LMFDB - Embedded newform 1000.2.bd.a.109.41

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1000,2,Mod(29,1000)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1000, base_ring=CyclotomicField(50))

chi = DirichletCharacter(H, H._module([0, 25, 31]))

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

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

chi := DirichletCharacter("1000.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$1000 = 2^{3} \cdot 5^{3}$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	1000.bd (of order $50$ , degree $20$ , minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$2960$
Relative dimension:	$148$ over $\Q(\zeta_{50})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{50}]$

Embedding invariants

Embedding label			109.41
Character	$\chi$	$=$	1000.109
Dual form			1000.2.bd.a.789.41

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.894681 + 1.09524i) q^{2} +(0.859509 + 1.03897i) q^{3} +(-0.399093 - 1.95978i) q^{4} +(0.254836 - 2.22150i) q^{5} +(-1.90690 + 0.0118226i) q^{6} +(4.65603 - 1.51284i) q^{7} +(2.50348 + 1.31627i) q^{8} +(0.221445 - 1.16086i) q^{9} +(2.20507 + 2.26664i) q^{10} +(-0.350697 + 2.77605i) q^{11} +(1.69312 - 2.09909i) q^{12} +(-0.189832 + 0.995136i) q^{13} +(-2.50875 + 6.45297i) q^{14} +(2.52710 - 1.64463i) q^{15} +(-3.68145 + 1.56427i) q^{16} +(-1.66441 - 6.48244i) q^{17} +(1.07329 + 1.28113i) q^{18} +(-1.29260 - 1.06933i) q^{19} +(-4.45535 + 0.387163i) q^{20} +(5.57369 + 3.53717i) q^{21} +(-2.72668 - 2.86778i) q^{22} +(0.102920 - 0.109598i) q^{23} +(0.784202 + 3.73239i) q^{24} +(-4.87012 - 1.13224i) q^{25} +(-0.920072 - 1.09824i) q^{26} +(4.94129 - 2.71650i) q^{27} +(-4.82301 - 8.52102i) q^{28} +(-2.65084 + 0.166777i) q^{29} +(-0.459685 + 4.23920i) q^{30} +(4.75898 - 1.22190i) q^{31} +(1.58048 - 5.43158i) q^{32} +(-3.18566 + 2.02168i) q^{33} +(8.58892 + 3.97679i) q^{34} +(-2.17424 - 10.7289i) q^{35} +(-2.36340 + 0.0293068i) q^{36} +(-4.28495 - 2.35567i) q^{37} +(2.32764 - 0.458995i) q^{38} +(-1.19708 + 0.658099i) q^{39} +(3.56208 - 5.22605i) q^{40} +(2.05023 - 1.92529i) q^{41} +(-8.86072 + 2.93988i) q^{42} +(0.729437 - 0.529967i) q^{43} +(5.58041 - 0.420616i) q^{44} +(-2.52241 - 0.787769i) q^{45} +(0.0279560 + 0.210777i) q^{46} +(2.32115 + 5.86254i) q^{47} +(-4.78946 - 2.48041i) q^{48} +(13.7268 - 9.97314i) q^{49} +(5.59727 - 4.32095i) q^{50} +(5.30447 - 7.30098i) q^{51} +(2.02601 - 0.0251231i) q^{52} +(-4.68128 + 7.37652i) q^{53} +(-1.44567 + 7.84229i) q^{54} +(6.07763 + 1.48651i) q^{55} +(13.6476 + 2.34124i) q^{56} -2.26207i q^{57} +(2.18900 - 3.05252i) q^{58} +(-3.28620 + 1.54637i) q^{59} +(-4.23166 - 4.29619i) q^{60} +(8.01345 - 8.53346i) q^{61} +(-2.91950 + 6.30542i) q^{62} +(-0.725130 - 5.74000i) q^{63} +(4.53486 + 6.59053i) q^{64} +(2.16232 + 0.675310i) q^{65} +(0.635925 - 5.29781i) q^{66} +(-0.269023 + 4.27600i) q^{67} +(-12.0399 + 5.84896i) q^{68} +(0.202329 + 0.0127295i) q^{69} +(13.6959 + 7.21763i) q^{70} +(-8.35992 + 3.30993i) q^{71} +(2.08239 - 2.61470i) q^{72} +(-0.209163 - 0.0984244i) q^{73} +(6.41368 - 2.58547i) q^{74} +(-3.00955 - 6.03307i) q^{75} +(-1.57978 + 2.95997i) q^{76} +(2.56686 + 13.4559i) q^{77} +(0.350227 - 1.89987i) q^{78} +(4.41669 + 5.33886i) q^{79} +(2.53685 + 8.57697i) q^{80} +(3.77304 + 1.49385i) q^{81} +(0.274354 + 3.96801i) q^{82} +(-0.0671268 + 0.0811423i) q^{83} +(4.70765 - 12.3349i) q^{84} +(-14.8249 + 2.04552i) q^{85} +(-0.0721730 + 1.27306i) q^{86} +(-2.45170 - 2.61080i) q^{87} +(-4.53201 + 6.48819i) q^{88} +(-5.81576 + 12.3591i) q^{89} +(3.11954 - 2.05784i) q^{90} +(0.621613 + 4.92057i) q^{91} +(-0.255863 - 0.157960i) q^{92} +(5.35990 + 3.89419i) q^{93} +(-8.49756 - 2.70290i) q^{94} +(-2.70492 + 2.59901i) q^{95} +(7.00168 - 3.02643i) q^{96} +(11.8143 - 0.743293i) q^{97} +(-1.35818 + 23.9569i) q^{98} +(3.14494 + 1.02185i) q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$2960 q - 20 q^{2} - 20 q^{4} - 20 q^{6} - 50 q^{7} - 35 q^{8} - 40 q^{9} - 20 q^{10} - 20 q^{12} - 30 q^{14} - 40 q^{15} - 40 q^{17} - 25 q^{18} - 20 q^{20} + 5 q^{22} - 40 q^{23} - 15 q^{24} - 40 q^{25}+ \cdots - 115 q^{98}+O(q^{100})$ 2960 * q - 20 * q^2 - 20 * q^4 - 20 * q^6 - 50 * q^7 - 35 * q^8 - 40 * q^9 - 20 * q^10 - 20 * q^12 - 30 * q^14 - 40 * q^15 - 40 * q^17 - 25 * q^18 - 20 * q^20 + 5 * q^22 - 40 * q^23 - 15 * q^24 - 40 * q^25 - 15 * q^26 - 40 * q^28 + 20 * q^30 - 40 * q^31 - 25 * q^32 - 40 * q^33 - 20 * q^34 + 180 * q^36 - 70 * q^38 - 40 * q^39 + 5 * q^40 - 40 * q^41 - 100 * q^42 + 15 * q^44 - 20 * q^46 - 40 * q^47 + 45 * q^48 + 650 * q^49 - 30 * q^50 + 75 * q^52 - 70 * q^54 - 40 * q^55 - 55 * q^56 - 295 * q^58 - 5 * q^60 - 45 * q^62 - 110 * q^63 - 5 * q^64 - 90 * q^65 - 95 * q^66 - 55 * q^70 - 40 * q^71 + 40 * q^72 - 40 * q^73 - 15 * q^74 - 15 * q^76 + 30 * q^78 - 40 * q^79 - 400 * q^80 - 40 * q^81 - 25 * q^82 - 95 * q^84 + 40 * q^86 - 40 * q^87 - 135 * q^88 - 90 * q^89 - 70 * q^90 - 115 * q^92 - 100 * q^94 + 60 * q^95 - 55 * q^96 - 115 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$ .

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{27}{50}\right)$	$-1$	$1$

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

)

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

$2$	−0.894681	+	1.09524i	−0.632635	+	0.774450i
$2$	−0.894681	+	1.09524i	−0.632635	+	0.774450i
$3$	0.859509	+	1.03897i	0.496238	+	0.599849i	0.957863	−	0.287227i	$-0.0927333\pi$
$3$	0.859509	+	1.03897i	0.496238	+	0.599849i	−0.461625	+	0.887075i	$0.652733\pi$
$4$	−0.399093	−	1.95978i	−0.199547	−	0.979888i
$5$	0.254836	−	2.22150i	0.113966	−	0.993485i
$5$	0.254836	−	2.22150i	0.113966	−	0.993485i
$6$	−1.90690	+	0.0118226i	−0.778490	+	0.00482657i
$7$	4.65603	−	1.51284i	1.75981	−	0.571799i	0.762634	−	0.646830i	$-0.223906\pi$
$7$	4.65603	−	1.51284i	1.75981	−	0.571799i	0.997181	+	0.0750320i	$0.0239059\pi$
$8$	2.50348	+	1.31627i	0.885115	+	0.465372i
$9$	0.221445	−	1.16086i	0.0738151	−	0.386952i
$10$	2.20507	+	2.26664i	0.697305	+	0.716774i
$11$	−0.350697	+	2.77605i	−0.105739	+	0.837012i	0.846655	+	0.532142i	$0.178613\pi$
$11$	−0.350697	+	2.77605i	−0.105739	+	0.837012i	−0.952394	+	0.304869i	$0.901387\pi$
$12$	1.69312	−	2.09909i	0.488762	−	0.605955i
$13$	−0.189832	+	0.995136i	−0.0526500	+	0.276001i	−0.998870	−	0.0475223i	$-0.984867\pi$
$13$	−0.189832	+	0.995136i	−0.0526500	+	0.276001i	0.946220	+	0.323524i	$0.104867\pi$
$14$	−2.50875	+	6.45297i	−0.670490	+	1.72463i
$15$	2.52710	−	1.64463i	0.652495	−	0.424642i
$16$	−3.68145	+	1.56427i	−0.920362	+	0.391067i
$17$	−1.66441	−	6.48244i	−0.403678	−	1.57222i	−0.767686	−	0.640826i	$-0.778592\pi$
$17$	−1.66441	−	6.48244i	−0.403678	−	1.57222i	0.364008	−	0.931396i	$-0.381408\pi$
$18$	1.07329	+	1.28113i	0.252977	+	0.301965i
$19$	−1.29260	−	1.06933i	−0.296543	−	0.245322i	0.477239	−	0.878773i	$-0.341637\pi$
$19$	−1.29260	−	1.06933i	−0.296543	−	0.245322i	−0.773782	+	0.633452i	$0.781637\pi$
$20$	−4.45535	+	0.387163i	−0.996246	+	0.0865722i
$21$	5.57369	+	3.53717i	1.21628	+	0.771874i
$22$	−2.72668	−	2.86778i	−0.581330	−	0.611412i
$23$	0.102920	−	0.109598i	0.0214602	−	0.0228528i	−0.718149	−	0.695889i	$-0.755010\pi$
$23$	0.102920	−	0.109598i	0.0214602	−	0.0228528i	0.739609	+	0.673037i	$0.235010\pi$
$24$	0.784202	+	3.73239i	0.160075	+	0.761870i
$25$	−4.87012	−	1.13224i	−0.974023	−	0.226448i
$26$	−0.920072	−	1.09824i	−0.180441	−	0.215383i
$27$	4.94129	−	2.71650i	0.950952	−	0.522790i
$28$	−4.82301	−	8.52102i	−0.911464	−	1.61032i
$29$	−2.65084	+	0.166777i	−0.492249	+	0.0309697i	−0.306976	−	0.951717i	$-0.599317\pi$
$29$	−2.65084	+	0.166777i	−0.492249	+	0.0309697i	−0.185273	+	0.982687i	$0.559317\pi$
$30$	−0.459685	+	4.23920i	−0.0839265	+	0.773968i
$31$	4.75898	−	1.22190i	0.854738	−	0.219459i	0.204196	−	0.978930i	$-0.434542\pi$
$31$	4.75898	−	1.22190i	0.854738	−	0.219459i	0.650542	+	0.759471i	$0.274542\pi$
$32$	1.58048	−	5.43158i	0.279391	−	0.960177i
$33$	−3.18566	+	2.02168i	−0.554552	+	0.351929i
$34$	8.58892	+	3.97679i	1.47299	+	0.682014i
$35$	−2.17424	−	10.7289i	−0.367513	−	1.81351i
$36$	−2.36340	+	0.0293068i	−0.393899	+	0.00488447i
$37$	−4.28495	−	2.35567i	−0.704442	−	0.387270i	0.0889052	−	0.996040i	$-0.471663\pi$
$37$	−4.28495	−	2.35567i	−0.704442	−	0.387270i	−0.793347	+	0.608770i	$0.791663\pi$
$38$	2.32764	−	0.458995i	0.377593	−	0.0744587i
$39$	−1.19708	+	0.658099i	−0.191686	+	0.105380i
$40$	3.56208	−	5.22605i	0.563214	−	0.826311i
$41$	2.05023	−	1.92529i	0.320192	−	0.300680i	−0.507738	−	0.861511i	$-0.669518\pi$
$41$	2.05023	−	1.92529i	0.320192	−	0.300680i	0.827930	+	0.560831i	$0.189518\pi$
$42$	−8.86072	+	2.93988i	−1.36724	+	0.453633i
$43$	0.729437	−	0.529967i	0.111238	−	0.0808192i	−0.530776	−	0.847512i	$-0.678099\pi$
$43$	0.729437	−	0.529967i	0.111238	−	0.0808192i	0.642014	+	0.766693i	$0.278099\pi$
$44$	5.58041	−	0.420616i	0.841278	−	0.0634103i
$45$	−2.52241	−	0.787769i	−0.376019	−	0.117434i
$46$	0.0279560	+	0.210777i	0.00412189	+	0.0310774i
$47$	2.32115	+	5.86254i	0.338574	+	0.855140i	0.994919	+	0.100679i	$0.0321015\pi$
$47$	2.32115	+	5.86254i	0.338574	+	0.855140i	−0.656345	+	0.754461i	$0.727898\pi$
$48$	−4.78946	−	2.48041i	−0.691300	−	0.358016i
$49$	13.7268	−	9.97314i	1.96098	−	1.42473i
$50$	5.59727	−	4.32095i	0.791573	−	0.611074i
$51$	5.30447	−	7.30098i	0.742775	−	1.02234i
$52$	2.02601	−	0.0251231i	0.280956	−	0.00348395i
$53$	−4.68128	+	7.37652i	−0.643024	+	1.01324i	0.353932	+	0.935271i	$0.384845\pi$
$53$	−4.68128	+	7.37652i	−0.643024	+	1.01324i	−0.996956	+	0.0779723i	$0.975155\pi$
$54$	−1.44567	+	7.84229i	−0.196730	+	1.06720i
$55$	6.07763	+	1.48651i	0.819507	+	0.200441i
$56$	13.6476	+	2.34124i	1.82374	+	0.312862i
$57$		−	2.26207i		−	0.299619i
$58$	2.18900	−	3.05252i	0.287430	−	0.400815i
$59$	−3.28620	+	1.54637i	−0.427827	+	0.201320i	−0.627623	−	0.778518i	$-0.715972\pi$
$59$	−3.28620	+	1.54637i	−0.427827	+	0.201320i	0.199796	+	0.979837i	$0.435972\pi$
$60$	−4.23166	−	4.29619i	−0.546305	−	0.554636i
$61$	8.01345	−	8.53346i	1.02602	−	1.09260i	0.0303569	−	0.999539i	$-0.490336\pi$
$61$	8.01345	−	8.53346i	1.02602	−	1.09260i	0.995661	−	0.0930586i	$-0.0296644\pi$
$62$	−2.91950	+	6.30542i	−0.370776	+	0.800789i
$63$	−0.725130	−	5.74000i	−0.0913578	−	0.723171i
$64$	4.53486	+	6.59053i	0.566857	+	0.823816i
$65$	2.16232	+	0.675310i	0.268203	+	0.0837619i
$66$	0.635925	−	5.29781i	0.0782770	−	0.652116i
$67$	−0.269023	+	4.27600i	−0.0328664	+	0.522396i	0.946808	+	0.321800i	$0.104288\pi$
$67$	−0.269023	+	4.27600i	−0.0328664	+	0.522396i	−0.979674	+	0.200596i	$0.935712\pi$
$68$	−12.0399	+	5.84896i	−1.46005	+	0.709291i
$69$	0.202329	+	0.0127295i	0.0243576	+	0.00153245i
$70$	13.6959	+	7.21763i	1.63698	+	0.862672i
$71$	−8.35992	+	3.30993i	−0.992140	+	0.392816i	−0.807421	−	0.589976i	$-0.799137\pi$
$71$	−8.35992	+	3.30993i	−0.992140	+	0.392816i	−0.184719	+	0.982791i	$0.559137\pi$
$72$	2.08239	−	2.61470i	0.245412	−	0.308146i
$73$	−0.209163	−	0.0984244i	−0.0244806	−	0.0115197i	0.413500	−	0.910504i	$-0.364306\pi$
$73$	−0.209163	−	0.0984244i	−0.0244806	−	0.0115197i	−0.437981	+	0.898984i	$0.644306\pi$
$74$	6.41368	−	2.58547i	0.745576	−	0.300555i
$75$	−3.00955	−	6.03307i	−0.347513	−	0.696638i
$76$	−1.57978	+	2.95997i	−0.181214	+	0.339532i
$77$	2.56686	+	13.4559i	0.292521	+	1.53345i
$78$	0.350227	−	1.89987i	0.0396554	−	0.215118i
$79$	4.41669	+	5.33886i	0.496916	+	0.600668i	0.958028	−	0.286674i	$-0.0925495\pi$
$79$	4.41669	+	5.33886i	0.496916	+	0.600668i	−0.461112	+	0.887342i	$0.652549\pi$
$80$	2.53685	+	8.57697i	0.283629	+	0.958934i
$81$	3.77304	+	1.49385i	0.419227	+	0.165984i
$82$	0.274354	+	3.96801i	0.0302974	+	0.438193i
$83$	−0.0671268	+	0.0811423i	−0.00736812	+	0.00890653i	−0.774184	−	0.632960i	$-0.781840\pi$
$83$	−0.0671268	+	0.0811423i	−0.00736812	+	0.00890653i	0.766816	+	0.641867i	$0.221840\pi$
$84$	4.70765	−	12.3349i	0.513646	−	1.34584i
$85$	−14.8249	+	2.04552i	−1.60798	+	0.221868i
$86$	−0.0721730	+	1.27306i	−0.00778262	+	0.137277i
$87$	−2.45170	−	2.61080i	−0.262850	−	0.279907i
$88$	−4.53201	+	6.48819i	−0.483113	+	0.691643i
$89$	−5.81576	+	12.3591i	−0.616469	+	1.31006i	0.315981	+	0.948765i	$0.397666\pi$
$89$	−5.81576	+	12.3591i	−0.616469	+	1.31006i	−0.932450	+	0.361298i	$0.882334\pi$
$90$	3.11954	−	2.05784i	0.328829	−	0.216915i
$91$	0.621613	+	4.92057i	0.0651627	+	0.515816i
$92$	−0.255863	−	0.157960i	−0.0266755	−	0.0164684i
$93$	5.35990	+	3.89419i	0.555796	+	0.403809i
$94$	−8.49756	−	2.70290i	−0.876457	−	0.278783i
$95$	−2.70492	+	2.59901i	−0.277519	+	0.266652i
$96$	7.00168	−	3.02643i	0.714606	−	0.308884i
$97$	11.8143	−	0.743293i	1.19956	−	0.0754700i	0.549594	−	0.835432i	$-0.314782\pi$
$97$	11.8143	−	0.743293i	1.19956	−	0.0754700i	0.649968	+	0.759962i	$0.274782\pi$
$98$	−1.35818	+	23.9569i	−0.137197	+	2.42002i
$99$	3.14494	+	1.02185i	0.316078	+	0.102700i
$100$	−0.275302	+	9.99621i	−0.0275302	+	0.999621i
$101$	2.30411	−	0.748652i	0.229268	−	0.0744936i	−0.192130	−	0.981369i	$-0.561540\pi$
$101$	2.30411	−	0.748652i	0.229268	−	0.0744936i	0.421398	+	0.906876i	$0.361540\pi$
$102$	3.25050	+	12.3417i	0.321848	+	1.22201i
$103$	3.01921	−	11.7590i	0.297492	−	1.15865i	−0.627485	−	0.778629i	$-0.715916\pi$
$103$	3.01921	−	11.7590i	0.297492	−	1.15865i	0.924976	−	0.380025i	$-0.124084\pi$
$104$	−1.78511	+	2.24144i	−0.175045	+	0.219791i
$105$	9.27821	−	11.4806i	0.905460	−	1.12039i
$106$	−3.89080	−	11.7268i	−0.377908	−	1.13900i
$107$	1.96491	−	6.04738i	0.189955	−	0.584622i	−0.810043	−	0.586370i	$-0.800556\pi$
$107$	1.96491	−	6.04738i	0.189955	−	0.584622i	0.999998	+	0.00174817i	$0.000556460\pi$
$108$	−7.29576	−	8.59969i	−0.702035	−	0.827506i
$109$	−7.71101	+	14.0263i	−0.738581	+	1.34347i	0.193456	+	0.981109i	$0.438030\pi$
$109$	−7.71101	+	14.0263i	−0.738581	+	1.34347i	−0.932037	+	0.362364i	$0.881970\pi$
$110$	−7.06562	+	5.32650i	−0.673681	+	0.507862i
$111$	−1.23549	−	6.47665i	−0.117267	−	0.614736i
$112$	−14.7745	+	12.8527i	−1.39606	+	1.21447i
$113$	−16.8944	+	7.94989i	−1.58929	+	0.747863i	−0.998270	−	0.0587947i	$-0.981274\pi$
$113$	−16.8944	+	7.94989i	−1.58929	+	0.747863i	−0.591019	+	0.806657i	$0.701274\pi$
$114$	2.47751	+	2.02383i	0.232040	+	0.189549i
$115$	−0.217245	−	0.256565i	−0.0202582	−	0.0239249i
$116$	1.38478	+	5.12850i	0.128574	+	0.476170i
$117$	1.11317	+	0.440736i	0.102913	+	0.0407461i
$118$	1.24646	−	4.98268i	0.114746	−	0.458693i
$119$	−17.5564	−	27.6645i	−1.60939	−	2.53600i
$120$	8.49134	−	0.790956i	0.775150	−	0.0722041i
$121$	3.07093	+	0.788481i	0.279175	+	0.0716801i
$122$	2.17669	+	16.4114i	0.197068	+	1.48581i
$123$	3.76251	+	0.475315i	0.339254	+	0.0428577i
$124$	−4.29392	−	8.83888i	−0.385606	−	0.793755i
$125$	−3.75635	+	10.5304i	−0.335978	+	0.941870i
$126$	6.93542	+	4.34127i	0.617856	+	0.386751i
$127$	−2.16944	+	17.1729i	−0.192507	+	1.52385i	0.539171	+	0.842196i	$0.318738\pi$
$127$	−2.16944	+	17.1729i	−0.192507	+	1.52385i	−0.731678	+	0.681651i	$0.761262\pi$
$128$	−11.2754	−	0.929671i	−0.996618	−	0.0821721i
$129$	1.17758	+	0.302350i	0.103680	+	0.0266205i
$130$	−2.67421	+	1.76407i	−0.234544	+	0.154719i
$131$	10.4741	−	6.64706i	0.915126	−	0.580757i	0.00723997	−	0.999974i	$-0.497695\pi$
$131$	10.4741	−	6.64706i	0.915126	−	0.580757i	0.907886	+	0.419217i	$0.137695\pi$
$132$	5.23342	+	5.43634i	0.455510	+	0.473173i
$133$	−7.63611	−	3.02335i	−0.662135	−	0.262158i
$134$	−4.44255	−	4.12030i	−0.383778	−	0.355939i
$135$	−4.77548	−	11.6693i	−0.411008	−	1.00434i
$136$	4.36584	−	18.4195i	0.374367	−	1.57946i
$137$	18.6872	−	8.79354i	1.59656	−	0.751283i	0.597826	−	0.801626i	$-0.296031\pi$
$137$	18.6872	−	8.79354i	1.59656	−	0.751283i	0.998732	+	0.0503427i	$0.0160314\pi$
$138$	−0.194962	+	0.210210i	−0.0165963	+	0.0178943i
$139$	15.3797	−	2.93383i	1.30449	−	0.248845i	0.512134	−	0.858905i	$-0.328855\pi$
$139$	15.3797	−	2.93383i	1.30449	−	0.248845i	0.792355	+	0.610061i	$0.208855\pi$
$140$	−20.1585	+	8.54285i	−1.70371	+	0.722003i
$141$	−4.09595	+	7.45051i	−0.344941	+	0.627446i
$142$	3.85430	−	12.1174i	0.323446	−	1.01687i
$143$	−2.69598	−	0.875976i	−0.225449	−	0.0732528i
$144$	1.00065	+	4.62003i	0.0833875	+	0.385003i
$145$	−0.305037	+	5.93135i	−0.0253319	+	0.492572i
$146$	0.294932	−	0.141024i	0.0244087	−	0.0116713i
$147$	22.1601	+	5.68975i	1.82774	+	0.469283i
$148$	−2.90649	+	9.33768i	−0.238912	+	0.767552i
$149$	22.6794	−	7.36899i	1.85797	−	0.603691i	0.862797	−	0.505550i	$-0.168710\pi$
$149$	22.6794	−	7.36899i	1.85797	−	0.603691i	0.995173	−	0.0981407i	$-0.0312895\pi$
$150$	9.30023	+	2.10149i	0.759361	+	0.171586i
$151$	−0.856420	+	2.63579i	−0.0696945	+	0.214498i	−0.979837	−	0.199797i	$-0.935972\pi$
$151$	−0.856420	+	2.63579i	−0.0696945	+	0.214498i	0.910143	+	0.414295i	$0.135972\pi$
$152$	−1.82847	−	4.37847i	−0.148309	−	0.355141i
$153$	−7.89375	+	0.496633i	−0.638172	+	0.0401504i
$154$	−17.0340	−	9.22745i	−1.37264	−	0.743569i
$155$	−1.50168	−	10.8834i	−0.120618	−	0.874180i
$156$	1.76747	+	2.08336i	0.141511	+	0.166802i
$157$	5.31333	+	3.86036i	0.424050	+	0.308090i	0.779265	−	0.626694i	$-0.215592\pi$
$157$	5.31333	+	3.86036i	0.424050	+	0.308090i	−0.355215	+	0.934785i	$0.615592\pi$
$158$	−9.79884	+	0.0607520i	−0.779554	+	0.00483317i
$159$	−11.6876	+	1.47648i	−0.926886	+	0.117093i
$160$	−11.6635	−	4.89519i	−0.922080	−	0.386999i
$161$	0.313393	−	0.665994i	0.0246988	−	0.0524877i
$162$	−5.01179	+	2.79586i	−0.393763	+	0.219663i
$163$	−6.88052	+	6.46124i	−0.538924	+	0.506083i	−0.905524	−	0.424295i	$-0.860522\pi$
$163$	−6.88052	+	6.46124i	−0.538924	+	0.506083i	0.366600	+	0.930379i	$0.380522\pi$
$164$	−4.59137	−	3.24962i	−0.358526	−	0.253752i
$165$	3.67934	+	7.59214i	0.286436	+	0.591047i
$166$	−0.0288132	−	0.146116i	−0.00223633	−	0.0113408i
$167$	3.68577	+	3.04913i	0.285213	+	0.235949i	0.769018	−	0.639227i	$-0.220746\pi$
$167$	3.68577	+	3.04913i	0.285213	+	0.235949i	−0.483805	+	0.875176i	$0.660746\pi$
$168$	9.29776	+	16.1917i	0.717338	+	1.24922i
$169$	11.1328	+	4.40780i	0.856372	+	0.339062i
$170$	11.0232	−	18.0669i	0.845441	−	1.38566i
$171$	−1.52758	+	1.26372i	−0.116817	+	0.0966394i
$172$	−1.32973	−	1.21803i	−0.101391	−	0.0928737i
$173$	3.60802	+	18.9139i	0.274313	+	1.43800i	0.806431	+	0.591328i	$0.201396\pi$
$173$	3.60802	+	18.9139i	0.274313	+	1.43800i	−0.532118	+	0.846670i	$0.678604\pi$
$174$	5.05293	−	0.349368i	0.383062	−	0.0264855i
$175$	−24.3883	+	2.09596i	−1.84358	+	0.158439i
$176$	−3.05142	−	10.7685i	−0.230009	−	0.811705i
$177$	−4.43115	−	2.08514i	−0.333065	−	0.156729i
$178$	−8.33293	−	17.4271i	−0.624579	−	1.30622i
$179$	−2.32881	−	5.88189i	−0.174063	−	0.439633i	0.816387	−	0.577505i	$-0.195974\pi$
$179$	−2.32881	−	5.88189i	−0.174063	−	0.439633i	−0.990450	+	0.137872i	$0.955974\pi$
$180$	−0.537174	+	5.25775i	−0.0400386	+	0.391890i
$181$	13.8945	+	0.874166i	1.03277	+	0.0649763i	0.570116	−	0.821564i	$-0.306898\pi$
$181$	13.8945	+	0.874166i	1.03277	+	0.0649763i	0.462652	+	0.886540i	$0.346898\pi$
$182$	−5.94534	−	3.72153i	−0.440698	−	0.275858i
$183$	15.7536	+	0.991134i	1.16454	+	0.0732668i
$184$	0.401919	−	0.138907i	0.0296298	−	0.0102404i
$185$	−6.32508	+	8.91870i	−0.465029	+	0.655716i
$186$	−9.06047	+	2.38631i	−0.664346	+	0.174972i
$187$	18.5793	−	2.34711i	1.35865	−	0.171638i
$188$	10.5629	−	6.88863i	0.770380	−	0.502405i
$189$	18.8972	−	20.1235i	1.37457	−	1.46377i
$190$	−0.426489	−	5.28781i	−0.0309408	−	0.383618i
$191$	−5.91175	−	12.5631i	−0.427759	−	0.909034i	−0.996264	−	0.0863546i	$-0.972478\pi$
$191$	−5.91175	−	12.5631i	−0.427759	−	0.909034i	0.568505	−	0.822679i	$-0.307522\pi$
$192$	−2.94960	+	10.3762i	−0.212869	+	0.748837i
$193$		−	20.7171i		−	1.49125i	−0.666368	−	0.745623i	$-0.732152\pi$
$193$		−	20.7171i		−	1.49125i	0.666368	−	0.745623i	$-0.267848\pi$
$194$	−9.75595	+	13.6045i	−0.700436	+	0.976746i
$195$	1.15691	+	2.82702i	0.0828479	+	0.202447i
$196$	−25.0234	−	22.9213i	−1.78739	−	1.63724i
$197$	−9.27206	+	14.6104i	−0.660607	+	1.04095i	0.334524	+	0.942387i	$0.391425\pi$
$197$	−9.27206	+	14.6104i	−0.660607	+	1.04095i	−0.995131	+	0.0985629i	$0.968575\pi$
$198$	−3.93289	+	2.53023i	−0.279498	+	0.179815i
$199$	10.0281	+	7.28587i	0.710876	+	0.516482i	0.883456	−	0.468514i	$-0.155210\pi$
$199$	10.0281	+	7.28587i	0.710876	+	0.516482i	−0.172580	+	0.984995i	$0.555210\pi$
$200$	−10.7019	−	9.24494i	−0.756740	−	0.653716i
$201$	−4.67385	+	3.39575i	−0.329668	+	0.239518i
$202$	−1.24149	+	3.19336i	−0.0873512	+	0.224684i
$203$	−12.0901	+	4.78681i	−0.848559	+	0.335968i
$204$	−16.4253	−	7.48181i	−1.15000	−	0.523831i
$205$	−3.75456	−	5.04521i	−0.262230	−	0.352373i
$206$	10.1777	+	13.8273i	0.709116	+	0.963397i
$207$	−0.104437	−	0.143745i	−0.00725886	−	0.00999096i
$208$	−0.857801	−	3.96049i	−0.0594778	−	0.274611i
$209$	3.42183	−	3.21332i	0.236693	−	0.222270i
$210$	4.27291	+	20.4333i	0.294859	+	1.41003i
$211$	−5.19111	−	9.44259i	−0.357371	−	0.650055i	0.635115	−	0.772418i	$-0.280953\pi$
$211$	−5.19111	−	9.44259i	−0.357371	−	0.650055i	−0.992485	+	0.122363i	$0.960953\pi$
$212$	16.3246	+	6.23035i	1.12118	+	0.427902i
$213$	−10.6243	−	5.84078i	−0.727967	−	0.400203i
$214$	4.86535	+	7.56252i	0.332588	+	0.516963i
$215$	−0.991434	−	1.75550i	−0.0676152	−	0.119724i
$216$	15.9461	−	0.296624i	1.08499	−	0.0201827i
$217$	20.3094	−	12.8888i	1.37869	−	0.874945i
$218$	−8.46322	−	20.9944i	−0.573201	−	1.42192i
$219$	−0.0775173	−	0.301910i	−0.00523813	−	0.0204012i
$220$	0.487692	−	12.5041i	0.0328802	−	0.843023i
$221$	6.76687	−	0.425735i	0.455189	−	0.0286381i
$222$	8.19884	+	4.44138i	0.550270	+	0.298086i
$223$	3.90520	+	7.10353i	0.261511	+	0.475687i	0.974168	−	0.225826i	$-0.0725081\pi$
$223$	3.90520	+	7.10353i	0.261511	+	0.475687i	−0.712656	+	0.701513i	$0.752508\pi$
$224$	−0.858352	−	27.6806i	−0.0573510	−	1.84949i
$225$	−2.39283	+	5.40278i	−0.159522	+	0.360185i
$226$	6.40805	−	25.6160i	0.426257	−	1.70395i
$227$	−15.7096	−	14.7523i	−1.04268	−	0.979145i	−0.0428827	−	0.999080i	$-0.513654\pi$
$227$	−15.7096	−	14.7523i	−1.04268	−	0.979145i	−0.999801	+	0.0199347i	$0.993654\pi$
$228$	−4.43315	+	0.902777i	−0.293593	+	0.0597879i
$229$	−20.9511	−	13.2960i	−1.38449	−	0.878622i	−0.385460	−	0.922725i	$-0.625957\pi$
$229$	−20.9511	−	13.2960i	−1.38449	−	0.878622i	−0.999027	+	0.0441026i	$0.985957\pi$
$230$	0.475365	−	0.00839062i	0.0313446	−	0.000553261i
$231$	−11.7741	+	14.2324i	−0.774676	+	0.936423i
$232$	−6.85587	−	3.07171i	−0.450110	−	0.201668i
$233$	0.614147	+	2.39195i	0.0402341	+	0.156702i	0.985526	−	0.169524i	$-0.0542231\pi$
$233$	0.614147	+	2.39195i	0.0402341	+	0.156702i	−0.945292	+	0.326226i	$0.894223\pi$
$234$	−1.47865	+	0.824871i	−0.0966621	+	0.0539235i
$235$	13.6151	−	3.66243i	0.888154	−	0.238911i
$236$	4.34204	+	5.82307i	0.282642	+	0.379050i
$237$	−1.75072	+	9.17759i	−0.113721	+	0.596149i
$238$	46.0065	+	5.52242i	2.98216	+	0.357965i
$239$	−17.7846	−	2.24672i	−1.15039	−	0.145328i	−0.473075	−	0.881022i	$-0.656856\pi$
$239$	−17.7846	−	2.24672i	−1.15039	−	0.145328i	−0.677314	+	0.735694i	$0.736856\pi$
$240$	−6.73075	+	10.0077i	−0.434468	+	0.645994i
$241$	−3.98367	+	20.8831i	−0.256611	+	1.34520i	0.587584	+	0.809163i	$0.300079\pi$
$241$	−3.98367	+	20.8831i	−0.256611	+	1.34520i	−0.844195	+	0.536037i	$0.819921\pi$
$242$	−3.61108	+	2.65796i	−0.232129	+	0.170860i
$243$	−3.53653	−	10.8843i	−0.226868	−	0.698229i
$244$	−19.9218	−	12.2989i	−1.27536	−	0.787358i
$245$	−18.6572	−	33.0357i	−1.19197	−	2.11057i
$246$	−3.88682	+	3.69559i	−0.247815	+	0.235622i
$247$	1.30951	−	1.08332i	0.0833220	−	0.0689300i
$248$	13.5224	+	3.20511i	0.858671	+	0.203525i
$249$	−0.142000			−0.00899891
$250$	−8.17259	−	13.5355i	−0.516880	−	0.856058i
$251$			27.4249i			1.73105i	0.500869	+	0.865523i	$0.333014\pi$
$251$			27.4249i			1.73105i	−0.500869	+	0.865523i	$0.666986\pi$
$252$	−10.9597	+	3.71189i	−0.690397	+	0.233827i
$253$	0.268157	+	0.324146i	0.0168589	+	0.0203789i
$254$	−16.8674	−	17.7403i	−1.05836	−	1.11313i
$255$	−14.8673	−	13.6444i	−0.931029	−	0.854448i
$256$	11.1061	−	11.5175i	0.694133	−	0.719846i
$257$	−11.9318	+	3.87686i	−0.744283	+	0.241832i	−0.656519	−	0.754309i	$-0.727972\pi$
$257$	−11.9318	+	3.87686i	−0.744283	+	0.241832i	−0.0877635	+	0.996141i	$0.527972\pi$
$258$	−1.38470	+	1.01922i	−0.0862077	+	0.0634539i
$259$	−23.5146	−	4.48565i	−1.46113	−	0.278725i
$260$	0.460489	−	4.50717i	0.0285583	−	0.279523i
$261$	−0.393413	+	3.11418i	−0.0243516	+	0.192763i
$262$	−2.09085	+	17.4186i	−0.129173	+	1.07613i
$263$	−14.9980	−	2.86102i	−0.924816	−	0.176418i	−0.297088	−	0.954850i	$-0.596015\pi$
$263$	−14.9980	−	2.86102i	−0.924816	−	0.176418i	−0.627729	+	0.778432i	$0.716015\pi$
$264$	−10.6363	+	0.868050i	−0.654620	+	0.0534248i
$265$	15.1940	+	12.2793i	0.933359	+	0.754310i
$266$	10.1432	−	5.65843i	0.621918	−	0.346941i
$267$	−17.8394	+	4.58039i	−1.09176	+	0.280315i
$268$	8.48737	−	1.17930i	0.518448	−	0.0720370i
$269$	15.5264	+	12.8446i	0.946662	+	0.783147i	0.976302	−	0.216414i	$-0.0694359\pi$
$269$	15.5264	+	12.8446i	0.946662	+	0.783147i	−0.0296396	+	0.999561i	$0.509436\pi$
$270$	17.0532	+	5.21004i	1.03783	+	0.317073i
$271$	−3.40141	+	5.35977i	−0.206621	+	0.325583i	−0.931796	−	0.362982i	$-0.881759\pi$
$271$	−3.40141	+	5.35977i	−0.206621	+	0.325583i	0.725175	+	0.688564i	$0.241759\pi$
$272$	16.2677	+	21.2612i	0.986374	+	1.28915i
$273$	−4.57804	+	4.87511i	−0.277075	+	0.295055i
$274$	−7.08808	+	28.3344i	−0.428207	+	1.71174i
$275$	4.85109	−	13.1226i	0.292532	−	0.791324i
$276$	−0.0558014	−	0.401601i	−0.00335885	−	0.0241735i
$277$	−9.05572	+	4.97842i	−0.544105	+	0.299124i	−0.730002	−	0.683445i	$-0.760481\pi$
$277$	−9.05572	+	4.97842i	−0.544105	+	0.299124i	0.185897	+	0.982569i	$0.440481\pi$
$278$	−10.5467	+	19.4693i	−0.632547	+	1.16769i
$279$	−0.364595	−	5.79507i	−0.0218277	−	0.346942i
$280$	8.67898	−	29.7215i	0.518668	−	1.77620i
$281$	−16.5039	+	4.23747i	−0.984538	+	0.252786i	−0.706445	−	0.707768i	$-0.749702\pi$
$281$	−16.5039	+	4.23747i	−0.984538	+	0.252786i	−0.278093	+	0.960554i	$0.589702\pi$
$282$	−4.49551	−	11.1519i	−0.267704	−	0.664084i
$283$	−5.35435	−	8.43711i	−0.318283	−	0.501534i	0.647087	−	0.762416i	$-0.275987\pi$
$283$	−5.35435	−	8.43711i	−0.318283	−	0.501534i	−0.965371	+	0.260881i	$0.915987\pi$
$284$	9.82310	+	15.0626i	0.582894	+	0.893801i
$285$	−5.02519	−	0.576458i	−0.297666	−	0.0341464i
$286$	3.37144	−	2.16902i	0.199358	−	0.128257i
$287$	6.63327	−	12.0659i	0.391550	−	0.712226i
$288$	−5.95530	−	3.03750i	−0.350919	−	0.178987i
$289$	−24.3545	+	13.3890i	−1.43262	+	0.787589i
$290$	−6.22333	−	5.64075i	−0.365446	−	0.331236i
$291$	10.9268	+	11.6358i	0.640538	+	0.682104i
$292$	−0.109415	+	0.449192i	−0.00640300	+	0.0262870i
$293$	−22.0475	+	16.0185i	−1.28803	+	0.935810i	−0.999764	−	0.0217403i	$-0.993079\pi$
$293$	−22.0475	+	16.0185i	−1.28803	+	0.935810i	−0.288268	+	0.957550i	$0.593079\pi$
$294$	−26.0579	+	19.1801i	−1.51973	+	1.11861i
$295$	2.59781	+	7.69436i	0.151250	+	0.447983i
$296$	−7.62660	−	11.5375i	−0.443287	−	0.670606i
$297$	5.80825	+	14.6700i	0.337029	+	0.851237i
$298$	−12.2200	+	31.4322i	−0.707887	+	1.82082i
$299$	0.0895277	+	0.123224i	0.00517752	+	0.00712625i
$300$	−10.6224	+	8.30580i	−0.613283	+	0.479536i
$301$	2.59453	−	3.57106i	0.149546	−	0.205833i
$302$	−2.12060	−	3.29618i	−0.122027	−	0.189674i
$303$	2.75823	+	1.75043i	0.158456	+	0.100559i
$304$	6.43136	+	1.91472i	0.368864	+	0.109817i
$305$	−16.9150	−	19.9765i	−0.968548	−	1.14385i
$306$	6.51846	−	9.08987i	0.372635	−	0.519633i
$307$	−26.8732			−1.53373			−0.766867	−	0.641806i	$-0.778185\pi$
$307$	−26.8732			−1.53373			−0.766867	+	0.641806i	$0.778185\pi$
$308$	25.3462	−	10.4006i	1.44424	−	0.592632i
$309$	14.8123	−	6.97015i	0.842643	−	0.396518i
$310$	13.2635	+	8.09251i	0.753316	+	0.459624i
$311$	1.42694	+	1.33999i	0.0809145	+	0.0759838i	0.723949	−	0.689853i	$-0.242325\pi$
$311$	1.42694	+	1.33999i	0.0809145	+	0.0759838i	−0.643035	+	0.765837i	$0.722325\pi$
$312$	−3.86310	+	0.0718601i	−0.218705	+	0.00406828i
$313$	−0.687304	−	5.44058i	−0.0388487	−	0.307519i	−0.999552	−	0.0299409i	$-0.990468\pi$
$313$	−0.687304	−	5.44058i	−0.0388487	−	0.307519i	0.960703	−	0.277579i	$-0.0895319\pi$
$314$	−8.98175	+	2.36557i	−0.506869	+	0.133497i
$315$	−12.9362	+	0.148116i	−0.728871	+	0.00834538i
$316$	8.70030	−	10.7864i	0.489430	−	0.606784i
$317$	−0.230137	+	3.65793i	−0.0129258	+	0.205450i	0.986263	+	0.165182i	$0.0528211\pi$
$317$	−0.230137	+	3.65793i	−0.0129258	+	0.205450i	−0.999189	+	0.0402679i	$0.987179\pi$
$318$	8.83955	−	14.1217i	0.495697	−	0.791904i
$319$	0.466662	−	7.41737i	0.0261280	−	0.415293i
$320$	15.7965	−	8.39467i	0.883051	−	0.469276i
$321$	7.97189	−	3.15629i	0.444948	−	0.176167i
$322$	0.449035	+	0.939091i	0.0250238	+	0.0523335i
$323$	−4.78046	+	10.1590i	−0.265992	+	0.565262i
$324$	1.42182	−	7.99050i	0.0789901	−	0.443917i
$325$	2.05124	−	4.63150i	0.113782	−	0.256909i
$326$	−0.920728	−	13.3166i	−0.0509944	−	0.737536i
$327$	−21.2005	+	4.04422i	−1.17239	+	0.223646i
$328$	7.66692	−	2.12128i	0.423335	−	0.117128i
$329$	19.6764	+	23.7847i	1.08479	+	1.31129i
$330$	−11.6070	−	2.76278i	−0.638946	−	0.152086i
$331$	4.82230	−	12.1797i	0.265057	−	0.669459i	−0.734905	−	0.678170i	$-0.762773\pi$
$331$	4.82230	−	12.1797i	0.265057	−	0.669459i	0.999962	+	0.00871188i	$0.00277311\pi$
$332$	0.185811	+	0.0991701i	0.0101977	+	0.00544267i
$333$	−3.68348	+	4.45256i	−0.201853	+	0.243999i
$334$	−6.63711	+	1.30879i	−0.363167	+	0.0716140i
$335$	9.43057	+	1.68731i	0.515247	+	0.0921878i
$336$	−26.0523	−	4.30318i	−1.42127	−	0.234758i
$337$	−3.20700	−	3.41510i	−0.174696	−	0.186033i	0.635662	−	0.771968i	$-0.280727\pi$
$337$	−3.20700	−	3.41510i	−0.174696	−	0.186033i	−0.810358	+	0.585935i	$0.800727\pi$
$338$	−14.7879	+	8.24953i	−0.804357	+	0.448715i
$339$	−22.7806	−	10.7197i	−1.23727	−	0.582215i
$340$	9.92527	+	28.2371i	0.538273	+	1.53137i
$341$	1.72309	+	13.6397i	0.0933108	+	0.738631i
$342$	−0.0173827	−	2.80369i	−0.000939947	−	0.151606i
$343$	28.6818	−	39.4771i	1.54867	−	2.13156i
$344$	2.52371	−	0.366626i	0.136070	−	0.0197671i
$345$	0.0798395	−	0.446231i	0.00429841	−	0.0240243i
$346$	−23.9433	−	12.9703i	−1.28720	−	0.697286i
$347$	0.694068	+	11.0319i	0.0372595	+	0.592223i	0.971717	+	0.236148i	$0.0758852\pi$
$347$	0.694068	+	11.0319i	0.0372595	+	0.592223i	−0.934457	+	0.356075i	$0.884115\pi$
$348$	−4.13812	+	5.84674i	−0.221827	+	0.313418i
$349$	11.2494	+	3.65515i	0.602166	+	0.195656i	0.594206	−	0.804313i	$-0.297466\pi$
$349$	11.2494	+	3.65515i	0.602166	+	0.195656i	0.00795995	+	0.999968i	$0.497466\pi$
$350$	19.5242	−	28.5862i	1.04361	−	1.52800i
$351$	1.76527	+	5.43294i	0.0942231	+	0.289989i
$352$	14.5241	+	6.29233i	0.774137	+	0.335382i
$353$	−0.616507	+	2.40113i	−0.0328133	+	0.127799i	−0.982880	−	0.184248i	$-0.941015\pi$
$353$	−0.616507	+	2.40113i	−0.0328133	+	0.127799i	0.950066	+	0.312048i	$0.101015\pi$
$354$	6.24818	−	2.98763i	0.332087	−	0.158791i
$355$	5.22259	+	19.4150i	0.277186	+	1.03044i
$356$	26.5421	+	6.46515i	1.40673	+	0.342652i
$357$	13.6526	−	42.0184i	0.722573	−	2.22385i
$358$	8.52561	+	2.71182i	0.450592	+	0.143324i
$359$	32.6388	+	17.9433i	1.72261	+	0.947012i	0.950066	+	0.312049i	$0.101015\pi$
$359$	32.6388	+	17.9433i	1.72261	+	0.947012i	0.772543	+	0.634963i	$0.218985\pi$
$360$	−5.27789	−	5.29234i	−0.278169	−	0.278931i
$361$	−3.03290	−	15.8990i	−0.159626	−	0.836791i
$362$	−13.3885	+	14.4357i	−0.703686	+	0.758721i
$363$	1.82029	+	3.86831i	0.0955403	+	0.203033i
$364$	9.39514	−	3.18199i	0.492439	−	0.166782i
$365$	−0.271952	+	0.439572i	−0.0142346	+	0.0230083i
$366$	−15.1800	+	16.3672i	−0.793471	+	0.855529i
$367$	−7.95866	+	20.1013i	−0.415439	+	1.04928i	0.559899	+	0.828561i	$0.310840\pi$
$367$	−7.95866	+	20.1013i	−0.415439	+	1.04928i	−0.975338	+	0.220718i	$0.929160\pi$
$368$	−0.207452	+	0.564474i	−0.0108142	+	0.0294253i
$369$	−1.78097	−	2.80637i	−0.0927138	−	0.146094i
$370$	−4.10917	−	14.9069i	−0.213626	−	0.774971i
$371$	−10.6367	+	41.4274i	−0.552232	+	2.15080i
$372$	5.49265	−	12.0583i	0.284781	−	0.625196i
$373$	−4.11003	−	0.519218i	−0.212809	−	0.0268841i	0.0182056	−	0.999834i	$-0.494205\pi$
$373$	−4.11003	−	0.519218i	−0.212809	−	0.0268841i	−0.231015	+	0.972950i	$0.574205\pi$
$374$	−14.0519	+	22.4487i	−0.726606	+	1.16079i
$375$	−14.1694	+	5.14827i	−0.731704	+	0.265856i
$376$	−1.90575	+	17.7320i	−0.0982817	+	0.914460i
$377$	0.337250	−	2.66961i	0.0173693	−	0.137492i
$378$	5.13304	+	38.7010i	0.264015	+	1.99056i
$379$	−2.96256	+	11.5384i	−0.152176	+	0.592688i	0.846047	+	0.533108i	$0.178976\pi$
$379$	−2.96256	+	11.5384i	−0.152176	+	0.592688i	−0.998224	+	0.0595799i	$0.981024\pi$
$380$	6.17299	+	4.26380i	0.316667	+	0.218728i
$381$	−19.7067	+	12.5063i	−1.00961	+	0.640716i
$382$	19.0487	+	4.76519i	0.974617	+	0.243808i
$383$	−6.14338	+	15.5164i	−0.313912	+	0.792851i	0.684074	+	0.729413i	$0.260207\pi$
$383$	−6.14338	+	15.5164i	−0.313912	+	0.792851i	−0.997986	+	0.0634384i	$0.979793\pi$
$384$	−8.72545	−	12.5139i	−0.445269	−	0.638597i
$385$	30.5465	−	2.27321i	1.55679	−	0.115853i
$386$	22.6901	+	18.5351i	1.15490	+	0.943414i
$387$	−0.453685	−	0.964130i	−0.0230621	−	0.0490095i
$388$	−6.17170	−	22.8568i	−0.313321	−	1.16038i
$389$	8.92513	−	1.70256i	0.452522	−	0.0863232i	0.0439184	−	0.999035i	$-0.486016\pi$
$389$	8.92513	−	1.70256i	0.452522	−	0.0863232i	0.408604	+	0.912712i	$0.366016\pi$
$390$	−4.13132	−	1.26219i	−0.209197	−	0.0639133i
$391$	−0.881764	−	0.484754i	−0.0445927	−	0.0245151i
$392$	47.4923	−	6.89932i	2.39872	−	0.348468i
$393$	15.9087	+	5.16904i	0.802486	+	0.260744i
$394$	−7.70637	−	23.2268i	−0.388241	−	1.17015i
$395$	12.9858	−	8.45113i	0.653386	−	0.425222i
$396$	0.747479	−	6.57119i	0.0375622	−	0.330215i
$397$	−22.4205	−	5.75661i	−1.12525	−	0.288916i	−0.360195	−	0.932877i	$-0.617290\pi$
$397$	−22.4205	−	5.75661i	−1.12525	−	0.288916i	−0.765058	+	0.643961i	$0.777290\pi$
$398$	−16.9517	+	4.46468i	−0.849714	+	0.223794i
$399$	−3.42214	−	10.5323i	−0.171321	−	0.527273i
$400$	19.7002	−	3.44989i	0.985010	−	0.172494i
$401$	0.595197	−	1.83183i	0.0297227	−	0.0914772i	−0.935095	−	0.354398i	$-0.884686\pi$
$401$	0.595197	−	1.83183i	0.0297227	−	0.0914772i	0.964817	+	0.262921i	$0.0846858\pi$
$402$	0.462447	−	8.15710i	0.0230648	−	0.406839i
$403$	0.312547	+	4.96779i	0.0155691	+	0.247463i
$404$	−2.38675	−	4.21677i	−0.118745	−	0.209792i
$405$	4.28010	−	8.00112i	0.212680	−	0.397579i
$406$	5.57409	−	17.5242i	0.276637	−	0.869712i
$407$	8.04219	−	11.0691i	0.398637	−	0.548676i
$408$	22.8897	−	11.2958i	1.13321	−	0.559223i
$409$	−6.09211	+	0.769613i	−0.301236	+	0.0380549i	−0.274498	−	0.961588i	$-0.588512\pi$
$409$	−6.09211	+	0.769613i	−0.301236	+	0.0380549i	−0.0267373	+	0.999642i	$0.508512\pi$
$410$	8.88484	+	0.401715i	0.438791	+	0.0198393i
$411$	25.1981	+	11.8573i	1.24293	+	0.584878i
$412$	−24.2501	−	1.22402i	−1.19471	−	0.0603032i
$413$	−12.9612	+	12.1714i	−0.637781	+	0.598917i
$414$	0.250872	+	0.0142226i	0.0123297	+	0.000699004i
$415$	0.163151	+	0.169800i	0.00800878	+	0.00833516i
$416$	5.10514	+	2.60388i	0.250300	+	0.127666i
$417$	16.2672	+	13.4574i	0.796606	+	0.659010i
$418$	0.457898	+	6.62261i	0.0223965	+	0.323923i
$419$	13.2660	−	33.5061i	0.648087	−	1.63688i	−0.117135	−	0.993116i	$-0.537371\pi$
$419$	13.2660	−	33.5061i	0.648087	−	1.63688i	0.765223	−	0.643766i	$-0.222629\pi$
$420$	−26.2022	−	13.6014i	−1.27854	−	0.663680i
$421$	1.30897	−	1.08287i	0.0637952	−	0.0527760i	−0.604980	−	0.796241i	$-0.706819\pi$
$421$	1.30897	−	1.08287i	0.0637952	−	0.0527760i	0.668775	+	0.743465i	$0.266819\pi$
$422$	14.9863	+	2.76260i	0.729520	+	0.134481i
$423$	7.31958	−	1.39628i	0.355890	−	0.0678896i
$424$	−21.4290	+	12.3052i	−1.04069	+	0.597591i
$425$	0.766196	+	33.4547i	0.0371659	+	1.62279i
$426$	15.9024	−	6.41055i	0.770475	−	0.310592i
$427$	24.4012	−	51.8551i	1.18086	−	2.50945i
$428$	−12.6357	−	1.43732i	−0.610769	−	0.0694755i
$429$	−1.40711	−	3.55395i	−0.0679357	−	0.171586i
$430$	2.80971	+	0.484754i	0.135496	+	0.0233769i
$431$	−1.94088	+	30.8495i	−0.0934891	+	1.48597i	0.619613	+	0.784907i	$0.287289\pi$
$431$	−1.94088	+	30.8495i	−0.0934891	+	1.48597i	−0.713103	+	0.701060i	$0.752711\pi$
$432$	−13.9418	+	17.7301i	−0.670774	+	0.853042i
$433$	−4.21270	−	0.265041i	−0.202449	−	0.0127370i	−0.0387580	−	0.999249i	$-0.512340\pi$
$433$	−4.21270	−	0.265041i	−0.202449	−	0.0127370i	−0.163691	+	0.986512i	$0.552340\pi$
$434$	−4.05419	+	33.7750i	−0.194608	+	1.62125i
$435$	−6.42466	+	4.78113i	−0.308039	+	0.229237i
$436$	30.5658	+	9.51406i	1.46383	+	0.455641i
$437$	−0.250231	+	0.0316115i	−0.0119702	+	0.00151218i
$438$	0.400016	+	0.185213i	0.0191135	+	0.00884982i
$439$	20.3520	+	19.1118i	0.971347	+	0.912156i	0.996161	−	0.0875365i	$-0.0278994\pi$
$439$	20.3520	+	19.1118i	0.971347	+	0.912156i	−0.0248143	+	0.999692i	$0.507899\pi$
$440$	13.2586	+	11.7213i	0.632078	+	0.558790i
$441$	−8.53764	−	18.1434i	−0.406554	−	0.863971i
$442$	−5.58790	+	7.79223i	−0.265789	+	0.370639i
$443$	7.10749			0.337687			0.168843	−	0.985643i	$-0.445997\pi$
$443$	7.10749			0.337687			0.168843	+	0.985643i	$0.445997\pi$
$444$	−12.1997	+	5.00606i	−0.578973	+	0.237577i
$445$	25.9737	+	16.0693i	1.23127	+	0.761756i
$446$	−11.2740	−	2.07827i	−0.533837	−	0.0984088i
$447$	27.1493	+	17.2295i	1.28412	+	0.814926i
$448$	31.0848	+	23.8252i	1.46862	+	1.12564i
$449$	−12.8919	−	9.36648i	−0.608404	−	0.442031i	0.240448	−	0.970662i	$-0.422706\pi$
$449$	−12.8919	−	9.36648i	−0.608404	−	0.442031i	−0.848852	+	0.528631i	$0.822706\pi$
$450$	−3.77651	−	7.45448i	−0.178026	−	0.351407i
$451$	4.62570	+	6.36674i	0.217816	+	0.299798i
$452$	22.3224	+	29.9365i	1.04996	+	1.40809i
$453$	−3.47460	+	1.37569i	−0.163251	+	0.0646357i
$454$	30.2124	−	4.00716i	1.41794	−	0.188066i
$455$	11.0895	−	0.126971i	0.519882	−	0.00595251i
$456$	2.97750	−	5.66306i	0.139434	−	0.265197i
$457$	−12.9178	−	17.7799i	−0.604271	−	0.831708i	0.391819	−	0.920042i	$-0.371846\pi$
$457$	−12.9178	−	17.7799i	−0.604271	−	0.831708i	−0.996091	+	0.0883338i	$0.971846\pi$
$458$	33.3068	−	11.0508i	1.55632	−	0.516369i
$459$	−25.8338	−	27.5102i	−1.20582	−	1.28407i
$460$	−0.416110	+	0.528145i	−0.0194012	+	0.0246249i
$461$	−17.3806	−	31.6152i	−0.809495	−	1.47247i	−0.880010	−	0.474954i	$-0.842465\pi$
$461$	−17.3806	−	31.6152i	−0.809495	−	1.47247i	0.0705159	−	0.997511i	$-0.477535\pi$
$462$	−5.05384	−	25.6288i	−0.235126	−	1.19236i
$463$	6.17864	−	11.2389i	0.287146	−	0.522316i	−0.692914	−	0.721021i	$-0.743673\pi$
$463$	6.17864	−	11.2389i	0.287146	−	0.522316i	0.980060	+	0.198704i	$0.0636733\pi$
$464$	9.49806	−	4.76061i	0.440937	−	0.221006i
$465$	10.0168	−	10.9146i	0.464520	−	0.506154i
$466$	−3.16922	−	1.46739i	−0.146811	−	0.0679755i
$467$	−22.5726	−	35.5687i	−1.04453	−	1.64592i	−0.711011	−	0.703181i	$-0.751762\pi$
$467$	−22.5726	−	35.5687i	−1.04453	−	1.64592i	−0.333523	−	0.942742i	$-0.608238\pi$
$468$	0.419485	−	2.35747i	0.0193907	−	0.108974i
$469$	5.21631	+	20.3162i	0.240867	+	0.938114i
$470$	−8.16997	+	18.1885i	−0.376853	+	0.838975i
$471$	0.556065	+	8.83840i	0.0256221	+	0.407252i
$472$	−10.2624	−	0.454226i	−0.472365	−	0.0209074i
$473$	1.21541	+	2.21081i	0.0558844	+	0.101653i
$474$	−8.48531	−	10.1285i	−0.389743	−	0.465216i
$475$	5.08438	+	6.67130i	0.233287	+	0.306100i
$476$	−47.2095	+	45.4473i	−2.16385	+	2.08307i
$477$	7.52644	+	7.06779i	0.344612	+	0.323612i
$478$	18.3722	−	17.4683i	0.840326	−	0.798980i
$479$	−8.87103	+	13.9785i	−0.405328	+	0.638694i	−0.984269	−	0.176675i	$-0.943466\pi$
$479$	−8.87103	+	13.9785i	−0.405328	+	0.638694i	0.578942	+	0.815369i	$0.303466\pi$
$480$	−4.93893	−	16.3255i	−0.225430	−	0.745152i
$481$	3.15764	−	3.81693i	0.143976	−	0.174037i
$482$	−19.3079	−	23.0468i	−0.879450	−	1.04975i
$483$	0.961310	−	0.246823i	0.0437411	−	0.0112308i
$484$	0.319659	−	6.33302i	0.0145299	−	0.287864i
$485$	1.35949	−	26.4349i	0.0617313	−	1.20035i
$486$	15.0850	+	5.86464i	0.684269	+	0.266026i
$487$	−0.872581	−	0.166454i	−0.0395404	−	0.00754274i	0.167573	−	0.985860i	$-0.446407\pi$
$487$	−0.872581	−	0.166454i	−0.0395404	−	0.00754274i	−0.207114	+	0.978317i	$0.566407\pi$
$488$	31.2939	−	10.8155i	1.41661	−	0.489594i
$489$	−12.6269	−	1.59515i	−0.571008	−	0.0721351i
$490$	52.8742	+	9.12230i	2.38861	+	0.412104i
$491$	−5.31015	−	1.01297i	−0.239644	−	0.0457145i	0.0661601	−	0.997809i	$-0.478925\pi$
$491$	−5.31015	−	1.01297i	−0.239644	−	0.0457145i	−0.305804	+	0.952095i	$0.598925\pi$
$492$	−0.570080	−	7.56337i	−0.0257012	−	0.340983i
$493$	5.49320	+	16.9063i	0.247401	+	0.761423i
$494$	0.0149012	+	2.40345i	0.000670436	+	0.108136i
$495$	3.07149	−	6.72607i	0.138053	−	0.302315i
$496$	−15.6086	+	11.9427i	−0.700845	+	0.536242i
$497$	−33.9167	+	28.0583i	−1.52137	+	1.25859i
$498$	0.127045	−	0.155524i	0.00569302	−	0.00696921i
$499$		−	30.6793i		−	1.37339i	−0.726944	−	0.686697i	$-0.759060\pi$
$499$		−	30.6793i		−	1.37339i	0.726944	−	0.686697i	$-0.240940\pi$
$500$	22.1364	+	3.15898i	0.989971	+	0.141274i
$501$			6.45015i			0.288172i
$502$	−30.0368	−	24.5366i	−1.34061	−	1.09512i
$503$	3.44109	−	2.84672i	0.153431	−	0.126929i	−0.557541	−	0.830149i	$-0.688255\pi$
$503$	3.44109	−	2.84672i	0.153431	−	0.126929i	0.710972	+	0.703220i	$0.248255\pi$
$504$	5.74004	−	15.3244i	0.255682	−	0.682605i
$505$	−1.07596	−	5.30937i	−0.0478795	−	0.236264i
$506$	−0.594932	+	0.00368853i	−0.0264480	+	0.000163975i
$507$	4.98921	+	15.3552i	0.221579	+	0.681949i
$508$	34.5208	−	2.60196i	1.53161	−	0.115444i
$509$	14.2129	+	2.71127i	0.629978	+	0.120175i	0.492475	−	0.870327i	$-0.336092\pi$
$509$	14.2129	+	2.71127i	0.629978	+	0.120175i	0.137503	+	0.990501i	$0.456092\pi$
$510$	28.2454	−	4.07587i	1.25073	−	0.180483i
$511$	−1.12277	−	0.141839i	−0.0496683	−	0.00627457i
$512$	2.67801	+	22.4684i	0.118352	+	0.992972i
$513$	−9.29195	−	1.77253i	−0.410250	−	0.0782593i
$514$	6.42903	−	16.5367i	0.283572	−	0.729402i
$515$	−25.3533	−	9.70381i	−1.11720	−	0.427601i
$516$	0.122576	−	2.42845i	0.00539611	−	0.106907i
$517$	−17.0888	+	4.38765i	−0.751562	+	0.192968i
$518$	25.9509	−	21.7409i	1.14022	−	0.955239i
$519$	−16.5498	+	20.0053i	−0.726457	+	0.878135i
$520$	4.52444	+	4.53683i	0.198410	+	0.198953i
$521$	17.6012	−	27.7351i	0.771123	−	1.21510i	−0.200762	−	0.979640i	$-0.564342\pi$
$521$	17.6012	−	27.7351i	0.771123	−	1.21510i	0.971885	−	0.235456i	$-0.0756582\pi$
$522$	−3.05879	−	3.21708i	−0.133880	−	0.140808i
$523$	−2.89834	−	2.72172i	−0.126736	−	0.119013i	0.618588	−	0.785716i	$-0.287705\pi$
$523$	−2.89834	−	2.72172i	−0.126736	−	0.119013i	−0.745324	+	0.666703i	$0.767705\pi$
$524$	−17.2069	−	17.8741i	−0.751687	−	0.780833i
$525$	−23.1396	−	23.5372i	−1.00990	−	1.02725i
$526$	16.5519	−	13.8667i	0.721698	−	0.604616i
$527$	−15.8417	−	28.8160i	−0.690077	−	1.25525i
$528$	8.56539	−	12.4259i	0.372761	−	0.540769i
$529$	1.44276	+	22.9321i	0.0627288	+	0.997046i
$530$	−27.0425	+	5.65500i	−1.17465	+	0.245637i
$531$	1.06740	+	4.15724i	0.0463211	+	0.180409i
$532$	−2.87757	+	16.1717i	−0.124759	+	0.701131i
$533$	1.52673	+	2.40574i	0.0661300	+	0.104204i
$534$	10.9440	−	23.6364i	0.473592	−	1.02285i
$535$	−12.9335	−	5.90614i	−0.559164	−	0.255345i
$536$	−6.30187	+	10.3508i	−0.272199	+	0.447086i
$537$	4.10947	−	7.47510i	0.177337	−	0.322574i
$538$	−27.9590	+	5.51334i	−1.20540	+	0.237697i
$539$	22.8720	+	41.6040i	0.985167	+	1.79201i
$540$	−20.9634	+	14.0160i	−0.902122	+	0.603153i
$541$	14.9405	+	15.9100i	0.642343	+	0.684026i	0.964928	−	0.262514i	$-0.0845517\pi$
$541$	14.9405	+	15.9100i	0.642343	+	0.684026i	−0.322585	+	0.946541i	$0.604552\pi$
$542$	−2.82705	−	8.52064i	−0.121432	−	0.365993i
$543$	11.0342	+	15.1873i	0.473523	+	0.651748i
$544$	−37.8405	−	1.20497i	−1.62240	−	0.0516626i
$545$	29.1943	+	20.7044i	1.25055	+	0.886879i
$546$	−1.24353	−	9.37571i	−0.0532182	−	0.401243i
$547$	27.9043	−	11.0481i	1.19310	−	0.472383i	0.314188	−	0.949361i	$-0.398268\pi$
$547$	27.9043	−	11.0481i	1.19310	−	0.472383i	0.878915	+	0.476978i	$0.158268\pi$
$548$	−24.6913	−	33.1134i	−1.05476	−	1.41453i
$549$	−8.13158	−	11.1922i	−0.347047	−	0.477670i
$550$	10.0322	+	17.0537i	0.427776	+	0.727171i
$551$	3.60482	+	2.61906i	0.153571	+	0.111576i
$552$	0.489773	+	0.298189i	0.0208461	+	0.0126918i
$553$	28.6411	+	18.1762i	1.21794	+	0.772929i
$554$	2.64942	−	14.3723i	0.112563	−	0.610619i
$555$	−14.7027	+	1.09415i	−0.624096	+	0.0464439i
$556$	−11.8876	−	28.9699i	−0.504146	−	1.22860i
$557$	−2.49509			−0.105720			−0.0528601	−	0.998602i	$-0.516834\pi$
$557$	−2.49509			−0.105720			−0.0528601	+	0.998602i	$0.516834\pi$
$558$	6.67318	+	4.78542i	0.282498	+	0.202583i
$559$	0.388919	+	0.826494i	0.0164495	+	0.0349570i
$560$	24.7872	+	36.0968i	1.04745	+	1.52537i
$561$	18.4076	+	17.2859i	0.777172	+	0.729813i
$562$	10.1246	−	21.8668i	0.427082	−	0.922397i
$563$	14.1410	−	1.78643i	0.595973	−	0.0752889i	0.178440	−	0.983951i	$-0.442895\pi$
$563$	14.1410	−	1.78643i	0.595973	−	0.0752889i	0.417533	+	0.908662i	$0.362895\pi$
$564$	16.2360	+	5.05370i	0.683659	+	0.212799i
$565$	13.3554	+	39.5568i	0.561865	+	1.66417i
$566$	14.0311	+	1.68423i	0.589771	+	0.0707934i
$567$	19.8274	+	1.24743i	0.832671	+	0.0523872i
$568$	−25.2857	−	2.71758i	−1.06096	−	0.114027i
$569$	−2.58014	+	41.0102i	−0.108165	+	1.71924i	0.452981	+	0.891520i	$0.350360\pi$
$569$	−2.58014	+	41.0102i	−0.108165	+	1.71924i	−0.561147	+	0.827716i	$0.689640\pi$
$570$	5.12730	−	4.98803i	0.214759	−	0.208926i
$571$	6.18914	+	15.6320i	0.259008	+	0.654178i	0.999847	−	0.0175040i	$-0.00557198\pi$
$571$	6.18914	+	15.6320i	0.259008	+	0.654178i	−0.740839	+	0.671682i	$0.765572\pi$
$572$	−0.640771	+	5.63311i	−0.0267920	+	0.235532i
$573$	7.97146	−	16.9402i	0.333013	−	0.707688i
$574$	7.28035	+	18.0601i	0.303876	+	0.753815i
$575$	−0.625322	+	0.417227i	−0.0260777	+	0.0173996i
$576$	8.65488	−	3.80488i	0.360620	−	0.158536i
$577$	−28.4701	+	5.43097i	−1.18523	+	0.226094i	−0.742053	−	0.670341i	$-0.766148\pi$
$577$	−28.4701	+	5.43097i	−1.18523	+	0.226094i	−0.443174	+	0.896435i	$0.646148\pi$
$578$	7.12536	−	38.6529i	0.296376	−	1.60775i
$579$	21.5244	−	17.8065i	0.894522	−	0.740013i
$580$	11.7459	−	1.76936i	0.487720	−	0.0734686i
$581$	−0.189789	+	0.479353i	−0.00787379	+	0.0198869i
$582$	−22.5200	+	1.55707i	−0.933483	+	0.0645424i
$583$	−18.8359	−	15.5824i	−0.780104	−	0.645358i
$584$	−0.394082	−	0.521719i	−0.0163072	−	0.0215889i
$585$	1.26277	−	2.36060i	0.0522092	−	0.0975987i
$586$	2.18146	−	38.4787i	0.0901153	−	1.58954i
$587$	30.3308	−	28.4826i	1.25189	−	1.17560i	0.275094	−	0.961417i	$-0.411291\pi$
$587$	30.3308	−	28.4826i	1.25189	−	1.17560i	0.976793	−	0.214184i	$-0.0687091\pi$
$588$	2.30669	−	45.6996i	0.0951262	−	1.88462i
$589$	−7.45807	−	3.50950i	−0.307304	−	0.144606i
$590$	−10.7514	−	4.03877i	−0.442627	−	0.166274i
$591$	−23.1492	+	2.92442i	−0.952231	+	0.120295i
$592$	19.4597	+	1.96948i	0.799790	+	0.0809450i
$593$	−23.5725	+	32.4448i	−0.968008	+	1.33235i	−0.0249607	+	0.999688i	$0.507946\pi$
$593$	−23.5725	+	32.4448i	−0.968008	+	1.33235i	−0.943047	+	0.332660i	$0.892054\pi$
$594$	−21.2636	−	6.76351i	−0.872457	−	0.277510i
$595$	−65.9306	+	31.9516i	−2.70289	+	1.30989i
$596$	−23.4928	−	41.5057i	−0.962301	−	1.70014i
$597$	1.04949	+	16.6812i	0.0429528	+	0.682716i
$598$	−0.215059	−	0.0121922i	−0.00879441	−	0.000498578i
$599$	−1.17114	+	3.60439i	−0.0478514	+	0.147271i	−0.972127	−	0.234454i	$-0.924670\pi$
$599$	−1.17114	+	3.60439i	−0.0478514	+	0.147271i	0.924276	+	0.381725i	$0.124670\pi$
$600$	0.406794	−	19.0651i	0.0166073	−	0.778328i
$601$	0.236075	+	0.726564i	0.00962970	+	0.0296372i	0.955756	−	0.294161i	$-0.0950402\pi$
$601$	0.236075	+	0.726564i	0.00962970	+	0.0296372i	−0.946126	+	0.323798i	$0.895040\pi$
$602$	1.58989	+	6.03659i	0.0647991	+	0.246033i
$603$	4.90425	+	1.25920i	0.199716	+	0.0512784i
$604$	5.50735	+	0.626466i	0.224091	+	0.0254905i
$605$	2.53419	−	6.62114i	0.103030	−	0.269187i
$606$	−4.38487	+	1.45485i	−0.178123	+	0.0590991i
$607$	35.1764	+	11.4295i	1.42776	+	0.463909i	0.918060	−	0.396441i	$-0.129755\pi$
$607$	35.1764	+	11.4295i	1.42776	+	0.463909i	0.509704	+	0.860350i	$0.329755\pi$
$608$	−7.85109	+	5.33081i	−0.318404	+	0.216193i
$609$	−15.3649	−	8.44693i	−0.622617	−	0.342287i
$610$	37.0125	−	0.653304i	1.49859	−	0.0264515i
$611$	−6.27466	+	1.19696i	−0.253846	+	0.0484236i
$612$	4.12363	+	15.2718i	0.166688	+	0.617325i
$613$	2.91013	+	6.18433i	0.117539	+	0.249783i	0.954936	−	0.296812i	$-0.0959236\pi$
$613$	2.91013	+	6.18433i	0.117539	+	0.249783i	−0.837397	+	0.546595i	$0.815924\pi$
$614$	24.0429	−	29.4325i	0.970293	−	1.18780i
$615$	2.01474	−	8.23728i	0.0812420	−	0.332159i
$616$	−11.2856	+	37.0654i	−0.454710	+	1.49341i
$617$	2.52910	−	6.38779i	0.101818	−	0.257163i	−0.869934	−	0.493169i	$-0.835839\pi$
$617$	2.52910	−	6.38779i	0.101818	−	0.257163i	0.971752	+	0.236006i	$0.0758385\pi$
$618$	−5.61832	+	22.4591i	−0.226002	+	0.903436i
$619$	−17.4922	+	11.1009i	−0.703070	+	0.446182i	−0.838712	−	0.544576i	$-0.816691\pi$
$619$	−17.4922	+	11.1009i	−0.703070	+	0.446182i	0.135641	+	0.990758i	$0.456691\pi$
$620$	−20.7298	+	7.28648i	−0.832529	+	0.292632i
$621$	0.210832	−	0.821138i	0.00846041	−	0.0329511i
$622$	−2.74426	+	0.363980i	−0.110035	+	0.0145943i
$623$	−8.38104	+	66.3427i	−0.335779	+	2.65797i
$624$	3.37754	−	4.29531i	0.135210	−	0.171950i
$625$	22.4361	+	11.0283i	0.897443	+	0.441130i
$626$	6.57364	+	4.11481i	0.262736	+	0.164461i
$627$	6.27963	+	0.793302i	0.250784	+	0.0316814i
$628$	5.44493	−	11.9536i	0.217276	−	0.477000i
$629$	−8.13859	+	31.6977i	−0.324507	+	1.26387i
$630$	11.4115	−	14.3007i	0.454646	−	0.569754i
$631$	0.814431	+	1.28334i	0.0324220	+	0.0510889i	0.860152	−	0.510037i	$-0.170368\pi$
$631$	0.814431	+	1.28334i	0.0324220	+	0.0510889i	−0.827730	+	0.561126i	$0.810368\pi$
$632$	4.02971	+	19.1793i	0.160293	+	0.762911i
$633$	5.34875	−	13.5094i	0.212594	−	0.536950i
$634$	−3.80041	−	3.52474i	−0.150933	−	0.139985i
$635$	37.5967	+	9.19568i	1.49198	+	0.364920i
$636$	7.55802	+	22.3158i	0.299695	+	0.884879i
$637$	7.31883	+	15.5533i	0.289983	+	0.616245i
$638$	7.70628	+	7.14729i	0.305094	+	0.282964i
$639$	1.99108	+	10.4376i	0.0787661	+	0.412906i
$640$	−4.93866	+	24.8115i	−0.195218	+	0.980760i
$641$	−5.39494	−	2.96589i	−0.213087	−	0.117146i	0.371636	−	0.928378i	$-0.378797\pi$
$641$	−5.39494	−	2.96589i	−0.213087	−	0.117146i	−0.584723	+	0.811233i	$0.698797\pi$
$642$	−3.67540	+	11.5550i	−0.145057	+	0.456039i
$643$	−1.48746	+	4.57792i	−0.0586596	+	0.180536i	−0.976093	−	0.217354i	$-0.930257\pi$
$643$	−1.48746	+	4.57792i	−0.0586596	+	0.180536i	0.917433	+	0.397890i	$0.130257\pi$
$644$	−1.43027	−	0.348386i	−0.0563606	−	0.0137283i
$645$	0.971760	−	2.53894i	0.0382630	−	0.0999705i
$646$	−6.84954	−	14.3248i	−0.269491	−	0.563602i
$647$	−5.32342	+	20.7333i	−0.209285	+	0.815112i	0.774022	+	0.633159i	$0.218242\pi$
$647$	−5.32342	+	20.7333i	−0.209285	+	0.815112i	−0.983307	+	0.181953i	$0.941758\pi$
$648$	7.47943	+	8.70618i	0.293820	+	0.342011i
$649$	−3.14034	−	9.66497i	−0.123269	−	0.379383i
$650$	3.23739	+	6.39030i	0.126981	+	0.250648i
$651$	30.8471	+	10.0228i	1.20899	+	0.392826i
$652$	15.4086	+	10.9057i	0.603446	+	0.427098i
$653$	−0.0160731	−	0.255474i	−0.000628988	−	0.00999748i	0.997700	−	0.0677885i	$-0.0215943\pi$
$653$	−0.0160731	−	0.255474i	−0.000628988	−	0.00999748i	−0.998329	+	0.0577910i	$0.981594\pi$
$654$	14.5383	−	26.8379i	0.568493	−	1.04945i
$655$	−12.0973	−	24.9621i	−0.472679	−	0.975350i
$656$	−4.53614	+	10.2950i	−0.177106	+	0.401951i
$657$	−0.160575	+	0.221012i	−0.00626461	+	0.00862250i
$658$	−43.6540	+	0.270651i	−1.70181	+	0.0105511i
$659$	2.75868	+	21.8372i	0.107463	+	0.850656i	0.950050	+	0.312096i	$0.101031\pi$
$659$	2.75868	+	21.8372i	0.107463	+	0.850656i	−0.842588	+	0.538559i	$0.818969\pi$
$660$	13.4105	−	10.2407i	0.522003	−	0.398617i
$661$	−24.1881	−	11.3821i	−0.940808	−	0.442711i	−0.106687	−	0.994293i	$-0.534024\pi$
$661$	−24.1881	−	11.3821i	−0.940808	−	0.442711i	−0.834121	+	0.551582i	$0.814024\pi$
$662$	9.02529	+	16.1785i	0.350778	+	0.628797i
$663$	6.25851	+	6.66464i	0.243060	+	0.258833i
$664$	−0.274856	+	0.114781i	−0.0106665	+	0.00445438i
$665$	−8.66233	+	16.1932i	−0.335911	+	0.627944i
$666$	−1.58108	−	8.01790i	−0.0612655	−	0.310687i
$667$	−0.254545	+	0.307693i	−0.00985604	+	0.0119139i
$668$	4.50465	−	8.44017i	0.174290	−	0.326560i
$669$	−4.02378	+	10.1629i	−0.155569	+	0.392921i
$670$	−10.2854	+	8.81911i	−0.397358	+	0.340712i
$671$	20.8790	+	25.2384i	0.806027	+	0.974319i
$672$	28.0215	−	24.6836i	1.08095	−	0.952189i
$673$	−23.8154	+	4.54303i	−0.918015	+	0.175121i	−0.624673	−	0.780887i	$-0.714768\pi$
$673$	−23.8154	+	4.54303i	−0.918015	+	0.175121i	−0.293342	+	0.956007i	$0.594768\pi$
$674$	6.60959	−	0.456997i	0.254592	−	0.0176029i
$675$	−27.1404	+	7.63494i	−1.04463	+	0.293869i
$676$	4.19527	−	23.5770i	0.161356	−	0.906807i
$677$	15.6247	−	33.2042i	0.600507	−	1.27614i	−0.341290	−	0.939958i	$-0.610864\pi$
$677$	15.6247	−	33.2042i	0.600507	−	1.27614i	0.941797	−	0.336183i	$-0.109136\pi$
$678$	32.1220	−	15.3594i	1.23364	−	0.589875i
$679$	53.8833	−	21.3339i	2.06785	−	0.818721i
$680$	−39.8063	−	14.3927i	−1.52650	−	0.551933i
$681$	1.82462	−	29.0015i	0.0699197	−	1.11134i
$682$	−16.4803	−	10.3160i	−0.631064	−	0.395019i
$683$	−0.516761	+	8.21368i	−0.0197733	+	0.314288i	0.975691	+	0.219151i	$0.0703288\pi$
$683$	−0.516761	+	8.21368i	−0.0197733	+	0.314288i	−0.995464	+	0.0951365i	$0.969671\pi$
$684$	3.08627	+	2.48937i	0.118006	+	0.0951836i
$685$	−14.7727	−	43.7546i	−0.564434	−	1.67178i
$686$	17.5758	+	66.7328i	0.671047	+	2.54787i
$687$	−4.19357	−	33.1955i	−0.159995	−	1.26649i
$688$	−1.85637	+	3.09208i	−0.0707736	+	0.117884i
$689$	−6.45199	−	6.05882i	−0.245801	−	0.230823i
$690$	0.417298	+	0.486677i	0.0158863	+	0.0185275i
$691$	39.6426	−	18.6544i	1.50808	−	0.709647i	0.518691	−	0.854962i	$-0.326420\pi$
$691$	39.6426	−	18.6544i	1.50808	−	0.709647i	0.989385	+	0.145315i	$0.0464195\pi$
$692$	35.6271	−	14.6193i	1.35434	−	0.555743i
$693$	16.1888			0.614963
$694$	−12.7035	−	9.10985i	−0.482219	−	0.345805i
$695$	−2.59820	−	34.9136i	−0.0985554	−	1.32435i
$696$	−2.70127	−	9.76319i	−0.102392	−	0.370073i
$697$	−15.8930	−	10.0860i	−0.601990	−	0.382035i
$698$	−14.0679	+	9.05057i	−0.532477	+	0.342569i
$699$	−1.95729	+	2.69398i	−0.0740315	+	0.101896i
$700$	13.8408	+	46.9592i	0.523134	+	1.77489i
$701$	−25.0865	−	34.5286i	−0.947504	−	1.30413i	−0.952627	−	0.304140i	$-0.901631\pi$
$701$	−25.0865	−	34.5286i	−0.947504	−	1.30413i	0.00512367	−	0.999987i	$-0.498369\pi$
$702$	−7.52971	−	2.92735i	−0.284191	−	0.110486i
$703$	3.01973	+	7.62697i	0.113891	+	0.287657i
$704$	−19.8860	+	10.2777i	−0.749483	+	0.387356i
$705$	15.5075	+	10.9978i	0.584046	+	0.414202i
$706$	−2.07824	−	2.82347i	−0.0782155	−	0.106263i
$707$	9.59544	−	6.97149i	0.360874	−	0.262190i
$708$	−2.31797	+	9.51622i	−0.0871145	+	0.357641i
$709$	20.0290	+	21.3287i	0.752203	+	0.801015i	0.985190	−	0.171465i	$-0.0548500\pi$
$709$	20.0290	+	21.3287i	0.752203	+	0.801015i	−0.232987	+	0.972480i	$0.574850\pi$
$710$	−25.9366	−	11.6503i	−0.973385	−	0.437227i
$711$	7.17570	−	3.94487i	0.269110	−	0.147944i
$712$	−30.8276	+	23.2857i	−1.15531	+	0.872669i
$713$	0.355874	−	0.647333i	0.0133276	−	0.0242428i
$714$	33.8054	+	52.5459i	1.26514	+	1.96648i
$715$	−2.63301	+	5.76588i	−0.0984692	+	0.215632i
$716$	−10.5978	+	6.91136i	−0.396058	+	0.258290i
$717$	−12.9518	−	20.4087i	−0.483692	−	0.762177i
$718$	−48.8535	+	19.6937i	−1.82320	+	0.734962i
$719$	9.23401	−	2.37089i	0.344370	−	0.0884193i	−0.0725436	−	0.997365i	$-0.523112\pi$
$719$	9.23401	−	2.37089i	0.344370	−	0.0884193i	0.416914	+	0.908946i	$0.363112\pi$
$720$	10.5184	−	1.04559i	0.391998	−	0.0389669i
$721$	−3.73198	−	59.3181i	−0.138986	−	2.20912i
$722$	20.1267	+	10.9028i	0.749038	+	0.405760i
$723$	−25.1209	+	13.8103i	−0.934256	+	0.513612i
$724$	−3.83202	−	27.5789i	−0.142416	−	1.02496i
$725$	13.0988	+	2.18916i	0.486475	+	0.0813035i
$726$	−5.86529	−	1.46725i	−0.217681	−	0.0544548i
$727$	−29.0119	+	30.8946i	−1.07599	+	1.14582i	−0.0872505	+	0.996186i	$0.527808\pi$
$727$	−29.0119	+	30.8946i	−1.07599	+	1.14582i	−0.988742	+	0.149629i	$0.952192\pi$
$728$	−4.92062	+	13.1368i	−0.182370	+	0.486882i
$729$	14.7919	−	23.3084i	0.547850	−	0.863273i
$730$	−0.238126	−	0.691129i	−0.00881344	−	0.0255798i
$731$	−4.64956	−	3.84645i	−0.171970	−	0.142266i
$732$	−4.34477	−	31.2692i	−0.160587	−	1.15574i
$733$	−22.4245	+	5.75764i	−0.828269	+	0.212663i	−0.638946	−	0.769252i	$-0.720629\pi$
$733$	−22.4245	+	5.75764i	−0.828269	+	0.212663i	−0.189323	+	0.981915i	$0.560629\pi$
$734$	−14.8952	−	26.7009i	−0.549793	−	0.985547i
$735$	18.2870	−	47.7787i	0.674526	−	1.76235i
$736$	−0.432630	−	0.732234i	−0.0159470	−	0.0269905i
$737$	−11.7761	−	2.24640i	−0.433777	−	0.0827473i
$738$	4.66704	+	0.560211i	0.171796	+	0.0206216i
$739$	−5.41723	+	42.8818i	−0.199276	+	1.57743i	0.502207	+	0.864747i	$0.332522\pi$
$739$	−5.41723	+	42.8818i	−0.199276	+	1.57743i	−0.701483	+	0.712686i	$0.747478\pi$
$740$	20.0030	+	8.83636i	0.735324	+	0.324831i
$741$	2.25107	+	0.429414i	0.0826951	+	0.0157749i
$742$	−35.8563	−	48.7140i	−1.31633	−	1.78835i
$743$	1.06917	−	0.347395i	0.0392241	−	0.0127447i	−0.289339	−	0.957227i	$-0.593436\pi$
$743$	1.06917	−	0.347395i	0.0392241	−	0.0127447i	0.328563	+	0.944482i	$0.393436\pi$
$744$	8.29260	+	16.8041i	0.304021	+	0.616069i
$745$	−10.5907	−	52.2602i	−0.388012	−	1.91466i
$746$	4.24583	−	4.03693i	0.155451	−	0.147803i
$747$	0.0793297	+	0.0958931i	0.00290252	+	0.00350855i
$748$	−12.0147	−	35.4746i	−0.439300	−	1.29708i
$749$		−	31.1294i		−	1.13744i
$750$	7.03850	−	20.1249i	0.257010	−	0.734858i
$751$	19.3582			0.706391			0.353195	−	0.935550i	$-0.385095\pi$
$751$	19.3582			0.706391			0.353195	+	0.935550i	$0.385095\pi$
$752$	−17.7158	−	17.9518i	−0.646027	−	0.654633i
$753$	−28.4936	+	23.5720i	−1.03837	+	0.859011i
$754$	2.62213	+	2.75782i	0.0954923	+	0.100434i
$755$	5.63716	+	2.57423i	0.205157	+	0.0936859i
$756$	−46.9792	−	29.0031i	−1.70862	−	1.05483i
$757$	0.0718018	+	0.220983i	0.00260968	+	0.00803178i	0.952353	−	0.304998i	$-0.0986559\pi$
$757$	0.0718018	+	0.220983i	0.00260968	+	0.00803178i	−0.949743	+	0.313030i	$0.898656\pi$
$758$	−9.98676	−	13.5679i	−0.362735	−	0.492808i
$759$	−0.106294	+	0.557213i	−0.00385823	+	0.0202256i
$760$	−10.1927	+	2.94615i	−0.369729	+	0.106868i
$761$	35.5995	+	4.49727i	1.29048	+	0.163026i	0.740446	−	0.672115i	$-0.234614\pi$
$761$	35.5995	+	4.49727i	1.29048	+	0.163026i	0.550036	+	0.835141i	$0.314614\pi$
$762$	3.93388	−	32.7727i	0.142510	−	1.18723i
$763$	−14.6832	+	76.9723i	−0.531569	+	2.78658i
$764$	−22.2615	+	16.5996i	−0.805394	+	0.600551i
$765$	−0.908346	+	17.6625i	−0.0328413	+	0.638590i
$766$	−11.4978	−	20.6107i	−0.415432	−	0.744694i
$767$	−0.915020	−	3.56377i	−0.0330395	−	0.128680i
$768$	21.5122	+	1.63949i	0.776254	+	0.0591599i
$769$	−7.98595	+	9.65335i	−0.287981	+	0.348109i	−0.894587	−	0.446893i	$-0.852530\pi$
$769$	−7.98595	+	9.65335i	−0.287981	+	0.348109i	0.606607	+	0.795002i	$0.292530\pi$
$770$	−24.8397	+	35.4895i	−0.895159	+	1.27895i
$771$	−14.2834	−	9.06452i	−0.514404	−	0.326451i
$772$	−40.6008	+	8.26804i	−1.46125	+	0.297573i
$773$	13.2535	+	12.4458i	0.476694	+	0.447645i	0.885269	−	0.465080i	$-0.153974\pi$
$773$	13.2535	+	12.4458i	0.476694	+	0.447645i	−0.408575	+	0.912725i	$0.633974\pi$
$774$	1.46186	+	0.365695i	0.0525453	+	0.0131446i
$775$	−24.5603	+	0.562490i	−0.882230	+	0.0202052i
$776$	30.5553	+	13.6900i	1.09687	+	0.491443i
$777$	−15.5506	−	28.2864i	−0.557874	−	1.01477i
$778$	−6.12043	+	11.2984i	−0.219428	+	0.405067i
$779$	−4.70890	+	0.296259i	−0.168714	+	0.0106146i
$780$	5.07860	−	3.39552i	0.181843	−	0.121579i
$781$	−6.25673	−	24.3684i	−0.223883	−	0.871969i
$782$	1.31982	−	0.532042i	0.0471966	−	0.0190258i
$783$	−12.6455	+	8.02510i	−0.451915	+	0.286794i
$784$	−34.9340	+	58.1881i	−1.24764	+	2.07814i
$785$	9.92982	−	10.8198i	0.354410	−	0.386175i
$786$	−19.8945	+	12.7991i	−0.709614	+	0.456530i
$787$	−4.21385	−	2.31658i	−0.150207	−	0.0825772i	0.404877	−	0.914371i	$-0.367314\pi$
$787$	−4.21385	−	2.31658i	−0.150207	−	0.0825772i	−0.555085	+	0.831794i	$0.687314\pi$
$788$	32.3336	+	12.3402i	1.15184	+	0.439603i
$789$	−9.91841	−	18.0415i	−0.353105	−	0.642295i
$790$	−2.36214	+	21.7836i	−0.0840412	+	0.775026i
$791$	−66.6339	+	62.5734i	−2.36923	+	2.22485i
$792$	6.52827	+	6.69779i	0.231972	+	0.237995i
$793$	6.97074	+	9.59441i	0.247538	+	0.340707i
$794$	26.3640	−	19.4055i	0.935625	−	0.688674i
$795$	0.301588	+	26.3402i	0.0106962	+	0.934191i
$796$	10.2765	−	22.5607i	0.364241	−	0.799641i
$797$	13.3074	−	5.26877i	0.471372	−	0.186629i	−0.120415	−	0.992724i	$-0.538423\pi$
$797$	13.3074	−	5.26877i	0.471372	−	0.186629i	0.591787	+	0.806094i	$0.298423\pi$
$798$	14.5971	+	5.67496i	0.516731	+	0.200891i
$799$	34.1402	−	24.8043i	1.20779	−	0.877514i
$800$	−13.8469	+	24.6630i	−0.489563	+	0.871968i
$801$	13.0593	+	9.48813i	0.461427	+	0.335246i
$802$	1.47378	+	2.29078i	0.0520409	+	0.0808904i
$803$	0.346584	−	0.546129i	0.0122307	−	0.0192725i
$804$	8.52022	+	7.80449i	0.300485	+	0.275243i
$805$	−1.39964	−	0.865921i	−0.0493308	−	0.0305197i
$806$	−5.72054	−	4.10227i	−0.201497	−	0.144496i
$807$			27.1715i			0.956481i
$808$	6.75374	+	1.15860i	0.237596	+	0.0407595i
$809$	1.51097	+	3.21098i	0.0531230	+	0.112892i	0.929626	−	0.368504i	$-0.120130\pi$
$809$	1.51097	+	3.21098i	0.0531230	+	0.112892i	−0.876503	+	0.481396i	$0.840130\pi$
$810$	4.93381	+	11.8462i	0.173356	+	0.416232i
$811$	−17.4089	+	18.5386i	−0.611309	+	0.650978i	−0.957921	−	0.287031i	$-0.907332\pi$
$811$	−17.4089	+	18.5386i	−0.611309	+	0.650978i	0.346613	+	0.938008i	$0.387332\pi$
$812$	14.2062	+	21.7835i	0.498539	+	0.764452i
$813$	−8.49218	+	1.07281i	−0.297834	+	0.0376251i
$814$	4.92814	+	18.7114i	0.172731	+	0.655836i
$815$	12.6002	+	16.9316i	0.441367	+	0.593089i
$816$	−8.10746	+	35.1758i	−0.283818	+	1.23140i
$817$	−1.50958	−	0.0949748i	−0.0528135	−	0.00332275i
$818$	4.60758	−	7.36087i	0.161100	−	0.257367i
$819$	5.84973	+	0.368034i	0.204406	+	0.0128601i
$820$	−8.38907	+	9.37161i	−0.292959	+	0.327271i
$821$	−8.91522	−	22.5173i	−0.311143	−	0.785858i	−0.998241	−	0.0592927i	$-0.981115\pi$
$821$	−8.91522	−	22.5173i	−0.311143	−	0.785858i	0.687097	−	0.726565i	$-0.258885\pi$
$822$	−35.5308	+	16.9894i	−1.23928	+	0.592573i
$823$	−48.7490	−	22.9396i	−1.69928	−	0.799623i	−0.996063	−	0.0886521i	$-0.971744\pi$
$823$	−48.7490	−	22.9396i	−1.69928	−	0.799623i	−0.703222	−	0.710971i	$-0.748256\pi$
$824$	23.0366	−	25.4645i	0.802520	−	0.887097i
$825$	17.8036	−	6.23890i	0.619840	−	0.217210i
$826$	−1.73443	−	25.0852i	−0.0603485	−	0.872825i
$827$	5.93156	+	31.0943i	0.206261	+	1.08126i	0.923258	+	0.384180i	$0.125516\pi$
$827$	5.93156	+	31.0943i	0.206261	+	1.08126i	−0.716998	+	0.697075i	$0.754484\pi$
$828$	−0.240028	+	0.262040i	−0.00834154	+	0.00910653i
$829$	16.1767	−	13.3825i	0.561839	−	0.464794i	−0.312630	−	0.949875i	$-0.601210\pi$
$829$	16.1767	−	13.3825i	0.561839	−	0.464794i	0.874469	+	0.485081i	$0.161210\pi$
$830$	−0.331940	+	0.0267726i	−0.0115218	+	0.000929292i
$831$	−12.9559	−	5.12960i	−0.449435	−	0.177944i
$832$	−7.41934	+	3.26170i	−0.257219	+	0.113079i
$833$	−87.4973	−	72.3841i	−3.03160	−	2.50796i
$834$	−29.2929	+	5.77637i	−1.01433	+	0.200019i
$835$	7.71291	−	7.41090i	0.266916	−	0.256465i
$836$	−7.66301	−	5.42362i	−0.265031	−	0.187580i
$837$	20.1962	−	18.9655i	0.698083	−	0.655544i
$838$	24.8283	+	44.5067i	0.857681	+	1.53746i
$839$	4.54691	−	9.66267i	0.156977	−	0.333592i	−0.810832	−	0.585279i	$-0.800985\pi$
$839$	4.54691	−	9.66267i	0.156977	−	0.333592i	0.967809	+	0.251686i	$0.0809851\pi$
$840$	38.3394	−	16.5287i	1.32283	−	0.570295i
$841$	−21.7722	+	2.75046i	−0.750764	+	0.0948436i
$842$	0.0148950	+	2.40246i	0.000513317	+	0.0827942i
$843$	−18.5878	−	13.5048i	−0.640198	−	0.465131i
$844$	−16.4336	+	13.9419i	−0.565669	+	0.479899i
$845$	12.6290	−	23.6083i	0.434450	−	0.812151i
$846$	−5.01942	+	9.26591i	−0.172571	+	0.318568i
$847$	15.4912	−	0.974623i	0.532284	−	0.0334885i
$848$	5.69506	−	34.4791i	0.195569	−	1.18402i
$849$	4.16377	−	12.8148i	0.142900	−	0.439802i
$850$	−37.3264	−	29.0921i	−1.28028	−	0.997852i
$851$	−0.699183	+	0.227178i	−0.0239677	+	0.00778757i
$852$	−7.20652	+	23.1523i	−0.246891	+	0.793186i
$853$	−29.1724	−	7.49020i	−0.998844	−	0.256460i	−0.286340	−	0.958128i	$-0.592439\pi$
$853$	−29.1724	−	7.49020i	−0.998844	−	0.256460i	−0.712504	+	0.701668i	$0.752439\pi$
$854$	34.9625	+	73.1189i	1.19639	+	2.50208i
$855$	2.41808	+	3.71556i	0.0826966	+	0.127070i
$856$	12.8791	−	12.5531i	0.440199	−	0.429058i
$857$	−22.9240	−	7.44846i	−0.783069	−	0.254434i	−0.109919	−	0.993941i	$-0.535059\pi$
$857$	−22.9240	−	7.44846i	−0.783069	−	0.254434i	−0.673150	+	0.739506i	$0.735059\pi$
$858$	5.15133	+	1.63853i	0.175863	+	0.0559385i
$859$	−0.615328	+	1.11928i	−0.0209947	+	0.0381892i	−0.886596	−	0.462545i	$-0.846936\pi$
$859$	−0.615328	+	1.11928i	−0.0209947	+	0.0381892i	0.865601	+	0.500734i	$0.166936\pi$
$860$	−3.04471	+	2.64360i	−0.103824	+	0.0901459i
$861$	18.2374	−	3.47898i	0.621530	−	0.118563i
$862$	−32.0511	−	29.7262i	−1.09166	−	1.01248i
$863$	42.9698	−	20.2201i	1.46271	−	0.688299i	0.480657	−	0.876909i	$-0.340398\pi$
$863$	42.9698	−	20.2201i	1.46271	−	0.688299i	0.982052	+	0.188610i	$0.0603982\pi$
$864$	−6.94529	−	31.1324i	−0.236284	−	1.05915i
$865$	42.9367	−	3.19526i	1.45989	−	0.108642i
$866$	4.05930	−	4.37678i	0.137941	−	0.148729i
$867$	−34.8437	−	13.7956i	−1.18335	−	0.468523i
$868$	−33.3644	−	34.6581i	−1.13246	−	1.17637i
$869$	−16.3699	+	10.3886i	−0.555310	+	0.352410i
$870$	0.511552	−	11.3141i	0.0173432	−	0.383585i
$871$	−4.20413	−	1.07944i	−0.142452	−	0.0365754i
$872$	−37.7668	+	24.9647i	−1.27894	+	0.845413i
$873$	1.75337	−	13.8793i	0.0593424	−	0.469744i
$874$	0.189255	−	0.302345i	0.00640163	−	0.0102270i
$875$	−1.55887	+	54.7127i	−0.0526994	+	1.84963i
$876$	−0.560739	+	0.272407i	−0.0189456	+	0.00920377i
$877$	10.2322	+	1.29263i	0.345517	+	0.0436490i	0.296177	−	0.955133i	$-0.404288\pi$
$877$	10.2322	+	1.29263i	0.345517	+	0.0436490i	0.0493401	+	0.998782i	$0.484288\pi$
$878$	−39.1405	+	5.19133i	−1.32093	+	0.175199i
$879$	−35.5928	−	9.13867i	−1.20051	−	0.308240i
$880$	−24.6998	+	4.03452i	−0.832630	+	0.136004i
$881$	14.9375	+	23.5378i	0.503259	+	0.793009i	0.997065	−	0.0765634i	$-0.0243948\pi$
$881$	14.9375	+	23.5378i	0.503259	+	0.793009i	−0.493806	+	0.869572i	$0.664395\pi$
$882$	27.5098	+	6.88180i	0.926303	+	0.231722i
$883$	−21.9054	−	8.67295i	−0.737175	−	0.291868i	−0.0306245	−	0.999531i	$-0.509750\pi$
$883$	−21.9054	−	8.67295i	−0.737175	−	0.291868i	−0.706550	+	0.707663i	$0.749750\pi$
$884$	−3.53496	−	13.0916i	−0.118893	−	0.440320i
$885$	−5.76135	+	9.31242i	−0.193666	+	0.313033i
$886$	−6.35893	+	7.78439i	−0.213632	+	0.261522i
$887$	35.8105	−	16.8512i	1.20240	−	0.565807i	0.282996	−	0.959121i	$-0.408672\pi$
$887$	35.8105	−	16.8512i	1.20240	−	0.565807i	0.919404	+	0.393314i	$0.128672\pi$
$888$	5.43201	−	17.8404i	0.182286	−	0.598685i
$889$	15.8788	+	83.2395i	0.532557	+	2.79176i
$890$	−40.8378	+	14.0705i	−1.36889	+	0.471645i
$891$	−5.47021	+	9.95027i	−0.183259	+	0.333347i
$892$	12.3628	−	10.4883i	0.413937	−	0.351174i
$893$	3.26869	−	10.0600i	0.109383	−	0.336645i
$894$	−43.1603	+	14.3201i	−1.44350	+	0.478935i
$895$	−13.6601	+	3.67452i	−0.456606	+	0.122826i
$896$	−53.9053	+	12.7293i	−1.80085	+	0.425257i
$897$	−0.0510763	+	0.198929i	−0.00170539	+	0.00664204i
$898$	21.7926	−	5.73964i	0.727229	−	0.191534i
$899$	−12.4115	+	4.03275i	−0.413947	+	0.134500i
$900$	11.5432	+	2.53320i	0.384773	+	0.0844400i
$901$	55.6094	+	18.0686i	1.85262	+	0.601952i
$902$	−11.1116	−	0.629947i	−0.369976	−	0.0209749i
$903$	5.94024	−	0.373728i	0.197679	−	0.0124369i
$904$	−52.7590	−	2.33518i	−1.75474	−	0.0776669i
$905$	5.48278	−	30.6438i	0.182254	−	1.01863i
$906$	1.60195	−	5.03632i	0.0532212	−	0.167321i
$907$	−14.4068	−	10.4671i	−0.478370	−	0.347556i	0.322325	−	0.946629i	$-0.395536\pi$
$907$	−14.4068	−	10.4671i	−0.478370	−	0.347556i	−0.800694	+	0.599073i	$0.795536\pi$
$908$	−22.6416	+	36.6749i	−0.751389	+	1.21710i
$909$	−0.358842	−	2.84053i	−0.0119020	−	0.0942144i
$910$	−9.78246	+	12.2592i	−0.324285	+	0.406388i
$911$	12.6215	−	26.8220i	0.418168	−	0.888652i	−0.579133	−	0.815233i	$-0.696609\pi$
$911$	12.6215	−	26.8220i	0.418168	−	0.888652i	0.997301	−	0.0734190i	$-0.0233911\pi$
$912$	3.53848	+	8.32770i	0.117171	+	0.275758i
$913$	−0.201714	−	0.214804i	−0.00667577	−	0.00710897i
$914$	31.0306	+	1.75920i	1.02640	+	0.0581893i
$915$	6.21640	−	34.7441i	0.205508	−	1.14860i
$916$	−17.6957	+	46.3658i	−0.584682	+	1.53197i
$917$	38.7118	−	46.7945i	1.27838	−	1.54529i
$918$	53.2433	−	3.68132i	1.75729	−	0.121502i
$919$	10.5105	+	4.16141i	0.346710	+	0.137272i	0.535024	−	0.844837i	$-0.320302\pi$
$919$	10.5105	+	4.16141i	0.346710	+	0.137272i	−0.188315	+	0.982109i	$0.560302\pi$
$920$	−0.206159	−	0.928261i	−0.00679685	−	0.0306038i
$921$	−23.0978	−	27.9204i	−0.761097	−	0.920008i
$922$	50.1762	+	9.24960i	1.65247	+	0.304619i
$923$	−1.70684	−	8.94759i	−0.0561815	−	0.294514i
$924$	32.5913	+	17.3945i	1.07217	+	0.572236i
$925$	18.2010	+	16.3240i	0.598446	+	0.536729i
$926$	6.78137	+	16.8223i	0.222850	+	0.552816i
$927$	−12.9820	−	6.10885i	−0.426384	−	0.200641i
$928$	−3.28373	+	14.6619i	−0.107794	+	0.481299i
$929$	−20.0995	+	7.95796i	−0.659443	+	0.261092i	−0.673921	−	0.738803i	$-0.735391\pi$
$929$	−20.0995	+	7.95796i	−0.659443	+	0.261092i	0.0144779	+	0.999895i	$0.495391\pi$
$930$	2.99224	+	20.7359i	0.0981193	+	0.679958i
$931$	−28.4079	−	1.78727i	−0.931032	−	0.0585756i
$932$	4.44258	−	2.15820i	0.145521	−	0.0706942i
$933$	−0.165735	+	2.63428i	−0.00542591	+	0.0862424i
$934$	59.1514	+	7.10027i	1.93549	+	0.232328i
$935$	−0.479423	−	41.8720i	−0.0156788	−	1.36936i
$936$	2.20668	+	2.56861i	0.0721276	+	0.0839578i
$937$	−6.51737	−	51.5903i	−0.212913	−	1.68538i	−0.630063	−	0.776544i	$-0.716971\pi$
$937$	−6.51737	−	51.5903i	−0.212913	−	1.68538i	0.417150	−	0.908838i	$-0.363029\pi$
$938$	−26.9180	−	12.4634i	−0.878903	−	0.406944i
$939$	5.06184	−	5.39031i	0.165187	−	0.175906i
$940$	−12.6113	−	25.2210i	−0.411334	−	0.822618i
$941$	−9.39079	+	4.41897i	−0.306131	+	0.144054i	−0.572708	−	0.819759i	$-0.694107\pi$
$941$	−9.39079	+	4.41897i	−0.306131	+	0.144054i	0.266577	+	0.963814i	$0.414107\pi$
$942$	−10.1777	−	7.29852i	−0.331606	−	0.237799i
$943$		−	0.422852i		−	0.0137699i
$944$	9.67904	−	10.8334i	0.315026	−	0.352596i
$945$	−39.8886	−	47.1083i	−1.29758	−	1.53243i
$946$	−3.50877	−	0.646814i	−0.114080	−	0.0210297i
$947$	−1.65689	+	2.61083i	−0.0538415	+	0.0848407i	−0.870182	−	0.492730i	$-0.835999\pi$
$947$	−1.65689	+	2.61083i	−0.0538415	+	0.0848407i	0.816341	+	0.577570i	$0.195999\pi$
$948$	18.6847	−	0.231696i	0.606852	−	0.00752515i
$949$	0.137652	−	0.189461i	0.00446836	−	0.00615017i
$950$	−11.8556	−	0.400082i	−0.384645	−	0.0129804i
$951$	−3.99828	+	2.90492i	−0.129653	+	0.0941985i
$952$	−7.53820	−	92.3665i	−0.244314	−	2.99362i
$953$	−10.1049	−	25.5220i	−0.327329	−	0.826739i	−0.996497	−	0.0836278i	$-0.973349\pi$
$953$	−10.1049	−	25.5220i	−0.327329	−	0.826739i	0.669168	−	0.743111i	$-0.266651\pi$
$954$	−14.4747	+	1.91982i	−0.468635	+	0.0621565i
$955$	−29.4154	+	9.93140i	−0.951862	+	0.321373i
$956$	2.69465	+	35.7505i	0.0871512	+	1.15625i
$957$	8.10751	−	5.89045i	0.262079	−	0.190411i
$958$	−7.37305	−	22.2222i	−0.238213	−	0.717966i
$959$	73.7052	−	69.2138i	2.38006	−	2.23503i
$960$	22.2990	+	9.19676i	0.719698	+	0.296824i
$961$	−6.01067	+	3.30440i	−0.193893	+	0.106593i
$962$	1.35537	+	6.87330i	0.0436988	+	0.221604i
$963$	−6.58501	−	3.62014i	−0.212199	−	0.116657i
$964$	42.5161	−	0.527213i	1.36935	−	0.0169804i
$965$	−46.0229	−	5.27946i	−1.48153	−	0.169952i
$966$	−0.589736	+	1.27369i	−0.0189744	+	0.0409803i
$967$	4.47459	−	2.83966i	0.143893	−	0.0913174i	−0.461931	−	0.886916i	$-0.652843\pi$
$967$	4.47459	−	2.83966i	0.143893	−	0.0913174i	0.605824	+	0.795598i	$0.292843\pi$
$968$	6.65017	+	6.01613i	0.213744	+	0.193366i
$969$	−14.6637	+	3.76501i	−0.471067	+	0.120949i
$970$	27.7362	+	25.1398i	0.890556	+	0.807189i
$971$	7.14558	−	0.449562i	0.229313	−	0.0144271i	0.0522816	−	0.998632i	$-0.483351\pi$
$971$	7.14558	−	0.449562i	0.229313	−	0.0144271i	0.177031	+	0.984205i	$0.443351\pi$
$972$	−19.9194	+	11.2747i	−0.638916	+	0.361635i
$973$	67.1700	−	36.9270i	2.15337	−	1.18383i
$974$	0.962987	−	0.806761i	0.0308561	−	0.0258503i
$975$	6.57503	−	1.84964i	0.210570	−	0.0592360i
$976$	−16.1525	+	43.9507i	−0.517029	+	1.40683i
$977$	20.3609	−	21.6821i	0.651402	−	0.693673i	−0.315470	−	0.948936i	$-0.602162\pi$
$977$	20.3609	−	21.6821i	0.651402	−	0.693673i	0.966872	+	0.255263i	$0.0821620\pi$
$978$	13.0441	−	12.4023i	0.417105	−	0.396582i
$979$	−32.2700	−	20.4792i	−1.03135	−	0.654517i
$980$	−57.2966	+	49.7483i	−1.83027	+	1.58915i
$981$	14.5749	+	12.0574i	0.465341	+	0.384964i
$982$	5.86033	−	4.90960i	0.187011	−	0.156672i
$983$	−9.67370	−	37.6766i	−0.308543	−	1.20170i	−0.913966	−	0.405791i	$-0.866996\pi$
$983$	−9.67370	−	37.6766i	−0.308543	−	1.20170i	0.605423	−	0.795904i	$-0.293004\pi$
$984$	8.79373	+	6.14243i	0.280334	+	0.195813i
$985$	30.0942	+	24.3211i	0.958881	+	0.774936i
$986$	−23.4311	−	9.10941i	−0.746199	−	0.290103i
$987$	−7.79948	+	40.8863i	−0.248260	+	1.30143i
$988$	−2.64568	−	2.13400i	−0.0841703	−	0.0678915i
$989$	0.0169899	−	0.134489i	0.000540248	−	0.00427650i
$990$	4.61865	+	9.38170i	0.146790	+	0.298170i
$991$	−8.58148	+	44.9857i	−0.272600	+	1.42902i	0.537766	+	0.843094i	$0.319268\pi$
$991$	−8.58148	+	44.9857i	−0.272600	+	1.42902i	−0.810366	+	0.585924i	$0.800732\pi$
$992$	0.884609	−	27.7800i	0.0280864	−	0.882015i
$993$	16.7992	−	5.45838i	0.533105	−	0.173216i
$994$	−0.385945	−	62.2501i	−0.0122414	−	1.97445i
$995$	18.7411	−	20.4208i	0.594133	−	0.647383i
$996$	0.0566714	+	0.278289i	0.00179570	+	0.00881792i
$997$	−1.86723	−	2.25709i	−0.0591356	−	0.0714827i	0.740116	−	0.672479i	$-0.234771\pi$
$997$	−1.86723	−	2.25709i	−0.0591356	−	0.0714827i	−0.799252	+	0.600996i	$0.794771\pi$
$998$	33.6011	+	27.4482i	1.06363	+	0.868857i
$999$	−27.5724			−0.872351

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Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.bd.a.109.41	✓	2960
8.5	even	2	inner	1000.2.bd.a.109.95	yes	2960
125.39	even	50	inner	1000.2.bd.a.789.95	yes	2960
1000.789	even	50	inner	1000.2.bd.a.789.41	yes	2960

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1000.2.bd.a.109.41	✓	2960	1.1	even	1	trivial
1000.2.bd.a.109.95	yes	2960	8.5	even	2	inner
1000.2.bd.a.789.41	yes	2960	1000.789	even	50	inner
1000.2.bd.a.789.95	yes	2960	125.39	even	50	inner

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

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Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	1000.2.bd.a.109.41

Level	$1000$
Weight	$2$
Character	1000.109
Analytic conductor	$7.985$
Analytic rank	$0$
Dimension	$2960$
Inner twists	$4$