LMFDB - Embedded newform 345.2.t.a.4.20

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			4.20
Character	$\chi$	$=$	345.4
Dual form			345.2.t.a.259.20

$q$-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 $\left(\mathbb{Z}/345\mathbb{Z}\right)^\times$.

$n$	$116$	$166$	$277$
$\chi(n)$	$1$	$e\left(\frac{2}{11}\right)$	$-1$

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	0.388848	−	0.921302i	$-0.372873\pi$
$2$	1.89471	−	0.865286i	1.33976	−	0.611849i	0.950915	+	0.309453i	$0.100146\pi$
$3$	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	0.530718	−	0.847548i	$-0.321922\pi$
$7$	3.38318	−	0.486427i	1.27872	−	0.183852i	0.748002	+	0.663696i	$0.231013\pi$
$8$	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	−0.568239	−	0.822863i	$-0.692375\pi$
$11$	1.41208	−	3.09202i	0.425757	−	0.932278i	0.993996	−	0.109414i	$-0.0348975\pi$
$12$	2.12731	+	0.971510i	0.614101	+	0.280451i
$13$	0.436083	+	0.0626993i	0.120948	+	0.0173897i	0.202523	−	0.979278i	$-0.435086\pi$
$13$	0.436083	+	0.0626993i	0.120948	+	0.0173897i	−0.0815751	+	0.996667i	$0.525995\pi$
$14$	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	−0.161322	−	0.986902i	$-0.551576\pi$
$17$	3.26787	−	2.83163i	0.792576	−	0.686771i	0.953898	+	0.300131i	$0.0970305\pi$
$18$	−1.12612	+	1.75228i	−0.265430	+	0.413017i
$19$	−5.10386	+	5.89017i	−1.17091	+	1.35130i	−0.246843	+	0.969055i	$0.579393\pi$
$19$	−5.10386	+	5.89017i	−1.17091	+	1.35130i	−0.924062	+	0.382242i	$0.875152\pi$
$20$	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	−0.976356	−	0.216168i	$-0.930644\pi$
$29$	−5.66182	−	6.53409i	−1.05137	−	1.21335i	−0.0750175	−	0.997182i	$-0.523901\pi$
$30$	−4.65707	+	0.0706006i	−0.850260	+	0.0128899i
$31$	−1.64386	−	0.482680i	−0.295245	−	0.0866919i	0.130755	−	0.991415i	$-0.458260\pi$
$31$	−1.64386	−	0.482680i	−0.295245	−	0.0866919i	−0.426001	+	0.904723i	$0.640078\pi$
$32$	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	0.995212	−	0.0977363i	$-0.0311602\pi$
$37$	2.99808	+	4.66511i	0.492882	+	0.766940i	−0.502330	+	0.864676i	$0.667524\pi$
$38$	−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	−0.994593	−	0.103852i	$-0.966883\pi$
$41$	−9.61896	−	6.18173i	−1.50223	−	0.965424i	−0.507636	−	0.861572i	$-0.669480\pi$
$42$	5.38050	+	4.66223i	0.830230	+	0.719398i
$43$	−1.46723	−	4.99691i	−0.223750	−	0.762022i	−0.992476	−	0.122443i	$-0.960927\pi$
$43$	−1.46723	−	4.99691i	−0.223750	−	0.762022i	0.768726	−	0.639579i	$-0.220891\pi$
$44$	−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	$-0.944270\pi$
$47$		−	2.38834i		−	0.348375i	0.984713	−	0.174187i	$-0.0557298\pi$
$48$	−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	−0.133817	−	0.991006i	$-0.542724\pi$
$53$	0.123648	−	0.0177779i	0.0169844	−	0.00244198i	0.150802	+	0.988564i	$0.451814\pi$
$54$	−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	0.661056	+	0.750337i	$0.270109\pi$
$59$	−1.41807	+	9.86289i	−0.184617	+	1.28404i	−0.845672	+	0.533702i	$0.820800\pi$
$60$	−4.72333	+	2.24422i	−0.609780	+	0.289727i
$61$	7.16403	+	2.10355i	0.917260	+	0.269332i	0.706094	−	0.708118i	$-0.250456\pi$
$61$	7.16403	+	2.10355i	0.917260	+	0.269332i	0.211166	+	0.977450i	$0.432274\pi$
$62$	−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	−0.0600765	−	0.998194i	$-0.519134\pi$
$67$	5.36113	−	2.44835i	0.654966	−	0.299113i	0.715043	+	0.699081i	$0.246407\pi$
$68$		−	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	0.893152	−	0.449755i	$-0.148489\pi$
$71$	−0.266610	−	0.583794i	−0.0316408	−	0.0692837i	−0.924793	+	0.380472i	$0.875762\pi$
$72$	0.198730	+	0.676813i	0.0234206	+	0.0797632i
$73$	4.88006	+	4.22859i	0.571168	+	0.494920i	0.891889	−	0.452254i	$-0.149380\pi$
$73$	4.88006	+	4.22859i	0.571168	+	0.494920i	−0.320722	+	0.947174i	$0.603925\pi$
$74$	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	−0.830571	−	0.556912i	$-0.811986\pi$
$79$	1.09553	−	7.61955i	0.123256	−	0.857267i	0.953828	−	0.300354i	$-0.0971049\pi$
$80$	−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	0.999405	+	0.0344848i	$0.0109790\pi$
$83$	5.60844	+	8.72690i	0.615606	+	0.957901i	−0.383799	+	0.923416i	$0.625385\pi$
$84$	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	0.792842	−	0.609427i	$-0.208600\pi$
$89$	16.8803	−	4.95649i	1.78930	−	0.525387i	0.996462	+	0.0840394i	$0.0267822\pi$
$90$	−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	−0.987055	−	0.160381i	$-0.948728\pi$
$97$	−4.24614	+	6.60712i	−0.431130	+	0.670851i	0.555925	+	0.831232i	$0.312364\pi$
$98$	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	−0.948372	−	0.317159i	$-0.897271\pi$
$101$	−10.5910	+	6.80641i	−1.05384	+	0.677263i	−0.105470	+	0.994422i	$0.533635\pi$
$102$	8.91500	+	1.28178i	0.882716	+	0.126915i
$103$	3.40973	+	1.55717i	0.335971	+	0.153433i	0.576255	−	0.817270i	$-0.304513\pi$
$103$	3.40973	+	1.55717i	0.335971	+	0.153433i	−0.240284	+	0.970703i	$0.577241\pi$
$104$	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	−0.952352	−	0.305000i	$-0.901344\pi$
$107$	0.141846	−	0.483083i	0.0137128	−	0.0467014i	0.966065	+	0.258298i	$0.0831618\pi$
$108$	−2.31484	+	0.332824i	−0.222746	+	0.0320260i
$109$	3.18360	+	3.67406i	0.304933	+	0.351912i	0.887447	−	0.460909i	$-0.152476\pi$
$109$	3.18360	+	3.67406i	0.304933	+	0.351912i	−0.582514	+	0.812820i	$0.697931\pi$
$110$	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	−0.775088	−	0.631854i	$-0.782294\pi$
$113$	−8.55874	+	3.90865i	−0.805139	+	0.367695i	−0.0300511	+	0.999548i	$0.509567\pi$
$114$	−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	−0.223087	−	0.974799i	$-0.571613\pi$
$127$	−12.4626	−	5.69150i	−1.10588	−	0.505039i	−0.882794	+	0.469760i	$0.844341\pi$
$128$	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	−0.878739	−	0.477303i	$-0.841614\pi$
$131$	−1.94651	−	13.5382i	−0.170067	−	1.18284i	0.708671	−	0.705539i	$-0.249295\pi$
$132$	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	$0.305584\pi$
$137$			19.1771i			1.63841i	−0.573503	+	0.819203i	$0.694416\pi$
$138$	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	−0.983495	−	0.180934i	$-0.942088\pi$
$149$	−2.47430	+	5.41796i	−0.202702	+	0.443856i	0.780793	+	0.624790i	$0.214815\pi$
$150$	6.57846	−	8.07404i	0.537129	−	0.659242i
$151$	−1.11988	+	7.78890i	−0.0911342	+	0.633852i	0.892145	+	0.451749i	$0.149200\pi$
$151$	−1.11988	+	7.78890i	−0.0911342	+	0.633852i	−0.983279	+	0.182103i	$0.941709\pi$
$152$	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	0.430255	−	0.902707i	$-0.358424\pi$
$157$	−5.03746	−	4.36498i	−0.402033	−	0.348363i	−0.832288	+	0.554344i	$0.812969\pi$
$158$	−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	0.0960405	−	0.995377i	$-0.469382\pi$
$163$	11.6333	−	5.31275i	0.911190	−	0.416126i	0.815149	+	0.579251i	$0.196655\pi$
$164$	−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	−0.546790	−	0.837270i	$-0.684150\pi$
$167$	2.63808	−	2.28591i	0.204141	−	0.176889i	0.750931	+	0.660381i	$0.229605\pi$
$168$	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	0.779935	−	0.625861i	$-0.215252\pi$
$173$	10.7550	+	4.91165i	0.817689	+	0.373426i	0.0377546	+	0.999287i	$0.487979\pi$
$174$	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	0.267116	−	0.963664i	$-0.413929\pi$
$179$	−6.66948	−	4.28621i	−0.498500	−	0.320366i	−0.765616	+	0.643298i	$0.777566\pi$
$180$	−3.48403	−	3.89974i	−0.259684	−	0.290669i
$181$	12.3255	−	3.61910i	0.916150	−	0.269006i	0.210522	−	0.977589i	$-0.432484\pi$
$181$	12.3255	−	3.61910i	0.916150	−	0.269006i	0.705627	+	0.708583i	$0.250665\pi$
$182$	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	−0.790011	−	0.613093i	$-0.789925\pi$
$191$	−2.82941	−	19.6790i	−0.204729	−	1.42392i	0.585282	−	0.810830i	$-0.300984\pi$
$192$	−2.94157	+	10.0181i	−0.212289	+	0.722991i
$193$	13.8929	+	21.6178i	1.00004	+	1.55609i	0.819951	+	0.572434i	$0.194001\pi$
$193$	13.8929	+	21.6178i	1.00004	+	1.55609i	0.180085	+	0.983651i	$0.442363\pi$
$194$	−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	−0.260944	−	0.965354i	$-0.584034\pi$
$197$	−10.9940	−	1.58070i	−0.783289	−	0.112620i	−0.522345	+	0.852734i	$0.674943\pi$
$198$	3.82791	+	5.95635i	0.272038	+	0.423299i
$199$	−15.4961	−	4.55005i	−1.09849	−	0.322545i	−0.318236	−	0.948012i	$-0.603090\pi$
$199$	−15.4961	−	4.55005i	−1.09849	−	0.322545i	−0.780251	+	0.625467i	$0.784908\pi$
$200$	−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	−0.613344	−	0.789816i	$-0.710176\pi$
$211$	3.71456	−	4.28683i	0.255721	−	0.295117i	0.869065	+	0.494699i	$0.164722\pi$
$212$	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	−0.424626	−	0.905369i	$-0.639595\pi$
$223$	−8.61616	+	1.23882i	−0.576981	+	0.0829573i	−0.152354	+	0.988326i	$0.548685\pi$
$224$	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	0.879550	+	0.475807i	$0.157844\pi$
$227$	5.97939	+	20.3639i	0.396866	+	1.35160i	−0.482683	+	0.875795i	$0.660338\pi$
$228$	−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	0.997770	−	0.0667494i	$-0.0212628\pi$
$233$	1.86690	+	6.35809i	0.122305	+	0.416533i	−0.875465	+	0.483282i	$0.839445\pi$
$234$	−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	−0.104411	−	0.994534i	$-0.533296\pi$
$239$	11.7010	−	7.51978i	0.756876	−	0.486414i	0.861286	+	0.508120i	$0.169659\pi$
$240$	1.91640	−	6.91262i	0.123703	−	0.446208i
$241$	7.88155	−	17.2582i	0.507695	−	1.11170i	−0.466196	−	0.884682i	$-0.654376\pi$
$241$	7.88155	−	17.2582i	0.507695	−	1.11170i	0.973891	−	0.227016i	$-0.0728970\pi$
$242$	−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	0.962867	−	0.269977i	$-0.0870163\pi$
$251$	2.03246	+	4.45047i	0.128288	+	0.280911i	−0.834579	+	0.550888i	$0.814289\pi$
$252$			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	0.607326	−	0.794452i	$-0.292242\pi$
$257$	−1.48462	−	1.28643i	−0.0926083	−	0.0802455i	−0.699935	+	0.714207i	$0.746788\pi$
$258$	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	0.701761	−	0.712412i	$-0.252397\pi$
$263$	19.0453	+	2.73831i	1.17439	+	0.168851i	0.472625	+	0.881264i	$0.343307\pi$
$264$	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	0.749389	+	0.662130i	$0.230348\pi$
$269$	3.55741	+	24.7423i	0.216899	+	1.50857i	−0.532489	+	0.846437i	$0.678743\pi$
$270$	3.87960	−	2.57719i	0.236105	−	0.156843i
$271$	10.6612	+	6.85155i	0.647623	+	0.416202i	0.822797	−	0.568335i	$-0.192412\pi$
$271$	10.6612	+	6.85155i	0.647623	+	0.416202i	−0.175174	+	0.984538i	$0.556049\pi$
$272$	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	$-0.923200\pi$
$277$		−	7.95353i		−	0.477881i	0.971034	−	0.238941i	$-0.0768002\pi$
$278$	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	0.130391	−	0.991463i	$-0.458377\pi$
$281$	−12.0243	−	7.72754i	−0.717309	−	0.460986i	−0.847700	+	0.530476i	$0.822013\pi$
$282$	3.75968	−	3.25778i	0.223886	−	0.193998i
$283$	−0.934447	+	0.134353i	−0.0555471	+	0.00798647i	−0.170032	−	0.985438i	$-0.554387\pi$
$283$	−0.934447	+	0.134353i	−0.0555471	+	0.00798647i	0.114485	+	0.993425i	$0.463478\pi$
$284$	−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	−0.760784	−	0.649005i	$-0.775185\pi$
$293$	−3.87972	+	3.36180i	−0.226656	+	0.196398i	0.534128	+	0.845403i	$0.320640\pi$
$294$	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	−0.845493	−	0.533987i	$-0.820693\pi$
$307$	2.70664	−	9.21798i	0.154476	−	0.526098i	0.999969	+	0.00788933i	$0.00251128\pi$
$308$	−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	−0.985090	−	0.172040i	$-0.944964\pi$
$311$	−3.70293	+	8.10828i	−0.209974	+	0.459778i	0.775116	+	0.631819i	$0.217691\pi$
$312$	0.307607	+	0.0442273i	0.0174148	+	0.00250388i
$313$	−6.52653	−	10.1555i	−0.368901	−	0.574022i	0.606329	−	0.795214i	$-0.292642\pi$
$313$	−6.52653	−	10.1555i	−0.368901	−	0.574022i	−0.975230	+	0.221192i	$0.929005\pi$
$314$	−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	−0.890140	−	0.455688i	$-0.849393\pi$
$317$	−1.88468	+	2.93262i	−0.105854	+	0.164713i	0.784285	+	0.620400i	$0.213030\pi$
$318$	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	−0.721643	−	0.692265i	$-0.756613\pi$
$331$	−7.12668	+	4.58004i	−0.391718	+	0.251742i	0.329925	+	0.944007i	$0.392976\pi$
$332$	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	−0.846126	−	0.532983i	$-0.821071\pi$
$337$	2.82399	−	9.61763i	0.153833	−	0.523906i	0.999959	+	0.00907691i	$0.00288931\pi$
$338$	−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	−0.544209	−	0.838950i	$-0.683170\pi$
$347$	−4.96536	+	2.26760i	−0.266554	+	0.121731i	0.277655	+	0.960681i	$0.410443\pi$
$348$	−5.69652	−	19.4005i	−0.305365	−	1.03998i
$349$	−22.8481	+	26.3681i	−1.22303	+	1.41145i	−0.341134	+	0.940015i	$0.610811\pi$
$349$	−22.8481	+	26.3681i	−1.22303	+	1.41145i	−0.881898	+	0.471440i	$0.843734\pi$
$350$	−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	−0.941591	−	0.336759i	$-0.890669\pi$
$353$	0.612338	−	2.08543i	0.0325915	−	0.110996i	0.974182	+	0.225763i	$0.0724874\pi$
$354$	−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	−0.318013	−	0.948086i	$-0.603015\pi$
$359$	7.81178	−	5.02033i	0.412290	−	0.264963i	0.730303	+	0.683124i	$0.239379\pi$
$360$	−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	$0.134973\pi$
$367$			15.7640i			0.822876i	−0.911438	+	0.411438i	$0.865027\pi$
$368$	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	0.320846	+	0.947131i	$0.396033\pi$
$373$	−13.0167	+	20.2544i	−0.673979	+	1.04873i	−0.994825	+	0.101601i	$0.967604\pi$
$374$	−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	−0.842272	−	0.539052i	$-0.818783\pi$
$379$	2.27166	−	4.97424i	0.116687	−	0.255509i	0.958960	+	0.283543i	$0.0915098\pi$
$380$	−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	−0.495639	−	0.868529i	$-0.665066\pi$
$383$	7.64969	−	26.0525i	0.390881	−	1.33122i	0.886520	−	0.462690i	$-0.153116\pi$
$384$	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	−0.952234	−	0.305369i	$-0.901220\pi$
$389$	−11.0338	−	24.1607i	−0.559436	−	1.22499i	0.392798	−	0.919625i	$-0.371507\pi$
$390$	−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	−0.695709	−	0.718324i	$-0.744909\pi$
$397$	−1.66782	+	1.44517i	−0.0837054	+	0.0725312i	0.612003	+	0.790855i	$0.290364\pi$
$398$	−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	−0.995192	−	0.0979394i	$-0.968775\pi$
$401$	−0.254709	+	1.77154i	−0.0127196	+	0.0884666i	0.982473	+	0.186406i	$0.0596840\pi$
$402$	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	0.993963	+	0.109718i	$0.0349947\pi$
$409$	30.4706	+	19.5822i	1.50667	+	0.968280i	0.512710	+	0.858562i	$0.328642\pi$
$410$	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	0.723077	−	0.690767i	$-0.242727\pi$
$419$	8.08772	+	5.19766i	0.395111	+	0.253922i	−0.327966	+	0.944689i	$0.606363\pi$
$420$	−14.8882	+	9.89014i	−0.726471	+	0.482589i
$421$	3.47769	+	24.1879i	0.169492	+	1.17885i	0.879936	+	0.475092i	$0.157585\pi$
$421$	3.47769	+	24.1879i	0.169492	+	1.17885i	−0.710444	+	0.703754i	$0.751506\pi$
$422$	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	0.458343	−	0.888776i	$-0.348443\pi$
$431$	−10.1024	−	11.6588i	−0.486615	−	0.561584i	−0.944958	+	0.327191i	$0.893898\pi$
$432$	1.73439	−	2.69876i	0.0834457	−	0.129844i
$433$	1.71929	+	1.48977i	0.0826236	+	0.0715937i	0.695193	−	0.718823i	$-0.255319\pi$
$433$	1.71929	+	1.48977i	0.0826236	+	0.0715937i	−0.612570	+	0.790416i	$0.709864\pi$
$434$	−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	0.941709	−	0.336429i	$-0.109219\pi$
$439$	1.48269	+	3.24664i	0.0707649	+	0.154954i	−0.870944	+	0.491382i	$0.836492\pi$
$440$	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	−0.315283	−	0.948998i	$-0.602099\pi$
$443$	12.1905	−	10.5631i	0.579186	−	0.501868i	0.894469	+	0.447130i	$0.147554\pi$
$444$	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	−0.797089	−	0.603862i	$-0.793628\pi$
$449$	3.84086	−	8.41031i	0.181261	−	0.396907i	0.978351	+	0.206954i	$0.0663552\pi$
$450$	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	0.939749	+	0.341865i	$0.111059\pi$
$457$	7.14028	+	24.3175i	0.334008	+	1.13753i	−0.605741	+	0.795662i	$0.707123\pi$
$458$	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	−0.896388	−	0.443271i	$-0.853818\pi$
$463$	−8.21856	−	27.9898i	−0.381949	−	1.30080i	0.514439	−	0.857527i	$-0.328000\pi$
$464$	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	0.192287	−	0.981339i	$-0.438410\pi$
$467$	14.1171	−	2.02973i	0.653260	−	0.0939246i	0.460973	+	0.887414i	$0.347500\pi$
$468$	−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	−0.951173	−	0.308659i	$-0.900120\pi$
$479$	−11.1682	+	12.8888i	−0.510290	+	0.588906i	0.440883	+	0.897564i	$0.354665\pi$
$480$	−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	0.557092	−	0.830451i	$-0.311917\pi$
$487$	−4.09636	−	3.54951i	−0.185624	−	0.160844i	−0.742716	+	0.669607i	$0.766463\pi$
$488$	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	0.984988	−	0.172621i	$-0.0552235\pi$
$491$	38.1190	+	11.1928i	1.72029	+	0.505122i	0.735299	+	0.677743i	$0.237042\pi$
$492$	−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	−0.825187	−	0.564860i	$-0.808930\pi$
$499$	−4.30158	−	29.9182i	−0.192565	−	1.33932i	0.632621	−	0.774461i	$-0.281979\pi$
$500$	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	−0.666909	−	0.745140i	$-0.732383\pi$
$503$	−11.4095	−	38.8570i	−0.508722	−	1.73255i	0.158186	−	0.987409i	$-0.449435\pi$
$504$	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	−0.319100	−	0.947721i	$-0.603381\pi$
$509$	−1.69586	+	0.497949i	−0.0751676	+	0.0220712i	0.243933	+	0.969792i	$0.421562\pi$
$510$	−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	0.172234	−	0.985056i	$-0.444901\pi$
$521$	−4.91738	−	1.44387i	−0.215434	−	0.0632572i	−0.387669	+	0.921799i	$0.626720\pi$
$522$	17.8255	−	2.56292i	0.780200	−	0.112176i
$523$	−11.7051	+	10.1425i	−0.511828	+	0.443501i	−0.872087	−	0.489351i	$-0.837234\pi$
$523$	−11.7051	+	10.1425i	−0.511828	+	0.443501i	0.360259	+	0.932852i	$0.382688\pi$
$524$	−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	−0.452179	−	0.891927i	$-0.649353\pi$
$541$	12.0486	−	26.3827i	0.518009	−	1.13428i	0.970188	−	0.242353i	$-0.0779194\pi$
$542$	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	−0.189946	−	0.981795i	$-0.560831\pi$
$547$	18.2902	−	28.4601i	0.782032	−	1.21687i	0.971978	−	0.235071i	$-0.0755323\pi$
$548$	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	−0.997978	−	0.0635563i	$-0.979756\pi$
$557$	−12.4044	+	19.3016i	−0.525590	+	0.817834i	0.472388	+	0.881391i	$0.343392\pi$
$558$	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	0.697573	−	0.716513i	$-0.254263\pi$
$563$	14.5422	+	6.64122i	0.612882	+	0.279894i	−0.0846912	+	0.996407i	$0.526990\pi$
$564$	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	0.999737	−	0.0229311i	$-0.00729985\pi$
$569$	19.9122	+	22.9799i	0.834762	+	0.963367i	−0.164975	+	0.986298i	$0.552754\pi$
$570$	23.3532	−	27.7912i	0.978156	−	1.16405i
$571$	−7.20782	+	8.31827i	−0.301638	+	0.348109i	−0.886253	−	0.463202i	$-0.846700\pi$
$571$	−7.20782	+	8.31827i	−0.301638	+	0.348109i	0.584615	+	0.811311i	$0.301246\pi$
$572$	−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	0.0702719	−	0.997528i	$-0.477613\pi$
$577$	20.9022	−	9.54573i	0.870171	−	0.397394i	0.799900	+	0.600134i	$0.204886\pi$
$578$	−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	0.645821	−	0.763488i	$-0.276515\pi$
$587$	11.9139	+	5.44089i	0.491738	+	0.224569i	−0.154083	+	0.988058i	$0.549242\pi$
$588$	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	−0.414191	−	0.910190i	$-0.635935\pi$
$593$	14.2654	−	22.1973i	0.585808	−	0.911535i	0.999999	−	0.00134514i	$-0.000428173\pi$
$594$	−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	−0.0974763	−	0.995238i	$-0.531077\pi$
$601$	8.79088	−	2.58124i	0.358588	−	0.105291i	0.456064	+	0.889947i	$0.349259\pi$
$602$	−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	0.892794	−	0.450465i	$-0.148742\pi$
$607$	2.76325	+	4.29971i	0.112157	+	0.174520i	−0.780637	+	0.624984i	$0.785105\pi$
$608$	−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	−0.250656	−	0.968076i	$-0.580646\pi$
$613$	11.9731	−	40.7768i	0.483591	−	1.64696i	0.734247	−	0.678882i	$-0.237535\pi$
$614$	−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	0.999458	+	0.0329059i	$0.0104762\pi$
$617$	29.1682	+	25.2744i	1.17427	+	1.01751i	0.174809	+	0.984602i	$0.444069\pi$
$618$	2.19973	+	7.49159i	0.0884860	+	0.301356i
$619$	−19.5414	−	42.7897i	−0.785435	−	1.71986i	−0.689278	−	0.724497i	$-0.742072\pi$
$619$	−19.5414	−	42.7897i	−0.785435	−	1.71986i	−0.0961573	−	0.995366i	$-0.530655\pi$
$620$	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	−0.587980	−	0.808875i	$-0.700077\pi$
$631$	5.12616	−	35.6532i	0.204069	−	1.41933i	0.792049	−	0.610457i	$-0.209014\pi$
$632$	−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	0.192991	−	0.981201i	$-0.438181\pi$
$641$	22.4272	−	6.58523i	0.885823	−	0.260101i	0.692832	+	0.721100i	$0.256363\pi$
$642$	0.953944	−	0.435652i	0.0376492	−	0.0171938i
$643$			25.5286i			1.00675i	0.864068	+	0.503375i	$0.167908\pi$
$643$			25.5286i			1.00675i	−0.864068	+	0.503375i	$0.832092\pi$
$644$	−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	−0.904373	−	0.426742i	$-0.859661\pi$
$647$	−9.52027	−	32.4231i	−0.374280	−	1.27468i	0.530093	−	0.847940i	$-0.322157\pi$
$648$	−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	0.961877	+	0.273483i	$0.0881758\pi$
$653$	20.7259	+	32.2502i	0.811068	+	1.26205i	−0.150809	+	0.988563i	$0.548188\pi$
$654$	−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	0.566837	−	0.823830i	$-0.308167\pi$
$659$	15.3588	+	4.50975i	0.598294	+	0.175675i	0.0314572	+	0.999505i	$0.489985\pi$
$660$	0.269446	+	17.7736i	0.0104882	+	0.691838i
$661$	−19.5755	−	22.5914i	−0.761400	−	0.878703i	0.234221	−	0.972183i	$-0.424746\pi$
$661$	−19.5755	−	22.5914i	−0.761400	−	0.878703i	−0.995621	+	0.0934806i	$0.970201\pi$
$662$	−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	0.365009	−	0.931004i	$-0.381066\pi$
$673$	34.7232	−	30.0879i	1.33848	−	1.15980i	0.973474	−	0.228798i	$-0.0734794\pi$
$674$	−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	−0.0968324	−	0.995301i	$-0.530871\pi$
$677$	−12.2330	−	1.75883i	−0.470151	−	0.0675975i	−0.373319	+	0.927703i	$0.621780\pi$
$678$	−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	−0.0224004	−	0.999749i	$-0.507131\pi$
$683$	6.21391	−	0.893425i	0.237769	−	0.0341860i	0.260169	+	0.965563i	$0.416222\pi$
$684$	−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	0.402415	+	0.915458i	$0.368171\pi$
$701$	−14.6406	+	32.0584i	−0.552968	+	1.21083i	−0.955382	+	0.295373i	$0.904556\pi$
$702$	−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	−0.503400	−	0.864054i	$-0.667918\pi$
$709$	11.2766	−	13.0139i	0.423501	−	0.488746i	0.926900	+	0.375308i	$0.122463\pi$
$710$	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	0.504904	−	0.863176i	$-0.331528\pi$
$719$	−11.2979	−	13.0385i	−0.421341	−	0.486254i	−0.926245	+	0.376922i	$0.876983\pi$
$720$	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	−0.937931	−	0.346823i	$-0.887260\pi$
$727$	−23.2901	−	36.2401i	−0.863781	−	1.34407i	0.0741491	−	0.997247i	$-0.476376\pi$
$728$	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	−0.750488	−	0.660884i	$-0.770182\pi$
$733$	−12.8991	−	43.9302i	−0.476438	−	1.62260i	0.274050	−	0.961715i	$-0.411637\pi$
$734$	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	−0.691583	−	0.722297i	$-0.743087\pi$
$739$	−24.0006	+	7.04722i	−0.882877	+	0.259236i	−0.191294	+	0.981533i	$0.561268\pi$
$740$	−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	−0.832554	−	0.553943i	$-0.813122\pi$
$743$	−40.2143	+	5.78195i	−1.47532	+	0.212119i	−0.642766	+	0.766062i	$0.722213\pi$
$744$	−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	0.417376	−	0.908734i	$-0.362950\pi$
$751$	7.59640	+	2.23050i	0.277196	+	0.0813922i	−0.140180	+	0.990126i	$0.544768\pi$
$752$	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	−0.0916535	−	0.995791i	$-0.529215\pi$
$757$	16.5328	−	7.55028i	0.600895	−	0.274419i	0.692548	+	0.721372i	$0.256488\pi$
$758$		−	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	0.920208	−	0.391430i	$-0.128019\pi$
$761$	0.600751	+	1.31546i	0.0217772	+	0.0476855i	−0.898431	+	0.439115i	$0.855292\pi$
$762$	−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	−0.997490	−	0.0708060i	$-0.977443\pi$
$769$	−0.567290	+	3.94559i	−0.0204570	+	0.142281i	0.977033	+	0.213088i	$0.0683520\pi$
$770$	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	−0.938219	−	0.346042i	$-0.887525\pi$
$773$	−24.0005	−	37.3456i	−0.863240	−	1.34323i	0.0749794	−	0.997185i	$-0.476111\pi$
$774$	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	−0.211773	−	0.977319i	$-0.567924\pi$
$787$	21.4666	−	33.4027i	0.765201	−	1.19068i	0.976974	−	0.213358i	$-0.0684400\pi$
$788$	−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	−0.972256	−	0.233920i	$-0.924845\pi$
$797$	−0.786966	+	2.68016i	−0.0278758	+	0.0949362i	0.944380	+	0.328856i	$0.106663\pi$
$798$	−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	−0.706069	−	0.708143i	$-0.749533\pi$
$809$	2.71204	−	3.12987i	0.0953504	−	0.110040i	0.801419	+	0.598103i	$0.204079\pi$
$810$	3.56581	+	2.99637i	0.125290	+	0.105282i
$811$	5.89521	+	6.80343i	0.207009	+	0.238901i	0.849754	−	0.527179i	$-0.176750\pi$
$811$	5.89521	+	6.80343i	0.207009	+	0.238901i	−0.642746	+	0.766080i	$0.722205\pi$
$812$	−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	0.963154	+	0.268951i	$0.0866768\pi$
$821$	3.28899	+	22.8754i	0.114787	+	0.798359i	−0.848367	+	0.529408i	$0.822414\pi$
$822$	−30.1882	+	26.1582i	−1.05293	+	0.912373i
$823$	21.2212	−	33.0208i	0.739723	−	1.15103i	−0.243725	−	0.969844i	$-0.578369\pi$
$823$	21.2212	−	33.0208i	0.739723	−	1.15103i	0.983449	−	0.181188i	$-0.0579941\pi$
$824$	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	$0.117327\pi$
$827$			20.7230i			0.720608i	−0.932835	+	0.360304i	$0.882673\pi$
$828$	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	−0.654728	−	0.755865i	$-0.727217\pi$
$839$	10.0010	−	21.8991i	0.345272	−	0.756040i	1.00000		0.000175692i	$-5.59246e-5\pi$
$840$	−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	−0.955645	−	0.294520i	$-0.904840\pi$
$853$	−39.6876	+	18.1247i	−1.35888	+	0.620578i	−0.403231	+	0.915098i	$0.632113\pi$
$854$	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	−0.718393	−	0.695638i	$-0.755122\pi$
$857$	−3.86638	+	3.35024i	−0.132073	+	0.114442i	0.586319	+	0.810080i	$0.300576\pi$
$858$	3.08761	−	0.443932i	0.105409	−	0.0151556i
$859$	−25.0891	−	7.36683i	−0.856029	−	0.251353i	−0.175867	−	0.984414i	$-0.556273\pi$
$859$	−25.0891	−	7.36683i	−0.856029	−	0.251353i	−0.680163	+	0.733061i	$0.738091\pi$
$860$	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	0.467291	−	0.884103i	$-0.345230\pi$
$863$	3.08871	+	1.41057i	0.105141	+	0.0480163i	−0.362150	+	0.932120i	$0.617957\pi$
$864$	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	0.887320	+	0.461154i	$0.152564\pi$
$877$	11.5548	+	39.3520i	0.390178	+	1.32882i	−0.497142	+	0.867669i	$0.665617\pi$
$878$	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	0.913747	+	0.406284i	$0.133176\pi$
$881$	4.49607	+	31.2709i	0.151477	+	1.05354i	−0.762270	+	0.647259i	$0.775915\pi$
$882$	−2.74784	+	9.35828i	−0.0925245	+	0.315110i
$883$	−4.44951	−	6.92358i	−0.149738	−	0.232997i	0.758279	−	0.651930i	$-0.226040\pi$
$883$	−4.44951	−	6.92358i	−0.149738	−	0.232997i	−0.908017	+	0.418933i	$0.862404\pi$
$884$	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	0.0134014	−	0.999910i	$-0.495734\pi$
$887$	−7.60787	−	1.09385i	−0.255447	−	0.0367278i	−0.268849	+	0.963182i	$0.586643\pi$
$888$	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	0.0552896	−	0.998470i	$-0.482392\pi$
$907$	−5.20900	−	0.748941i	−0.172962	−	0.0248682i	−0.228252	+	0.973602i	$0.573301\pi$
$908$	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	−0.654999	−	0.755629i	$-0.727331\pi$
$911$	−7.23635	+	4.65052i	−0.239751	+	0.154079i	0.415248	+	0.909708i	$0.363695\pi$
$912$	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	−0.795240	−	0.606295i	$-0.792655\pi$
$929$	−17.4980	+	11.2453i	−0.574089	+	0.368945i	0.221151	+	0.975240i	$0.429019\pi$
$930$	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	−0.814518	−	0.580139i	$-0.802998\pi$
$937$	−10.9035	+	9.44793i	−0.356202	+	0.308650i	0.458316	+	0.888789i	$0.348453\pi$
$938$	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	0.765883	−	0.642980i	$-0.222302\pi$
$941$	−6.79760	−	14.8847i	−0.221596	−	0.485227i	−0.987479	+	0.157753i	$0.949575\pi$
$942$		−	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	0.541517	−	0.840690i	$-0.317850\pi$
$947$	−6.57167	−	5.69438i	−0.213550	−	0.185043i	−0.755067	+	0.655647i	$0.772396\pi$
$948$	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	−0.348935	−	0.937147i	$-0.613457\pi$
$953$	−29.2580	−	4.20667i	−0.947761	−	0.136267i	−0.598826	+	0.800879i	$0.704366\pi$
$954$	−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	$0.117043\pi$
$967$			22.3567i			0.718943i	−0.933156	+	0.359472i	$0.882957\pi$
$968$	−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	0.517763	−	0.855524i	$-0.326765\pi$
$971$	−1.41351	−	0.908409i	−0.0453617	−	0.0291522i	−0.563125	+	0.826372i	$0.690401\pi$
$972$	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	0.817500	−	0.575928i	$-0.195359\pi$
$977$	28.6812	+	13.0983i	0.917592	+	0.419050i	0.100092	+	0.994978i	$0.468086\pi$
$978$	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	−0.968104	−	0.250548i	$-0.919389\pi$
$983$	−26.8970	+	23.3064i	−0.857882	+	0.743359i	0.110222	+	0.993907i	$0.464844\pi$
$984$	−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	0.675577	−	0.737289i	$-0.263895\pi$
$991$	−10.2008	−	22.3366i	−0.324038	−	0.709544i	−0.999615	+	0.0277452i	$0.991167\pi$
$992$	−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	−0.936374	−	0.351003i	$-0.885841\pi$
$997$	1.29839	−	4.42191i	0.0411205	−	0.140043i	0.977495	+	0.210960i	$0.0676589\pi$
$998$	−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.4.20	yes	240
5.4	even	2	inner	345.2.t.a.4.5	✓	240
23.6	even	11	inner	345.2.t.a.259.5	yes	240
115.29	even	22	inner	345.2.t.a.259.20	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
345.2.t.a.4.5	✓	240	5.4	even	2	inner
345.2.t.a.4.20	yes	240	1.1	even	1	trivial
345.2.t.a.259.5	yes	240	23.6	even	11	inner
345.2.t.a.259.20	yes	240	115.29	even	22	inner

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

Related objects

Downloads

Learn more