+	0.417863i
$927$	−17.3603	+	4.81067i	−0.570187	+	0.158003i
$928$			25.6952i			0.843487i
$929$	10.4088	+	6.00952i	0.341502	+	0.197166i	0.660936	−	0.750442i	$-0.270160\pi$
$929$	10.4088	+	6.00952i	0.341502	+	0.197166i	−0.319434	+	0.947608i	$0.603493\pi$
$930$	−0.608133	−	4.47185i	−0.0199415	−	0.146638i
$931$	−5.25068	−	3.03148i	−0.172084	−	0.0993527i
$932$	−20.7338			−0.679157
$933$	23.7107	+	30.6291i	0.776252	+	1.00275i
$934$		−	7.71316i		−	0.252382i
$935$	9.29984			0.304137
$936$	−2.98706	−	22.5255i	−0.0976352	−	0.736267i
$937$	−32.9241			−1.07558			−0.537791	−	0.843078i	$-0.680741\pi$
$937$	−32.9241			−1.07558			−0.537791	+	0.843078i	$0.680741\pi$
$938$			18.0345i			0.588848i
$939$	−57.8907	+	7.87264i	−1.88919	+	0.256914i
$940$	2.39995			0.0782777
$941$	−16.5053	−	9.52932i	−0.538056	−	0.310647i	0.206235	−	0.978503i	$-0.433879\pi$
$941$	−16.5053	−	9.52932i	−0.538056	−	0.310647i	−0.744291	+	0.667856i	$0.767212\pi$
$942$	−8.78448	+	6.80026i	−0.286214	+	0.221564i
$943$	4.03790	+	2.33128i	0.131492	+	0.0759171i
$944$		−	13.1193i		−	0.426996i
$945$	−7.39574	−	5.52614i	−0.240583	−	0.179765i
$946$	11.5263	−	19.9641i	0.374751	−	0.649088i
$947$			32.5855i			1.05889i	0.848345	+	0.529444i	$0.177599\pi$
$947$			32.5855i			1.05889i	−0.848345	+	0.529444i	$0.822401\pi$
$948$	−23.5356	+	3.20064i	−0.764400	+	0.103952i
$949$	24.9555	+	19.4515i	0.810089	+	0.631424i
$950$	2.20698	−	3.82261i	0.0716040	−	0.124022i
$951$	1.52685	+	11.2275i	0.0495115	+	0.364078i
$952$	−9.77073			−0.316671
$953$	17.6632	+	30.5936i	0.572168	+	0.991023i	0.996343	+	0.0854433i	$0.0272306\pi$
$953$	17.6632	+	30.5936i	0.572168	+	0.991023i	−0.424175	+	0.905580i	$0.639436\pi$
$954$	−4.92864	+	5.01340i	−0.159571	+	0.162315i
$955$	−13.6580	+	7.88545i	−0.441962	+	0.255167i
$956$	3.02624	+	1.74720i	0.0978757	+	0.0565086i
$957$	−31.9029	−	13.0556i	−1.03127	−	0.422027i
$958$	−4.33446			−0.140040
$959$	5.30491	+	9.18837i	0.171304	+	0.296708i
$960$	−1.49071	+	1.15399i	−0.0481125	+	0.0372449i
$961$	−3.22042	−	5.57793i	−0.103884	−	0.179933i
$962$	−0.858496	−	2.11789i	−0.0276790	−	0.0682836i
$963$	−28.0387	+	7.76974i	−0.903535	+	0.250376i
$964$	2.05013	+	1.18365i	0.0660304	+	0.0381226i
$965$	−3.14685			−0.101301
$966$	5.96396	−	14.5737i	0.191887	−	0.468900i
$967$	−25.1654	−	14.5293i	−0.809266	−	0.467230i	0.0374350	−	0.999299i	$-0.488081\pi$
$967$	−25.1654	−	14.5293i	−0.809266	−	0.467230i	−0.846701	+	0.532069i	$0.821415\pi$
$968$		−	14.0197i		−	0.450609i
$969$	6.12173	−	4.73896i	0.196658	−	0.152237i
$970$	−6.32475	+	3.65160i	−0.203076	+	0.117246i
$971$	−4.95021	−	8.57402i	−0.158860	−	0.275154i	0.775598	−	0.631227i	$-0.217448\pi$
$971$	−4.95021	−	8.57402i	−0.158860	−	0.275154i	−0.934458	+	0.356074i	$0.884115\pi$
$972$	−24.2996	−	9.46370i	−0.779411	−	0.303548i
$973$	−21.9642	−	12.6811i	−0.704141	−	0.406536i
$974$	−5.63530	−	9.76062i	−0.180567	−	0.312751i
$975$	13.0485	−	22.4281i	0.417885	−	0.718276i
$976$	−1.43532	+	2.48604i	−0.0459433	+	0.0795762i
$977$	−26.9796	+	15.5767i	−0.863154	+	0.498342i	−0.865067	−	0.501656i	$-0.832724\pi$
$977$	−26.9796	+	15.5767i	−0.863154	+	0.498342i	0.00191303	+	0.999998i	$0.499391\pi$
$978$	8.29222	−	1.12767i	0.265156	−	0.0360590i
$979$	27.8196	−	48.1849i	0.889117	−	1.54000i
$980$		−	5.01977i		−	0.160351i
$981$	−23.6473	+	24.0540i	−0.755000	+	0.767984i
$982$	−4.37929	+	2.52839i	−0.139749	+	0.0806841i
$983$	−5.27019	+	3.04274i	−0.168093	+	0.0970485i	−0.581686	−	0.813413i	$-0.697607\pi$
$983$	−5.27019	+	3.04274i	−0.168093	+	0.0970485i	0.413593	+	0.910462i	$0.364274\pi$
$984$	2.04405	−	0.277973i	0.0651619	−	0.00886147i
$985$	12.1526	+	21.0489i	0.387213	+	0.670673i
$986$	5.64275	−	3.25784i	0.179702	−	0.103751i
$987$	1.97877	−	4.83536i	0.0629848	−	0.153911i
$988$	1.54650	−	11.0958i	0.0492008	−	0.353003i
$989$	78.8451			2.50713
$990$	1.77079	+	6.39027i	0.0562795	+	0.203096i
$991$	21.0497	−	36.4591i	0.668665	−	1.15816i	−0.309612	−	0.950863i	$-0.600199\pi$
$991$	21.0497	−	36.4591i	0.668665	−	1.15816i	0.978278	−	0.207300i	$-0.0664675\pi$
$992$	−13.4494	+	23.2950i	−0.427018	+	0.739617i
$993$	9.00532	−	6.97121i	0.285775	−	0.221225i
$994$			13.5481i			0.429719i
$995$			14.8207i			0.469848i
$996$	1.04323	+	7.67131i	0.0330561	+	0.243075i
$997$	25.9420	−	44.9329i	0.821593	−	1.42304i	−0.0829033	−	0.996558i	$-0.526419\pi$
$997$	25.9420	−	44.9329i	0.821593	−	1.42304i	0.904496	−	0.426482i	$-0.140247\pi$
$998$	2.37738	−	4.11774i	0.0752546	−	0.130345i
$999$	−5.71810	−	0.678534i	−0.180913	−	0.0214679i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.2.l.b.4.7	✓	22
3.2	odd	2		351.2.l.b.199.5		22
9.2	odd	6		351.2.r.b.316.5		22
9.7	even	3		117.2.r.b.43.7	yes	22
13.10	even	6		117.2.r.b.49.7	yes	22
39.23	odd	6		351.2.r.b.10.5		22
117.88	even	6	inner	117.2.l.b.88.5	yes	22
117.101	odd	6		351.2.l.b.127.7		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.2.l.b.4.7	✓	22	1.1	even	1	trivial
117.2.l.b.88.5	yes	22	117.88	even	6	inner
117.2.r.b.43.7	yes	22	9.7	even	3
117.2.r.b.49.7	yes	22	13.10	even	6
351.2.l.b.127.7		22	117.101	odd	6
351.2.l.b.199.5		22	3.2	odd	2
351.2.r.b.10.5		22	39.23	odd	6
351.2.r.b.316.5		22	9.2	odd	6

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	117.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.571953i q^{2} +(-0.656000 + 1.60302i) q^{3} +1.67287 q^{4} +(0.796103 + 0.459630i) q^{5} +(-0.916851 - 0.375201i) q^{6} +(-1.67386 - 0.966405i) q^{7} +2.10071i q^{8} +(-2.13933 - 2.10316i) q^{9} +(-0.262887 + 0.455333i) q^{10} +4.20402i q^{11} +(-1.09740 + 2.68164i) q^{12} +(2.21656 - 2.84374i) q^{13} +(0.552738 - 0.957371i) q^{14} +(-1.25904 + 0.974649i) q^{15} +2.14423 q^{16} +(-1.20321 - 2.08402i) q^{17} +(1.20291 - 1.22360i) q^{18} +(1.60854 - 0.928692i) q^{19} +(1.33178 + 0.768901i) q^{20} +(2.64722 - 2.04927i) q^{21} -2.40450 q^{22} +(-4.11198 - 7.12216i) q^{23} +(-3.36747 - 1.37807i) q^{24} +(-2.07748 - 3.59830i) q^{25} +(1.62649 + 1.26777i) q^{26} +(4.77480 - 2.04971i) q^{27} +(-2.80015 - 1.61667i) q^{28} +4.73399 q^{29} +(-0.557453 - 0.720111i) q^{30} +(4.29178 + 2.47786i) q^{31} +5.42782i q^{32} +(-6.73911 - 2.75784i) q^{33} +(1.19196 - 0.688181i) q^{34} +(-0.888377 - 1.53871i) q^{35} +(-3.57882 - 3.51831i) q^{36} +(-0.959703 - 0.554085i) q^{37} +(0.531168 + 0.920010i) q^{38} +(3.10451 + 5.41867i) q^{39} +(-0.965549 + 1.67238i) q^{40} +(-0.490992 + 0.283475i) q^{41} +(1.17209 + 1.51408i) q^{42} +(-4.79362 + 8.30280i) q^{43} +7.03277i q^{44} +(-0.736449 - 2.65763i) q^{45} +(4.07354 - 2.35186i) q^{46} +(1.35155 - 0.780318i) q^{47} +(-1.40662 + 3.43724i) q^{48} +(-1.63212 - 2.82692i) q^{49} +(2.05806 - 1.18822i) q^{50} +(4.13003 - 0.561649i) q^{51} +(3.70801 - 4.75721i) q^{52} -4.09727 q^{53} +(1.17234 + 2.73096i) q^{54} +(-1.93229 + 3.34683i) q^{55} +(2.03014 - 3.51630i) q^{56} +(0.433505 + 3.18774i) q^{57} +2.70762i q^{58} -6.11841i q^{59} +(-2.10621 + 1.63046i) q^{60} +(-0.669384 + 1.15941i) q^{61} +(-1.41722 + 2.45470i) q^{62} +(1.54844 + 5.58785i) q^{63} +1.18401 q^{64} +(3.07168 - 1.24512i) q^{65} +(1.57735 - 3.85446i) q^{66} +(-14.1282 + 8.15690i) q^{67} +(-2.01282 - 3.48630i) q^{68} +(14.1144 - 1.91944i) q^{69} +(0.880073 - 0.508110i) q^{70} +(-10.6135 + 6.12771i) q^{71} +(4.41813 - 4.49411i) q^{72} +8.77557i q^{73} +(0.316911 - 0.548905i) q^{74} +(7.13097 - 0.969750i) q^{75} +(2.69088 - 1.55358i) q^{76} +(4.06278 - 7.03695i) q^{77} +(-3.09923 + 1.77563i) q^{78} +(4.09875 + 7.09924i) q^{79} +(1.70703 + 0.985554i) q^{80} +(0.153446 + 8.99869i) q^{81} +(-0.162134 - 0.280825i) q^{82} +(2.31396 - 1.33597i) q^{83} +(4.42845 - 3.42816i) q^{84} -2.21213i q^{85} +(-4.74881 - 2.74173i) q^{86} +(-3.10550 + 7.58867i) q^{87} -8.83142 q^{88} +(-11.4616 - 6.61737i) q^{89} +(1.52004 - 0.421215i) q^{90} +(-6.45842 + 2.61794i) q^{91} +(-6.87881 - 11.9144i) q^{92} +(-6.78746 + 5.25432i) q^{93} +(0.446305 + 0.773023i) q^{94} +1.70742 q^{95} +(-8.70089 - 3.56065i) q^{96} +(12.0294 + 6.94519i) q^{97} +(1.61687 - 0.933498i) q^{98} +(8.84172 - 8.99377i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q - q^{3} - 20 q^{4} - 3 q^{5} - 18 q^{6} - 6 q^{7} + 7 q^{9} - 7 q^{10} - 11 q^{12} - 9 q^{14} - 6 q^{15} + 24 q^{16} + 9 q^{17} + 30 q^{18} - 6 q^{19} - 24 q^{20} - 12 q^{21} + 26 q^{22} + 6 q^{23}+ \cdots + 18 q^{99}+O(q^{100}) \) 22 * q - q^3 - 20 * q^4 - 3 * q^5 - 18 * q^6 - 6 * q^7 + 7 * q^9 - 7 * q^10 - 11 * q^12 - 9 * q^14 - 6 * q^15 + 24 * q^16 + 9 * q^17 + 30 * q^18 - 6 * q^19 - 24 * q^20 - 12 * q^21 + 26 * q^22 + 6 * q^23 + 24 * q^24 + 4 * q^25 - 12 * q^26 + 14 * q^27 + 3 * q^28 + 48 * q^29 + 9 * q^30 - 27 * q^31 - 3 * q^33 + 15 * q^34 - 27 * q^35 - 34 * q^36 + 6 * q^37 + 21 * q^38 + 19 * q^39 + 13 * q^40 + 6 * q^41 - 30 * q^42 - 4 * q^43 + 6 * q^45 - 15 * q^46 - 6 * q^47 - 13 * q^48 + 7 * q^49 + 18 * q^50 + 12 * q^51 - 22 * q^52 - 24 * q^53 + 21 * q^54 - 13 * q^55 - 9 * q^56 - 42 * q^57 + 6 * q^60 + 3 * q^61 - 54 * q^63 - 24 * q^64 - 57 * q^65 + 30 * q^66 - 45 * q^67 - 69 * q^68 + 42 * q^69 - 24 * q^70 + 9 * q^71 - 24 * q^72 - 6 * q^74 - 8 * q^75 + 18 * q^76 + 42 * q^77 + 6 * q^78 - 6 * q^79 + 105 * q^80 + 19 * q^81 - 16 * q^82 + 42 * q^83 + 66 * q^84 + 45 * q^86 - 6 * q^87 + 22 * q^88 - 30 * q^89 + 30 * q^90 + 15 * q^91 - 3 * q^92 + 39 * q^93 + 44 * q^94 + 6 * q^95 - 9 * q^96 - 27 * q^97 + 117 * q^98 + 18 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more