LMFDB - Embedded newform 345.2.t.a.259.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [345,2,Mod(4,345)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(345, base_ring=CyclotomicField(22)) chi = DirichletCharacter(H, H._module([0, 11, 4])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("345.4"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 345 = 3 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	345.t (of order $22$, degree $10$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$2.75483886973$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$24$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			259.20
Character	$\chi$	$=$	345.259
Dual form			345.2.t.a.4.20

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.89471 + 0.865286i) q^{2} +(0.281733 - 0.959493i) q^{3} +(1.53149 + 1.76743i) q^{4} +(-1.43853 - 1.71191i) q^{5} +(1.36404 - 1.57418i) q^{6} +(3.38318 + 0.486427i) q^{7} +(0.198730 + 0.676813i) q^{8} +(-0.841254 - 0.540641i) q^{9} +(-1.24431 - 4.48831i) q^{10} +(1.41208 + 3.09202i) q^{11} +(2.12731 - 0.971510i) q^{12} +(0.436083 - 0.0626993i) q^{13} +(5.98924 + 3.84905i) q^{14} +(-2.04785 + 0.897958i) q^{15} +(0.456549 - 3.17537i) q^{16} +(3.26787 + 2.83163i) q^{17} +(-1.12612 - 1.75228i) q^{18} +(-5.10386 - 5.89017i) q^{19} +(0.822593 - 5.16427i) q^{20} +(1.41987 - 3.10909i) q^{21} +7.08033i q^{22} +(-3.61427 + 3.15230i) q^{23} +0.705386 q^{24} +(-0.861269 + 4.92526i) q^{25} +(0.880505 + 0.258540i) q^{26} +(-0.755750 + 0.654861i) q^{27} +(4.32157 + 6.72449i) q^{28} +(-5.66182 + 6.53409i) q^{29} +(-4.65707 - 0.0706006i) q^{30} +(-1.64386 + 0.482680i) q^{31} +(4.37535 - 6.80817i) q^{32} +(3.36460 - 0.483756i) q^{33} +(3.74151 + 8.19276i) q^{34} +(-4.03408 - 6.49143i) q^{35} +(-0.332824 - 2.31484i) q^{36} +(2.99808 - 4.66511i) q^{37} +(-4.57366 - 15.5765i) q^{38} +(0.0626993 - 0.436083i) q^{39} +(0.872764 - 1.31382i) q^{40} +(-9.61896 + 6.18173i) q^{41} +(5.38050 - 4.66223i) q^{42} +(-1.46723 + 4.99691i) q^{43} +(-3.30235 + 7.23114i) q^{44} +(0.284639 + 2.21788i) q^{45} +(-9.57565 + 2.84532i) q^{46} +2.38834i q^{47} +(-2.91812 - 1.33266i) q^{48} +(4.49282 + 1.31921i) q^{49} +(-5.89361 + 8.58671i) q^{50} +(3.63759 - 2.33774i) q^{51} +(0.778674 + 0.674725i) q^{52} +(0.123648 + 0.0177779i) q^{53} +(-1.99857 + 0.586833i) q^{54} +(3.26194 - 6.86530i) q^{55} +(0.343119 + 2.38645i) q^{56} +(-7.08950 + 3.23767i) q^{57} +(-16.3814 + 7.48112i) q^{58} +(-1.41807 - 9.86289i) q^{59} +(-4.72333 - 2.24422i) q^{60} +(7.16403 - 2.10355i) q^{61} +(-3.53229 - 0.507867i) q^{62} +(-2.58313 - 2.23829i) q^{63} +(8.78352 - 5.64482i) q^{64} +(-0.734654 - 0.656341i) q^{65} +(6.79352 + 1.99476i) q^{66} +(5.36113 + 2.44835i) q^{67} +10.1124i q^{68} +(2.00635 + 4.35598i) q^{69} +(-2.02647 - 15.7900i) q^{70} +(-0.266610 + 0.583794i) q^{71} +(0.198730 - 0.676813i) q^{72} +(4.88006 - 4.22859i) q^{73} +(9.71716 - 6.24484i) q^{74} +(4.48311 + 2.21399i) q^{75} +(2.59397 - 18.0415i) q^{76} +(3.27326 + 11.1477i) q^{77} +(0.496134 - 0.771999i) q^{78} +(1.09553 + 7.61955i) q^{79} +(-6.09270 + 3.78629i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-23.5741 + 3.38944i) q^{82} +(5.60844 - 8.72690i) q^{83} +(7.66963 - 2.25201i) q^{84} +(0.146561 - 9.66768i) q^{85} +(-7.10372 + 8.19813i) q^{86} +(4.67429 + 7.27334i) q^{87} +(-1.81209 + 1.57019i) q^{88} +(16.8803 + 4.95649i) q^{89} +(-1.37979 + 4.44853i) q^{90} +1.50585 q^{91} +(-11.1067 - 1.56027i) q^{92} +1.71326i q^{93} +(-2.06659 + 4.52521i) q^{94} +(-2.74138 + 17.2105i) q^{95} +(-5.29972 - 6.11620i) q^{96} +(-4.24614 - 6.60712i) q^{97} +(7.37109 + 6.38709i) q^{98} +(0.483756 - 3.36460i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q + 28 q^{4} - 4 q^{5} - 4 q^{6} + 24 q^{9} + 8 q^{14} + 4 q^{15} - 36 q^{16} - 8 q^{19} - 92 q^{20} + 8 q^{21} + 12 q^{24} - 44 q^{25} + 32 q^{26} - 12 q^{29} + 8 q^{30} - 20 q^{31} - 54 q^{34} + 36 q^{35}+ \cdots + 44 q^{99}+O(q^{100}) $ 240 * q + 28 * q^4 - 4 * q^5 - 4 * q^6 + 24 * q^9 + 8 * q^14 + 4 * q^15 - 36 * q^16 - 8 * q^19 - 92 * q^20 + 8 * q^21 + 12 * q^24 - 44 * q^25 + 32 * q^26 - 12 * q^29 + 8 * q^30 - 20 * q^31 - 54 * q^34 + 36 * q^35 - 28 * q^36 - 36 * q^39 - 24 * q^40 - 28 * q^41 - 224 * q^44 + 4 * q^45 - 8 * q^46 + 52 * q^49 - 48 * q^50 - 18 * q^54 - 22 * q^55 - 56 * q^59 - 36 * q^60 + 44 * q^61 + 12 * q^64 - 16 * q^65 + 8 * q^66 + 8 * q^69 - 152 * q^70 + 4 * q^71 + 88 * q^74 - 8 * q^75 - 100 * q^76 - 84 * q^79 + 122 * q^80 - 24 * q^81 - 56 * q^84 + 186 * q^85 - 392 * q^86 + 48 * q^89 - 304 * q^91 + 80 * q^94 + 190 * q^95 + 16 * q^96 + 44 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/345\mathbb{Z}\right)^\times$.

$n$	$116$	$166$	$277$
$\chi(n)$	$1$	$e\left(\frac{9}{11}\right)$	$-1$

Coefficient data

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

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

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

$2$	1.89471	+	0.865286i	1.33976	+	0.611849i	0.950915	−	0.309453i	$-0.100146\pi$
$2$	1.89471	+	0.865286i	1.33976	+	0.611849i	0.388848	+	0.921302i	$0.372873\pi$
$3$	0.281733	−	0.959493i	0.162658	−	0.553964i
$3$	0.281733	−	0.959493i	0.162658	−	0.553964i
$4$	1.53149	+	1.76743i	0.765745	+	0.883716i
$5$	−1.43853	−	1.71191i	−0.643330	−	0.765589i
$5$	−1.43853	−	1.71191i	−0.643330	−	0.765589i
$6$	1.36404	−	1.57418i	0.556866	−	0.642657i
$7$	3.38318	+	0.486427i	1.27872	+	0.183852i	0.748002	−	0.663696i	$-0.231013\pi$
$7$	3.38318	+	0.486427i	1.27872	+	0.183852i	0.530718	+	0.847548i	$0.321922\pi$
$8$	0.198730	+	0.676813i	0.0702618	+	0.239290i
$9$	−0.841254	−	0.540641i	−0.280418	−	0.180214i
$10$	−1.24431	−	4.48831i	−0.393484	−	1.41933i
$11$	1.41208	+	3.09202i	0.425757	+	0.932278i	0.993996	+	0.109414i	$0.0348975\pi$
$11$	1.41208	+	3.09202i	0.425757	+	0.932278i	−0.568239	+	0.822863i	$0.692375\pi$
$12$	2.12731	−	0.971510i	0.614101	−	0.280451i
$13$	0.436083	−	0.0626993i	0.120948	−	0.0173897i	−0.0815751	−	0.996667i	$-0.525995\pi$
$13$	0.436083	−	0.0626993i	0.120948	−	0.0173897i	0.202523	+	0.979278i	$0.435086\pi$
$14$	5.98924	+	3.84905i	1.60069	+	1.02870i
$15$	−2.04785	+	0.897958i	−0.528751	+	0.231852i
$16$	0.456549	−	3.17537i	0.114137	−	0.793841i
$17$	3.26787	+	2.83163i	0.792576	+	0.686771i	0.953898	−	0.300131i	$-0.0970305\pi$
$17$	3.26787	+	2.83163i	0.792576	+	0.686771i	−0.161322	+	0.986902i	$0.551576\pi$
$18$	−1.12612	−	1.75228i	−0.265430	−	0.413017i
$19$	−5.10386	−	5.89017i	−1.17091	−	1.35130i	−0.924062	−	0.382242i	$-0.875152\pi$
$19$	−5.10386	−	5.89017i	−1.17091	−	1.35130i	−0.246843	−	0.969055i	$-0.579393\pi$
$20$	0.822593	−	5.16427i	0.183937	−	1.15477i
$21$	1.41987	−	3.10909i	0.309842	−	0.678459i
$22$			7.08033i			1.50953i
$23$	−3.61427	+	3.15230i	−0.753628	+	0.657301i
$23$	−3.61427	+	3.15230i	−0.753628	+	0.657301i
$24$	0.705386			0.143986
$25$	−0.861269	+	4.92526i	−0.172254	+	0.985053i
$26$	0.880505	+	0.258540i	0.172681	+	0.0507038i
$27$	−0.755750	+	0.654861i	−0.145444	+	0.126028i
$28$	4.32157	+	6.72449i	0.816700	+	1.27081i
$29$	−5.66182	+	6.53409i	−1.05137	+	1.21335i	−0.0750175	+	0.997182i	$0.523901\pi$
$29$	−5.66182	+	6.53409i	−1.05137	+	1.21335i	−0.976356	+	0.216168i	$0.930644\pi$
$30$	−4.65707	−	0.0706006i	−0.850260	−	0.0128899i
$31$	−1.64386	+	0.482680i	−0.295245	+	0.0866919i	−0.426001	−	0.904723i	$-0.640078\pi$
$31$	−1.64386	+	0.482680i	−0.295245	+	0.0866919i	0.130755	+	0.991415i	$0.458260\pi$
$32$	4.37535	−	6.80817i	0.773459	−	1.20353i
$33$	3.36460	−	0.483756i	0.585701	−	0.0842111i
$34$	3.74151	+	8.19276i	0.641663	+	1.40505i
$35$	−4.03408	−	6.49143i	−0.681883	−	1.09725i
$36$	−0.332824	−	2.31484i	−0.0554707	−	0.385807i
$37$	2.99808	−	4.66511i	0.492882	−	0.766940i	−0.502330	−	0.864676i	$-0.667524\pi$
$37$	2.99808	−	4.66511i	0.492882	−	0.766940i	0.995212	+	0.0977363i	$0.0311602\pi$
$38$	−4.57366	−	15.5765i	−0.741946	−	2.52684i
$39$	0.0626993	−	0.436083i	0.0100399	−	0.0698292i
$40$	0.872764	−	1.31382i	0.137996	−	0.207734i
$41$	−9.61896	+	6.18173i	−1.50223	+	0.965424i	−0.507636	+	0.861572i	$0.669480\pi$
$41$	−9.61896	+	6.18173i	−1.50223	+	0.965424i	−0.994593	+	0.103852i	$0.966883\pi$
$42$	5.38050	−	4.66223i	0.830230	−	0.719398i
$43$	−1.46723	+	4.99691i	−0.223750	+	0.762022i	0.768726	+	0.639579i	$0.220891\pi$
$43$	−1.46723	+	4.99691i	−0.223750	+	0.762022i	−0.992476	+	0.122443i	$0.960927\pi$
$44$	−3.30235	+	7.23114i	−0.497848	+	1.09014i
$45$	0.284639	+	2.21788i	0.0424315	+	0.330622i
$46$	−9.57565	+	2.84532i	−1.41185	+	0.419520i
$47$			2.38834i			0.348375i	0.984713	+	0.174187i	$0.0557298\pi$
$47$			2.38834i			0.348375i	−0.984713	+	0.174187i	$0.944270\pi$
$48$	−2.91812	−	1.33266i	−0.421194	−	0.192353i
$49$	4.49282	+	1.31921i	0.641831	+	0.188459i
$50$	−5.89361	+	8.58671i	−0.833483	+	1.21434i
$51$	3.63759	−	2.33774i	0.509365	−	0.327349i
$52$	0.778674	+	0.674725i	0.107983	+	0.0935675i
$53$	0.123648	+	0.0177779i	0.0169844	+	0.00244198i	0.150802	−	0.988564i	$-0.451814\pi$
$53$	0.123648	+	0.0177779i	0.0169844	+	0.00244198i	−0.133817	+	0.991006i	$0.542724\pi$
$54$	−1.99857	+	0.586833i	−0.271971	+	0.0798578i
$55$	3.26194	−	6.86530i	0.439840	−	0.925717i
$56$	0.343119	+	2.38645i	0.0458512	+	0.318902i
$57$	−7.08950	+	3.23767i	−0.939027	+	0.428839i
$58$	−16.3814	+	7.48112i	−2.15098	+	0.982319i
$59$	−1.41807	−	9.86289i	−0.184617	−	1.28404i	−0.845672	−	0.533702i	$-0.820800\pi$
$59$	−1.41807	−	9.86289i	−0.184617	−	1.28404i	0.661056	−	0.750337i	$-0.270109\pi$
$60$	−4.72333	−	2.24422i	−0.609780	−	0.289727i
$61$	7.16403	−	2.10355i	0.917260	−	0.269332i	0.211166	−	0.977450i	$-0.432274\pi$
$61$	7.16403	−	2.10355i	0.917260	−	0.269332i	0.706094	+	0.708118i	$0.250456\pi$
$62$	−3.53229	−	0.507867i	−0.448601	−	0.0644991i
$63$	−2.58313	−	2.23829i	−0.325443	−	0.281998i
$64$	8.78352	−	5.64482i	1.09794	−	0.705603i
$65$	−0.734654	−	0.656341i	−0.0911226	−	0.0814090i
$66$	6.79352	+	1.99476i	0.836225	+	0.245538i
$67$	5.36113	+	2.44835i	0.654966	+	0.299113i	0.715043	−	0.699081i	$-0.246407\pi$
$67$	5.36113	+	2.44835i	0.654966	+	0.299113i	−0.0600765	+	0.998194i	$0.519134\pi$
$68$			10.1124i			1.22630i
$69$	2.00635	+	4.35598i	0.241537	+	0.524398i
$70$	−2.02647	−	15.7900i	−0.242209	−	1.88727i
$71$	−0.266610	+	0.583794i	−0.0316408	+	0.0692837i	−0.924793	−	0.380472i	$-0.875762\pi$
$71$	−0.266610	+	0.583794i	−0.0316408	+	0.0692837i	0.893152	+	0.449755i	$0.148489\pi$
$72$	0.198730	−	0.676813i	0.0234206	−	0.0797632i
$73$	4.88006	−	4.22859i	0.571168	−	0.494920i	−0.320722	−	0.947174i	$-0.603925\pi$
$73$	4.88006	−	4.22859i	0.571168	−	0.494920i	0.891889	+	0.452254i	$0.149380\pi$
$74$	9.71716	−	6.24484i	1.12960	−	0.725948i
$75$	4.48311	+	2.21399i	0.517665	+	0.255649i
$76$	2.59397	−	18.0415i	0.297549	−	2.06950i
$77$	3.27326	+	11.1477i	0.373023	+	1.27040i
$78$	0.496134	−	0.771999i	0.0561761	−	0.0874117i
$79$	1.09553	+	7.61955i	0.123256	+	0.857267i	0.953828	+	0.300354i	$0.0971049\pi$
$79$	1.09553	+	7.61955i	0.123256	+	0.857267i	−0.830571	+	0.556912i	$0.811986\pi$
$80$	−6.09270	+	3.78629i	−0.681184	+	0.423320i
$81$	0.415415	+	0.909632i	0.0461572	+	0.101070i
$82$	−23.5741	+	3.38944i	−2.60332	+	0.374301i
$83$	5.60844	−	8.72690i	0.615606	−	0.957901i	−0.383799	−	0.923416i	$-0.625385\pi$
$83$	5.60844	−	8.72690i	0.615606	−	0.957901i	0.999405	−	0.0344848i	$-0.0109790\pi$
$84$	7.66963	−	2.25201i	0.836825	−	0.245714i
$85$	0.146561	−	9.66768i	0.0158968	−	1.04861i
$86$	−7.10372	+	8.19813i	−0.766014	+	0.884027i
$87$	4.67429	+	7.27334i	0.501137	+	0.779784i
$88$	−1.81209	+	1.57019i	−0.193170	+	0.167383i
$89$	16.8803	+	4.95649i	1.78930	+	0.525387i	0.996462	−	0.0840394i	$-0.0267822\pi$
$89$	16.8803	+	4.95649i	1.78930	+	0.525387i	0.792842	+	0.609427i	$0.208600\pi$
$90$	−1.37979	+	4.44853i	−0.145442	+	0.468916i
$91$	1.50585			0.157856
$92$	−11.1067	−	1.56027i	−1.15795	−	0.162669i
$93$			1.71326i			0.177656i
$94$	−2.06659	+	4.52521i	−0.213153	+	0.466739i
$95$	−2.74138	+	17.2105i	−0.281260	+	1.76576i
$96$	−5.29972	−	6.11620i	−0.540900	−	0.624232i
$97$	−4.24614	−	6.60712i	−0.431130	−	0.670851i	0.555925	−	0.831232i	$-0.312364\pi$
$97$	−4.24614	−	6.60712i	−0.431130	−	0.670851i	−0.987055	+	0.160381i	$0.948728\pi$
$98$	7.37109	+	6.38709i	0.744593	+	0.645193i
$99$	0.483756	−	3.36460i	0.0486193	−	0.338155i
$100$	−10.0241	+	6.02075i	−1.00241	+	0.602075i
$101$	−10.5910	−	6.80641i	−1.05384	−	0.677263i	−0.105470	−	0.994422i	$-0.533635\pi$
$101$	−10.5910	−	6.80641i	−1.05384	−	0.677263i	−0.948372	+	0.317159i	$0.897271\pi$
$102$	8.91500	−	1.28178i	0.882716	−	0.126915i
$103$	3.40973	−	1.55717i	0.335971	−	0.153433i	−0.240284	−	0.970703i	$-0.577241\pi$
$103$	3.40973	−	1.55717i	0.335971	−	0.153433i	0.576255	+	0.817270i	$0.304513\pi$
$104$	0.129099	+	0.282687i	0.0126592	+	0.0277197i
$105$	−7.36501	+	2.04182i	−0.718752	+	0.199261i
$106$	0.218894	+	0.140675i	0.0212609	+	0.0136635i
$107$	0.141846	+	0.483083i	0.0137128	+	0.0467014i	0.966065	−	0.258298i	$-0.0831618\pi$
$107$	0.141846	+	0.483083i	0.0137128	+	0.0467014i	−0.952352	+	0.305000i	$0.901344\pi$
$108$	−2.31484	−	0.332824i	−0.222746	−	0.0320260i
$109$	3.18360	−	3.67406i	0.304933	−	0.351912i	−0.582514	−	0.812820i	$-0.697931\pi$
$109$	3.18360	−	3.67406i	0.304933	−	0.351912i	0.887447	+	0.460909i	$0.152476\pi$
$110$	12.1209	−	10.1853i	1.15568	−	0.971126i
$111$	−3.63148	−	4.19096i	−0.344685	−	0.397788i
$112$	3.08917	−	10.5207i	0.291899	−	0.994117i
$113$	−8.55874	−	3.90865i	−0.805139	−	0.367695i	−0.0300511	−	0.999548i	$-0.509567\pi$
$113$	−8.55874	−	3.90865i	−0.805139	−	0.367695i	−0.775088	+	0.631854i	$0.782294\pi$
$114$	−16.2341			−1.52046
$115$	10.5957	+	1.65263i	0.988054	+	0.154109i
$116$	−20.2196			−1.87734
$117$	−0.400755	−	0.183018i	−0.0370498	−	0.0169201i
$118$	5.84739	−	19.9144i	0.538295	−	1.83327i
$119$	9.67841	+	11.1695i	0.887218	+	1.02390i
$120$	−1.01472	−	1.20756i	−0.0926307	−	0.110234i
$121$	−0.363133	+	0.419078i	−0.0330121	+	0.0380980i
$122$	15.3939	+	2.21331i	1.39370	+	0.200384i
$123$	3.22135	+	10.9709i	0.290459	+	0.989214i
$124$	−3.37065	−	2.16619i	−0.302694	−	0.194529i
$125$	9.67056	−	5.61072i	0.864962	−	0.501838i
$126$	−2.95752	−	6.47606i	−0.263476	−	0.576933i
$127$	−12.4626	+	5.69150i	−1.10588	+	0.505039i	−0.882794	−	0.469760i	$-0.844341\pi$
$127$	−12.4626	+	5.69150i	−1.10588	+	0.505039i	−0.223087	+	0.974799i	$0.571613\pi$
$128$	5.50558	−	0.791583i	0.486629	−	0.0699667i
$129$	4.38114	+	2.81558i	0.385737	+	0.247898i
$130$	−0.824036	−	1.87926i	−0.0722727	−	0.164822i
$131$	−1.94651	+	13.5382i	−0.170067	+	1.18284i	0.708671	+	0.705539i	$0.249295\pi$
$131$	−1.94651	+	13.5382i	−0.170067	+	1.18284i	−0.878739	+	0.477303i	$0.841614\pi$
$132$	6.00785	+	5.20583i	0.522916	+	0.453109i
$133$	−14.4021	−	22.4101i	−1.24882	−	1.94320i
$134$	8.03927	+	9.27782i	0.694487	+	0.801481i
$135$	2.20823	+	0.351739i	0.190054	+	0.0302729i
$136$	−1.26706	+	2.77447i	−0.108649	+	0.237909i
$137$		−	19.1771i		−	1.63841i	−0.573503	−	0.819203i	$-0.694416\pi$
$137$		−	19.1771i		−	1.63841i	0.573503	−	0.819203i	$-0.305584\pi$
$138$	0.0322967	+	9.98939i	0.00274928	+	0.850353i
$139$	0.913586			0.0774893			0.0387447	−	0.999249i	$-0.487664\pi$
$139$	0.913586			0.0774893			0.0387447	+	0.999249i	$0.487664\pi$
$140$	5.29502	−	17.0715i	0.447511	−	1.44281i
$141$	2.29159	+	0.672872i	0.192987	+	0.0566661i
$142$	−1.01030	+	0.875428i	−0.0847823	+	0.0734643i
$143$	0.809650	+	1.25984i	0.0677064	+	0.105353i
$144$	−2.10081	+	2.42446i	−0.175067	+	0.202038i
$145$	19.3305	+	0.293048i	1.60531	+	0.0243363i
$146$	12.9052	−	3.78932i	1.06805	−	0.313606i
$147$	2.53154	−	3.93916i	0.208798	−	0.324896i
$148$	12.8368	−	1.84565i	1.05518	−	0.151712i
$149$	−2.47430	−	5.41796i	−0.202702	−	0.443856i	0.780793	−	0.624790i	$-0.214815\pi$
$149$	−2.47430	−	5.41796i	−0.202702	−	0.443856i	−0.983495	+	0.180934i	$0.942088\pi$
$150$	6.57846	+	8.07404i	0.537129	+	0.659242i
$151$	−1.11988	−	7.78890i	−0.0911342	−	0.633852i	−0.983279	−	0.182103i	$-0.941709\pi$
$151$	−1.11988	−	7.78890i	−0.0911342	−	0.633852i	0.892145	−	0.451749i	$-0.149200\pi$
$152$	2.97225	−	4.62491i	0.241081	−	0.375130i
$153$	−1.21822	−	4.14886i	−0.0984869	−	0.335416i
$154$	−3.44406	+	23.9540i	−0.277531	+	1.93027i
$155$	3.19104	+	2.11979i	0.256311	+	0.170265i
$156$	0.866772	−	0.557040i	0.0693973	−	0.0445989i
$157$	−5.03746	+	4.36498i	−0.402033	+	0.348363i	−0.832288	−	0.554344i	$-0.812969\pi$
$157$	−5.03746	+	4.36498i	−0.402033	+	0.348363i	0.430255	+	0.902707i	$0.358424\pi$
$158$	−4.51738	+	15.3848i	−0.359384	+	1.22395i
$159$	0.0518934	−	0.113631i	0.00411542	−	0.00901150i
$160$	−17.9490	+	2.30356i	−1.41900	+	0.182112i
$161$	−13.7611	+	8.90671i	−1.08453	+	0.701947i
$162$			2.08294i			0.163651i
$163$	11.6333	+	5.31275i	0.911190	+	0.416126i	0.815149	−	0.579251i	$-0.196655\pi$
$163$	11.6333	+	5.31275i	0.911190	+	0.416126i	0.0960405	+	0.995377i	$0.469382\pi$
$164$	−25.6571	−	7.53361i	−2.00348	−	0.588276i
$165$	−5.66821	−	5.06399i	−0.441270	−	0.394231i
$166$	18.1776	−	11.6820i	1.41086	−	0.906703i
$167$	2.63808	+	2.28591i	0.204141	+	0.176889i	0.750931	−	0.660381i	$-0.229605\pi$
$167$	2.63808	+	2.28591i	0.204141	+	0.176889i	−0.546790	+	0.837270i	$0.684150\pi$
$168$	2.38645	+	0.343119i	0.184118	+	0.0264722i
$169$	−12.2872	+	3.60784i	−0.945167	+	0.277526i
$170$	8.64300	−	18.1906i	0.662887	−	1.39516i
$171$	1.10917	+	7.71448i	0.0848207	+	0.589941i
$172$	−11.0787	+	5.05949i	−0.844746	+	0.385783i
$173$	10.7550	−	4.91165i	0.817689	−	0.373426i	0.0377546	−	0.999287i	$-0.487979\pi$
$173$	10.7550	−	4.91165i	0.817689	−	0.373426i	0.779935	+	0.625861i	$0.215252\pi$
$174$	2.56292	+	17.8255i	0.194294	+	1.35135i
$175$	−5.30961	+	16.2441i	−0.401368	+	1.22794i
$176$	10.4630	−	3.07220i	0.788675	−	0.231576i
$177$	−9.86289	−	1.41807i	−0.741340	−	0.106589i
$178$	27.6944	+	23.9974i	2.07579	+	1.79868i
$179$	−6.66948	+	4.28621i	−0.498500	+	0.320366i	−0.765616	−	0.643298i	$-0.777566\pi$
$179$	−6.66948	+	4.28621i	−0.498500	+	0.320366i	0.267116	+	0.963664i	$0.413929\pi$
$180$	−3.48403	+	3.89974i	−0.259684	+	0.290669i
$181$	12.3255	+	3.61910i	0.916150	+	0.269006i	0.705627	−	0.708583i	$-0.250665\pi$
$181$	12.3255	+	3.61910i	0.916150	+	0.269006i	0.210522	+	0.977589i	$0.432484\pi$
$182$	2.85314	+	1.30299i	0.211489	+	0.0965838i
$183$		−	7.46647i		−	0.551937i
$184$	−2.85179	−	1.81973i	−0.210236	−	0.134152i
$185$	−12.2991	+	1.57845i	−0.904246	+	0.116050i
$186$	−1.48246	+	3.24613i	−0.108699	+	0.238017i
$187$	−4.14095	+	14.1028i	−0.302816	+	1.03130i
$188$	−4.22122	+	3.65771i	−0.307864	+	0.266766i
$189$	−2.87538	+	1.84789i	−0.209153	+	0.134414i
$190$	−20.0861	+	30.2369i	−1.45720	+	2.19361i
$191$	−2.82941	+	19.6790i	−0.204729	+	1.42392i	0.585282	+	0.810830i	$0.300984\pi$
$191$	−2.82941	+	19.6790i	−0.204729	+	1.42392i	−0.790011	+	0.613093i	$0.789925\pi$
$192$	−2.94157	−	10.0181i	−0.212289	−	0.722991i
$193$	13.8929	−	21.6178i	1.00004	−	1.55609i	0.180085	−	0.983651i	$-0.442363\pi$
$193$	13.8929	−	21.6178i	1.00004	−	1.55609i	0.819951	−	0.572434i	$-0.194001\pi$
$194$	−2.32816	−	16.1927i	−0.167152	−	1.16257i
$195$	−0.836730	+	0.519983i	−0.0599195	+	0.0372368i
$196$	4.54908	+	9.96111i	0.324935	+	0.711508i
$197$	−10.9940	+	1.58070i	−0.783289	+	0.112620i	−0.522345	−	0.852734i	$-0.674943\pi$
$197$	−10.9940	+	1.58070i	−0.783289	+	0.112620i	−0.260944	+	0.965354i	$0.584034\pi$
$198$	3.82791	−	5.95635i	0.272038	−	0.423299i
$199$	−15.4961	+	4.55005i	−1.09849	+	0.322545i	−0.780251	−	0.625467i	$-0.784908\pi$
$199$	−15.4961	+	4.55005i	−1.09849	+	0.322545i	−0.318236	+	0.948012i	$0.603090\pi$
$200$	−3.50464	+	0.395881i	−0.247816	+	0.0279930i
$201$	3.85958	−	4.45419i	0.272233	−	0.314174i
$202$	−14.1774	−	22.0604i	−0.997516	−	1.55217i
$203$	−22.3333	+	19.3519i	−1.56749	+	1.35824i
$204$	9.70273	+	2.84898i	0.679327	+	0.199468i
$205$	24.4197	+	7.57419i	1.70555	+	0.529004i
$206$	7.80786			0.543999
$207$	4.74479	−	0.697862i	0.329785	−	0.0485048i
$208$		−	1.41335i		−	0.0979982i
$209$	11.0055	−	24.0986i	0.761263	−	1.66693i
$210$	−15.7213	−	2.50418i	−1.08487	−	0.172805i
$211$	3.71456	+	4.28683i	0.255721	+	0.295117i	0.869065	−	0.494699i	$-0.164722\pi$
$211$	3.71456	+	4.28683i	0.255721	+	0.295117i	−0.613344	+	0.789816i	$0.710176\pi$
$212$	0.157944	+	0.245766i	0.0108477	+	0.0168793i
$213$	0.485034	+	0.420284i	0.0332340	+	0.0287974i
$214$	−0.149248	+	1.03804i	−0.0102024	+	0.0709589i
$215$	10.6649	−	4.67644i	0.727341	−	0.318931i
$216$	−0.593409	−	0.381361i	−0.0403763	−	0.0259483i
$217$	−5.79625	+	0.833374i	−0.393475	+	0.0565731i
$218$	9.21111	−	4.20657i	0.623855	−	0.284905i
$219$	−2.68244	−	5.87371i	−0.181262	−	0.396909i
$220$	17.1296	−	4.74888i	1.15488	−	0.320169i
$221$	1.60261	+	1.02993i	0.107803	+	0.0692808i
$222$	−3.25424	−	11.0829i	−0.218410	−	0.743837i
$223$	−8.61616	−	1.23882i	−0.576981	−	0.0829573i	−0.152354	−	0.988326i	$-0.548685\pi$
$223$	−8.61616	−	1.23882i	−0.576981	−	0.0829573i	−0.424626	+	0.905369i	$0.639595\pi$
$224$	18.1142	−	20.9050i	1.21031	−	1.39677i
$225$	3.38734	−	3.67776i	0.225823	−	0.245184i
$226$	−12.8342	−	14.8115i	−0.853721	−	0.985247i
$227$	5.97939	−	20.3639i	0.396866	−	1.35160i	−0.482683	−	0.875795i	$-0.660338\pi$
$227$	5.97939	−	20.3639i	0.396866	−	1.35160i	0.879550	−	0.475807i	$-0.157844\pi$
$228$	−16.5798	−	7.57176i	−1.09803	−	0.501452i
$229$	1.02911			0.0680054			0.0340027	−	0.999422i	$-0.489175\pi$
$229$	1.02911			0.0680054			0.0340027	+	0.999422i	$0.489175\pi$
$230$	18.6458	+	12.2996i	1.22947	+	0.811009i
$231$	11.6183			0.764430
$232$	−5.54753	−	2.53347i	−0.364213	−	0.166331i
$233$	1.86690	−	6.35809i	0.122305	−	0.416533i	−0.875465	−	0.483282i	$-0.839445\pi$
$233$	1.86690	−	6.35809i	0.122305	−	0.416533i	0.997770	+	0.0667494i	$0.0212628\pi$
$234$	−0.600951	−	0.693534i	−0.0392854	−	0.0453378i
$235$	4.08862	−	3.43569i	0.266712	−	0.224120i
$236$	15.2602	−	17.6113i	0.993357	−	1.14640i
$237$	7.61955	+	1.09553i	0.494943	+	0.0711621i
$238$	8.67300	+	29.5375i	0.562187	+	1.91463i
$239$	11.7010	+	7.51978i	0.756876	+	0.486414i	0.861286	−	0.508120i	$-0.169659\pi$
$239$	11.7010	+	7.51978i	0.756876	+	0.486414i	−0.104411	+	0.994534i	$0.533296\pi$
$240$	1.91640	+	6.91262i	0.123703	+	0.446208i
$241$	7.88155	+	17.2582i	0.507695	+	1.11170i	0.973891	+	0.227016i	$0.0728970\pi$
$241$	7.88155	+	17.2582i	0.507695	+	1.11170i	−0.466196	+	0.884682i	$0.654376\pi$
$242$	−1.05066	+	0.479818i	−0.0675387	+	0.0308439i
$243$	0.989821	−	0.142315i	0.0634971	−	0.00912950i
$244$	14.6895	+	9.44038i	0.940400	+	0.604358i
$245$	−4.20468	−	9.58901i	−0.268627	−	0.612620i
$246$	−3.38944	+	23.5741i	−0.216103	+	1.50303i
$247$	−2.59502	−	2.24860i	−0.165117	−	0.143075i
$248$	−0.653368	−	1.01666i	−0.0414889	−	0.0645580i
$249$	−6.79332	−	7.83990i	−0.430509	−	0.496834i
$250$	23.1778	−	2.26289i	1.46589	−	0.143118i
$251$	2.03246	−	4.45047i	0.128288	−	0.280911i	−0.834579	−	0.550888i	$-0.814289\pi$
$251$	2.03246	−	4.45047i	0.128288	−	0.280911i	0.962867	+	0.269977i	$0.0870163\pi$
$252$		−	7.99342i		−	0.503538i
$253$	−14.8506	−	6.72410i	−0.933649	−	0.422741i
$254$	−28.5379			−1.79063
$255$	−9.23478	−	2.86432i	−0.578304	−	0.179371i
$256$	−8.91968	−	2.61906i	−0.557480	−	0.163691i
$257$	−1.48462	+	1.28643i	−0.0926083	+	0.0802455i	−0.699935	−	0.714207i	$-0.746788\pi$
$257$	−1.48462	+	1.28643i	−0.0926083	+	0.0802455i	0.607326	+	0.794452i	$0.292242\pi$
$258$	5.86470	+	9.12565i	0.365120	+	0.568138i
$259$	12.4123	−	14.3245i	0.771262	−	0.890084i
$260$	0.0349228	−	2.30363i	0.00216582	−	0.142865i
$261$	8.29562	−	2.43581i	0.513486	−	0.150773i
$262$	−15.4025	+	23.9668i	−0.951571	+	1.48067i
$263$	19.0453	−	2.73831i	1.17439	−	0.168851i	0.472625	−	0.881264i	$-0.343307\pi$
$263$	19.0453	−	2.73831i	1.17439	−	0.168851i	0.701761	+	0.712412i	$0.252397\pi$
$264$	0.996059	+	2.18107i	0.0613032	+	0.134235i
$265$	−0.147437	−	0.237248i	−0.00905698	−	0.0145740i
$266$	−7.89669	−	54.9227i	−0.484177	−	3.36752i
$267$	9.51144	−	14.8001i	0.582091	−	0.905751i
$268$	3.88323	+	13.2251i	0.237206	+	0.807849i
$269$	3.55741	−	24.7423i	0.216899	−	1.50857i	−0.532489	−	0.846437i	$-0.678743\pi$
$269$	3.55741	−	24.7423i	0.216899	−	1.50857i	0.749389	−	0.662130i	$-0.230348\pi$
$270$	3.87960	+	2.57719i	0.236105	+	0.156843i
$271$	10.6612	−	6.85155i	0.647623	−	0.416202i	−0.175174	−	0.984538i	$-0.556049\pi$
$271$	10.6612	−	6.85155i	0.647623	−	0.416202i	0.822797	+	0.568335i	$0.192412\pi$
$272$	10.4834	−	9.08392i	0.635649	−	0.550793i
$273$	0.424246	−	1.44485i	0.0256765	−	0.0874462i
$274$	16.5936	−	36.3350i	1.00246	−	2.19508i
$275$	−16.4452	+	4.29179i	−0.991681	+	0.258805i
$276$	−4.62619	+	10.2172i	−0.278464	+	0.615005i
$277$			7.95353i			0.477881i	0.971034	+	0.238941i	$0.0768002\pi$
$277$			7.95353i			0.477881i	−0.971034	+	0.238941i	$0.923200\pi$
$278$	1.73098	+	0.790513i	0.103817	+	0.0474118i
$279$	1.64386	+	0.482680i	0.0984152	+	0.0288973i
$280$	3.59179	−	4.02036i	0.214651	−	0.240262i
$281$	−12.0243	+	7.72754i	−0.717309	+	0.460986i	−0.847700	−	0.530476i	$-0.822013\pi$
$281$	−12.0243	+	7.72754i	−0.717309	+	0.460986i	0.130391	+	0.991463i	$0.458377\pi$
$282$	3.75968	+	3.25778i	0.223886	+	0.193998i
$283$	−0.934447	−	0.134353i	−0.0555471	−	0.00798647i	0.114485	−	0.993425i	$-0.463478\pi$
$283$	−0.934447	−	0.134353i	−0.0555471	−	0.00798647i	−0.170032	+	0.985438i	$0.554387\pi$
$284$	−1.44013	+	0.422860i	−0.0854559	+	0.0250921i
$285$	15.7410	+	7.47910i	0.932419	+	0.443024i
$286$	0.443932	+	3.08761i	0.0262502	+	0.182574i
$287$	−35.5496	+	16.2349i	−2.09843	+	0.958319i
$288$	−7.36155	+	3.36191i	−0.433784	+	0.198102i
$289$	0.241523	+	1.67983i	0.0142073	+	0.0988137i
$290$	36.3721	+	17.2816i	2.13584	+	1.01481i
$291$	−7.53576	+	2.21270i	−0.441754	+	0.129711i
$292$	14.9475	+	2.14913i	0.874737	+	0.125768i
$293$	−3.87972	−	3.36180i	−0.226656	−	0.196398i	0.534128	−	0.845403i	$-0.320640\pi$
$293$	−3.87972	−	3.36180i	−0.226656	−	0.196398i	−0.760784	+	0.649005i	$0.775185\pi$
$294$	8.20504	−	5.27306i	0.478528	−	0.307531i
$295$	−14.8444	+	16.6157i	−0.864277	+	0.967401i
$296$	3.75322	+	1.10204i	0.218151	+	0.0640550i
$297$	−3.09202	−	1.41208i	−0.179417	−	0.0819370i
$298$		−	12.4064i		−	0.718685i
$299$	−1.37848	+	1.60128i	−0.0797194	+	0.0926044i
$300$	2.95276	+	11.3143i	0.170477	+	0.653231i
$301$	−7.39451	+	16.1917i	−0.426213	+	0.933276i
$302$	4.61779	−	15.7267i	0.265724	−	0.904972i
$303$	−9.51453	+	8.24439i	−0.546596	+	0.473628i
$304$	−21.0336	+	13.5175i	−1.20636	+	0.775280i
$305$	−13.9067	−	9.23815i	−0.796298	−	0.528975i
$306$	1.28178	−	8.91500i	0.0732747	−	0.509637i
$307$	2.70664	+	9.21798i	0.154476	+	0.526098i	0.999969	−	0.00788933i	$-0.00251128\pi$
$307$	2.70664	+	9.21798i	0.154476	+	0.526098i	−0.845493	+	0.533987i	$0.820693\pi$
$308$	−14.6899	+	22.8579i	−0.837032	+	1.30245i
$309$	−0.533464	−	3.71032i	−0.0303477	−	0.211073i
$310$	4.21188	+	6.77754i	0.239219	+	0.384939i
$311$	−3.70293	−	8.10828i	−0.209974	−	0.459778i	0.775116	−	0.631819i	$-0.217691\pi$
$311$	−3.70293	−	8.10828i	−0.209974	−	0.459778i	−0.985090	+	0.172040i	$0.944964\pi$
$312$	0.307607	−	0.0442273i	0.0174148	−	0.00250388i
$313$	−6.52653	+	10.1555i	−0.368901	+	0.574022i	−0.975230	−	0.221192i	$-0.929005\pi$
$313$	−6.52653	+	10.1555i	−0.368901	+	0.574022i	0.606329	+	0.795214i	$0.292642\pi$
$314$	−13.3215	+	3.91154i	−0.751774	+	0.220741i
$315$	−0.115851	+	7.64193i	−0.00652745	+	0.430574i
$316$	−11.7893	+	13.6055i	−0.663198	+	0.765371i
$317$	−1.88468	−	2.93262i	−0.105854	−	0.164713i	0.784285	−	0.620400i	$-0.213030\pi$
$317$	−1.88468	−	2.93262i	−0.105854	−	0.164713i	−0.890140	+	0.455688i	$0.849393\pi$
$318$	0.196646	−	0.170395i	0.0110274	−	0.00955526i
$319$	−28.1984	−	8.27981i	−1.57881	−	0.463580i
$320$	−22.2988	−	6.91635i	−1.24654	−	0.386635i
$321$	0.503477			0.0281014
$322$	−33.7801	+	4.96838i	−1.88249	+	0.276877i
$323$		−	33.7006i		−	1.87515i
$324$	−0.971510	+	2.12731i	−0.0539728	+	0.118184i
$325$	−0.0667743	+	2.20183i	−0.00370397	+	0.122135i
$326$	17.4447	+	20.1322i	0.966172	+	1.11502i
$327$	−2.62832	−	4.08974i	−0.145346	−	0.226163i
$328$	−6.09545	−	5.28174i	−0.336565	−	0.291635i
$329$	−1.16175	+	8.08016i	−0.0640494	+	0.445474i
$330$	−6.35783	−	14.4994i	−0.349987	−	0.798166i
$331$	−7.12668	−	4.58004i	−0.391718	−	0.251742i	0.329925	−	0.944007i	$-0.392976\pi$
$331$	−7.12668	−	4.58004i	−0.391718	−	0.251742i	−0.721643	+	0.692265i	$0.756613\pi$
$332$	24.0135	−	3.45261i	1.31791	−	0.189487i
$333$	−5.04430	+	2.30365i	−0.276426	+	0.126239i
$334$	3.02044	+	6.61383i	0.165271	+	0.361893i
$335$	−3.52079	−	12.6998i	−0.192362	−	0.693863i
$336$	−9.22426	−	5.92807i	−0.503225	−	0.323403i
$337$	2.82399	+	9.61763i	0.153833	+	0.523906i	0.999959	−	0.00907691i	$-0.00288931\pi$
$337$	2.82399	+	9.61763i	0.153833	+	0.523906i	−0.846126	+	0.532983i	$0.821071\pi$
$338$	−26.4024	−	3.79610i	−1.43610	−	0.206481i
$339$	−6.16160	+	7.11086i	−0.334652	+	0.386209i
$340$	17.3114	−	14.5469i	0.938844	−	0.788917i
$341$	−3.81371	−	4.40125i	−0.206524	−	0.238341i
$342$	−4.57366	+	15.5765i	−0.247315	+	0.842279i
$343$	−7.20535	−	3.29057i	−0.389052	−	0.177674i
$344$	−3.67356			−0.198065
$345$	4.57084	−	9.70090i	0.246086	−	0.522279i
$346$	24.6276			1.32399
$347$	−4.96536	−	2.26760i	−0.266554	−	0.121731i	0.277655	−	0.960681i	$-0.410443\pi$
$347$	−4.96536	−	2.26760i	−0.266554	−	0.121731i	−0.544209	+	0.838950i	$0.683170\pi$
$348$	−5.69652	+	19.4005i	−0.305365	+	1.03998i
$349$	−22.8481	−	26.3681i	−1.22303	−	1.41145i	−0.881898	−	0.471440i	$-0.843734\pi$
$349$	−22.8481	−	26.3681i	−1.22303	−	1.41145i	−0.341134	−	0.940015i	$-0.610811\pi$
$350$	−24.1159	+	26.1835i	−1.28905	+	1.39957i
$351$	−0.288511	+	0.332959i	−0.0153996	+	0.0177720i
$352$	27.2293	+	3.91498i	1.45133	+	0.208669i
$353$	0.612338	+	2.08543i	0.0325915	+	0.110996i	0.974182	−	0.225763i	$-0.0724874\pi$
$353$	0.612338	+	2.08543i	0.0325915	+	0.110996i	−0.941591	+	0.336759i	$0.890669\pi$
$354$	−17.4603	−	11.2211i	−0.928004	−	0.596392i
$355$	1.38293	−	0.383393i	0.0733983	−	0.0203484i
$356$	17.0917	+	37.4256i	0.905857	+	1.98355i
$357$	13.4438	−	6.13956i	0.711519	−	0.324940i
$358$	−16.3455	+	2.35013i	−0.863888	+	0.124208i
$359$	7.81178	+	5.02033i	0.412290	+	0.264963i	0.730303	−	0.683124i	$-0.239379\pi$
$359$	7.81178	+	5.02033i	0.412290	+	0.264963i	−0.318013	+	0.948086i	$0.603015\pi$
$360$	−1.44452	+	0.633407i	−0.0761330	+	0.0333835i
$361$	−5.94071	+	41.3186i	−0.312669	+	2.17466i
$362$	20.2218	+	17.5223i	1.06283	+	0.920949i
$363$	0.299796	+	0.466492i	0.0157352	+	0.0244845i
$364$	2.30619	+	2.66148i	0.120877	+	0.139500i
$365$	−14.2591	−	2.27126i	−0.746354	−	0.118883i
$366$	6.46063	−	14.1468i	0.337703	−	0.739465i
$367$		−	15.7640i		−	0.822876i	−0.911438	−	0.411438i	$-0.865027\pi$
$367$		−	15.7640i		−	0.822876i	0.911438	−	0.411438i	$-0.134973\pi$
$368$	8.35962	+	12.9158i	0.435776	+	0.673284i
$369$	11.4341			0.595234
$370$	−24.6690	−	7.65151i	−1.28248	−	0.397783i
$371$	0.409675	+	0.120291i	0.0212693	+	0.00624522i
$372$	−3.02807	+	2.62383i	−0.156998	+	0.136039i
$373$	−13.0167	−	20.2544i	−0.673979	−	1.04873i	−0.994825	−	0.101601i	$-0.967604\pi$
$373$	−13.0167	−	20.2544i	−0.673979	−	1.04873i	0.320846	−	0.947131i	$-0.396033\pi$
$374$	−20.0488	+	23.1376i	−1.03670	+	1.19642i
$375$	−2.65893	−	10.8596i	−0.137307	−	0.560785i
$376$	−1.61646	+	0.474635i	−0.0833624	+	0.0244774i
$377$	−2.05934	+	3.20440i	−0.106062	+	0.165035i
$378$	−7.04696	+	1.01320i	−0.362457	+	0.0521134i
$379$	2.27166	+	4.97424i	0.116687	+	0.255509i	0.958960	−	0.283543i	$-0.0915098\pi$
$379$	2.27166	+	4.97424i	0.116687	+	0.255509i	−0.842272	+	0.539052i	$0.818783\pi$
$380$	−34.6168	+	21.5125i	−1.77581	+	1.10357i
$381$	1.94982	+	13.5613i	0.0998924	+	0.694767i
$382$	−22.3889	+	34.8378i	−1.14551	+	1.78246i
$383$	7.64969	+	26.0525i	0.390881	+	1.33122i	0.886520	+	0.462690i	$0.153116\pi$
$383$	7.64969	+	26.0525i	0.390881	+	1.33122i	−0.495639	+	0.868529i	$0.665066\pi$
$384$	0.791583	−	5.50558i	0.0403953	−	0.280955i
$385$	14.3752	−	21.6398i	0.732627	−	1.10287i
$386$	45.0287	−	28.9382i	2.29190	−	1.47291i
$387$	3.93584	−	3.41043i	0.200070	−	0.173362i
$388$	5.17473	−	17.6235i	0.262707	−	0.894697i
$389$	−11.0338	+	24.1607i	−0.559436	+	1.22499i	0.392798	+	0.919625i	$0.371507\pi$
$389$	−11.0338	+	24.1607i	−0.559436	+	1.22499i	−0.952234	+	0.305369i	$0.901220\pi$
$390$	−2.03530	+	0.261207i	−0.103061	+	0.0132267i
$391$	−20.7371	+	0.0670452i	−1.04872	+	0.00339062i
$392$			3.30296i			0.166825i
$393$	12.4415	+	5.68182i	0.627589	+	0.286610i
$394$	−22.1982	−	6.51797i	−1.11833	−	0.328371i
$395$	11.4680	−	12.8364i	0.577020	−	0.645869i
$396$	6.68756	−	4.29784i	0.336063	−	0.215974i
$397$	−1.66782	−	1.44517i	−0.0837054	−	0.0725312i	0.612003	−	0.790855i	$-0.290364\pi$
$397$	−1.66782	−	1.44517i	−0.0837054	−	0.0725312i	−0.695709	+	0.718324i	$0.744909\pi$
$398$	−33.2976	−	4.78748i	−1.66906	−	0.239975i
$399$	−25.5599	+	7.50507i	−1.27960	+	0.375723i
$400$	15.2463	+	4.98347i	0.762315	+	0.249173i
$401$	−0.254709	−	1.77154i	−0.0127196	−	0.0884666i	0.982473	−	0.186406i	$-0.0596840\pi$
$401$	−0.254709	−	1.77154i	−0.0127196	−	0.0884666i	−0.995192	+	0.0979394i	$0.968775\pi$
$402$	11.1669	−	5.09976i	0.556956	−	0.254353i
$403$	−0.686595	+	0.313558i	−0.0342017	+	0.0156194i
$404$	−4.19010	−	29.1428i	−0.208465	−	1.44991i
$405$	0.959621	−	2.01968i	0.0476840	−	0.100359i
$406$	−59.0601	+	17.3416i	−2.93110	+	0.860649i
$407$	18.6581	+	2.68263i	0.924849	+	0.132973i
$408$	2.30511	+	1.99739i	0.114120	+	0.0988856i
$409$	30.4706	−	19.5822i	1.50667	−	0.968280i	0.512710	−	0.858562i	$-0.328642\pi$
$409$	30.4706	−	19.5822i	1.50667	−	0.968280i	0.993963	−	0.109718i	$-0.0349947\pi$
$410$	39.7144	+	35.4809i	1.96136	+	1.75228i
$411$	−18.4002	−	5.40280i	−0.907617	−	0.266500i
$412$	7.97417	+	3.64168i	0.392859	+	0.179413i
$413$		−	34.0577i		−	1.67587i
$414$	9.59385	+	2.78335i	0.471512	+	0.136794i
$415$	−23.0076	+	2.95276i	−1.12940	+	0.144945i
$416$	1.48115	−	3.24326i	0.0726193	−	0.159014i
$417$	0.257387	−	0.876579i	0.0126043	−	0.0429263i
$418$	41.7043	−	36.1370i	2.03982	−	1.76752i
$419$	8.08772	−	5.19766i	0.395111	−	0.253922i	−0.327966	−	0.944689i	$-0.606363\pi$
$419$	8.08772	−	5.19766i	0.395111	−	0.253922i	0.723077	+	0.690767i	$0.242727\pi$
$420$	−14.8882	−	9.89014i	−0.726471	−	0.482589i
$421$	3.47769	−	24.1879i	0.169492	−	1.17885i	−0.710444	−	0.703754i	$-0.751506\pi$
$421$	3.47769	−	24.1879i	0.169492	−	1.17885i	0.879936	−	0.475092i	$-0.157585\pi$
$422$	3.32868	+	11.3364i	0.162038	+	0.551850i
$423$	1.29123	−	2.00920i	0.0627819	−	0.0976905i
$424$	0.0125403	+	0.0872196i	0.000609010	+	0.00423576i
$425$	−16.7610	+	13.6563i	−0.813029	+	0.662430i
$426$	0.555333	+	1.21601i	0.0269060	+	0.0589159i
$427$	25.2604	−	3.63189i	1.22244	−	0.175760i
$428$	−0.636581	+	0.990539i	−0.0307703	+	0.0478795i
$429$	1.43691	−	0.421916i	0.0693748	−	0.0203703i
$430$	24.2534	+	0.367679i	1.16960	+	0.0177310i
$431$	−10.1024	+	11.6588i	−0.486615	+	0.561584i	−0.944958	−	0.327191i	$-0.893898\pi$
$431$	−10.1024	+	11.6588i	−0.486615	+	0.561584i	0.458343	+	0.888776i	$0.348443\pi$
$432$	1.73439	+	2.69876i	0.0834457	+	0.129844i
$433$	1.71929	−	1.48977i	0.0826236	−	0.0715937i	−0.612570	−	0.790416i	$-0.709864\pi$
$433$	1.71929	−	1.48977i	0.0826236	−	0.0715937i	0.695193	+	0.718823i	$0.255319\pi$
$434$	−11.7033	−	3.43640i	−0.561777	−	0.164953i
$435$	5.72720	−	18.4649i	0.274598	−	0.885323i
$436$	11.3693			0.544491
$437$	37.0143	+	5.19977i	1.77064	+	0.248739i
$438$		−	13.4501i		−	0.642669i
$439$	1.48269	−	3.24664i	0.0707649	−	0.154954i	−0.870944	−	0.491382i	$-0.836492\pi$
$439$	1.48269	−	3.24664i	0.0707649	−	0.154954i	0.941709	+	0.336429i	$0.109219\pi$
$440$	5.29477	+	0.843380i	0.252418	+	0.0402066i
$441$	−3.06638	−	3.53879i	−0.146018	−	0.168514i
$442$	2.14529	+	3.33814i	0.102041	+	0.158779i
$443$	12.1905	+	10.5631i	0.579186	+	0.501868i	0.894469	−	0.447130i	$-0.147554\pi$
$443$	12.1905	+	10.5631i	0.579186	+	0.501868i	−0.315283	+	0.948998i	$0.602099\pi$
$444$	1.84565	−	12.8368i	0.0875909	−	0.609208i
$445$	−15.7977	−	36.0276i	−0.748882	−	1.70787i
$446$	−15.2532	−	9.80264i	−0.722260	−	0.464168i
$447$	−5.89558	+	0.847656i	−0.278851	+	0.0400928i
$448$	32.4620	−	14.8249i	1.53368	−	0.700410i
$449$	3.84086	+	8.41031i	0.181261	+	0.396907i	0.978351	−	0.206954i	$-0.0663552\pi$
$449$	3.84086	+	8.41031i	0.181261	+	0.396907i	−0.797089	+	0.603862i	$0.793628\pi$
$450$	9.60035	−	4.03727i	0.452565	−	0.190319i
$451$	−32.6967	−	21.0129i	−1.53963	−	0.989458i
$452$	−6.19935	−	21.1131i	−0.291593	−	0.993074i
$453$	−7.78890	−	1.11988i	−0.365955	−	0.0526163i
$454$	28.9498	−	33.4099i	1.35868	−	1.56800i
$455$	−2.16620	−	2.57787i	−0.101553	−	0.120852i
$456$	−3.60019	−	4.15484i	−0.168594	−	0.194568i
$457$	7.14028	−	24.3175i	0.334008	−	1.13753i	−0.605741	−	0.795662i	$-0.707123\pi$
$457$	7.14028	−	24.3175i	0.334008	−	1.13753i	0.939749	−	0.341865i	$-0.111059\pi$
$458$	1.94986	+	0.890472i	0.0911111	+	0.0416090i
$459$	−4.32402			−0.201828
$460$	13.3063	+	21.2582i	0.620409	+	0.991167i
$461$	−32.7564			−1.52562			−0.762810	−	0.646623i	$-0.776181\pi$
$461$	−32.7564			−1.52562			−0.762810	+	0.646623i	$0.776181\pi$
$462$	22.0134	+	10.0532i	1.02415	+	0.467716i
$463$	−8.21856	+	27.9898i	−0.381949	+	1.30080i	0.514439	+	0.857527i	$0.328000\pi$
$463$	−8.21856	+	27.9898i	−0.381949	+	1.30080i	−0.896388	+	0.443271i	$0.853818\pi$
$464$	18.1632	+	20.9615i	0.843207	+	0.973112i
$465$	2.93294	−	2.46457i	0.136012	−	0.114292i
$466$	9.03881	−	10.4313i	0.418715	−	0.483223i
$467$	14.1171	+	2.02973i	0.653260	+	0.0939246i	0.460973	−	0.887414i	$-0.347500\pi$
$467$	14.1171	+	2.02973i	0.653260	+	0.0939246i	0.192287	+	0.981339i	$0.438410\pi$
$468$	−0.290278	−	0.988598i	−0.0134181	−	0.0456979i
$469$	16.9467	+	10.8910i	0.782526	+	0.502899i
$470$	10.7196	−	2.97182i	0.494458	−	0.137080i
$471$	2.76895	+	6.06316i	0.127587	+	0.279376i
$472$	6.39352	−	2.91982i	0.294286	−	0.134396i
$473$	−17.5224	+	2.51934i	−0.805679	+	0.115839i
$474$	13.4889	+	8.66879i	0.619566	+	0.398171i
$475$	33.4064	−	20.0648i	1.53279	−	0.920638i
$476$	−4.91892	+	34.2119i	−0.225459	+	1.56810i
$477$	−0.0944078	−	0.0818048i	−0.00432264	−	0.00374559i
$478$	15.6633	+	24.3725i	0.716422	+	1.11477i
$479$	−11.1682	−	12.8888i	−0.510290	−	0.588906i	0.440883	−	0.897564i	$-0.354665\pi$
$479$	−11.1682	−	12.8888i	−0.510290	−	0.588906i	−0.951173	+	0.308659i	$0.900120\pi$
$480$	−2.84658	+	17.8710i	−0.129928	+	0.815694i
$481$	1.01492	−	2.22236i	0.0462762	−	0.101331i
$482$			39.5191i			1.80004i
$483$	4.66898	+	15.7130i	0.212446	+	0.714966i
$484$	−1.29683			−0.0589467
$485$	−5.20260	+	16.7735i	−0.236238	+	0.761647i
$486$	1.99857	+	0.586833i	0.0906569	+	0.0266193i
$487$	−4.09636	+	3.54951i	−0.185624	+	0.160844i	−0.742716	−	0.669607i	$-0.766463\pi$
$487$	−4.09636	+	3.54951i	−0.185624	+	0.160844i	0.557092	+	0.830451i	$0.311917\pi$
$488$	2.84742	+	4.43067i	0.128897	+	0.200567i
$489$	8.37502	−	9.66529i	0.378732	−	0.437079i
$490$	0.330587	−	21.8067i	0.0149344	−	0.985124i
$491$	38.1190	−	11.1928i	1.72029	−	0.505122i	0.735299	−	0.677743i	$-0.237042\pi$
$491$	38.1190	−	11.1928i	1.72029	−	0.505122i	0.984988	+	0.172621i	$0.0552235\pi$
$492$	−14.4569	+	22.4954i	−0.651767	+	1.01417i
$493$	−37.0042	+	5.32040i	−1.66659	+	0.239619i
$494$	−2.97113	−	6.50587i	−0.133678	−	0.292713i
$495$	−6.45578	+	4.01192i	−0.290166	+	0.180322i
$496$	0.782185	+	5.44022i	0.0351211	+	0.244273i
$497$	−1.18596	+	1.84539i	−0.0531977	+	0.0827772i
$498$	−6.08761	−	20.7325i	−0.272793	−	0.929046i
$499$	−4.30158	+	29.9182i	−0.192565	+	1.33932i	0.632621	+	0.774461i	$0.281979\pi$
$499$	−4.30158	+	29.9182i	−0.192565	+	1.33932i	−0.825187	+	0.564860i	$0.808930\pi$
$500$	24.7269	+	8.49932i	1.10582	+	0.380101i
$501$	2.93655	−	1.88720i	0.131195	−	0.0843141i
$502$	7.70185	−	6.67369i	0.343750	−	0.297861i
$503$	−11.4095	+	38.8570i	−0.508722	+	1.73255i	0.158186	+	0.987409i	$0.449435\pi$
$503$	−11.4095	+	38.8570i	−0.508722	+	1.73255i	−0.666909	+	0.745140i	$0.732383\pi$
$504$	1.00156	−	2.19311i	0.0446130	−	0.0976889i
$505$	3.58348	+	27.9220i	0.159463	+	1.24251i
$506$	−22.3193	−	25.5902i	−0.992215	−	1.13763i
$507$			12.8059i			0.568730i
$508$	−29.1458	−	13.3104i	−1.29313	−	0.590554i
$509$	−1.69586	−	0.497949i	−0.0751676	−	0.0220712i	0.243933	−	0.969792i	$-0.421562\pi$
$509$	−1.69586	−	0.497949i	−0.0751676	−	0.0220712i	−0.319100	+	0.947721i	$0.603381\pi$
$510$	−15.0188	−	13.4178i	−0.665043	−	0.594150i
$511$	18.5670	−	11.9323i	0.821356	−	0.527853i
$512$	−23.0412	−	19.9654i	−1.01829	−	0.882352i
$513$	7.71448	+	1.10917i	0.340603	+	0.0489713i
$514$	−3.92607	+	1.15280i	−0.173171	+	0.0508477i
$515$	−7.57074	−	3.59712i	−0.333607	−	0.158508i
$516$	1.73331	+	12.0554i	0.0763045	+	0.530709i
$517$	−7.38477	+	3.37251i	−0.324782	+	0.148323i
$518$	35.9125	−	16.4007i	1.57791	−	0.720605i
$519$	−1.68266	−	11.7031i	−0.0738605	−	0.513711i
$520$	0.298222	−	0.627658i	0.0130779	−	0.0275246i
$521$	−4.91738	+	1.44387i	−0.215434	+	0.0632572i	−0.387669	−	0.921799i	$-0.626720\pi$
$521$	−4.91738	+	1.44387i	−0.215434	+	0.0632572i	0.172234	+	0.985056i	$0.444901\pi$
$522$	17.8255	+	2.56292i	0.780200	+	0.112176i
$523$	−11.7051	−	10.1425i	−0.511828	−	0.443501i	0.360259	−	0.932852i	$-0.382688\pi$
$523$	−11.7051	−	10.1425i	−0.511828	−	0.443501i	−0.872087	+	0.489351i	$0.837234\pi$
$524$	−26.9090	+	17.2934i	−1.17552	+	0.755464i
$525$	14.0902	+	9.67102i	0.614947	+	0.422078i
$526$	38.4548	+	11.2914i	1.67671	+	0.492327i
$527$	−6.73869	−	3.07746i	−0.293542	−	0.134056i
$528$		−	10.9047i		−	0.474565i
$529$	3.12597	−	22.7866i	0.135912	−	0.990721i
$530$	−0.0740632	−	0.577092i	−0.00321710	−	0.0250673i
$531$	−4.13933	+	9.06386i	−0.179631	+	0.393338i
$532$	17.5517	−	59.7757i	0.760963	−	2.59160i
$533$	−3.80708	+	3.29885i	−0.164903	+	0.142889i
$534$	30.8277	−	19.8118i	1.33405	−	0.857340i
$535$	0.622945	−	0.937756i	0.0269322	−	0.0405427i
$536$	−0.591654	+	4.11504i	−0.0255556	+	0.177743i
$537$	2.23358	+	7.60688i	0.0963862	+	0.328261i
$538$	28.1495	−	43.8014i	1.21361	−	1.88841i
$539$	2.26518	+	15.7547i	0.0975683	+	0.678602i
$540$	2.76021	+	4.44158i	0.118780	+	0.191135i
$541$	12.0486	+	26.3827i	0.518009	+	1.13428i	0.970188	+	0.242353i	$0.0779194\pi$
$541$	12.0486	+	26.3827i	0.518009	+	1.13428i	−0.452179	+	0.891927i	$0.649353\pi$
$542$	26.1285	−	3.75671i	1.12231	−	0.161364i
$543$	6.94501	−	10.8066i	0.298039	−	0.463757i
$544$	33.5763	−	9.85889i	1.43957	−	0.422696i
$545$	−10.8694	−	0.164778i	−0.465592	−	0.00705833i
$546$	2.05403	−	2.37048i	0.0879043	−	0.101447i
$547$	18.2902	+	28.4601i	0.782032	+	1.21687i	0.971978	+	0.235071i	$0.0755323\pi$
$547$	18.2902	+	28.4601i	0.782032	+	1.21687i	−0.189946	+	0.981795i	$0.560831\pi$
$548$	33.8942	−	29.3695i	1.44789	−	1.25460i
$549$	−7.16403	−	2.10355i	−0.305753	−	0.0897772i
$550$	−34.8725	−	6.09806i	−1.48697	−	0.260022i
$551$	67.3840			2.87066
$552$	−2.54946	+	2.22359i	−0.108512	+	0.0946423i
$553$			26.3112i			1.11887i
$554$	−6.88208	+	15.0696i	−0.292391	+	0.640248i
$555$	−1.95054	+	12.2456i	−0.0827959	+	0.519796i
$556$	1.39915	+	1.61470i	0.0593371	+	0.0684786i
$557$	−12.4044	−	19.3016i	−0.525590	−	0.817834i	0.472388	−	0.881391i	$-0.343392\pi$
$557$	−12.4044	−	19.3016i	−0.525590	−	0.817834i	−0.997978	+	0.0635563i	$0.979756\pi$
$558$	2.69698	+	2.33695i	0.114172	+	0.0989308i
$559$	−0.326530	+	2.27106i	−0.0138107	+	0.0960558i
$560$	−22.4544	+	9.84602i	−0.948872	+	0.416070i
$561$	12.3649	+	7.94643i	0.522046	+	0.335498i
$562$	−29.4691	+	4.23701i	−1.24308	+	0.178728i
$563$	14.5422	−	6.64122i	0.612882	−	0.279894i	−0.0846912	−	0.996407i	$-0.526990\pi$
$563$	14.5422	−	6.64122i	0.612882	−	0.279894i	0.697573	+	0.716513i	$0.254263\pi$
$564$	2.32029	+	5.08073i	0.0977019	+	0.213937i
$565$	5.62075	+	20.2745i	0.236467	+	0.852954i
$566$	−1.65425	−	1.06312i	−0.0695335	−	0.0446865i
$567$	0.962952	+	3.27951i	0.0404402	+	0.137727i
$568$	−0.448103	−	0.0644275i	−0.0188020	−	0.00270332i
$569$	19.9122	−	22.9799i	0.834762	−	0.963367i	−0.164975	−	0.986298i	$-0.552754\pi$
$569$	19.9122	−	22.9799i	0.834762	−	0.963367i	0.999737	+	0.0229311i	$0.00729985\pi$
$570$	23.3532	+	27.7912i	0.978156	+	1.16405i
$571$	−7.20782	−	8.31827i	−0.301638	−	0.348109i	0.584615	−	0.811311i	$-0.301246\pi$
$571$	−7.20782	−	8.31827i	−0.301638	−	0.348109i	−0.886253	+	0.463202i	$0.846700\pi$
$572$	−0.986713	+	3.36044i	−0.0412565	+	0.140507i
$573$	18.0847	+	8.25902i	0.755500	+	0.345025i
$574$	−81.4040			−3.39774
$575$	−12.4131	−	20.5162i	−0.517660	−	0.855586i
$576$	−10.4410			−0.435041
$577$	20.9022	+	9.54573i	0.870171	+	0.397394i	0.799900	−	0.600134i	$-0.204886\pi$
$577$	20.9022	+	9.54573i	0.870171	+	0.397394i	0.0702719	+	0.997528i	$0.477613\pi$
$578$	−0.995918	+	3.39178i	−0.0414247	+	0.141080i
$579$	−16.8281	−	19.4206i	−0.699350	−	0.807093i
$580$	29.0865	+	34.6141i	1.20775	+	1.43727i
$581$	23.2193	−	26.7965i	0.963300	−	1.11171i
$582$	−16.1927	−	2.32816i	−0.671209	−	0.0965053i
$583$	0.119631	+	0.407425i	0.00495460	+	0.0168738i
$584$	3.83178	+	2.46254i	0.158560	+	0.101901i
$585$	0.263186	+	0.949333i	0.0108814	+	0.0392501i
$586$	−4.44203	−	9.72670i	−0.183499	−	0.401806i
$587$	11.9139	−	5.44089i	0.491738	−	0.224569i	−0.154083	−	0.988058i	$-0.549242\pi$
$587$	11.9139	−	5.44089i	0.491738	−	0.224569i	0.645821	+	0.763488i	$0.276515\pi$
$588$	10.8392	−	1.55845i	0.447003	−	0.0642693i
$589$	11.2331	+	7.21906i	0.462851	+	0.297456i
$590$	−42.5032	+	18.6372i	−1.74983	+	0.767281i
$591$	−1.58070	+	10.9940i	−0.0650212	+	0.452232i
$592$	−13.4447	−	11.6499i	−0.552572	−	0.478807i
$593$	14.2654	+	22.1973i	0.585808	+	0.911535i	0.999999	+	0.00134514i	$0.000428173\pi$
$593$	14.2654	+	22.1973i	0.585808	+	0.911535i	−0.414191	+	0.910190i	$0.635935\pi$
$594$	−4.63663	−	5.35095i	−0.190243	−	0.219552i
$595$	5.19846	−	32.6362i	0.213116	−	1.33795i
$596$	5.78651	−	12.6707i	0.237025	−	0.519012i
$597$			16.1503i			0.660986i
$598$	−3.99738	+	1.84119i	−0.163465	+	0.0752917i
$599$	−44.4449			−1.81597			−0.907984	−	0.419005i	$-0.862379\pi$
$599$	−44.4449			−1.81597			−0.907984	+	0.419005i	$0.862379\pi$
$600$	−0.607527	+	3.47421i	−0.0248022	+	0.141834i
$601$	8.79088	+	2.58124i	0.358588	+	0.105291i	0.456064	−	0.889947i	$-0.349259\pi$
$601$	8.79088	+	2.58124i	0.358588	+	0.105291i	−0.0974763	+	0.995238i	$0.531077\pi$
$602$	−28.0209	+	24.2803i	−1.14205	+	0.989590i
$603$	−3.18639	−	4.95812i	−0.129760	−	0.201910i
$604$	12.0513	−	13.9079i	0.490360	−	0.565906i
$605$	1.23980	+	0.0187953i	0.0504051	+	0.000764136i
$606$	−25.1610	+	7.38795i	−1.02210	+	0.300115i
$607$	2.76325	−	4.29971i	0.112157	−	0.174520i	−0.780637	−	0.624984i	$-0.785105\pi$
$607$	2.76325	−	4.29971i	0.112157	−	0.174520i	0.892794	+	0.450465i	$0.148742\pi$
$608$	−62.4324	+	8.97643i	−2.53197	+	0.364042i
$609$	12.2760	+	26.8807i	0.497449	+	1.08926i
$610$	−18.3556	−	29.5369i	−0.743197	−	1.19592i
$611$	0.149747	+	1.04151i	0.00605812	+	0.0421351i
$612$	5.46715	−	8.50705i	0.220996	−	0.343877i
$613$	11.9731	+	40.7768i	0.483591	+	1.64696i	0.734247	+	0.678882i	$0.237535\pi$
$613$	11.9731	+	40.7768i	0.483591	+	1.64696i	−0.250656	+	0.968076i	$0.580646\pi$
$614$	−2.84788	+	19.8074i	−0.114931	+	0.799362i
$615$	14.1472	−	21.2966i	0.570470	−	0.858763i
$616$	−6.89442	+	4.43077i	−0.277784	+	0.178521i
$617$	29.1682	−	25.2744i	1.17427	−	1.01751i	0.174809	−	0.984602i	$-0.444069\pi$
$617$	29.1682	−	25.2744i	1.17427	−	1.01751i	0.999458	−	0.0329059i	$-0.0104762\pi$
$618$	2.19973	−	7.49159i	0.0884860	−	0.301356i
$619$	−19.5414	+	42.7897i	−0.785435	+	1.71986i	−0.0961573	+	0.995366i	$0.530655\pi$
$619$	−19.5414	+	42.7897i	−0.785435	+	1.71986i	−0.689278	+	0.724497i	$0.742072\pi$
$620$	1.14047	+	8.88638i	0.0458022	+	0.356886i
$621$	0.667167	−	4.74920i	0.0267725	−	0.190579i
$622$		−	18.5669i		−	0.744466i
$623$	54.6979	+	24.9797i	2.19143	+	1.00079i
$624$	−1.35610	−	0.398187i	−0.0542874	−	0.0159402i
$625$	−23.5164	−	8.48395i	−0.940657	−	0.339358i
$626$	−21.1533	+	13.5944i	−0.845455	+	0.543341i
$627$	−20.0218	−	17.3490i	−0.799595	−	0.692853i
$628$	−15.4296	−	2.21844i	−0.615709	−	0.0885256i
$629$	23.0072	−	6.75553i	0.917358	−	0.269361i
$630$	−6.83195	+	14.3790i	−0.272191	+	0.572873i
$631$	5.12616	+	35.6532i	0.204069	+	1.41933i	0.792049	+	0.610457i	$0.209014\pi$
$631$	5.12616	+	35.6532i	0.204069	+	1.41933i	−0.587980	+	0.808875i	$0.700077\pi$
$632$	−4.93930	+	2.25570i	−0.196475	+	0.0897270i
$633$	5.15969	−	2.35635i	0.205079	−	0.0936566i
$634$	−1.03337	−	7.18727i	−0.0410405	−	0.285443i
$635$	27.6712	+	13.1475i	1.09810	+	0.521744i
$636$	0.280309	−	0.0823061i	0.0111150	−	0.00326365i
$637$	2.04196	+	0.293589i	0.0809052	+	0.0116324i
$638$	−46.2635	−	40.0875i	−1.83159	−	1.58708i
$639$	0.539910	−	0.346979i	0.0213585	−	0.0137263i
$640$	−9.27505	−	8.28634i	−0.366629	−	0.327546i
$641$	22.4272	+	6.58523i	0.885823	+	0.260101i	0.692832	−	0.721100i	$-0.256363\pi$
$641$	22.4272	+	6.58523i	0.885823	+	0.260101i	0.192991	+	0.981201i	$0.438181\pi$
$642$	0.953944	+	0.435652i	0.0376492	+	0.0171938i
$643$		−	25.5286i		−	1.00675i	−0.864068	−	0.503375i	$-0.832092\pi$
$643$		−	25.5286i		−	1.00675i	0.864068	−	0.503375i	$-0.167908\pi$
$644$	−36.8170	−	10.6813i	−1.45079	−	0.420901i
$645$	−1.48236	−	11.5504i	−0.0583680	−	0.454797i
$646$	29.1606	−	63.8528i	1.14731	−	2.51225i
$647$	−9.52027	+	32.4231i	−0.374280	+	1.27468i	0.530093	+	0.847940i	$0.322157\pi$
$647$	−9.52027	+	32.4231i	−0.374280	+	1.27468i	−0.904373	+	0.426742i	$0.859661\pi$
$648$	−0.533095	+	0.461930i	−0.0209420	+	0.0181463i
$649$	28.4938	−	18.3118i	1.11848	−	0.718803i
$650$	−2.03173	+	4.11405i	−0.0796909	+	0.161366i
$651$	−0.833374	+	5.79625i	−0.0326625	+	0.227173i
$652$	8.42634	+	28.6975i	0.330001	+	1.12388i
$653$	20.7259	−	32.2502i	0.811068	−	1.26205i	−0.150809	−	0.988563i	$-0.548188\pi$
$653$	20.7259	−	32.2502i	0.811068	−	1.26205i	0.961877	−	0.273483i	$-0.0881758\pi$
$654$	−1.44111	−	10.0231i	−0.0563518	−	0.391935i
$655$	25.9764	−	16.1429i	1.01498	−	0.630756i
$656$	15.2377	+	33.3660i	0.594933	+	1.30272i
$657$	−6.39152	+	0.918961i	−0.249357	+	0.0358521i
$658$	−9.19283	+	14.3043i	−0.358374	+	0.557641i
$659$	15.3588	−	4.50975i	0.598294	−	0.175675i	0.0314572	−	0.999505i	$-0.489985\pi$
$659$	15.3588	−	4.50975i	0.598294	−	0.175675i	0.566837	+	0.823830i	$0.308167\pi$
$660$	0.269446	−	17.7736i	0.0104882	−	0.691838i
$661$	−19.5755	+	22.5914i	−0.761400	+	0.878703i	−0.995621	−	0.0934806i	$-0.970201\pi$
$661$	−19.5755	+	22.5914i	−0.761400	+	0.878703i	0.234221	+	0.972183i	$0.424746\pi$
$662$	−9.53996	−	14.8445i	−0.370781	−	0.576947i
$663$	1.43972	−	1.24752i	0.0559141	−	0.0484498i
$664$	7.02104	+	2.06156i	0.272469	+	0.0800042i
$665$	−17.6463	+	56.8927i	−0.684292	+	2.20621i
$666$	−11.5508			−0.447585
$667$	−0.134056	−	41.4638i	−0.00519069	−	1.60548i
$668$			8.16348i			0.315854i
$669$	−3.61609	+	7.91813i	−0.139806	+	0.306132i
$670$	4.31805	−	27.1089i	0.166821	−	1.04731i
$671$	16.6204	+	19.1809i	0.641622	+	0.740471i
$672$	−14.9548	−	23.2701i	−0.576893	−	0.897664i
$673$	34.7232	+	30.0879i	1.33848	+	1.15980i	0.973474	+	0.228798i	$0.0734794\pi$
$673$	34.7232	+	30.0879i	1.33848	+	1.15980i	0.365009	+	0.931004i	$0.381066\pi$
$674$	−2.97135	+	20.6662i	−0.114452	+	0.796032i
$675$	−2.57446	−	4.28628i	−0.0990909	−	0.164979i
$676$	−25.1943	−	16.1914i	−0.969011	−	0.622746i
$677$	−12.2330	+	1.75883i	−0.470151	+	0.0675975i	−0.373319	−	0.927703i	$-0.621780\pi$
$677$	−12.2330	+	1.75883i	−0.470151	+	0.0675975i	−0.0968324	+	0.995301i	$0.530871\pi$
$678$	−17.8274	+	8.14149i	−0.684656	+	0.312672i
$679$	−11.1515	−	24.4185i	−0.427957	−	0.937095i
$680$	6.57234	−	1.82207i	0.252038	−	0.0698731i
$681$	−17.8545	−	11.4744i	−0.684185	−	0.439699i
$682$	−3.41753	−	11.6390i	−0.130864	−	0.445682i
$683$	6.21391	+	0.893425i	0.237769	+	0.0341860i	0.260169	−	0.965563i	$-0.416222\pi$
$683$	6.21391	+	0.893425i	0.237769	+	0.0341860i	−0.0224004	+	0.999749i	$0.507131\pi$
$684$	−11.9361	+	13.7750i	−0.456390	+	0.526702i
$685$	−32.8294	+	27.5867i	−1.25435	+	1.05404i
$686$	−10.8048	−	12.4694i	−0.412528	−	0.476083i
$687$	0.289933	−	0.987422i	0.0110616	−	0.0376725i
$688$	15.1972	+	6.94031i	0.579386	+	0.264597i
$689$	0.0550355			0.00209669
$690$	17.0545	−	14.4253i	0.649253	−	0.549162i
$691$	−2.24407			−0.0853684			−0.0426842	−	0.999089i	$-0.513591\pi$
$691$	−2.24407			−0.0853684			−0.0426842	+	0.999089i	$0.513591\pi$
$692$	25.1522	+	11.4866i	0.956144	+	0.436656i
$693$	3.27326	−	11.1477i	0.124341	−	0.423466i
$694$	−7.44579	−	8.59290i	−0.282638	−	0.326182i
$695$	−1.31422	−	1.56398i	−0.0498512	−	0.0593250i
$696$	−3.99377	+	4.60906i	−0.151383	+	0.174706i
$697$	−48.9379	−	7.03620i	−1.85365	−	0.266515i
$698$	−20.4746	−	69.7302i	−0.774976	−	2.63933i
$699$	−5.57458	−	3.58256i	−0.210850	−	0.135505i
$700$	−36.8419	+	15.4933i	−1.39249	+	0.585591i
$701$	−14.6406	−	32.0584i	−0.552968	−	1.21083i	−0.955382	−	0.295373i	$-0.904556\pi$
$701$	−14.6406	−	32.0584i	−0.552968	−	1.21083i	0.402415	−	0.915458i	$-0.368171\pi$
$702$	−0.834749	+	0.381217i	−0.0315056	+	0.0143881i
$703$	−42.7801	+	6.15085i	−1.61348	+	0.231984i
$704$	29.8569	+	19.1879i	1.12527	+	0.723169i
$705$	−2.14463	−	4.89094i	−0.0807713	−	0.184204i
$706$	−0.644290	+	4.48114i	−0.0242482	+	0.168650i
$707$	−32.5203	−	28.1790i	−1.22305	−	1.05978i
$708$	−12.5986	−	19.6038i	−0.473483	−	0.736754i
$709$	11.2766	+	13.0139i	0.423501	+	0.488746i	0.926900	−	0.375308i	$-0.122463\pi$
$709$	11.2766	+	13.0139i	0.423501	+	0.488746i	−0.503400	+	0.864054i	$0.667918\pi$
$710$	2.95200	+	0.470210i	0.110786	+	0.0176467i
$711$	3.19783	−	7.00226i	0.119928	−	0.262605i
$712$			12.4098i			0.465077i
$713$	4.41980	−	6.92648i	0.165523	−	0.259399i
$714$	30.7845			1.15208
$715$	0.992028	−	3.19837i	0.0370997	−	0.119612i
$716$	−17.7898	−	5.22356i	−0.664837	−	0.195214i
$717$	10.5117	−	9.10847i	0.392568	−	0.340162i
$718$	10.4571	+	16.2715i	0.390254	+	0.607247i
$719$	−11.2979	+	13.0385i	−0.421341	+	0.486254i	−0.926245	−	0.376922i	$-0.876983\pi$
$719$	−11.2979	+	13.0385i	−0.421341	+	0.486254i	0.504904	+	0.863176i	$0.331528\pi$
$720$	7.17252	+	0.108735i	0.267304	+	0.00405230i
$721$	12.2932	−	3.60960i	0.457822	−	0.134429i
$722$	−47.0083	+	73.1464i	−1.74947	+	2.72223i
$723$	18.7796	−	2.70010i	0.698421	−	0.100418i
$724$	12.4799	+	27.3272i	0.463812	+	1.01561i
$725$	−27.3058	−	33.5136i	−1.01411	−	1.24466i
$726$	0.164378	+	1.14328i	0.00610065	+	0.0424310i
$727$	−23.2901	+	36.2401i	−0.863781	+	1.34407i	0.0741491	+	0.997247i	$0.476376\pi$
$727$	−23.2901	+	36.2401i	−0.863781	+	1.34407i	−0.937931	+	0.346823i	$0.887260\pi$
$728$	0.299257	+	1.01918i	0.0110912	+	0.0377732i
$729$	0.142315	−	0.989821i	0.00527092	−	0.0366601i
$730$	−25.0515	−	16.6416i	−0.927199	−	0.615932i
$731$	−18.9441	+	12.1746i	−0.700673	+	0.450295i
$732$	13.1965	−	11.4348i	0.487756	−	0.422643i
$733$	−12.8991	+	43.9302i	−0.476438	+	1.62260i	0.274050	+	0.961715i	$0.411637\pi$
$733$	−12.8991	+	43.9302i	−0.476438	+	1.62260i	−0.750488	+	0.660884i	$0.770182\pi$
$734$	13.6404	−	29.8683i	0.503476	−	1.10246i
$735$	−10.3852	+	1.33282i	−0.383063	+	0.0491618i
$736$	5.64772	+	38.3990i	0.208178	+	1.41541i
$737$			20.0339i			0.737960i
$738$	21.6643	+	9.89374i	0.797473	+	0.364194i
$739$	−24.0006	−	7.04722i	−0.882877	−	0.259236i	−0.191294	−	0.981533i	$-0.561268\pi$
$739$	−24.0006	−	7.04722i	−0.882877	−	0.259236i	−0.691583	+	0.722297i	$0.743087\pi$
$740$	−21.6257	−	19.3204i	−0.794977	−	0.710233i
$741$	−2.88861	+	1.85640i	−0.106116	+	0.0681965i
$742$	0.672129	+	0.582403i	0.0246746	+	0.0213807i
$743$	−40.2143	−	5.78195i	−1.47532	−	0.212119i	−0.642766	−	0.766062i	$-0.722213\pi$
$743$	−40.2143	−	5.78195i	−1.47532	−	0.212119i	−0.832554	+	0.553943i	$0.813122\pi$
$744$	−1.15955	+	0.340476i	−0.0425113	+	0.0124825i
$745$	−5.71570	+	12.0297i	−0.209407	+	0.440733i
$746$	−7.13706	−	49.6394i	−0.261306	−	1.81743i
$747$	−9.43623	+	4.30938i	−0.345254	+	0.157672i
$748$	−31.2676	+	14.2794i	−1.14326	+	0.522107i
$749$	0.244905	+	1.70335i	0.00894864	+	0.0622391i
$750$	4.35871	−	22.8765i	0.159158	−	0.835330i
$751$	7.59640	−	2.23050i	0.277196	−	0.0813922i	−0.140180	−	0.990126i	$-0.544768\pi$
$751$	7.59640	−	2.23050i	0.277196	−	0.0813922i	0.417376	+	0.908734i	$0.362950\pi$
$752$	7.58384	+	1.09039i	0.276554	+	0.0397625i
$753$	−3.69758	−	3.20397i	−0.134747	−	0.116759i
$754$	−6.67458	+	4.28949i	−0.243074	+	0.156214i
$755$	−11.7229	+	13.1217i	−0.426641	+	0.477547i
$756$	−7.66963	−	2.25201i	−0.278942	−	0.0819047i
$757$	16.5328	+	7.55028i	0.600895	+	0.274419i	0.692548	−	0.721372i	$-0.256488\pi$
$757$	16.5328	+	7.55028i	0.600895	+	0.274419i	−0.0916535	+	0.995791i	$0.529215\pi$
$758$			11.3904i			0.413717i
$759$	−10.6356	+	12.3547i	−0.386049	+	0.448445i
$760$	−12.1931	+	1.56485i	−0.442290	+	0.0567630i
$761$	0.600751	−	1.31546i	0.0217772	−	0.0476855i	−0.898431	−	0.439115i	$-0.855292\pi$
$761$	0.600751	−	1.31546i	0.0217772	−	0.0476855i	0.920208	+	0.391430i	$0.128019\pi$
$762$	−8.04005	+	27.3819i	−0.291260	+	0.991942i
$763$	12.5578	−	10.8814i	0.454624	−	0.393934i
$764$	−39.1145	+	25.1374i	−1.41511	+	0.909439i
$765$	−5.35004	+	8.05373i	−0.193431	+	0.291183i
$766$	−8.04886	+	55.9811i	−0.290817	+	2.02268i
$767$	−1.23679	−	4.21213i	−0.0446580	−	0.152091i
$768$	−5.02593	+	7.82050i	−0.181358	+	0.282198i
$769$	−0.567290	−	3.94559i	−0.0204570	−	0.142281i	0.977033	−	0.213088i	$-0.0683520\pi$
$769$	−0.567290	−	3.94559i	−0.0204570	−	0.142281i	−0.997490	+	0.0708060i	$0.977443\pi$
$770$	45.9614	−	28.5626i	1.65634	−	1.02932i
$771$	0.816057	+	1.78692i	0.0293896	+	0.0643542i
$772$	59.4849	−	8.55264i	2.14091	−	0.307816i
$773$	−24.0005	+	37.3456i	−0.863240	+	1.34323i	0.0749794	+	0.997185i	$0.476111\pi$
$773$	−24.0005	+	37.3456i	−0.863240	+	1.34323i	−0.938219	+	0.346042i	$0.887525\pi$
$774$	10.4083	−	3.05615i	0.374118	−	0.109851i
$775$	−0.961524	−	8.51215i	−0.0345389	−	0.305765i
$776$	3.62795	−	4.18688i	0.130236	−	0.150300i
$777$	−10.2474	−	15.9452i	−0.367622	−	0.572031i
$778$	−41.8117	+	36.2301i	−1.49902	+	1.29891i
$779$	85.5052	+	25.1066i	3.06354	+	0.899537i
$780$	−2.20048	−	0.682516i	−0.0787898	−	0.0244380i
$781$	−2.18158			−0.0780629
$782$	−39.3489	−	17.8165i	−1.40711	−	0.637117i
$783$		−	8.64584i		−	0.308977i
$784$	6.24016	−	13.6640i	0.222863	−	0.488002i
$785$	14.7190	+	2.34452i	0.525343	+	0.0836794i
$786$	18.6566	+	21.5308i	0.665458	+	0.767979i
$787$	21.4666	+	33.4027i	0.765201	+	1.19068i	0.976974	+	0.213358i	$0.0684400\pi$
$787$	21.4666	+	33.4027i	0.765201	+	1.19068i	−0.211773	+	0.977319i	$0.567924\pi$
$788$	−19.6309	−	17.0103i	−0.699324	−	0.605967i
$789$	2.73831	−	19.0453i	0.0974863	−	0.678032i
$790$	32.8358	−	14.3981i	1.16824	−	0.512262i
$791$	−27.0545	−	17.3868i	−0.961946	−	0.618205i
$792$	2.37334	−	0.341235i	0.0843329	−	0.0121252i
$793$	2.99222	−	1.36650i	0.106257	−	0.0485259i
$794$	−1.90955	−	4.18133i	−0.0677673	−	0.148390i
$795$	−0.269176	+	0.0746243i	−0.00954668	+	0.00264665i
$796$	−31.7740	−	20.4199i	−1.12620	−	0.723763i
$797$	−0.786966	−	2.68016i	−0.0278758	−	0.0949362i	0.944380	−	0.328856i	$-0.106663\pi$
$797$	−0.786966	−	2.68016i	−0.0278758	−	0.0949362i	−0.972256	+	0.233920i	$0.924845\pi$
$798$	−54.9227	−	7.89669i	−1.94424	−	0.279540i
$799$	−6.76288	+	7.80478i	−0.239253	+	0.276113i
$800$	29.7637	+	27.4134i	1.05231	+	0.969210i
$801$	−11.5209	−	13.2958i	−0.407071	−	0.469785i
$802$	1.05029	−	3.57696i	0.0370870	−	0.126307i
$803$	19.9659	+	9.11812i	0.704581	+	0.321771i
$804$	13.7834			0.486102
$805$	35.0432	+	10.7452i	1.23511	+	0.378718i
$806$	−1.57222			−0.0553790
$807$	−22.7379	−	10.3840i	−0.800411	−	0.365535i
$808$	2.50192	−	8.52076i	0.0880173	−	0.299759i
$809$	2.71204	+	3.12987i	0.0953504	+	0.110040i	0.801419	−	0.598103i	$-0.204079\pi$
$809$	2.71204	+	3.12987i	0.0953504	+	0.110040i	−0.706069	+	0.708143i	$0.749533\pi$
$810$	3.56581	−	2.99637i	0.125290	−	0.105282i
$811$	5.89521	−	6.80343i	0.207009	−	0.238901i	−0.642746	−	0.766080i	$-0.722205\pi$
$811$	5.89521	−	6.80343i	0.207009	−	0.238901i	0.849754	+	0.527179i	$0.176750\pi$
$812$	−68.4064	−	9.83536i	−2.40059	−	0.345153i
$813$	−3.57040	−	12.1597i	−0.125219	−	0.426458i
$814$	33.0305	+	21.2274i	1.15772	+	0.744021i
$815$	−7.63989	−	27.5577i	−0.267614	−	0.965304i
$816$	−5.76244	−	12.6180i	−0.201726	−	0.441718i
$817$	36.9212	−	16.8613i	1.29171	−	0.589903i
$818$	74.6772	−	10.7370i	2.61103	−	0.375409i
$819$	−1.26680	−	0.814122i	−0.0442655	−	0.0284477i
$820$	24.0116	+	54.7600i	0.838523	+	1.91230i
$821$	3.28899	−	22.8754i	0.114787	−	0.798359i	−0.848367	−	0.529408i	$-0.822414\pi$
$821$	3.28899	−	22.8754i	0.114787	−	0.798359i	0.963154	−	0.268951i	$-0.0866768\pi$
$822$	−30.1882	−	26.1582i	−1.05293	−	0.912373i
$823$	21.2212	+	33.0208i	0.739723	+	1.15103i	0.983449	+	0.181188i	$0.0579941\pi$
$823$	21.2212	+	33.0208i	0.739723	+	1.15103i	−0.243725	+	0.969844i	$0.578369\pi$
$824$	1.73153	+	1.99830i	0.0603208	+	0.0696139i
$825$	−0.515196	+	16.9882i	−0.0179368	+	0.591452i
$826$	29.4696	−	64.5295i	1.02538	−	2.24527i
$827$		−	20.7230i		−	0.720608i	−0.932835	−	0.360304i	$-0.882673\pi$
$827$		−	20.7230i		−	0.720608i	0.932835	−	0.360304i	$-0.117327\pi$
$828$	8.50001	+	7.31732i	0.295396	+	0.254295i
$829$	8.00708			0.278097			0.139049	−	0.990286i	$-0.455596\pi$
$829$	8.00708			0.278097			0.139049	+	0.990286i	$0.455596\pi$
$830$	−46.1476	−	14.3135i	−1.60181	−	0.496828i
$831$	7.63136	+	2.24077i	0.264729	+	0.0777314i
$832$	3.47642	−	3.01234i	0.120523	−	0.104434i
$833$	10.9464	+	17.0330i	0.379272	+	0.590158i
$834$	1.24617	−	1.43815i	0.0431512	−	0.0497991i
$835$	0.118315	−	7.80450i	0.00409447	−	0.270086i
$836$	59.4474	−	17.4553i	2.05603	−	0.603705i
$837$	0.926256	−	1.44128i	0.0320161	−	0.0498180i
$838$	19.8214	−	2.84988i	0.684717	−	0.0984475i
$839$	10.0010	+	21.8991i	0.345272	+	0.756040i	1.00000		0.000175692i	$5.59246e-5\pi$
$839$	10.0010	+	21.8991i	0.345272	+	0.756040i	−0.654728	+	0.755865i	$0.727217\pi$
$840$	−2.84558	−	4.57897i	−0.0981819	−	0.157989i
$841$	−6.51098	−	45.2849i	−0.224517	−	1.56155i
$842$	27.5187	−	42.8199i	0.948356	−	1.47567i
$843$	4.02689	+	13.7143i	0.138693	+	0.472346i
$844$	−1.88787	+	13.1305i	−0.0649833	+	0.451969i
$845$	23.8517	+	15.8445i	0.820525	+	0.545069i
$846$	4.18504	−	2.68956i	0.143885	−	0.0924690i
$847$	−1.43240	+	1.24118i	−0.0492177	+	0.0426474i
$848$	0.112903	−	0.384511i	0.00387709	−	0.0132042i
$849$	−0.392175	+	0.858744i	−0.0134594	+	0.0294720i
$850$	−43.5739	+	11.3717i	−1.49457	+	0.390048i
$851$	3.86994	+	26.3119i	0.132660	+	0.901959i
$852$			1.50093i			0.0514209i
$853$	−39.6876	−	18.1247i	−1.35888	−	0.620578i	−0.403231	−	0.915098i	$-0.632113\pi$
$853$	−39.6876	−	18.1247i	−1.35888	−	0.620578i	−0.955645	+	0.294520i	$0.904840\pi$
$854$	51.0038	+	14.9761i	1.74531	+	0.512470i
$855$	11.6109	−	12.9963i	0.397085	−	0.444464i
$856$	−0.298768	+	0.192006i	−0.0102117	+	0.00656264i
$857$	−3.86638	−	3.35024i	−0.132073	−	0.114442i	0.586319	−	0.810080i	$-0.300576\pi$
$857$	−3.86638	−	3.35024i	−0.132073	−	0.114442i	−0.718393	+	0.695638i	$0.755122\pi$
$858$	3.08761	+	0.443932i	0.105409	+	0.0151556i
$859$	−25.0891	+	7.36683i	−0.856029	+	0.251353i	−0.680163	−	0.733061i	$-0.738091\pi$
$859$	−25.0891	+	7.36683i	−0.856029	+	0.251353i	−0.175867	+	0.984414i	$0.556273\pi$
$860$	24.5985	+	11.6876i	0.838802	+	0.398543i
$861$	5.56185	+	38.6835i	0.189547	+	1.31833i
$862$	−29.2293	+	13.3486i	−0.995554	+	0.454654i
$863$	3.08871	−	1.41057i	0.105141	−	0.0480163i	−0.362150	−	0.932120i	$-0.617957\pi$
$863$	3.08871	−	1.41057i	0.105141	−	0.0480163i	0.467291	+	0.884103i	$0.345230\pi$
$864$	1.15174	+	8.01052i	0.0391829	+	0.272523i
$865$	−23.8797	−	11.3461i	−0.811935	−	0.385778i
$866$	4.54662	−	1.33501i	0.154501	−	0.0453655i
$867$	1.67983	+	0.241523i	0.0570501	+	0.00820257i
$868$	−10.3498	−	8.96817i	−0.351296	−	0.304400i
$869$	−22.0128	+	14.1468i	−0.746733	+	0.479896i
$870$	26.8288	−	30.0300i	0.909581	−	1.01811i
$871$	2.49141	+	0.731544i	0.0844182	+	0.0247874i
$872$	3.11933	+	1.42455i	0.105634	+	0.0482414i
$873$			7.85390i			0.265814i
$874$	65.6322	+	41.8800i	2.22004	+	1.41661i
$875$	35.4464	−	14.2780i	1.19831	−	0.482685i
$876$	6.27327	−	13.7366i	0.211954	−	0.464115i
$877$	11.5548	−	39.3520i	0.390178	−	1.32882i	−0.497142	−	0.867669i	$-0.665617\pi$
$877$	11.5548	−	39.3520i	0.390178	−	1.32882i	0.887320	−	0.461154i	$-0.152564\pi$
$878$	5.61854	−	4.86849i	0.189616	−	0.164304i
$879$	−4.31866	+	2.77544i	−0.145665	+	0.0936131i
$880$	−20.3106	−	13.4922i	−0.684670	−	0.454822i
$881$	4.49607	−	31.2709i	0.151477	−	1.05354i	−0.762270	−	0.647259i	$-0.775915\pi$
$881$	4.49607	−	31.2709i	0.151477	−	1.05354i	0.913747	−	0.406284i	$-0.133176\pi$
$882$	−2.74784	−	9.35828i	−0.0925245	−	0.315110i
$883$	−4.44951	+	6.92358i	−0.149738	+	0.232997i	−0.908017	−	0.418933i	$-0.862404\pi$
$883$	−4.44951	+	6.92358i	−0.149738	+	0.232997i	0.758279	+	0.651930i	$0.226040\pi$
$884$	0.634038	+	4.40983i	0.0213250	+	0.148319i
$885$	11.7604	+	18.9243i	0.395323	+	0.636134i
$886$	13.9573	+	30.5622i	0.468905	+	1.02676i
$887$	−7.60787	+	1.09385i	−0.255447	+	0.0367278i	−0.268849	−	0.963182i	$-0.586643\pi$
$887$	−7.60787	+	1.09385i	−0.255447	+	0.0367278i	0.0134014	+	0.999910i	$0.495734\pi$
$888$	2.11481	−	3.29071i	0.0709683	−	0.110429i
$889$	−44.9318	+	13.1932i	−1.50697	+	0.442485i
$890$	1.24207	−	81.9313i	0.0416343	−	2.74634i
$891$	−2.22600	+	2.56894i	−0.0745738	+	0.0860627i
$892$	−11.0060	−	17.1257i	−0.368509	−	0.573411i
$893$	14.0677	−	12.1897i	0.470758	−	0.407914i
$894$	−11.9039	−	3.49530i	−0.398125	−	0.116900i
$895$	16.9318	+	5.25170i	0.565969	+	0.175545i
$896$	19.0114			0.635126
$897$	1.14805	+	1.77377i	0.0383324	+	0.0592245i
$898$			19.2586i			0.642666i
$899$	6.15335	−	13.4740i	0.205226	−	0.449382i
$900$	11.6879	+	0.354455i	0.389596	+	0.0118152i
$901$	0.353725	+	0.408221i	0.0117843	+	0.0135998i
$902$	−43.7686	−	68.1053i	−1.45734	−	2.26766i
$903$	13.4526	+	11.6567i	0.447674	+	0.387911i
$904$	0.944542	−	6.56944i	0.0314150	−	0.218496i
$905$	−11.5351	−	26.3064i	−0.383438	−	0.874454i
$906$	−13.7887	−	8.86147i	−0.458099	−	0.294403i
$907$	−5.20900	+	0.748941i	−0.172962	+	0.0248682i	−0.228252	−	0.973602i	$-0.573301\pi$
$907$	−5.20900	+	0.748941i	−0.172962	+	0.0248682i	0.0552896	+	0.998470i	$0.482392\pi$
$908$	45.1493	−	20.6190i	1.49833	−	0.684265i
$909$	5.22988	+	11.4518i	0.173464	+	0.379834i
$910$	−1.87373	−	6.75871i	−0.0621136	−	0.224049i
$911$	−7.23635	−	4.65052i	−0.239751	−	0.154079i	0.415248	−	0.909708i	$-0.363695\pi$
$911$	−7.23635	−	4.65052i	−0.239751	−	0.154079i	−0.654999	+	0.755629i	$0.727331\pi$
$912$	7.04407	+	23.9899i	0.233253	+	0.794385i
$913$	34.9032	+	5.01833i	1.15513	+	0.166082i
$914$	34.5704	−	39.8963i	1.14349	−	1.31965i
$915$	−12.7819	+	10.7407i	−0.422557	+	0.355078i
$916$	1.57607	+	1.81888i	0.0520747	+	0.0600975i
$917$	−13.1707	+	44.8554i	−0.434936	+	1.48126i
$918$	−8.19276	−	3.74151i	−0.270401	−	0.123488i
$919$	53.6290			1.76906			0.884528	−	0.466486i	$-0.154480\pi$
$919$	53.6290			1.76906			0.884528	+	0.466486i	$0.154480\pi$
$920$	0.987163	+	7.49974i	0.0325458	+	0.247259i
$921$	9.60713			0.316566
$922$	−62.0640	−	28.3437i	−2.04397	−	0.933449i
$923$	−0.0796607	+	0.271299i	−0.00262206	+	0.00892993i
$924$	17.7933	+	20.5346i	0.585358	+	0.675539i
$925$	20.3947	+	18.7843i	0.670575	+	0.617623i
$926$	−39.7910	+	45.9213i	−1.30761	+	1.50907i
$927$	−3.71032	−	0.533464i	−0.121863	−	0.0175212i
$928$	19.7128	+	67.1356i	0.647104	+	2.20383i
$929$	−17.4980	−	11.2453i	−0.574089	−	0.368945i	0.221151	−	0.975240i	$-0.429019\pi$
$929$	−17.4980	−	11.2453i	−0.574089	−	0.368945i	−0.795240	+	0.606295i	$0.792655\pi$
$930$	7.68963	−	2.13182i	0.252153	−	0.0699050i
$931$	−15.1603	−	33.1965i	−0.496860	−	1.08797i
$932$	14.0966	−	6.43772i	0.461751	−	0.210875i
$933$	−8.82307	+	1.26857i	−0.288854	+	0.0415310i
$934$	24.9915	+	16.0610i	0.817746	+	0.525533i
$935$	30.0996	−	13.1983i	0.984361	−	0.431632i
$936$	0.0442273	−	0.307607i	0.00144561	−	0.0100545i
$937$	−10.9035	−	9.44793i	−0.356202	−	0.308650i	0.458316	−	0.888789i	$-0.348453\pi$
$937$	−10.9035	−	9.44793i	−0.356202	−	0.308650i	−0.814518	+	0.580139i	$0.802998\pi$
$938$	22.6853	+	35.2990i	0.740701	+	1.15255i
$939$	7.90538	+	9.12329i	0.257982	+	0.297727i
$940$	12.3340	+	1.96463i	0.402292	+	0.0640792i
$941$	−6.79760	+	14.8847i	−0.221596	+	0.485227i	−0.987479	−	0.157753i	$-0.949575\pi$
$941$	−6.79760	+	14.8847i	−0.221596	+	0.485227i	0.765883	+	0.642980i	$0.222302\pi$
$942$			13.8839i			0.452361i
$943$	15.2789	−	52.6643i	0.497548	−	1.71499i
$944$	−31.9657			−1.04040
$945$	7.29973	+	2.26414i	0.237460	+	0.0736524i
$946$	−35.3798	−	10.3884i	−1.15029	−	0.337757i
$947$	−6.57167	+	5.69438i	−0.213550	+	0.185043i	−0.755067	−	0.655647i	$-0.772396\pi$
$947$	−6.57167	+	5.69438i	−0.213550	+	0.185043i	0.541517	+	0.840690i	$0.317850\pi$
$948$	9.73299	+	15.1448i	0.316113	+	0.491881i
$949$	1.86298	−	2.15000i	0.0604750	−	0.0697918i
$950$	80.6573	−	9.11097i	2.61687	−	0.295599i
$951$	−3.34481	+	0.982125i	−0.108463	+	0.0318476i
$952$	−5.63626	+	8.77019i	−0.182672	+	0.284243i
$953$	−29.2580	+	4.20667i	−0.947761	+	0.136267i	−0.598826	−	0.800879i	$-0.704366\pi$
$953$	−29.2580	+	4.20667i	−0.947761	+	0.136267i	−0.348935	+	0.937147i	$0.613457\pi$
$954$	−0.108091	−	0.236686i	−0.00349958	−	0.00766300i
$955$	37.7589	−	23.4651i	1.22185	−	0.759313i
$956$	4.62926	+	32.1972i	0.149721	+	1.04133i
$957$	−15.8888	+	24.7235i	−0.513613	+	0.799197i
$958$	−10.0081	−	34.0843i	−0.323346	−	1.10121i
$959$	9.32824	−	64.8793i	0.301225	−	2.09506i
$960$	−12.9185	+	19.4470i	−0.416942	+	0.627648i
$961$	−23.6096	+	15.1730i	−0.761599	+	0.489450i
$962$	3.84594	−	3.33253i	0.123998	−	0.107445i
$963$	0.141846	−	0.483083i	0.00457092	−	0.0155671i
$964$	−18.4322	+	40.3608i	−0.593661	+	1.29994i
$965$	−56.9932	+	7.31443i	−1.83467	+	0.235460i
$966$	−4.74985	+	33.8116i	−0.152824	+	1.08787i
$967$		−	22.3567i		−	0.718943i	−0.933156	−	0.359472i	$-0.882957\pi$
$967$		−	22.3567i		−	0.718943i	0.933156	−	0.359472i	$-0.117043\pi$
$968$	−0.355803	−	0.162490i	−0.0114360	−	0.00522262i
$969$	−32.3354	−	9.49454i	−1.03876	−	0.305009i
$970$	−24.3713	+	27.2793i	−0.782516	+	0.875885i
$971$	−1.41351	+	0.908409i	−0.0453617	+	0.0291522i	−0.563125	−	0.826372i	$-0.690401\pi$
$971$	−1.41351	+	0.908409i	−0.0453617	+	0.0291522i	0.517763	+	0.855524i	$0.326765\pi$
$972$	1.76743	+	1.53149i	0.0566904	+	0.0491225i
$973$	3.09082	+	0.444393i	0.0990872	+	0.0142466i
$974$	−10.8328	+	3.18078i	−0.347104	+	0.101919i
$975$	2.09382	+	0.684396i	0.0670561	+	0.0219182i
$976$	−3.40881	−	23.7088i	−0.109113	−	0.758900i
$977$	28.6812	−	13.0983i	0.917592	−	0.419050i	0.100092	−	0.994978i	$-0.468086\pi$
$977$	28.6812	−	13.0983i	0.917592	−	0.419050i	0.817500	+	0.575928i	$0.195359\pi$
$978$	24.2315	−	11.0661i	0.774837	−	0.353856i
$979$	8.51067	+	59.1930i	0.272002	+	1.89182i
$980$	10.5085	−	22.1170i	0.335682	−	0.706500i
$981$	−4.66456	+	1.36964i	−0.148928	+	0.0437292i
$982$	81.9095	+	11.7768i	2.61384	+	0.375813i
$983$	−26.8970	−	23.3064i	−0.857882	−	0.743359i	0.110222	−	0.993907i	$-0.464844\pi$
$983$	−26.8970	−	23.3064i	−0.857882	−	0.743359i	−0.968104	+	0.250548i	$0.919389\pi$
$984$	−6.78508	+	4.36051i	−0.216300	+	0.139008i
$985$	18.5212	+	16.5468i	0.590134	+	0.527226i
$986$	−74.7160	−	21.9386i	−2.37944	−	0.698667i
$987$	7.42555	+	3.39114i	0.236358	+	0.107941i
$988$		−	8.03022i		−	0.255475i
$989$	−10.4488	−	22.6853i	−0.332253	−	0.721352i
$990$	−15.7033	+	2.01534i	−0.499083	+	0.0640517i
$991$	−10.2008	+	22.3366i	−0.324038	+	0.709544i	−0.999615	−	0.0277452i	$-0.991167\pi$
$991$	−10.2008	+	22.3366i	−0.324038	+	0.709544i	0.675577	+	0.737289i	$0.263895\pi$
$992$	−3.90628	+	13.3036i	−0.124024	+	0.422388i
$993$	−6.40233	+	5.54765i	−0.203172	+	0.176049i
$994$	−3.84385	+	2.47029i	−0.121919	+	0.0783529i
$995$	30.0808	+	19.9825i	0.953625	+	0.633487i
$996$	3.45261	−	24.0135i	0.109400	−	0.760896i
$997$	1.29839	+	4.42191i	0.0411205	+	0.140043i	0.977495	−	0.210960i	$-0.0676589\pi$
$997$	1.29839	+	4.42191i	0.0411205	+	0.140043i	−0.936374	+	0.351003i	$0.885841\pi$
$998$	−34.0380	+	52.9642i	−1.07745	+	1.67655i
$999$	0.789197	+	5.48898i	0.0249691	+	0.173664i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	345.2.t.a.259.20	yes	240
5.4	even	2	inner	345.2.t.a.259.5	yes	240
23.4	even	11	inner	345.2.t.a.4.5	✓	240
115.4	even	22	inner	345.2.t.a.4.20	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.t.a.4.5	✓	240	23.4	even	11	inner
345.2.t.a.4.20	yes	240	115.4	even	22	inner
345.2.t.a.259.5	yes	240	5.4	even	2	inner
345.2.t.a.259.20	yes	240	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 345 = 3 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	345.t (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(1.89471 + 0.865286i) q^{2} +(0.281733 - 0.959493i) q^{3} +(1.53149 + 1.76743i) q^{4} +(-1.43853 - 1.71191i) q^{5} +(1.36404 - 1.57418i) q^{6} +(3.38318 + 0.486427i) q^{7} +(0.198730 + 0.676813i) q^{8} +(-0.841254 - 0.540641i) q^{9} +(-1.24431 - 4.48831i) q^{10} +(1.41208 + 3.09202i) q^{11} +(2.12731 - 0.971510i) q^{12} +(0.436083 - 0.0626993i) q^{13} +(5.98924 + 3.84905i) q^{14} +(-2.04785 + 0.897958i) q^{15} +(0.456549 - 3.17537i) q^{16} +(3.26787 + 2.83163i) q^{17} +(-1.12612 - 1.75228i) q^{18} +(-5.10386 - 5.89017i) q^{19} +(0.822593 - 5.16427i) q^{20} +(1.41987 - 3.10909i) q^{21} +7.08033i q^{22} +(-3.61427 + 3.15230i) q^{23} +0.705386 q^{24} +(-0.861269 + 4.92526i) q^{25} +(0.880505 + 0.258540i) q^{26} +(-0.755750 + 0.654861i) q^{27} +(4.32157 + 6.72449i) q^{28} +(-5.66182 + 6.53409i) q^{29} +(-4.65707 - 0.0706006i) q^{30} +(-1.64386 + 0.482680i) q^{31} +(4.37535 - 6.80817i) q^{32} +(3.36460 - 0.483756i) q^{33} +(3.74151 + 8.19276i) q^{34} +(-4.03408 - 6.49143i) q^{35} +(-0.332824 - 2.31484i) q^{36} +(2.99808 - 4.66511i) q^{37} +(-4.57366 - 15.5765i) q^{38} +(0.0626993 - 0.436083i) q^{39} +(0.872764 - 1.31382i) q^{40} +(-9.61896 + 6.18173i) q^{41} +(5.38050 - 4.66223i) q^{42} +(-1.46723 + 4.99691i) q^{43} +(-3.30235 + 7.23114i) q^{44} +(0.284639 + 2.21788i) q^{45} +(-9.57565 + 2.84532i) q^{46} +2.38834i q^{47} +(-2.91812 - 1.33266i) q^{48} +(4.49282 + 1.31921i) q^{49} +(-5.89361 + 8.58671i) q^{50} +(3.63759 - 2.33774i) q^{51} +(0.778674 + 0.674725i) q^{52} +(0.123648 + 0.0177779i) q^{53} +(-1.99857 + 0.586833i) q^{54} +(3.26194 - 6.86530i) q^{55} +(0.343119 + 2.38645i) q^{56} +(-7.08950 + 3.23767i) q^{57} +(-16.3814 + 7.48112i) q^{58} +(-1.41807 - 9.86289i) q^{59} +(-4.72333 - 2.24422i) q^{60} +(7.16403 - 2.10355i) q^{61} +(-3.53229 - 0.507867i) q^{62} +(-2.58313 - 2.23829i) q^{63} +(8.78352 - 5.64482i) q^{64} +(-0.734654 - 0.656341i) q^{65} +(6.79352 + 1.99476i) q^{66} +(5.36113 + 2.44835i) q^{67} +10.1124i q^{68} +(2.00635 + 4.35598i) q^{69} +(-2.02647 - 15.7900i) q^{70} +(-0.266610 + 0.583794i) q^{71} +(0.198730 - 0.676813i) q^{72} +(4.88006 - 4.22859i) q^{73} +(9.71716 - 6.24484i) q^{74} +(4.48311 + 2.21399i) q^{75} +(2.59397 - 18.0415i) q^{76} +(3.27326 + 11.1477i) q^{77} +(0.496134 - 0.771999i) q^{78} +(1.09553 + 7.61955i) q^{79} +(-6.09270 + 3.78629i) q^{80} +(0.415415 + 0.909632i) q^{81} +(-23.5741 + 3.38944i) q^{82} +(5.60844 - 8.72690i) q^{83} +(7.66963 - 2.25201i) q^{84} +(0.146561 - 9.66768i) q^{85} +(-7.10372 + 8.19813i) q^{86} +(4.67429 + 7.27334i) q^{87} +(-1.81209 + 1.57019i) q^{88} +(16.8803 + 4.95649i) q^{89} +(-1.37979 + 4.44853i) q^{90} +1.50585 q^{91} +(-11.1067 - 1.56027i) q^{92} +1.71326i q^{93} +(-2.06659 + 4.52521i) q^{94} +(-2.74138 + 17.2105i) q^{95} +(-5.29972 - 6.11620i) q^{96} +(-4.24614 - 6.60712i) q^{97} +(7.37109 + 6.38709i) q^{98} +(0.483756 - 3.36460i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q + 28 q^{4} - 4 q^{5} - 4 q^{6} + 24 q^{9} + 8 q^{14} + 4 q^{15} - 36 q^{16} - 8 q^{19} - 92 q^{20} + 8 q^{21} + 12 q^{24} - 44 q^{25} + 32 q^{26} - 12 q^{29} + 8 q^{30} - 20 q^{31} - 54 q^{34} + 36 q^{35}+ \cdots + 44 q^{99}+O(q^{100}) \) 240 * q + 28 * q^4 - 4 * q^5 - 4 * q^6 + 24 * q^9 + 8 * q^14 + 4 * q^15 - 36 * q^16 - 8 * q^19 - 92 * q^20 + 8 * q^21 + 12 * q^24 - 44 * q^25 + 32 * q^26 - 12 * q^29 + 8 * q^30 - 20 * q^31 - 54 * q^34 + 36 * q^35 - 28 * q^36 - 36 * q^39 - 24 * q^40 - 28 * q^41 - 224 * q^44 + 4 * q^45 - 8 * q^46 + 52 * q^49 - 48 * q^50 - 18 * q^54 - 22 * q^55 - 56 * q^59 - 36 * q^60 + 44 * q^61 + 12 * q^64 - 16 * q^65 + 8 * q^66 + 8 * q^69 - 152 * q^70 + 4 * q^71 + 88 * q^74 - 8 * q^75 - 100 * q^76 - 84 * q^79 + 122 * q^80 - 24 * q^81 - 56 * q^84 + 186 * q^85 - 392 * q^86 + 48 * q^89 - 304 * q^91 + 80 * q^94 + 190 * q^95 + 16 * q^96 + 44 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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