LMFDB - Embedded newform 570.2.bf.a.89.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(29,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([9, 9, 17]))

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

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

chi := DirichletCharacter("570.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.bf (of order $18$, degree $6$, 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:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$40$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			89.9
Character	$\chi$	$=$	570.89
Dual form			570.2.bf.a.269.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.642788 - 0.766044i) q^{2} +(-0.213600 - 1.71883i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-2.00927 - 0.981251i) q^{5} +(-1.17940 + 1.26847i) q^{6} +(-3.44103 - 1.98668i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-2.90875 + 0.734285i) q^{9} +O(q^{10})$	\(q+(-0.642788 - 0.766044i) q^{2} +(-0.213600 - 1.71883i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-2.00927 - 0.981251i) q^{5} +(-1.17940 + 1.26847i) q^{6} +(-3.44103 - 1.98668i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-2.90875 + 0.734285i) q^{9} +(0.539849 + 2.16992i) q^{10} +(3.19095 - 1.84230i) q^{11} +(1.72981 + 0.0881164i) q^{12} +(-2.53956 + 0.924323i) q^{13} +(0.689967 + 3.91300i) q^{14} +(-1.25742 + 3.66318i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(4.70060 - 3.94427i) q^{17} +(2.43220 + 1.75624i) q^{18} +(-0.557630 + 4.32308i) q^{19} +(1.31525 - 1.80835i) q^{20} +(-2.67976 + 6.33890i) q^{21} +(-3.46239 - 1.26021i) q^{22} +(-1.43032 + 8.11177i) q^{23} +(-1.04440 - 1.38175i) q^{24} +(3.07429 + 3.94319i) q^{25} +(2.34047 + 1.35127i) q^{26} +(1.88342 + 4.84280i) q^{27} +(2.55403 - 3.04377i) q^{28} +(-2.49722 - 2.09542i) q^{29} +(3.61441 - 1.39140i) q^{30} +(-5.40828 - 3.12247i) q^{31} +(0.342020 + 0.939693i) q^{32} +(-3.84819 - 5.09119i) q^{33} +(-6.04297 - 1.06554i) q^{34} +(4.96451 + 7.36828i) q^{35} +(-0.218030 - 2.99207i) q^{36} +5.48605 q^{37} +(3.67011 - 2.35165i) q^{38} +(2.13120 + 4.16763i) q^{39} +(-2.23070 + 0.154844i) q^{40} +(5.54983 + 2.01997i) q^{41} +(6.57840 - 2.02175i) q^{42} +(-9.57801 + 1.68886i) q^{43} +(1.26021 + 3.46239i) q^{44} +(6.56497 + 1.37884i) q^{45} +(7.13337 - 4.11845i) q^{46} +(-8.28350 - 6.95068i) q^{47} +(-0.387156 + 1.68823i) q^{48} +(4.39380 + 7.61029i) q^{49} +(1.04454 - 4.88968i) q^{50} +(-7.78357 - 7.23703i) q^{51} +(-0.469291 - 2.66148i) q^{52} +(-7.81317 - 1.37767i) q^{53} +(2.49916 - 4.55568i) q^{54} +(-8.21923 + 0.570539i) q^{55} -3.97336 q^{56} +(7.54975 + 0.0350595i) q^{57} +3.25989i q^{58} +(3.14279 - 2.63711i) q^{59} +(-3.38918 - 1.87442i) q^{60} +(-0.625224 + 3.54582i) q^{61} +(1.08442 + 6.15007i) q^{62} +(11.4679 + 3.25206i) q^{63} +(0.500000 - 0.866025i) q^{64} +(6.00963 + 0.634732i) q^{65} +(-1.42651 + 6.22044i) q^{66} +(4.03846 + 3.38867i) q^{67} +(3.06810 + 5.31410i) q^{68} +(14.2483 + 0.725806i) q^{69} +(2.45331 - 8.53928i) q^{70} +(0.156103 + 0.885303i) q^{71} +(-2.15191 + 2.09028i) q^{72} +(0.0635095 - 0.174491i) q^{73} +(-3.52637 - 4.20256i) q^{74} +(6.12100 - 6.12645i) q^{75} +(-4.16057 - 1.29985i) q^{76} -14.6402 q^{77} +(1.82268 - 4.31150i) q^{78} +(-2.72968 + 7.49975i) q^{79} +(1.55248 + 1.60928i) q^{80} +(7.92165 - 4.27170i) q^{81} +(-2.01997 - 5.54983i) q^{82} +(2.29598 - 3.97675i) q^{83} +(-5.77727 - 3.73979i) q^{84} +(-13.3151 + 3.31262i) q^{85} +(7.45037 + 6.25160i) q^{86} +(-3.06826 + 4.73988i) q^{87} +(1.84230 - 3.19095i) q^{88} +(-6.92216 + 2.51946i) q^{89} +(-3.16363 - 5.91536i) q^{90} +(10.5750 + 1.86466i) q^{91} +(-7.74016 - 2.81719i) q^{92} +(-4.21178 + 9.96287i) q^{93} +10.8133i q^{94} +(5.36246 - 8.13905i) q^{95} +(1.54212 - 0.788593i) q^{96} +(-6.07708 + 5.09928i) q^{97} +(3.00554 - 8.25764i) q^{98} +(-7.92892 + 7.70185i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q+O(q^{10}) $ 240 * q	$ 240 q - 30 q^{15} + 48 q^{19} + 12 q^{25} - 48 q^{39} + 36 q^{45} - 72 q^{46} + 216 q^{49} - 180 q^{51} + 36 q^{54} + 60 q^{55} + 6 q^{60} - 72 q^{61} + 120 q^{64} - 156 q^{66} + 48 q^{79} - 120 q^{81} - 108 q^{84} - 48 q^{85} - 36 q^{90} - 24 q^{91} - 216 q^{99}+O(q^{100}) $ 240 * q - 30 * q^15 + 48 * q^19 + 12 * q^25 - 48 * q^39 + 36 * q^45 - 72 * q^46 + 216 * q^49 - 180 * q^51 + 36 * q^54 + 60 * q^55 + 6 * q^60 - 72 * q^61 + 120 * q^64 - 156 * q^66 + 48 * q^79 - 120 * q^81 - 108 * q^84 - 48 * q^85 - 36 * q^90 - 24 * q^91 - 216 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$-1$	$e\left(\frac{5}{18}\right)$	$-1$

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 $

$2$	−0.642788	−	0.766044i	−0.454519	−	0.541675i
$2$	−0.642788	−	0.766044i	−0.454519	−	0.541675i
$3$	−0.213600	−	1.71883i	−0.123322	−	0.992367i
$3$	−0.213600	−	1.71883i	−0.123322	−	0.992367i
$4$	−0.173648	+	0.984808i	−0.0868241	+	0.492404i
$5$	−2.00927	−	0.981251i	−0.898571	−	0.438829i
$5$	−2.00927	−	0.981251i	−0.898571	−	0.438829i
$6$	−1.17940	+	1.26847i	−0.481488	+	0.517851i
$7$	−3.44103	−	1.98668i	−1.30059	−	0.750895i	−0.320083	−	0.947390i	$-0.603711\pi$
$7$	−3.44103	−	1.98668i	−1.30059	−	0.750895i	−0.980505	+	0.196495i	$0.937044\pi$
$8$	0.866025	−	0.500000i	0.306186	−	0.176777i
$9$	−2.90875	+	0.734285i	−0.969583	+	0.244762i
$10$	0.539849	+	2.16992i	0.170715	+	0.686190i
$11$	3.19095	−	1.84230i	0.962109	−	0.555474i	0.0652874	−	0.997866i	$-0.479204\pi$
$11$	3.19095	−	1.84230i	0.962109	−	0.555474i	0.896821	+	0.442393i	$0.145870\pi$
$12$	1.72981	+	0.0881164i	0.499353	+	0.0254370i
$13$	−2.53956	+	0.924323i	−0.704346	+	0.256361i	−0.669265	−	0.743023i	$-0.733391\pi$
$13$	−2.53956	+	0.924323i	−0.704346	+	0.256361i	−0.0350807	+	0.999384i	$0.511169\pi$
$14$	0.689967	+	3.91300i	0.184401	+	1.04579i
$15$	−1.25742	+	3.66318i	−0.324665	+	0.945829i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	4.70060	−	3.94427i	1.14006	−	0.956626i	0.140621	−	0.990063i	$-0.455090\pi$
$17$	4.70060	−	3.94427i	1.14006	−	0.956626i	0.999441	+	0.0334378i	$0.0106456\pi$
$18$	2.43220	+	1.75624i	0.573276	+	0.413950i
$19$	−0.557630	+	4.32308i	−0.127929	+	0.991783i
$19$	−0.557630	+	4.32308i	−0.127929	+	0.991783i
$20$	1.31525	−	1.80835i	0.294099	−	0.404359i
$21$	−2.67976	+	6.33890i	−0.584772	+	1.38326i
$22$	−3.46239	−	1.26021i	−0.738184	−	0.268677i
$23$	−1.43032	+	8.11177i	−0.298243	+	1.69142i	0.355477	+	0.934685i	$0.384318\pi$
$23$	−1.43032	+	8.11177i	−0.298243	+	1.69142i	−0.653720	+	0.756736i	$0.726793\pi$
$24$	−1.04440	−	1.38175i	−0.213187	−	0.282049i
$25$	3.07429	+	3.94319i	0.614859	+	0.788637i
$26$	2.34047	+	1.35127i	0.459003	+	0.265006i
$27$	1.88342	+	4.84280i	0.362464	+	0.931998i
$28$	2.55403	−	3.04377i	0.482666	−	0.575219i
$29$	−2.49722	−	2.09542i	−0.463722	−	0.389109i	0.380776	−	0.924667i	$-0.375657\pi$
$29$	−2.49722	−	2.09542i	−0.463722	−	0.389109i	−0.844498	+	0.535558i	$0.820101\pi$
$30$	3.61441	−	1.39140i	0.659899	−	0.254035i
$31$	−5.40828	−	3.12247i	−0.971355	−	0.560812i	−0.0717061	−	0.997426i	$-0.522844\pi$
$31$	−5.40828	−	3.12247i	−0.971355	−	0.560812i	−0.899649	+	0.436614i	$0.856178\pi$
$32$	0.342020	+	0.939693i	0.0604612	+	0.166116i
$33$	−3.84819	−	5.09119i	−0.669883	−	0.886263i
$34$	−6.04297	−	1.06554i	−1.03636	−	0.182738i
$35$	4.96451	+	7.36828i	0.839156	+	1.24547i
$36$	−0.218030	−	2.99207i	−0.0363384	−	0.498678i
$37$	5.48605			0.901901			0.450951	−	0.892549i	$-0.351085\pi$
$37$	5.48605			0.901901			0.450951	+	0.892549i	$0.351085\pi$
$38$	3.67011	−	2.35165i	0.595371	−	0.381489i
$39$	2.13120	+	4.16763i	0.341266	+	0.667355i
$40$	−2.23070	+	0.154844i	−0.352705	+	0.0244830i
$41$	5.54983	+	2.01997i	0.866738	+	0.315467i	0.736846	−	0.676061i	$-0.236314\pi$
$41$	5.54983	+	2.01997i	0.866738	+	0.315467i	0.129893	+	0.991528i	$0.458537\pi$
$42$	6.57840	−	2.02175i	1.01507	−	0.311963i
$43$	−9.57801	+	1.68886i	−1.46063	+	0.257549i	−0.846811	−	0.531895i	$-0.821480\pi$
$43$	−9.57801	+	1.68886i	−1.46063	+	0.257549i	−0.613823	+	0.789444i	$0.710369\pi$
$44$	1.26021	+	3.46239i	0.189983	+	0.521975i
$45$	6.56497	+	1.37884i	0.978648	+	0.205545i
$46$	7.13337	−	4.11845i	1.05176	−	0.607233i
$47$	−8.28350	−	6.95068i	−1.20827	−	1.01386i	−0.999354	−	0.0359278i	$-0.988561\pi$
$47$	−8.28350	−	6.95068i	−1.20827	−	1.01386i	−0.208918	−	0.977933i	$-0.566994\pi$
$48$	−0.387156	+	1.68823i	−0.0558811	+	0.243675i
$49$	4.39380	+	7.61029i	0.627686	+	1.08718i
$50$	1.04454	−	4.88968i	0.147720	−	0.691505i
$51$	−7.78357	−	7.23703i	−1.08992	−	1.01339i
$52$	−0.469291	−	2.66148i	−0.0650789	−	0.369081i
$53$	−7.81317	−	1.37767i	−1.07322	−	0.189238i	−0.391006	−	0.920388i	$-0.627873\pi$
$53$	−7.81317	−	1.37767i	−1.07322	−	0.189238i	−0.682216	+	0.731150i	$0.738984\pi$
$54$	2.49916	−	4.55568i	0.340093	−	0.619949i
$55$	−8.21923	+	0.570539i	−1.10828	+	0.0769315i
$56$	−3.97336			−0.530963
$57$	7.54975	+	0.0350595i	0.999989	+	0.00464374i
$58$			3.25989i			0.428044i
$59$	3.14279	−	2.63711i	0.409157	−	0.343323i	−0.414864	−	0.909884i	$-0.636171\pi$
$59$	3.14279	−	2.63711i	0.409157	−	0.343323i	0.824020	+	0.566561i	$0.191726\pi$
$60$	−3.38918	−	1.87442i	−0.437541	−	0.241987i
$61$	−0.625224	+	3.54582i	−0.0800517	+	0.453996i	0.918263	+	0.395970i	$0.129592\pi$
$61$	−0.625224	+	3.54582i	−0.0800517	+	0.453996i	−0.998315	+	0.0580256i	$0.981520\pi$
$62$	1.08442	+	6.15007i	0.137722	+	0.781059i
$63$	11.4679	+	3.25206i	1.44482	+	0.409721i
$64$	0.500000	−	0.866025i	0.0625000	−	0.108253i
$65$	6.00963	+	0.634732i	0.745403	+	0.0787288i
$66$	−1.42651	+	6.22044i	−0.175592	+	0.765683i
$67$	4.03846	+	3.38867i	0.493377	+	0.413992i	0.855235	−	0.518241i	$-0.173413\pi$
$67$	4.03846	+	3.38867i	0.493377	+	0.413992i	−0.361858	+	0.932233i	$0.617857\pi$
$68$	3.06810	+	5.31410i	0.372061	+	0.644429i
$69$	14.2483	+	0.725806i	1.71529	+	0.0873768i
$70$	2.45331	−	8.53928i	0.293226	−	1.02064i
$71$	0.156103	+	0.885303i	0.0185260	+	0.105066i	0.992669	−	0.120868i	$-0.0385677\pi$
$71$	0.156103	+	0.885303i	0.0185260	+	0.105066i	−0.974143	+	0.225934i	$0.927457\pi$
$72$	−2.15191	+	2.09028i	−0.253605	+	0.246342i
$73$	0.0635095	−	0.174491i	0.00743323	−	0.0204226i	−0.935921	−	0.352211i	$-0.885430\pi$
$73$	0.0635095	−	0.174491i	0.00743323	−	0.0204226i	0.943354	+	0.331789i	$0.107652\pi$
$74$	−3.52637	−	4.20256i	−0.409932	−	0.488538i
$75$	6.12100	−	6.12645i	0.706792	−	0.707422i
$76$	−4.16057	−	1.29985i	−0.477251	−	0.149103i
$77$	−14.6402			−1.66841
$78$	1.82268	−	4.31150i	0.206378	−	0.488181i
$79$	−2.72968	+	7.49975i	−0.307114	+	0.843788i	0.686103	+	0.727505i	$0.259320\pi$
$79$	−2.72968	+	7.49975i	−0.307114	+	0.843788i	−0.993216	+	0.116283i	$0.962902\pi$
$80$	1.55248	+	1.60928i	0.173573	+	0.179923i
$81$	7.92165	−	4.27170i	0.880183	−	0.474634i
$82$	−2.01997	−	5.54983i	−0.223069	−	0.612877i
$83$	2.29598	−	3.97675i	0.252016	−	0.436505i	−0.712065	−	0.702114i	$-0.752240\pi$
$83$	2.29598	−	3.97675i	0.252016	−	0.436505i	0.964081	+	0.265609i	$0.0855731\pi$
$84$	−5.77727	−	3.73979i	−0.630351	−	0.408044i
$85$	−13.3151	+	3.31262i	−1.44422	+	0.359304i
$86$	7.45037	+	6.25160i	0.803394	+	0.674128i
$87$	−3.06826	+	4.73988i	−0.328952	+	0.508168i
$88$	1.84230	−	3.19095i	0.196390	−	0.340157i
$89$	−6.92216	+	2.51946i	−0.733748	+	0.267062i	−0.681750	−	0.731585i	$-0.738781\pi$
$89$	−6.92216	+	2.51946i	−0.733748	+	0.267062i	−0.0519974	+	0.998647i	$0.516559\pi$
$90$	−3.16363	−	5.91536i	−0.333476	−	0.623534i
$91$	10.5750	+	1.86466i	1.10856	+	0.195470i
$92$	−7.74016	−	2.81719i	−0.806968	−	0.293712i
$93$	−4.21178	+	9.96287i	−0.436742	+	1.03310i
$94$			10.8133i			1.11531i
$95$	5.36246	−	8.13905i	0.550176	−	0.835048i
$96$	1.54212	−	0.788593i	0.157392	−	0.0804854i
$97$	−6.07708	+	5.09928i	−0.617034	+	0.517753i	−0.896870	−	0.442295i	$-0.854164\pi$
$97$	−6.07708	+	5.09928i	−0.617034	+	0.517753i	0.279836	+	0.960048i	$0.409720\pi$
$98$	3.00554	−	8.25764i	0.303605	−	0.834148i
$99$	−7.92892	+	7.70185i	−0.796886	+	0.774066i
$100$	−4.41713	+	2.34286i	−0.441713	+	0.234286i
$101$	−2.30123	−	6.32259i	−0.228981	−	0.629121i	0.770989	−	0.636849i	$-0.219762\pi$
$101$	−2.30123	−	6.32259i	−0.228981	−	0.629121i	−0.999970	+	0.00772758i	$0.997540\pi$
$102$	−0.540699	+	10.6144i	−0.0535372	+	1.05099i
$103$	−7.95354	−	13.7759i	−0.783686	−	1.35738i	−0.929781	−	0.368113i	$-0.880004\pi$
$103$	−7.95354	−	13.7759i	−0.783686	−	1.35738i	0.146096	−	0.989270i	$-0.453329\pi$
$104$	−1.73716	+	2.07026i	−0.170342	+	0.203006i
$105$	11.6044	−	10.1070i	1.13247	−	0.986344i
$106$	3.96685	+	6.87079i	0.385295	+	0.667350i
$107$	−11.3788	−	6.56958i	−1.10003	−	0.635105i	−0.163804	−	0.986493i	$-0.552377\pi$
$107$	−11.3788	−	6.56958i	−1.10003	−	0.635105i	−0.936230	+	0.351388i	$0.885710\pi$
$108$	−5.09628	+	1.01386i	−0.490390	+	0.0975591i
$109$	2.03175	−	0.358253i	0.194607	−	0.0343144i	−0.0754951	−	0.997146i	$-0.524054\pi$
$109$	2.03175	−	0.358253i	0.194607	−	0.0343144i	0.270102	+	0.962832i	$0.412943\pi$
$110$	5.72028	+	5.92956i	0.545407	+	0.565361i
$111$	−1.17182	−	9.42959i	−0.111224	−	0.895017i
$112$	2.55403	+	3.04377i	0.241333	+	0.287609i
$113$			4.74390i			0.446269i	0.974788	+	0.223134i	$0.0716289\pi$
$113$			4.74390i			0.446269i	−0.974788	+	0.223134i	$0.928371\pi$
$114$	−4.82603	−	5.80598i	−0.451999	−	0.543780i
$115$	10.8336	−	14.8952i	1.01024	−	1.38898i
$116$	2.49722	−	2.09542i	0.231861	−	0.194554i
$117$	6.70822	−	4.55338i	0.620175	−	0.420960i
$118$	−4.04029	−	0.712413i	−0.371939	−	0.0655829i
$119$	−24.0109	+	4.23377i	−2.20108	+	0.388109i
$120$	0.742629	+	3.80112i	0.0677925	+	0.346993i
$121$	1.28813	−	2.23110i	0.117102	−	0.202827i
$122$	3.11814	−	1.80026i	0.282303	−	0.162988i
$123$	2.28654	−	9.97068i	0.206171	−	0.899026i
$124$	4.01417	−	4.78390i	0.360483	−	0.429607i
$125$	−2.30782	−	10.9396i	−0.206417	−	0.978464i
$126$	−4.88020	−	10.8753i	−0.434762	−	0.968848i
$127$	2.92253	−	1.06371i	0.259332	−	0.0943893i	−0.209082	−	0.977898i	$-0.567048\pi$
$127$	2.92253	−	1.06371i	0.259332	−	0.0943893i	0.468415	+	0.883509i	$0.344825\pi$
$128$	−0.984808	+	0.173648i	−0.0870455	+	0.0153485i
$129$	4.94873	+	16.1022i	0.435712	+	1.41772i
$130$	−3.37669	−	5.01164i	−0.296155	−	0.439550i
$131$	−10.7385	−	12.7976i	−0.938223	−	1.11813i	−0.992819	−	0.119622i	$-0.961832\pi$
$131$	−10.7385	−	12.7976i	−0.938223	−	1.11813i	0.0545962	−	0.998509i	$-0.482613\pi$
$132$	5.68207	−	2.90565i	0.494561	−	0.252904i
$133$	10.5074	−	13.7680i	0.911108	−	1.19384i
$134$		−	5.27184i		−	0.455417i
$135$	0.967712	−	11.5786i	0.0832874	−	0.996526i
$136$	2.09870	−	5.76613i	0.179962	−	0.494442i
$137$	−1.03098	+	5.84696i	−0.0880822	+	0.499539i	0.908567	+	0.417740i	$0.137178\pi$
$137$	−1.03098	+	5.84696i	−0.0880822	+	0.499539i	−0.996649	+	0.0817992i	$0.973933\pi$
$138$	−8.60261	−	11.3813i	−0.732303	−	0.968845i
$139$	−14.3234	+	5.21328i	−1.21489	+	0.442184i	−0.868398	−	0.495868i	$-0.834850\pi$
$139$	−14.3234	+	5.21328i	−1.21489	+	0.442184i	−0.346493	+	0.938052i	$0.612628\pi$
$140$	−8.11842	+	3.60960i	−0.686132	+	0.305067i
$141$	−10.1777	+	15.7226i	−0.857115	+	1.32408i
$142$	0.577840	−	0.688643i	0.0484913	−	0.0577897i
$143$	−6.40073	+	7.62809i	−0.535256	+	0.637893i
$144$	2.98447	+	0.304849i	0.248706	+	0.0254041i
$145$	2.96145	+	6.66064i	0.245935	+	0.553136i
$146$	−0.174491	+	0.0635095i	−0.0144410	+	0.00525609i
$147$	12.1423	−	9.17775i	1.00148	−	0.756968i
$148$	−0.952643	+	5.40271i	−0.0783067	+	0.444100i
$149$	5.53602	−	15.2101i	0.453529	−	1.24606i	−0.476696	−	0.879068i	$-0.658166\pi$
$149$	5.53602	−	15.2101i	0.453529	−	1.24606i	0.930224	−	0.366991i	$-0.119612\pi$
$150$	−8.62763	−	0.750947i	−0.704443	−	0.0613146i
$151$		−	2.92592i		−	0.238108i	−0.992888	−	0.119054i	$-0.962014\pi$
$151$		−	2.92592i		−	0.238108i	0.992888	−	0.119054i	$-0.0379861\pi$
$152$	1.67862	+	4.02272i	0.136154	+	0.326285i
$153$	−10.7766	+	14.9245i	−0.871240	+	1.20657i
$154$	9.41056	+	11.2151i	0.758325	+	0.903736i
$155$	7.80274	+	11.5807i	0.626731	+	0.930188i
$156$	−4.47439	+	1.37512i	−0.358238	+	0.110098i
$157$	−16.5618	+	2.92028i	−1.32177	+	0.233064i	−0.789626	−	0.613589i	$-0.789725\pi$
$157$	−16.5618	+	2.92028i	−1.32177	+	0.233064i	−0.532146	+	0.846653i	$0.678614\pi$
$158$	7.49975	−	2.72968i	0.596648	−	0.217162i
$159$	−0.699089	+	13.7238i	−0.0554414	+	1.08837i
$160$	0.234865	−	2.22370i	0.0185677	−	0.175799i
$161$	21.0373	−	25.0713i	1.65797	−	1.97589i
$162$	−8.36425	−	3.32254i	−0.657158	−	0.261043i
$163$	−4.78129	+	2.76048i	−0.374499	+	0.216217i	−0.675422	−	0.737431i	$-0.736039\pi$
$163$	−4.78129	+	2.76048i	−0.374499	+	0.216217i	0.300923	+	0.953648i	$0.402705\pi$
$164$	−2.95300	+	5.11475i	−0.230591	+	0.399395i
$165$	2.73629	+	14.0056i	0.213020	+	1.09033i
$166$	−4.52219	+	0.797384i	−0.350990	+	0.0618890i
$167$	9.00117	+	1.58715i	0.696531	+	0.122817i	0.510693	−	0.859763i	$-0.329389\pi$
$167$	9.00117	+	1.58715i	0.696531	+	0.122817i	0.185838	+	0.982580i	$0.440500\pi$
$168$	0.848711	+	6.82953i	0.0654795	+	0.526910i
$169$	−4.36361	+	3.66150i	−0.335662	+	0.281654i
$170$	11.0964	+	8.07062i	0.851053	+	0.618988i
$171$	−1.55237	−	12.9842i	−0.118713	−	0.992929i
$172$		−	9.72577i		−	0.741583i
$173$	11.1541	+	13.2930i	0.848032	+	1.01065i	0.999753	+	0.0222218i	$0.00707402\pi$
$173$	11.1541	+	13.2930i	0.848032	+	1.01065i	−0.151721	+	0.988423i	$0.548482\pi$
$174$	5.60319	−	0.696313i	0.424777	−	0.0527874i
$175$	−2.74489	−	19.6763i	−0.207494	−	1.48739i
$176$	−3.62862	+	0.639823i	−0.273517	+	0.0482285i
$177$	−5.20405	−	4.83863i	−0.391160	−	0.363694i
$178$	6.37950	+	3.68321i	0.478164	+	0.276068i
$179$	−4.24912	−	7.35969i	−0.317594	−	0.550089i	0.662391	−	0.749158i	$-0.269542\pi$
$179$	−4.24912	−	7.35969i	−0.317594	−	0.550089i	−0.979986	+	0.199069i	$0.936208\pi$
$180$	−2.49789	+	6.22580i	−0.186182	+	0.464044i
$181$	7.15652	−	8.52881i	0.531940	−	0.633941i	−0.431421	−	0.902151i	$-0.641987\pi$
$181$	7.15652	−	8.52881i	0.531940	−	0.633941i	0.963361	+	0.268209i	$0.0864319\pi$
$182$	−5.36908	−	9.29952i	−0.397983	−	0.689326i
$183$	6.22821	+	0.317265i	0.460402	+	0.0234529i
$184$	2.81719	+	7.74016i	0.207686	+	0.570612i
$185$	−11.0229	−	5.38319i	−0.810422	−	0.395780i
$186$	10.3393	−	3.17759i	0.758113	−	0.232992i
$187$	7.73287	−	21.2459i	0.565483	−	1.55365i
$188$	8.28350	−	6.95068i	0.604136	−	0.506930i
$189$	3.14019	−	20.4060i	0.228415	−	1.48432i
$190$	−9.68179	+	1.12380i	−0.702391	+	0.0815289i
$191$			10.7405i			0.777158i	0.921415	+	0.388579i	$0.127034\pi$
$191$			10.7405i			0.777158i	−0.921415	+	0.388579i	$0.872966\pi$
$192$	−1.59535	−	0.674431i	−0.115134	−	0.0486729i
$193$	−2.36363	−	0.860293i	−0.170138	−	0.0619252i	0.255547	−	0.966797i	$-0.417745\pi$
$193$	−2.36363	−	0.860293i	−0.170138	−	0.0619252i	−0.425685	+	0.904871i	$0.639967\pi$
$194$	7.81254	+	1.37756i	0.560908	+	0.0989032i
$195$	−0.192664	−	10.4651i	−0.0137969	−	0.749422i
$196$	−8.25764	+	3.00554i	−0.589832	+	0.214681i
$197$	−2.03754	+	3.52912i	−0.145168	+	0.251439i	−0.929436	−	0.368984i	$-0.879706\pi$
$197$	−2.03754	+	3.52912i	−0.145168	+	0.251439i	0.784267	+	0.620423i	$0.213039\pi$
$198$	10.9966	+	1.12324i	0.781492	+	0.0798255i
$199$	14.4450	+	12.1208i	1.02398	+	0.859219i	0.990122	−	0.140207i	$-0.0447769\pi$
$199$	14.4450	+	12.1208i	1.02398	+	0.859219i	0.0338557	+	0.999427i	$0.489221\pi$
$200$	4.63401	+	1.87775i	0.327674	+	0.132777i
$201$	4.96193	−	7.66525i	0.349988	−	0.540665i
$202$	−3.36418	+	5.82693i	−0.236703	+	0.409981i
$203$	4.43009	+	12.1716i	0.310931	+	0.854277i
$204$	8.47868	−	6.40863i	0.593627	−	0.448694i
$205$	−9.16899	−	9.50444i	−0.640390	−	0.663819i
$206$	−5.44054	+	14.9478i	−0.379061	+	1.04146i
$207$	−1.79590	−	24.6454i	−0.124823	−	1.71297i
$208$	2.70254			0.187387
$209$	6.18504	+	14.8221i	0.427828	+	1.02526i
$210$	−15.2016	−	2.39282i	−1.04901	−	0.165120i
$211$	−11.8644	−	14.1394i	−0.816776	−	0.973396i	0.183177	−	0.983080i	$-0.441362\pi$
$211$	−11.8644	−	14.1394i	−0.816776	−	0.973396i	−0.999953	+	0.00968393i	$0.996917\pi$
$212$	2.71349	−	7.45524i	0.186363	−	0.512028i
$213$	1.48834	−	0.457415i	0.101979	−	0.0313416i
$214$	2.28159	+	12.9395i	0.155966	+	0.884529i
$215$	20.9020	+	6.00506i	1.42550	+	0.409542i
$216$	4.05249	+	3.25228i	0.275737	+	0.221290i
$217$	12.4067	+	21.4890i	0.842222	+	1.45877i
$218$	−1.58042	−	1.32613i	−0.107040	−	0.0898171i
$219$	−0.313486	−	0.0718907i	−0.0211834	−	0.00485793i
$220$	0.865383	−	8.19343i	0.0583441	−	0.552401i
$221$	−8.29165	+	14.3616i	−0.557757	+	0.966063i
$222$	−6.47025	+	6.95889i	−0.434255	+	0.467050i
$223$	4.09234	+	23.2088i	0.274043	+	1.55418i	0.741984	+	0.670418i	$0.233885\pi$
$223$	4.09234	+	23.2088i	0.274043	+	1.55418i	−0.467940	+	0.883760i	$0.655004\pi$
$224$	0.689967	−	3.91300i	0.0461004	−	0.261448i
$225$	−11.8378	−	9.21234i	−0.789185	−	0.614156i
$226$	3.63404	−	3.04932i	0.241733	−	0.202838i
$227$			13.1734i			0.874346i	0.899377	+	0.437173i	$0.144020\pi$
$227$			13.1734i			0.874346i	−0.899377	+	0.437173i	$0.855980\pi$
$228$	−1.34553	+	7.42897i	−0.0891097	+	0.491995i
$229$	5.99830			0.396379			0.198189	−	0.980164i	$-0.436494\pi$
$229$	5.99830			0.396379			0.198189	+	0.980164i	$0.436494\pi$
$230$	−18.3741	+	1.27544i	−1.21155	+	0.0841000i
$231$	3.12716	+	25.1641i	0.205752	+	1.65567i
$232$	−3.21036	−	0.566074i	−0.210771	−	0.0371646i
$233$	−2.18985	−	12.4192i	−0.143462	−	0.813612i	−0.968589	−	0.248666i	$-0.920008\pi$
$233$	−2.18985	−	12.4192i	−0.143462	−	0.813612i	0.825128	−	0.564946i	$-0.191103\pi$
$234$	−7.80005	−	2.21193i	−0.509905	−	0.144599i
$235$	9.82338	+	22.0940i	0.640807	+	1.44125i
$236$	2.05131	+	3.55297i	0.133529	+	0.231279i
$237$	13.4738	+	3.08991i	0.875221	+	0.200712i
$238$	18.6772	+	15.6720i	1.21066	+	1.01587i
$239$	−8.75603	+	5.05530i	−0.566381	+	0.327000i	−0.755703	−	0.654915i	$-0.772704\pi$
$239$	−8.75603	+	5.05530i	−0.566381	+	0.327000i	0.189322	+	0.981915i	$0.439371\pi$
$240$	2.43447	−	3.01220i	0.157145	−	0.194437i
$241$	−4.41995	−	12.1437i	−0.284714	−	0.782246i	−0.996784	−	0.0801370i	$-0.974464\pi$
$241$	−4.41995	−	12.1437i	−0.284714	−	0.782246i	0.712070	−	0.702109i	$-0.247758\pi$
$242$	−2.53711	+	0.447361i	−0.163092	+	0.0287575i
$243$	−9.03440	−	12.7035i	−0.579557	−	0.814932i
$244$	−3.38338	−	1.23145i	−0.216599	−	0.0788355i
$245$	−1.36071	−	19.6025i	−0.0869326	−	1.25236i
$246$	−9.10775	+	4.65744i	−0.580689	+	0.296947i
$247$	−2.57979	−	11.4941i	−0.164148	−	0.731355i
$248$	−6.24494			−0.396554
$249$	−7.32577	−	3.09696i	−0.464252	−	0.196262i
$250$	−6.89675	+	8.79970i	−0.436189	+	0.556542i
$251$	−10.9660	−	1.93359i	−0.692165	−	0.122047i	−0.183510	−	0.983018i	$-0.558746\pi$
$251$	−10.9660	−	1.93359i	−0.692165	−	0.122047i	−0.508655	+	0.860970i	$0.669857\pi$
$252$	−5.19403	+	10.7290i	−0.327193	+	0.675861i
$253$	10.3802	+	28.5194i	0.652598	+	1.79300i
$254$	−2.69342	−	1.55504i	−0.169000	−	0.0975722i
$255$	8.53793	+	22.1787i	0.534666	+	1.38889i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	0.457732	−	0.545503i	0.0285525	−	0.0340276i	−0.751579	−	0.659643i	$-0.770708\pi$
$257$	0.457732	−	0.545503i	0.0285525	−	0.0340276i	0.780132	+	0.625615i	$0.215152\pi$
$258$	9.15404	−	14.1413i	0.569906	−	0.880397i
$259$	−18.8777	−	10.8990i	−1.17300	−	0.677233i
$260$	−1.66865	+	5.80811i	−0.103485	+	0.360204i
$261$	8.80242	+	4.26137i	0.544856	+	0.263772i
$262$	−2.90098	+	16.4523i	−0.179223	+	1.01642i
$263$	−14.9588	−	5.44456i	−0.922400	−	0.335726i	−0.163207	−	0.986592i	$-0.552184\pi$
$263$	−14.9588	−	5.44456i	−0.922400	−	0.335726i	−0.759193	+	0.650866i	$0.774406\pi$
$264$	−5.87822	−	2.48501i	−0.361780	−	0.152942i
$265$	14.3469	+	10.4348i	0.881323	+	0.641004i
$266$	−17.3010	+	0.800779i	−1.06079	+	0.0490989i
$267$	5.80910	+	11.3599i	0.355511	+	0.695212i
$268$	−4.03846	+	3.38867i	−0.246688	+	0.206996i
$269$	18.9131	+	6.88381i	1.15315	+	0.419713i	0.846646	−	0.532156i	$-0.178618\pi$
$269$	18.9131	+	6.88381i	1.15315	+	0.419713i	0.306506	+	0.951869i	$0.400840\pi$
$270$	−9.49174	+	6.70126i	−0.577649	+	0.407826i
$271$	−1.80247	−	10.2223i	−0.109492	−	0.620963i	−0.989330	−	0.145689i	$-0.953460\pi$
$271$	−1.80247	−	10.2223i	−0.109492	−	0.620963i	0.879838	−	0.475274i	$-0.157651\pi$
$272$	−5.76613	+	2.09870i	−0.349623	+	0.127252i
$273$	0.946208	−	18.5750i	0.0572671	−	1.12421i
$274$	5.14173	−	2.96858i	0.310623	−	0.179338i
$275$	17.0745	+	6.91876i	1.02963	+	0.417217i
$276$	−3.18897	+	13.9058i	−0.191953	+	0.837029i
$277$	4.79388	−	2.76775i	0.288036	−	0.166298i	−0.349020	−	0.937115i	$-0.613485\pi$
$277$	4.79388	−	2.76775i	0.288036	−	0.166298i	0.637056	+	0.770818i	$0.280152\pi$
$278$	13.2005	+	7.62130i	0.791712	+	0.457095i
$279$	18.0241	+	5.11127i	1.07908	+	0.306004i
$280$	7.98354	+	3.89886i	0.477108	+	0.233002i
$281$	−4.66377	+	26.4496i	−0.278217	+	1.57785i	0.450335	+	0.892860i	$0.351305\pi$
$281$	−4.66377	+	26.4496i	−0.278217	+	1.57785i	−0.728553	+	0.684990i	$0.759807\pi$
$282$	18.5863	−	2.30973i	1.10680	−	0.137543i
$283$	−11.5989	−	13.8230i	−0.689483	−	0.821693i	0.301810	−	0.953368i	$-0.402409\pi$
$283$	−11.5989	−	13.8230i	−0.689483	−	0.821693i	−0.991293	+	0.131675i	$0.957965\pi$
$284$	−0.898960			−0.0533435
$285$	−15.1351	−	7.47865i	−0.896523	−	0.442997i
$286$	9.95776			0.588815
$287$	−15.0841	−	17.9765i	−0.890387	−	1.06112i
$288$	−1.68485	−	2.48219i	−0.0992809	−	0.146264i
$289$	3.58633	−	20.3391i	0.210961	−	1.19642i
$290$	3.19877	−	6.54998i	0.187838	−	0.384628i
$291$	10.0629	+	9.35626i	0.589895	+	0.548474i
$292$	0.160812	+	0.0928447i	0.00941080	+	0.00543333i
$293$	6.53655	−	3.77388i	0.381870	−	0.220472i	−0.296762	−	0.954952i	$-0.595907\pi$
$293$	6.53655	−	3.77388i	0.381870	−	0.220472i	0.678631	+	0.734479i	$0.262573\pi$
$294$	−14.8355	−	3.40217i	−0.865222	−	0.198419i
$295$	−8.90237	+	2.21480i	−0.518316	+	0.128950i
$296$	4.75106	−	2.74303i	0.276150	−	0.159435i
$297$	14.9318	+	11.9833i	0.866431	+	0.695344i
$298$	−15.2101	+	5.53602i	−0.881097	+	0.320693i
$299$	−3.86551	−	21.9224i	−0.223548	−	1.26780i
$300$	4.97048	+	7.09185i	0.286971	+	0.409448i
$301$	36.3135	+	13.2170i	2.09307	+	0.761817i
$302$	−2.24138	+	1.88074i	−0.128977	+	0.108225i
$303$	−10.3759	+	5.30594i	−0.596080	+	0.304818i
$304$	2.00258	−	3.87165i	0.114856	−	0.222054i
$305$	4.73558	−	6.51099i	0.271158	−	0.372818i
$306$	18.3599	−	1.33788i	1.04957	−	0.0764813i
$307$	25.8542	+	9.41014i	1.47557	+	0.537065i	0.949608	−	0.313440i	$-0.101481\pi$
$307$	25.8542	+	9.41014i	1.47557	+	0.537065i	0.525967	+	0.850505i	$0.323704\pi$
$308$	2.54225	−	14.4178i	0.144858	−	0.821531i
$309$	−21.9796	+	16.6133i	−1.25038	+	0.945099i
$310$	3.85587	−	13.4212i	0.218998	−	0.762273i
$311$	−13.6726	−	7.89390i	−0.775304	−	0.447622i	0.0594596	−	0.998231i	$-0.481062\pi$
$311$	−13.6726	−	7.89390i	−0.775304	−	0.447622i	−0.834763	+	0.550609i	$0.814396\pi$
$312$	3.92949	+	2.54367i	0.222464	+	0.144007i
$313$	8.66681	−	10.3287i	0.489877	−	0.583813i	−0.463309	−	0.886197i	$-0.653338\pi$
$313$	8.66681	−	10.3287i	0.489877	−	0.583813i	0.953186	+	0.302384i	$0.0977825\pi$
$314$	12.8828	+	10.8099i	0.727016	+	0.610039i
$315$	−19.8509	−	17.7871i	−1.11847	−	1.00219i
$316$	−6.91180	−	3.99053i	−0.388819	−	0.224485i
$317$	5.96430	+	16.3868i	0.334988	+	0.920373i	0.986793	+	0.161986i	$0.0517899\pi$
$317$	5.96430	+	16.3868i	0.334988	+	0.920373i	−0.651805	+	0.758387i	$0.725988\pi$
$318$	10.9624	−	8.28595i	0.614741	−	0.464653i
$319$	−11.8289	−	2.08575i	−0.662291	−	0.116780i
$320$	−1.85442	+	1.24945i	−0.103665	+	0.0698463i
$321$	−8.86146	+	20.9616i	−0.494598	+	1.16996i
$322$	−32.7282			−1.82387
$323$	14.4302	+	22.5205i	0.802918	+	1.25307i
$324$	2.83123	+	8.54308i	0.157290	+	0.474615i
$325$	−11.4521	−	7.17230i	−0.635249	−	0.397848i
$326$	5.18800	+	1.88828i	0.287337	+	0.104582i
$327$	−1.04976	−	3.41572i	−0.0580518	−	0.188890i
$328$	5.81628	−	1.02557i	0.321151	−	0.0566275i
$329$	14.6950	+	40.3742i	0.810162	+	2.22590i
$330$	8.97005	−	11.0987i	0.493785	−	0.610965i
$331$	−10.3770	+	5.99116i	−0.570371	+	0.329304i	−0.757297	−	0.653070i	$-0.773481\pi$
$331$	−10.3770	+	5.99116i	−0.570371	+	0.329304i	0.186927	+	0.982374i	$0.440147\pi$
$332$	3.51764	+	2.95165i	0.193056	+	0.161993i
$333$	−15.9575	+	4.02832i	−0.874468	+	0.220751i
$334$	−4.57001	−	7.91549i	−0.250060	−	0.433117i
$335$	−4.78920	−	10.7715i	−0.261662	−	0.588509i
$336$	4.68618	−	5.04009i	0.255652	−	0.274959i
$337$	3.86733	+	21.9327i	0.210667	+	1.19475i	0.888270	+	0.459323i	$0.151908\pi$
$337$	3.86733	+	21.9327i	0.210667	+	1.19475i	−0.677603	+	0.735428i	$0.736981\pi$
$338$	5.60974	+	0.989149i	0.305130	+	0.0538026i
$339$	8.15396	−	1.01330i	0.442862	−	0.0550349i
$340$	−0.950155	−	13.6880i	−0.0515294	−	0.742336i
$341$	−23.0101			−1.24607
$342$	−8.94865	+	9.53528i	−0.483888	+	0.515609i
$343$		−	7.10278i		−	0.383514i
$344$	−7.45037	+	6.25160i	−0.401697	+	0.337064i
$345$	−27.9164	−	15.4395i	−1.50297	−	0.831233i
$346$	3.01327	−	17.0891i	0.161994	−	0.918716i
$347$	0.402185	+	2.28090i	0.0215904	+	0.122445i	0.993698	−	0.112090i	$-0.0357544\pi$
$347$	0.402185	+	2.28090i	0.0215904	+	0.122445i	−0.972108	+	0.234535i	$0.924643\pi$
$348$	−4.13507	−	3.84471i	−0.221663	−	0.206098i
$349$	4.07912	−	7.06525i	0.218350	−	0.378194i	−0.735953	−	0.677032i	$-0.763266\pi$
$349$	4.07912	−	7.06525i	0.218350	−	0.378194i	0.954304	+	0.298838i	$0.0965991\pi$
$350$	−13.3085	+	14.7504i	−0.711370	+	0.788440i
$351$	−9.25936	−	10.5577i	−0.494228	−	0.563527i
$352$	2.82256	+	2.36841i	0.150443	+	0.126237i
$353$	−1.15242	−	1.99605i	−0.0613372	−	0.106239i	0.833726	−	0.552178i	$-0.186203\pi$
$353$	−1.15242	−	1.99605i	−0.0613372	−	0.106239i	−0.895063	+	0.445939i	$0.852870\pi$
$354$	−0.361508	+	7.09675i	−0.0192139	+	0.377188i
$355$	0.555052	−	1.93198i	0.0294591	−	0.102539i
$356$	−1.27916	−	7.25450i	−0.0677956	−	0.384488i
$357$	12.4059	+	40.3663i	0.656588	+	2.13641i
$358$	−2.90657	+	7.98573i	−0.153617	+	0.422059i
$359$	8.80452	+	10.4928i	0.464685	+	0.553790i	0.946593	−	0.322432i	$-0.104500\pi$
$359$	8.80452	+	10.4928i	0.464685	+	0.553790i	−0.481908	+	0.876222i	$0.660056\pi$
$360$	6.37485	−	2.08837i	0.335984	−	0.110067i
$361$	−18.3781	−	4.82136i	−0.967268	−	0.253756i
$362$	−11.1336			−0.585167
$363$	−4.11002	−	1.73751i	−0.215720	−	0.0911954i
$364$	−3.67267	+	10.0906i	−0.192500	+	0.528890i
$365$	−0.298827	+	0.288280i	−0.0156413	+	0.0150893i
$366$	−3.76038	−	4.97502i	−0.196558	−	0.260048i
$367$	−1.22644	−	3.36962i	−0.0640197	−	0.175893i	0.903558	−	0.428465i	$-0.140946\pi$
$367$	−1.22644	−	3.36962i	−0.0640197	−	0.175893i	−0.967578	+	0.252573i	$0.918723\pi$
$368$	4.11845	−	7.13337i	0.214689	−	0.371853i
$369$	−17.6263	−	1.80044i	−0.917589	−	0.0937272i
$370$	2.96164	+	11.9043i	0.153968	+	0.618875i
$371$	24.1484	+	20.2629i	1.25372	+	1.05200i
$372$	−9.08014	−	5.87783i	−0.470783	−	0.304751i
$373$	15.6386	−	27.0868i	0.809734	−	1.40250i	−0.103314	−	0.994649i	$-0.532945\pi$
$373$	15.6386	−	27.0868i	0.809734	−	1.40250i	0.913048	−	0.407852i	$-0.133722\pi$
$374$	−21.2459	+	7.73287i	−1.09860	+	0.399857i
$375$	−18.3103	+	6.30343i	−0.945539	+	0.325508i
$376$	−10.6491	−	1.87772i	−0.549183	−	0.0968358i
$377$	8.27867	+	3.01319i	0.426373	+	0.155187i
$378$	−17.6504	+	10.7112i	−0.907837	+	0.550924i
$379$		−	25.0952i		−	1.28906i	−0.764581	−	0.644528i	$-0.777054\pi$
$379$		−	25.0952i		−	1.28906i	0.764581	−	0.644528i	$-0.222946\pi$
$380$	7.08421	+	6.69432i	0.363413	+	0.343411i
$381$	−2.45259	−	4.79612i	−0.125650	−	0.245713i
$382$	8.22773	−	6.90388i	0.420967	−	0.353233i
$383$	7.67222	−	21.0793i	0.392032	−	1.07710i	−0.574040	−	0.818827i	$-0.694625\pi$
$383$	7.67222	−	21.0793i	0.392032	−	1.07710i	0.966072	−	0.258272i	$-0.0831532\pi$
$384$	0.508827	+	1.65563i	0.0259660	+	0.0844883i
$385$	29.4161	+	14.3657i	1.49918	+	0.732146i
$386$	0.860293	+	2.36363i	0.0437877	+	0.120306i
$387$	26.6199	−	11.9455i	1.35317	−	0.607222i
$388$	−3.96653	−	6.87024i	−0.201370	−	0.348783i
$389$	14.4837	−	17.2610i	0.734351	−	0.875166i	−0.261589	−	0.965179i	$-0.584247\pi$
$389$	14.4837	−	17.2610i	0.734351	−	0.875166i	0.995941	+	0.0900135i	$0.0286910\pi$
$390$	−7.89290	+	6.87443i	−0.399673	+	0.348101i
$391$	25.2716	+	43.7717i	1.27804	+	2.21363i
$392$	7.61029	+	4.39380i	0.384377	+	0.221920i
$393$	−19.7031	+	21.1911i	−0.993892	+	1.06895i
$394$	4.01316	−	0.707629i	0.202180	−	0.0356498i
$395$	12.8438	−	12.3905i	0.646241	−	0.623433i
$396$	−6.20800	−	9.14587i	−0.311964	−	0.459597i
$397$	−4.43134	−	5.28107i	−0.222403	−	0.265049i	0.643293	−	0.765620i	$-0.277568\pi$
$397$	−4.43134	−	5.28107i	−0.222403	−	0.265049i	−0.865695	+	0.500571i	$0.833123\pi$
$398$		−	18.8566i		−	0.945195i
$399$	−25.9093	−	15.1196i	−1.29709	−	0.756926i
$400$	−1.54024	−	4.75685i	−0.0770121	−	0.237843i
$401$	−7.74218	+	6.49646i	−0.386626	+	0.324418i	−0.815297	−	0.579043i	$-0.803426\pi$
$401$	−7.74218	+	6.49646i	−0.386626	+	0.324418i	0.428671	+	0.903461i	$0.358982\pi$
$402$	−9.06139	+	1.12607i	−0.451941	+	0.0561631i
$403$	16.6208	+	2.93069i	0.827941	+	0.145988i
$404$	6.62614	−	1.16837i	0.329663	−	0.0581284i
$405$	−20.1083	+	0.809857i	−0.999190	+	0.0402421i
$406$	6.47636	−	11.2174i	0.321416	−	0.556709i
$407$	17.5057	−	10.1069i	0.867727	−	0.500983i
$408$	−10.3593	−	2.37566i	−0.512861	−	0.117613i
$409$	1.87803	−	2.23815i	0.0928625	−	0.110669i	−0.717612	−	0.696443i	$-0.754765\pi$
$409$	1.87803	−	2.23815i	0.0928625	−	0.110669i	0.810475	+	0.585774i	$0.199209\pi$
$410$	−1.38712	+	13.1332i	−0.0685047	+	0.648602i
$411$	10.2701	+	0.523161i	0.506589	+	0.0258056i
$412$	14.9478	−	5.44054i	0.736424	−	0.268036i
$413$	−16.0535	+	2.83067i	−0.789943	+	0.139288i
$414$	−17.7251	+	17.2175i	−0.871140	+	0.846193i
$415$	−8.51541	+	5.73741i	−0.418005	+	0.281638i
$416$	−1.73716	−	2.07026i	−0.0851712	−	0.101503i
$417$	12.0202	+	23.5059i	0.588632	+	1.15109i
$418$	7.37871	−	14.2655i	0.360904	−	0.697747i
$419$		−	36.0163i		−	1.75951i	−0.475426	−	0.879755i	$-0.657706\pi$
$419$		−	36.0163i		−	1.75951i	0.475426	−	0.879755i	$-0.342294\pi$
$420$	7.93839	+	13.1832i	0.387354	+	0.643273i
$421$	7.36495	−	20.2350i	0.358946	−	0.986195i	−0.620450	−	0.784246i	$-0.713050\pi$
$421$	7.36495	−	20.2350i	0.358946	−	0.986195i	0.979396	−	0.201949i	$-0.0647276\pi$
$422$	−3.20514	+	18.1773i	−0.156024	+	0.884855i
$423$	29.1984	+	14.1353i	1.41968	+	0.687284i
$424$	−7.45524	+	2.71349i	−0.362059	+	0.131779i
$425$	30.0040	+	6.40949i	1.45541	+	0.310906i
$426$	−1.30709	−	0.846115i	−0.0633286	−	0.0409944i
$427$	9.19583	−	10.9592i	0.445017	−	0.530351i
$428$	8.44569	−	10.0652i	0.408238	−	0.486519i
$429$	14.4786	+	9.37240i	0.699033	+	0.452504i
$430$	−8.83538	−	19.8718i	−0.426080	−	0.958304i
$431$	−1.58649	+	0.577434i	−0.0764184	+	0.0278140i	−0.379946	−	0.925008i	$-0.624058\pi$
$431$	−1.58649	+	0.577434i	−0.0764184	+	0.0278140i	0.303528	+	0.952822i	$0.401835\pi$
$432$	−0.113501	−	5.19491i	−0.00546081	−	0.249940i
$433$	−0.787161	+	4.46421i	−0.0378285	+	0.214536i	−0.997863	−	0.0653468i	$-0.979185\pi$
$433$	−0.787161	+	4.46421i	−0.0378285	+	0.214536i	0.960034	+	0.279883i	$0.0902957\pi$
$434$	8.48668	−	23.3170i	0.407374	−	1.11925i
$435$	10.8159	−	6.51294i	0.518585	−	0.312271i
$436$			2.06310i			0.0988045i
$437$	−34.2703	−	10.7068i	−1.63937	−	0.512175i
$438$	0.146433	+	0.286355i	0.00699686	+	0.0136826i
$439$	1.65001	+	1.96640i	0.0787507	+	0.0938514i	0.803981	−	0.594655i	$-0.202711\pi$
$439$	1.65001	+	1.96640i	0.0787507	+	0.0938514i	−0.725230	+	0.688506i	$0.758267\pi$
$440$	−6.83279	+	4.60372i	−0.325741	+	0.219474i
$441$	−18.3686	−	18.9101i	−0.874694	−	0.900482i
$442$	16.3314	−	2.87966i	0.776804	−	0.136971i
$443$	−1.87712	+	0.683216i	−0.0891846	+	0.0324606i	−0.386227	−	0.922404i	$-0.626222\pi$
$443$	−1.87712	+	0.683216i	−0.0891846	+	0.0324606i	0.297043	+	0.954864i	$0.404000\pi$
$444$	9.48981	+	0.483411i	0.450367	+	0.0229417i
$445$	16.3807	+	1.73011i	0.776519	+	0.0820152i
$446$	15.1485	−	18.0533i	0.717301	−	0.854847i
$447$	−27.3261	−	6.26660i	−1.29248	−	0.296400i
$448$	−3.44103	+	1.98668i	−0.162573	+	0.0938618i
$449$	−1.10040	+	1.90595i	−0.0519313	+	0.0899476i	−0.890822	−	0.454352i	$-0.849871\pi$
$449$	−1.10040	+	1.90595i	−0.0519313	+	0.0899476i	0.838891	+	0.544299i	$0.183204\pi$
$450$	0.552115	+	14.9898i	0.0260270	+	0.706628i
$451$	21.4307	−	3.77880i	1.00913	−	0.177937i
$452$	−4.67183	−	0.823770i	−0.219745	−	0.0387469i
$453$	−5.02915	+	0.624977i	−0.236290	+	0.0293640i
$454$	10.0914	−	8.46767i	0.473612	−	0.397407i
$455$	−19.4183	−	14.1234i	−0.910345	−	0.662113i
$456$	6.55581	−	3.74451i	0.307004	−	0.175353i
$457$			8.79212i			0.411278i	0.978628	+	0.205639i	$0.0659273\pi$
$457$			8.79212i			0.411278i	−0.978628	+	0.205639i	$0.934073\pi$
$458$	−3.85563	−	4.59496i	−0.180162	−	0.214709i
$459$	27.9545	+	15.3353i	1.30480	+	0.715792i
$460$	12.7877	+	13.2555i	0.596228	+	0.618042i
$461$	24.2749	−	4.28032i	1.13060	−	0.199355i	0.423108	−	0.906079i	$-0.360939\pi$
$461$	24.2749	−	4.28032i	1.13060	−	0.199355i	0.707488	+	0.706725i	$0.249828\pi$
$462$	17.2667	−	18.5707i	0.803319	−	0.863987i
$463$	−32.2406	−	18.6141i	−1.49835	−	0.865072i	−0.498350	−	0.866976i	$-0.666061\pi$
$463$	−32.2406	−	18.6141i	−1.49835	−	0.865072i	−0.999998	+	0.00190400i	$0.999394\pi$
$464$	1.62994	+	2.82315i	0.0756683	+	0.131061i
$465$	18.2387	−	15.8852i	0.845798	−	0.736660i
$466$	−8.10609	+	9.66046i	−0.375507	+	0.447512i
$467$	−13.7662	−	23.8438i	−0.637024	−	1.10336i	−0.986082	−	0.166257i	$-0.946832\pi$
$467$	−13.7662	−	23.8438i	−0.637024	−	1.10336i	0.349058	−	0.937101i	$-0.386502\pi$
$468$	3.31934	+	7.39699i	0.153436	+	0.341926i
$469$	−7.16427	−	19.6837i	−0.330815	−	0.908907i
$470$	10.6106	−	21.7269i	0.489430	−	1.00219i
$471$	8.55707	+	27.8431i	0.394289	+	1.28294i
$472$	1.40318	−	3.85520i	0.0645866	−	0.177450i
$473$	−27.4516	+	23.0346i	−1.26223	+	1.05913i
$474$	−6.29381	−	12.3077i	−0.289084	−	0.565313i
$475$	−18.7610	+	11.0916i	−0.860816	+	0.508917i
$476$		−	24.3813i		−	1.11752i
$477$	23.7382	−	1.72979i	1.08690	−	0.0792016i
$478$	9.50085	+	3.45803i	0.434559	+	0.158167i
$479$	−31.5808	−	5.56855i	−1.44296	−	0.254434i	−0.603289	−	0.797522i	$-0.706144\pi$
$479$	−31.5808	−	5.56855i	−1.44296	−	0.254434i	−0.839675	+	0.543089i	$0.817255\pi$
$480$	−3.87233	+	0.0712898i	−0.176747	+	0.00325392i
$481$	−13.9321	+	5.07088i	−0.635251	+	0.231212i
$482$	−6.46154	+	11.1917i	−0.294315	+	0.509769i
$483$	−47.5868	−	30.8043i	−2.16527	−	1.40164i
$484$	1.97352	+	1.65598i	0.0897056	+	0.0752719i
$485$	17.2141	−	4.28266i	0.781654	−	0.194465i
$486$	−3.92427	+	15.0864i	−0.178009	+	0.684334i
$487$	−13.4375	+	23.2745i	−0.608913	+	1.05467i	0.382507	+	0.923953i	$0.375061\pi$
$487$	−13.4375	+	23.2745i	−0.608913	+	1.05467i	−0.991420	+	0.130716i	$0.958272\pi$
$488$	1.23145	+	3.38338i	0.0557451	+	0.153158i
$489$	5.76607	+	7.62858i	0.260751	+	0.344976i
$490$	−14.1417	+	13.6426i	−0.638859	+	0.616310i
$491$	5.69402	−	15.6442i	0.256968	−	0.706013i	−0.742383	−	0.669976i	$-0.766304\pi$
$491$	5.69402	−	15.6442i	0.256968	−	0.706013i	0.999350	−	0.0360368i	$-0.0114734\pi$
$492$	9.42215	+	3.98320i	0.424783	+	0.179576i
$493$	−20.0033			−0.900903
$494$	−7.14677	+	9.36453i	−0.321548	+	0.421330i
$495$	23.4887	−	7.69481i	1.05574	−	0.345856i
$496$	4.01417	+	4.78390i	0.180242	+	0.214804i
$497$	1.22166	−	3.35648i	0.0547989	−	0.150559i
$498$	2.33651	+	7.60255i	0.104701	+	0.340679i
$499$	0.205740	+	1.16681i	0.00921017	+	0.0522335i	0.989066	−	0.147470i	$-0.0471131\pi$
$499$	0.205740	+	1.16681i	0.00921017	+	0.0522335i	−0.979856	+	0.199704i	$0.936002\pi$
$500$	11.1741	−	0.373120i	0.499721	−	0.0166864i
$501$	0.805386	−	15.8105i	0.0359820	−	0.706361i
$502$	5.56756	+	9.64330i	0.248492	+	0.430402i
$503$	−20.2377	−	16.9814i	−0.902352	−	0.757163i	0.0682965	−	0.997665i	$-0.478244\pi$
$503$	−20.2377	−	16.9814i	−0.902352	−	0.757163i	−0.970649	+	0.240502i	$0.922688\pi$
$504$	11.5575	−	2.91758i	0.514813	−	0.129959i
$505$	−1.58026	+	14.9618i	−0.0703205	+	0.665793i
$506$	15.1748	−	26.2836i	0.674604	−	1.16845i
$507$	7.22556	+	6.71820i	0.320899	+	0.298366i
$508$	0.540061	+	3.06284i	0.0239613	+	0.135892i
$509$	4.16341	−	23.6119i	0.184540	−	1.04658i	−0.742005	−	0.670394i	$-0.766125\pi$
$509$	4.16341	−	23.6119i	0.184540	−	1.04658i	0.926545	−	0.376183i	$-0.122764\pi$
$510$	11.5018	−	20.7967i	0.509310	−	0.920891i
$511$	−0.565196	+	0.474256i	−0.0250028	+	0.0209798i
$512$		−	1.00000i		−	0.0441942i
$513$	−21.9861	+	5.44169i	−0.970709	+	0.240257i
$514$	−0.712104			−0.0314096
$515$	2.46312	+	35.4839i	0.108538	+	1.56361i
$516$	−16.7169	+	2.07743i	−0.735922	+	0.0914536i
$517$	−39.2375	−	6.91863i	−1.72566	−	0.304281i
$518$	3.78519	+	21.4669i	0.166312	+	0.943201i
$519$	20.4658	−	22.0114i	0.898349	−	0.966194i
$520$	5.52186	−	2.45512i	0.242150	−	0.107664i
$521$	−2.79411	−	4.83955i	−0.122412	−	0.212024i	0.798306	−	0.602252i	$-0.205730\pi$
$521$	−2.79411	−	4.83955i	−0.122412	−	0.212024i	−0.920718	+	0.390227i	$0.872396\pi$
$522$	−2.39369	−	9.48220i	−0.104769	−	0.415025i
$523$	34.6659	+	29.0881i	1.51583	+	1.27193i	0.851306	+	0.524669i	$0.175811\pi$
$523$	34.6659	+	29.0881i	1.51583	+	1.27193i	0.664526	+	0.747265i	$0.268634\pi$
$524$	14.4679	−	8.35304i	0.632032	−	0.364904i
$525$	−33.2338	+	8.92085i	−1.45044	+	0.389338i
$526$	5.44456	+	14.9588i	0.237394	+	0.652235i
$527$	−37.7380	+	6.65423i	−1.64389	+	0.289863i
$528$	1.87482	+	6.10031i	0.0815911	+	0.265482i
$529$	−42.1421	−	15.3385i	−1.83226	−	0.666889i
$530$	−1.22849	−	17.6977i	−0.0533622	−	0.768740i
$531$	−7.20520	+	9.97841i	−0.312679	+	0.433026i
$532$	11.7343	+	12.7386i	0.508745	+	0.552287i
$533$	−15.9612			−0.691357
$534$	4.96814	−	11.7520i	0.214992	−	0.508559i
$535$	16.4167	+	24.3655i	0.709756	+	1.05341i
$536$	5.19175	+	0.915445i	0.224249	+	0.0395412i
$537$	−11.7424	+	8.87554i	−0.506724	+	0.383008i
$538$	−6.88381	−	18.9131i	−0.296782	−	0.815402i
$539$	28.0408	+	16.1894i	1.20780	+	0.697326i
$540$	11.2346	+	2.96361i	0.483462	+	0.127533i
$541$	15.9737	+	13.4035i	0.686764	+	0.576263i	0.917974	−	0.396641i	$-0.129824\pi$
$541$	15.9737	+	13.4035i	0.686764	+	0.576263i	−0.231210	+	0.972904i	$0.574269\pi$
$542$	−6.67215	+	7.95156i	−0.286594	+	0.341549i
$543$	−16.1882	−	10.4791i	−0.694702	−	0.449701i
$544$	5.31410	+	3.06810i	0.227840	+	0.131544i
$545$	−4.43387	−	1.27384i	−0.189926	−	0.0545651i
$546$	−14.8375	+	11.2149i	−0.634984	+	0.479954i
$547$	2.31953	−	13.1547i	0.0991757	−	0.562454i	−0.894212	−	0.447644i	$-0.852263\pi$
$547$	2.31953	−	13.1547i	0.0991757	−	0.562454i	0.993388	−	0.114809i	$-0.0366257\pi$
$548$	−5.57910	−	2.03063i	−0.238327	−	0.0867441i
$549$	−0.785023	−	10.7730i	−0.0335040	−	0.459780i
$550$	−5.67517	−	17.5271i	−0.241990	−	0.747357i
$551$	10.4512	−	9.62722i	0.445235	−	0.410133i
$552$	12.7023	−	6.49557i	0.540644	−	0.276470i
$553$	24.2925	−	20.3839i	1.03302	−	0.866810i
$554$	−5.20166	−	1.89325i	−0.220997	−	0.0804365i
$555$	−6.89829	+	20.0964i	−0.292816	+	0.853044i
$556$	−2.64685	−	15.0110i	−0.112251	−	0.636609i
$557$	22.1081	−	8.04668i	0.936749	−	0.340949i	0.171868	−	0.985120i	$-0.445020\pi$
$557$	22.1081	−	8.04668i	0.936749	−	0.340949i	0.764881	+	0.644171i	$0.222798\pi$
$558$	−7.67021	−	17.0927i	−0.324706	−	0.723593i
$559$	22.7628	−	13.1421i	0.962766	−	0.555853i
$560$	−2.14502	−	8.62189i	−0.0906434	−	0.364341i
$561$	−38.1698	−	8.75336i	−1.61153	−	0.369567i
$562$	23.2594	−	13.4288i	0.981137	−	0.566460i
$563$	23.3674	+	13.4912i	0.984819	+	0.568585i	0.903721	−	0.428121i	$-0.140824\pi$
$563$	23.3674	+	13.4912i	0.984819	+	0.568585i	0.0810972	+	0.996706i	$0.474158\pi$
$564$	−13.7164	−	12.7533i	−0.577564	−	0.537009i
$565$	4.65496	−	9.53176i	0.195836	−	0.401004i
$566$	−3.13342	+	17.7705i	−0.131708	+	0.746951i
$567$	−35.7452	−	1.03873i	−1.50116	−	0.0436224i
$568$	0.577840	+	0.688643i	0.0242456	+	0.0288948i
$569$	−7.48774			−0.313902			−0.156951	−	0.987606i	$-0.550167\pi$
$569$	−7.48774			−0.313902			−0.156951	+	0.987606i	$0.550167\pi$
$570$	3.99965	+	16.4013i	0.167527	+	0.686975i
$571$	−28.5942			−1.19663			−0.598314	−	0.801262i	$-0.704162\pi$
$571$	−28.5942			−1.19663			−0.598314	+	0.801262i	$0.704162\pi$
$572$	−6.40073	−	7.62809i	−0.267628	−	0.318946i
$573$	18.4612	−	2.29418i	0.771226	−	0.0958408i
$574$	−4.07495	+	23.1102i	−0.170085	+	0.964601i
$575$	−36.3835	+	19.2979i	−1.51730	+	0.804779i
$576$	−0.818465	+	2.88619i	−0.0341027	+	0.120258i
$577$	−13.9903	−	8.07731i	−0.582424	−	0.336263i	0.179672	−	0.983727i	$-0.442496\pi$
$577$	−13.9903	−	8.07731i	−0.582424	−	0.336263i	−0.762096	+	0.647464i	$0.775830\pi$
$578$	−17.8859	+	10.3264i	−0.743955	+	0.429523i
$579$	−0.973823	+	4.24644i	−0.0404707	+	0.176476i
$580$	−7.07370	+	1.75985i	−0.293720	+	0.0730737i
$581$	−15.8011	+	9.12274i	−0.655538	+	0.378475i
$582$	0.699033	−	13.7227i	0.0289758	−	0.568823i
$583$	−27.4696	+	9.99810i	−1.13767	+	0.414079i
$584$	−0.0322446	−	0.182868i	−0.00133429	−	0.00756715i
$585$	−17.9466	+	2.56651i	−0.742000	+	0.106112i
$586$	−7.09258	−	2.58149i	−0.292992	−	0.106640i
$587$	9.43356	−	7.91569i	0.389365	−	0.326716i	−0.427001	−	0.904251i	$-0.640430\pi$
$587$	9.43356	−	7.91569i	0.389365	−	0.326716i	0.816366	+	0.577536i	$0.195985\pi$
$588$	6.92984	+	13.5515i	0.285782	+	0.558854i
$589$	16.5145	−	21.6392i	0.680469	−	0.891630i
$590$	7.41897	+	5.39597i	0.305434	+	0.222149i
$591$	6.50117	+	2.74836i	0.267422	+	0.113052i
$592$	−5.15520	−	1.87634i	−0.211877	−	0.0771171i
$593$	5.38493	−	30.5395i	0.221133	−	1.25411i	−0.648809	−	0.760951i	$-0.724733\pi$
$593$	5.38493	−	30.5395i	0.221133	−	1.25411i	0.869942	−	0.493155i	$-0.164156\pi$
$594$	−0.418205	−	19.1412i	−0.0171591	−	0.785371i
$595$	52.3987	+	15.0540i	2.14814	+	0.617152i
$596$	14.0177	+	8.09312i	0.574187	+	0.331507i
$597$	17.7481	−	27.4175i	0.726382	−	1.12212i
$598$	−14.3088	+	17.0526i	−0.585131	+	0.697332i
$599$	1.36518	+	1.14552i	0.0557797	+	0.0468047i	0.670251	−	0.742134i	$-0.266186\pi$
$599$	1.36518	+	1.14552i	0.0557797	+	0.0468047i	−0.614472	+	0.788939i	$0.710631\pi$
$600$	2.23771	−	8.36616i	0.0913542	−	0.341547i
$601$	32.7412	+	18.9032i	1.33554	+	0.771076i	0.986143	−	0.165897i	$-0.0530520\pi$
$601$	32.7412	+	18.9032i	1.33554	+	0.771076i	0.349400	+	0.936974i	$0.386385\pi$
$602$	−13.2170	−	36.3135i	−0.538686	−	1.48003i
$603$	−14.2351	−	6.89142i	−0.579699	−	0.280640i
$604$	2.88147	+	0.508080i	0.117245	+	0.0206735i
$605$	−4.77745	+	3.21890i	−0.194231	+	0.130867i
$606$	10.7341	+	4.53782i	0.436043	+	0.184336i
$607$	−19.9070			−0.807999			−0.404000	−	0.914759i	$-0.632380\pi$
$607$	−19.9070			−0.807999			−0.404000	+	0.914759i	$0.632380\pi$
$608$	−4.25309	+	0.954580i	−0.172486	+	0.0387134i
$609$	19.9746	−	10.2144i	0.809411	−	0.413909i
$610$	−8.03168	+	0.557520i	−0.325193	+	0.0225733i
$611$	27.4611	+	9.99502i	1.11096	+	0.404355i
$612$	−12.8264	−	13.2045i	−0.518476	−	0.533761i
$613$	−20.7106	+	3.65183i	−0.836492	+	0.147496i	−0.575456	−	0.817833i	$-0.695175\pi$
$613$	−20.7106	+	3.65183i	−0.836492	+	0.147496i	−0.261036	+	0.965329i	$0.584064\pi$
$614$	−9.41014	−	25.8542i	−0.379762	−	1.04339i
$615$	−14.3780	+	17.7901i	−0.579778	+	0.717365i
$616$	−12.6788	+	7.32012i	−0.510844	+	0.294936i
$617$	−22.1287	−	18.5681i	−0.890866	−	0.747525i	0.0775176	−	0.996991i	$-0.475301\pi$
$617$	−22.1287	−	18.5681i	−0.890866	−	0.747525i	−0.968384	+	0.249466i	$0.919745\pi$
$618$	26.8548	+	6.15852i	1.08026	+	0.247732i
$619$	−8.36494	−	14.4885i	−0.336215	−	0.582342i	0.647502	−	0.762064i	$-0.275814\pi$
$619$	−8.36494	−	14.4885i	−0.336215	−	0.582342i	−0.983717	+	0.179722i	$0.942480\pi$
$620$	−12.7597	+	5.67322i	−0.512444	+	0.227842i
$621$	−41.9776	+	8.35110i	−1.68450	+	0.335118i
$622$	2.74152	+	15.5479i	0.109925	+	0.623416i
$623$	28.8248	+	5.08258i	1.15484	+	0.203629i
$624$	−0.577263	−	4.64520i	−0.0231090	−	0.185957i
$625$	−6.09744	+	24.2450i	−0.243898	+	0.969801i
$626$	−13.4832			−0.538896
$627$	24.1555	−	13.7970i	0.964678	−	0.551000i
$628$		−	16.8172i		−	0.671081i
$629$	25.7877	−	21.6385i	1.02822	−	0.862782i
$630$	−0.865786	+	26.6401i	−0.0344938	+	1.06137i
$631$	−2.07442	+	11.7646i	−0.0825814	+	0.468343i	0.915271	+	0.402839i	$0.131977\pi$
$631$	−2.07442	+	11.7646i	−0.0825814	+	0.468343i	−0.997852	+	0.0655037i	$0.979135\pi$
$632$	1.38590	+	7.85981i	0.0551280	+	0.312647i
$633$	−21.7690	+	23.4130i	−0.865239	+	0.930583i
$634$	8.71922	−	15.1021i	0.346284	−	0.599782i
$635$	−6.91590	−	0.730451i	−0.274449	−	0.0289871i
$636$	−13.3939	−	3.07158i	−0.531102	−	0.121796i
$637$	−18.1927	−	15.2655i	−0.720819	−	0.604839i
$638$	6.00569	+	10.4022i	0.237767	+	0.411825i
$639$	−1.10413	−	2.46050i	−0.0436786	−	0.0973359i
$640$	2.14913	+	0.617438i	0.0849519	+	0.0244064i
$641$	−6.13216	−	34.7772i	−0.242206	−	1.37362i	−0.826894	−	0.562358i	$-0.809894\pi$
$641$	−6.13216	−	34.7772i	−0.242206	−	1.37362i	0.584688	−	0.811258i	$-0.301217\pi$
$642$	21.7535	−	6.68555i	0.858543	−	0.263858i
$643$	4.40966	−	12.1154i	0.173900	−	0.477786i	−0.821869	−	0.569676i	$-0.807069\pi$
$643$	4.40966	−	12.1154i	0.173900	−	0.477786i	0.995769	+	0.0918902i	$0.0292909\pi$
$644$	21.0373	+	25.0713i	0.828985	+	0.987946i
$645$	5.85701	−	37.2096i	0.230620	−	1.46513i
$646$	7.97616	−	25.5301i	0.313818	−	1.00447i
$647$	−11.5209			−0.452933			−0.226467	−	0.974019i	$-0.572717\pi$
$647$	−11.5209			−0.452933			−0.226467	+	0.974019i	$0.572717\pi$
$648$	4.72450	−	7.66023i	0.185596	−	0.300922i
$649$	5.17015	−	14.2049i	0.202946	−	0.557590i
$650$	1.86698	+	13.3831i	0.0732288	+	0.524928i
$651$	34.2859	−	25.9151i	1.34377	−	1.01569i
$652$	−1.88828	−	5.18800i	−0.0739507	−	0.203178i
$653$	−3.89684	+	6.74953i	−0.152495	+	0.264129i	−0.932144	−	0.362087i	$-0.882064\pi$
$653$	−3.89684	+	6.74953i	−0.152495	+	0.264129i	0.779649	+	0.626217i	$0.215398\pi$
$654$	−1.94182	+	2.99974i	−0.0759311	+	0.117299i
$655$	9.01876	+	36.2509i	0.352392	+	1.41644i
$656$	−4.52427	−	3.79631i	−0.176643	−	0.148221i
$657$	−0.0566072	+	0.554185i	−0.00220846	+	0.0216208i
$658$	21.4827	−	37.2090i	0.837481	−	1.45056i
$659$	−34.9568	+	12.7233i	−1.36173	+	0.495627i	−0.916587	−	0.399834i	$-0.869068\pi$
$659$	−34.9568	+	12.7233i	−1.36173	+	0.495627i	−0.445138	+	0.895462i	$0.646845\pi$
$660$	−14.2680	+	0.262674i	−0.555380	+	0.0102246i
$661$	−23.7504	−	4.18784i	−0.923784	−	0.162888i	−0.308528	−	0.951215i	$-0.599836\pi$
$661$	−23.7504	−	4.18784i	−0.923784	−	0.162888i	−0.615256	+	0.788327i	$0.710947\pi$
$662$	11.2597	+	4.09819i	0.437620	+	0.159281i
$663$	26.4562	+	11.1843i	1.02747	+	0.434362i
$664$		−	4.59195i		−	0.178202i
$665$	−34.6221	+	17.3532i	−1.34259	+	0.672929i
$666$	13.3432	+	9.63483i	0.517038	+	0.373342i
$667$	20.5694	−	17.2597i	0.796449	−	0.668300i
$668$	−3.12607	+	8.58881i	−0.120951	+	0.332311i
$669$	39.0179	−	11.9914i	1.50852	−	0.463616i
$670$	−5.17300	+	10.5925i	−0.199850	+	0.409225i
$671$	4.53740	+	12.4664i	0.175164	+	0.481260i
$672$	−6.87315	−	0.350118i	−0.265138	−	0.0135061i
$673$	6.32197	+	10.9500i	0.243694	+	0.422090i	0.961764	−	0.273881i	$-0.0883074\pi$
$673$	6.32197	+	10.9500i	0.243694	+	0.422090i	−0.718070	+	0.695971i	$0.754974\pi$
$674$	14.3156	−	17.0606i	0.551415	−	0.657150i
$675$	−13.3059	+	22.3149i	−0.512144	+	0.858900i
$676$	−2.84814	−	4.93313i	−0.109544	−	0.189736i
$677$	−13.5989	−	7.85134i	−0.522649	−	0.301751i	0.215369	−	0.976533i	$-0.430905\pi$
$677$	−13.5989	−	7.85134i	−0.522649	−	0.301751i	−0.738018	+	0.674781i	$0.764238\pi$
$678$	−6.01750	−	5.59496i	−0.231101	−	0.214873i
$679$	31.0421	−	5.47355i	1.19128	−	0.210056i
$680$	−9.87487	+	9.52634i	−0.378684	+	0.365319i
$681$	22.6428	−	2.81383i	0.867672	−	0.107826i
$682$	14.7906	+	17.6267i	0.566361	+	0.674963i
$683$			33.8066i			1.29357i	0.762671	+	0.646787i	$0.223888\pi$
$683$			33.8066i			1.29357i	−0.762671	+	0.646787i	$0.776112\pi$
$684$	13.0565	+	0.725903i	0.499229	+	0.0277556i
$685$	7.80884	−	10.7364i	0.298360	−	0.410218i
$686$	−5.44105	+	4.56558i	−0.207740	+	0.174315i
$687$	−1.28124	−	10.3101i	−0.0488823	−	0.393353i
$688$	9.57801	+	1.68886i	0.365158	+	0.0643873i
$689$	21.1154	−	3.72322i	0.804433	−	0.141843i
$690$	6.11697	+	31.3095i	0.232869	+	1.19193i
$691$	−17.2678	+	29.9088i	−0.656899	+	1.13778i	0.324515	+	0.945881i	$0.394799\pi$
$691$	−17.2678	+	29.9088i	−0.656899	+	1.13778i	−0.981414	+	0.191902i	$0.938534\pi$
$692$	−15.0279	+	8.67636i	−0.571275	+	0.329826i
$693$	42.5848	−	10.7501i	1.61766	−	0.408363i
$694$	1.48875	−	1.77423i	0.0565123	−	0.0673487i
$695$	33.8950	+	3.57995i	1.28571	+	0.135795i
$696$	−0.287250	+	5.63898i	−0.0108882	+	0.213745i
$697$	34.0548	−	12.3949i	1.28992	−	0.469492i
$698$	−8.03431	+	1.41666i	−0.304103	+	0.0536216i
$699$	−20.8788	+	6.41673i	−0.789709	+	0.242703i
$700$	19.8540	+	0.713561i	0.750410	+	0.0269701i
$701$	5.25804	+	6.26629i	0.198593	+	0.236674i	0.856146	−	0.516735i	$-0.172853\pi$
$701$	5.25804	+	6.26629i	0.198593	+	0.236674i	−0.657552	+	0.753409i	$0.728408\pi$
$702$	−2.13585	+	13.8794i	−0.0806123	+	0.523845i
$703$	−3.05919	+	23.7167i	−0.115379	+	0.894491i
$704$		−	3.68460i		−	0.138868i
$705$	35.8775	−	21.6040i	1.35122	−	0.813654i
$706$	−0.788302	+	2.16584i	−0.0296682	+	0.0815126i
$707$	−4.64235	+	26.3281i	−0.174593	+	0.990168i
$708$	5.66880	−	4.28477i	0.213046	−	0.161032i
$709$	−12.8266	+	4.66852i	−0.481715	+	0.175330i	−0.571452	−	0.820636i	$-0.693620\pi$
$709$	−12.8266	+	4.66852i	−0.481715	+	0.175330i	0.0897371	+	0.995965i	$0.471397\pi$
$710$	−1.83677	+	0.816661i	−0.0689326	+	0.0306487i
$711$	2.43302	−	23.8193i	0.0912453	−	0.893292i
$712$	−4.73504	+	5.64300i	−0.177453	+	0.211480i
$713$	33.0644	−	39.4046i	1.23827	−	1.47571i
$714$	22.9481	−	35.4504i	0.858809	−	1.32670i
$715$	20.3458	−	9.04614i	0.760891	−	0.338306i
$716$	7.98573	−	2.90657i	0.298441	−	0.108624i
$717$	10.5595	+	13.9703i	0.394351	+	0.521731i
$718$	2.37853	−	13.4893i	0.0887659	−	0.503417i
$719$	−8.44358	+	23.1985i	−0.314892	+	0.865159i	0.676758	+	0.736205i	$0.263384\pi$
$719$	−8.44358	+	23.1985i	−0.314892	+	0.865159i	−0.991651	+	0.128954i	$0.958838\pi$
$720$	−5.69746	−	3.54104i	−0.212332	−	0.131967i
$721$			63.2046i			2.35386i
$722$	8.11983	+	17.1776i	0.302189	+	0.639282i
$723$	−19.9289	+	10.1910i	−0.741163	+	0.379009i
$724$	7.15652	+	8.52881i	0.265970	+	0.316971i
$725$	0.585431	−	16.2889i	0.0217424	−	0.604955i
$726$	1.31087	+	4.26531i	0.0486508	+	0.158300i
$727$	−19.0343	+	3.35626i	−0.705942	+	0.124477i	−0.515082	−	0.857141i	$-0.672239\pi$
$727$	−19.0343	+	3.35626i	−0.705942	+	0.124477i	−0.190860	+	0.981617i	$0.561128\pi$
$728$	10.0906	−	3.67267i	0.373982	−	0.136118i
$729$	−19.9055	+	18.2421i	−0.737239	+	0.675632i
$730$	0.412917	+	0.0436120i	0.0152828	+	0.00161415i
$731$	−38.3611	+	45.7169i	−1.41883	+	1.69090i
$732$	−1.39396	+	6.07849i	−0.0515223	+	0.224668i
$733$	−17.7218	+	10.2317i	−0.654571	+	0.377917i	−0.790205	−	0.612842i	$-0.790026\pi$
$733$	−17.7218	+	10.2317i	−0.654571	+	0.377917i	0.135634	+	0.990759i	$0.456693\pi$
$734$	−1.79294	+	3.10546i	−0.0661785	+	0.114625i
$735$	−33.4027	+	6.52593i	−1.23208	+	0.240713i
$736$	−8.11177	+	1.43032i	−0.299004	+	0.0527224i
$737$	19.1295	+	3.37305i	0.704644	+	0.124248i
$738$	9.95076	+	14.6598i	0.366292	+	0.539636i
$739$	26.6430	−	22.3561i	0.980077	−	0.822382i	−0.00402407	−	0.999992i	$-0.501281\pi$
$739$	26.6430	−	22.3561i	0.980077	−	0.822382i	0.984101	+	0.177610i	$0.0568365\pi$
$740$	7.21552	−	9.92069i	0.265248	−	0.364692i
$741$	−19.2054	+	6.88937i	−0.705529	+	0.253087i
$742$		−	31.5235i		−	1.15726i
$743$	18.2065	+	21.6977i	0.667933	+	0.796011i	0.988501	−	0.151214i	$-0.0483184\pi$
$743$	18.2065	+	21.6977i	0.667933	+	0.796011i	−0.320568	+	0.947225i	$0.603874\pi$
$744$	1.33392	+	10.7340i	0.0489039	+	0.393527i
$745$	−26.0483	+	25.1289i	−0.954334	+	0.920651i
$746$	−30.8020	+	5.43122i	−1.12774	+	0.198851i
$747$	−3.75835	+	13.2533i	−0.137511	+	0.484912i
$748$	19.5803	+	11.3047i	0.715927	+	0.413341i
$749$	26.1033	+	45.2123i	0.953794	+	1.65202i
$750$	16.5983	+	9.97473i	0.606086	+	0.364226i
$751$	13.6425	−	16.2585i	0.497822	−	0.593281i	−0.457367	−	0.889278i	$-0.651207\pi$
$751$	13.6425	−	16.2585i	0.497822	−	0.593281i	0.955189	+	0.295997i	$0.0956519\pi$
$752$	5.40667	+	9.36463i	0.197161	+	0.341493i
$753$	−0.981187	+	19.2616i	−0.0357564	+	0.701933i
$754$	−3.01319	−	8.27867i	−0.109734	−	0.301491i
$755$	−2.87106	+	5.87894i	−0.104489	+	0.213957i
$756$	19.5507	+	6.63595i	0.711052	+	0.241347i
$757$	−12.0089	+	32.9943i	−0.436472	+	1.19920i	0.505299	+	0.862944i	$0.331382\pi$
$757$	−12.0089	+	32.9943i	−0.436472	+	1.19920i	−0.941771	+	0.336254i	$0.890840\pi$
$758$	−19.2241	+	16.1309i	−0.698250	+	0.585901i
$759$	46.8027	−	23.9335i	1.69883	−	0.868733i
$760$	0.574501	−	9.72985i	0.0208393	−	0.352939i
$761$		−	18.1845i		−	0.659188i	−0.944123	−	0.329594i	$-0.893088\pi$
$761$		−	18.1845i		−	0.659188i	0.944123	−	0.329594i	$-0.106912\pi$
$762$	−2.09754	+	4.96168i	−0.0759859	+	0.179743i
$763$	−7.70307	−	2.80369i	−0.278870	−	0.101500i
$764$	−10.5774	−	1.86507i	−0.382676	−	0.0674760i
$765$	36.2978	−	19.4126i	1.31235	−	0.701865i
$766$	−21.0793	+	7.67222i	−0.761624	+	0.277209i
$767$	−5.54375	+	9.60205i	−0.200173	+	0.346710i
$768$	0.941215	−	1.45400i	0.0339632	−	0.0524667i
$769$	−20.2543	−	16.9953i	−0.730387	−	0.612868i	0.199850	−	0.979827i	$-0.435955\pi$
$769$	−20.2543	−	16.9953i	−0.730387	−	0.612868i	−0.930237	+	0.366959i	$0.880399\pi$
$770$	−7.90352	−	31.7682i	−0.284823	−	1.14485i
$771$	−1.03540	−	0.670243i	−0.0372890	−	0.0241382i
$772$	1.25766	−	2.17834i	0.0452643	−	0.0784001i
$773$	−9.81302	−	26.9611i	−0.352950	−	0.969722i	−0.981417	−	0.191886i	$-0.938540\pi$
$773$	−9.81302	−	26.9611i	−0.352950	−	0.969722i	0.628467	−	0.777836i	$-0.283683\pi$
$774$	−26.2617	−	12.7137i	−0.943958	−	0.456983i
$775$	−4.31415	−	30.9252i	−0.154969	−	1.11087i
$776$	−2.71327	+	7.45464i	−0.0974006	+	0.267606i
$777$	−14.7013	+	34.7755i	−0.527406	+	1.24757i
$778$	−22.5326			−0.807833
$779$	−11.8273	+	22.8660i	−0.423756	+	0.819259i
$780$	10.3396	+	1.62751i	0.370216	+	0.0582743i
$781$	2.12911	+	2.53737i	0.0761855	+	0.0907943i
$782$	17.2868	−	47.4951i	0.618175	−	1.69842i
$783$	5.44437	−	16.0401i	0.194566	−	0.573226i
$784$	−1.52595	−	8.65410i	−0.0544982	−	0.309075i
$785$	36.1425	+	10.3836i	1.28998	+	0.370607i
$786$	28.8983	+	1.47208i	1.03077	+	0.0525073i
$787$	14.5974	+	25.2834i	0.520341	+	0.901257i	0.999720	+	0.0236495i	$0.00752857\pi$
$787$	14.5974	+	25.2834i	0.520341	+	0.901257i	−0.479379	+	0.877608i	$0.659138\pi$
$788$	−3.12169	−	2.61941i	−0.111205	−	0.0933125i
$789$	−6.16307	+	26.8746i	−0.219411	+	0.956761i
$790$	−17.7475	−	1.87447i	−0.631427	−	0.0666908i
$791$	9.42462	−	16.3239i	0.335101	−	0.580412i
$792$	−3.01571	+	10.6345i	−0.107159	+	0.377879i
$793$	−1.68969	−	9.58271i	−0.0600027	−	0.340292i
$794$	−1.19712	+	6.78921i	−0.0424842	+	0.240940i
$795$	14.8711	−	26.8887i	0.527425	−	0.953645i
$796$	−14.4450	+	12.1208i	−0.511989	+	0.429610i
$797$		−	6.65442i		−	0.235712i	−0.993031	−	0.117856i	$-0.962398\pi$
$797$		−	6.65442i		−	0.235712i	0.993031	−	0.117856i	$-0.0376021\pi$
$798$	5.07189	+	29.5664i	0.179543	+	1.04664i
$799$	−66.3527			−2.34739
$800$	−2.65391	+	4.23754i	−0.0938300	+	0.149820i
$801$	18.2848	−	12.4113i	0.646063	−	0.438533i
$802$	9.95315	+	1.75501i	0.351458	+	0.0619715i
$803$	−0.118808	−	0.673796i	−0.00419266	−	0.0237778i
$804$	6.68717	+	6.21761i	0.235838	+	0.219278i
$805$	−66.8707	+	29.7320i	−2.35688	+	1.04791i
$806$	−8.43860	−	14.6161i	−0.297237	−	0.514829i
$807$	7.79224	−	33.9788i	0.274300	−	1.19611i
$808$	−5.15422	−	4.32491i	−0.181325	−	0.152150i
$809$	−18.2678	+	10.5469i	−0.642261	+	0.370809i	−0.785485	−	0.618881i	$-0.787586\pi$
$809$	−18.2678	+	10.5469i	−0.642261	+	0.370809i	0.143224	+	0.989690i	$0.454253\pi$
$810$	13.5458	+	14.8833i	0.475949	+	0.522946i
$811$	−15.3572	−	42.1936i	−0.539265	−	1.48162i	−0.847753	−	0.530391i	$-0.822045\pi$
$811$	−15.3572	−	42.1936i	−0.539265	−	1.48162i	0.308488	−	0.951228i	$-0.400177\pi$
$812$	−12.7559	+	2.24922i	−0.447645	+	0.0789320i
$813$	−17.1854	+	5.28164i	−0.602720	+	0.185235i
$814$	−18.9948	−	6.91356i	−0.665769	−	0.242320i
$815$	12.3156	−	0.854889i	0.431396	−	0.0299455i
$816$	4.83896	+	9.46272i	0.169397	+	0.331261i
$817$	−1.96010	−	42.3483i	−0.0685753	−	1.48158i
$818$	−2.92169			−0.102155
$819$	−32.1293	+	2.34125i	−1.12269	+	0.0818098i
$820$	10.9522	−	7.37926i	0.382468	−	0.257695i
$821$	24.0955	+	4.24868i	0.840938	+	0.148280i	0.577494	−	0.816395i	$-0.304031\pi$
$821$	24.0955	+	4.24868i	0.840938	+	0.148280i	0.263443	+	0.964675i	$0.415142\pi$
$822$	−6.20075	−	8.20366i	−0.216276	−	0.286136i
$823$	12.3282	+	33.8715i	0.429734	+	1.18069i	0.945974	+	0.324242i	$0.105109\pi$
$823$	12.3282	+	33.8715i	0.429734	+	1.18069i	−0.516240	+	0.856444i	$0.672669\pi$
$824$	−13.7759	−	7.95354i	−0.479907	−	0.277075i
$825$	8.24506	−	30.8259i	0.287056	−	1.07322i
$826$	12.4874	+	10.4782i	0.434494	+	0.364584i
$827$	2.86781	−	3.41773i	0.0997237	−	0.118846i	−0.713874	−	0.700274i	$-0.753061\pi$
$827$	2.86781	−	3.41773i	0.0997237	−	0.118846i	0.813598	+	0.581428i	$0.197506\pi$
$828$	24.5828	+	2.51101i	0.854312	+	0.0872637i
$829$	14.2324	+	8.21710i	0.494313	+	0.285392i	0.726362	−	0.687312i	$-0.241210\pi$
$829$	14.2324	+	8.21710i	0.494313	+	0.285392i	−0.232049	+	0.972704i	$0.574543\pi$
$830$	9.86871	+	2.83525i	0.342548	+	0.0984129i
$831$	−5.78126	−	7.64867i	−0.200550	−	0.265329i
$832$	−0.469291	+	2.66148i	−0.0162697	+	0.0922703i
$833$	50.6705	+	18.4426i	1.75563	+	0.638996i
$834$	10.2801	−	24.3173i	0.355970	−	0.842039i
$835$	−16.5283	−	12.0214i	−0.571987	−	0.416018i
$836$	−15.6709	+	3.51724i	−0.541990	+	0.121646i
$837$	4.93544	−	32.0721i	0.170594	−	1.10858i
$838$	−27.5901	+	23.1508i	−0.953083	+	0.799732i
$839$	1.22898	+	0.447310i	0.0424289	+	0.0154429i	0.363147	−	0.931732i	$-0.381702\pi$
$839$	1.22898	+	0.447310i	0.0424289	+	0.0154429i	−0.320719	+	0.947175i	$0.603924\pi$
$840$	4.99620	−	14.5551i	0.172385	−	0.502200i
$841$	−3.19046	−	18.0940i	−0.110016	−	0.623931i
$842$	−20.2350	+	7.36495i	−0.697345	+	0.253813i
$843$	46.4585	+	2.36659i	1.60012	+	0.0815099i
$844$	15.9848	−	9.22883i	0.550220	−	0.317670i
$845$	12.3605	−	3.07513i	0.425214	−	0.105788i
$846$	−7.94007	−	31.4533i	−0.272985	−	1.08139i
$847$	−8.86496	+	5.11819i	−0.304604	+	0.175863i
$848$	6.87079	+	3.96685i	0.235944	+	0.136222i
$849$	−21.2819	+	22.8891i	−0.730393	+	0.785553i
$850$	−14.3762	−	27.1043i	−0.493101	−	0.929671i
$851$	−7.84683	+	44.5016i	−0.268986	+	1.52549i
$852$	0.192018	+	1.54516i	0.00657843	+	0.0529363i
$853$	−12.6044	−	15.0213i	−0.431566	−	0.514321i	0.505807	−	0.862646i	$-0.331195\pi$
$853$	−12.6044	−	15.0213i	−0.431566	−	0.514321i	−0.937373	+	0.348326i	$0.886750\pi$
$854$	−14.3062			−0.489547
$855$	−9.62166	+	27.6120i	−0.329054	+	0.944311i
$856$	−13.1392			−0.449087
$857$	9.94573	+	11.8529i	0.339740	+	0.404886i	0.908680	−	0.417493i	$-0.137091\pi$
$857$	9.94573	+	11.8529i	0.339740	+	0.404886i	−0.568941	+	0.822379i	$0.692647\pi$
$858$	−2.12698	−	17.1157i	−0.0726140	−	0.584320i
$859$	5.77959	−	32.7777i	0.197197	−	1.11836i	−0.712058	−	0.702121i	$-0.752237\pi$
$859$	5.77959	−	32.7777i	0.197197	−	1.11836i	0.909255	−	0.416240i	$-0.136652\pi$
$860$	−9.54342	+	19.5417i	−0.325428	+	0.666365i
$861$	−27.6766	+	29.7668i	−0.943217	+	1.01445i
$862$	1.46211	+	0.844152i	0.0497998	+	0.0287519i
$863$	28.7361	−	16.5908i	0.978187	−	0.564756i	0.0764644	−	0.997072i	$-0.475637\pi$
$863$	28.7361	−	16.5908i	0.978187	−	0.564756i	0.901722	+	0.432316i	$0.142304\pi$
$864$	−3.90658	+	3.42617i	−0.132904	+	0.116561i
$865$	−9.36785	−	37.6541i	−0.318517	−	1.28028i
$866$	3.92576	−	2.26654i	0.133403	−	0.0770202i
$867$	−35.7255	−	1.81986i	−1.21330	−	0.0618055i
$868$	−23.3170	+	8.48668i	−0.791430	+	0.288057i
$869$	5.10647	+	28.9602i	0.173225	+	0.982409i
$870$	−11.9416	−	4.09906i	−0.404857	−	0.138971i
$871$	−13.3881	−	4.87288i	−0.453639	−	0.165111i
$872$	1.58042	−	1.32613i	0.0535199	−	0.0449086i
$873$	13.9324	−	19.2948i	0.471540	−	0.653031i
$874$	13.8266	+	33.1347i	0.467693	+	1.12080i
$875$	−13.7921	+	42.2283i	−0.466260	+	1.42758i
$876$	0.125235	−	0.296240i	0.00423129	−	0.0100090i
$877$	10.8359	+	3.94393i	0.365901	+	0.133177i	0.518426	−	0.855123i	$-0.326518\pi$
$877$	10.8359	+	3.94393i	0.365901	+	0.133177i	−0.152525	+	0.988300i	$0.548740\pi$
$878$	0.445748	−	2.52796i	0.0150433	−	0.0853146i
$879$	−7.88287	−	10.4291i	−0.265883	−	0.351765i
$880$	7.91869	+	2.27501i	0.266939	+	0.0766906i
$881$	3.26100	+	1.88274i	0.109866	+	0.0634310i	0.553926	−	0.832566i	$-0.313129\pi$
$881$	3.26100	+	1.88274i	0.109866	+	0.0634310i	−0.444060	+	0.895997i	$0.646462\pi$
$882$	−2.67889	+	26.2263i	−0.0902029	+	0.883087i
$883$	−10.3156	+	12.2937i	−0.347149	+	0.413716i	−0.911161	−	0.412051i	$-0.864813\pi$
$883$	−10.3156	+	12.2937i	−0.347149	+	0.413716i	0.564012	+	0.825767i	$0.309257\pi$
$884$	−12.7035	−	10.6595i	−0.427266	−	0.358519i
$885$	5.70841	+	14.8286i	0.191886	+	0.498457i
$886$	1.72996	+	0.998794i	0.0581192	+	0.0335552i
$887$	−9.65622	−	26.5302i	−0.324224	−	0.890799i	−0.989543	−	0.144239i	$-0.953927\pi$
$887$	−9.65622	−	26.5302i	−0.324224	−	0.890799i	0.665319	−	0.746559i	$-0.268296\pi$
$888$	−5.72962	−	7.58035i	−0.192273	−	0.254380i
$889$	−12.1698	−	2.14586i	−0.408161	−	0.0719698i
$890$	−9.20396	−	13.6604i	−0.308517	−	0.457899i
$891$	17.4079	−	28.2249i	0.583186	−	0.945568i
$892$	−23.5669			−0.789077
$893$	34.6675	−	31.9343i	1.16010	−	1.06864i
$894$	12.7644	+	24.9611i	0.426904	+	0.834823i
$895$	1.31590	+	18.9570i	0.0439858	+	0.633663i
$896$	3.73374	+	1.35897i	0.124735	+	0.0454000i
$897$	−36.8552	+	11.3268i	−1.23056	+	0.378190i
$898$	2.16737	−	0.382166i	0.0723261	−	0.0127530i
$899$	6.96278	+	19.1301i	0.232222	+	0.638024i
$900$	11.1280	−	10.0582i	0.370933	−	0.335274i
$901$	−42.1605	+	24.3414i	−1.40457	+	0.810929i
$902$	−16.6701	−	13.9879i	−0.555053	−	0.465745i
$903$	14.9612	−	65.2398i	0.497879	−	2.17105i
$904$	2.37195	+	4.10834i	0.0788899	+	0.136641i
$905$	−22.7483	+	10.1143i	−0.756177	+	0.336211i
$906$	3.71144	+	3.45083i	0.123304	+	0.114646i
$907$	−2.38433	−	13.5222i	−0.0791704	−	0.448998i	−0.998463	−	0.0554229i	$-0.982349\pi$
$907$	−2.38433	−	13.5222i	−0.0791704	−	0.448998i	0.919293	−	0.393575i	$-0.128762\pi$
$908$	−12.9732	−	2.28753i	−0.430532	−	0.0759143i
$909$	11.3363	+	16.7011i	0.376001	+	0.553939i
$910$	1.66274	+	23.9536i	0.0551194	+	0.794055i
$911$	−22.1623			−0.734269			−0.367135	−	0.930168i	$-0.619661\pi$
$911$	−22.1623			−0.734269			−0.367135	+	0.930168i	$0.619661\pi$
$912$	−7.08246	−	2.61511i	−0.234524	−	0.0865950i
$913$		−	16.9195i		−	0.559953i
$914$	6.73516	−	5.65147i	0.222779	−	0.186934i
$915$	−12.2028	−	6.74890i	−0.403412	−	0.223112i
$916$	−1.04159	+	5.90717i	−0.0344152	+	0.195178i
$917$	11.5266	+	65.3708i	0.380643	+	2.15873i
$918$	−6.22126	−	31.2718i	−0.205332	−	1.03212i
$919$	−21.3905	+	37.0495i	−0.705608	+	1.22215i	0.260863	+	0.965376i	$0.415993\pi$
$919$	−21.3905	+	37.0495i	−0.705608	+	1.22215i	−0.966472	+	0.256774i	$0.917340\pi$
$920$	1.93456	−	18.3164i	0.0637806	−	0.603874i
$921$	10.6520	−	46.4489i	0.350995	−	1.53054i
$922$	−18.8825	−	15.8443i	−0.621863	−	0.521805i
$923$	−1.21474	−	2.10399i	−0.0399836	−	0.0692536i
$924$	−25.3248	−	1.29004i	−0.833124	−	0.0424393i
$925$	16.8657	+	21.6325i	0.554542	+	0.711273i
$926$	6.46462	+	36.6627i	0.212441	+	1.20481i
$927$	33.2503	+	34.2306i	1.09208	+	1.12428i
$928$	1.11495	−	3.06329i	0.0365999	−	0.100558i
$929$	2.28335	+	2.72119i	0.0749142	+	0.0892792i	0.802200	−	0.597056i	$-0.203663\pi$
$929$	2.28335	+	2.72119i	0.0749142	+	0.0892792i	−0.727286	+	0.686335i	$0.759218\pi$
$930$	−23.8924	−	3.76080i	−0.783462	−	0.123322i
$931$	−35.3500	+	14.7510i	−1.15855	+	0.483446i
$932$	12.6108			0.413082
$933$	−10.6478	+	25.1871i	−0.348593	+	0.824587i
$934$	−9.41664	+	25.8720i	−0.308122	+	0.846558i
$935$	−36.3849	+	35.1007i	−1.18991	+	1.14792i
$936$	3.53279	−	7.29745i	0.115473	−	0.238525i
$937$	−4.22542	−	11.6092i	−0.138038	−	0.379257i	0.851341	−	0.524613i	$-0.175790\pi$
$937$	−4.22542	−	11.6092i	−0.138038	−	0.379257i	−0.989380	+	0.145355i	$0.953568\pi$
$938$	−10.4735	+	18.1406i	−0.341971	+	0.592310i
$939$	−19.6045	−	12.6906i	−0.639769	−	0.414141i
$940$	−23.4641	+	5.83757i	−0.765315	+	0.190401i
$941$	−23.3760	−	19.6148i	−0.762037	−	0.639425i	0.176619	−	0.984279i	$-0.443484\pi$
$941$	−23.3760	−	19.6148i	−0.762037	−	0.639425i	−0.938656	+	0.344854i	$0.887928\pi$
$942$	15.8286	−	24.4523i	0.515725	−	0.796698i
$943$	−24.3236	+	42.1298i	−0.792086	+	1.37193i
$944$	−3.85520	+	1.40318i	−0.125476	+	0.0456696i
$945$	−26.3329	+	37.9197i	−0.856608	+	1.23353i
$946$	35.2911	+	6.22278i	1.14741	+	0.202320i
$947$	−25.4271	−	9.25472i	−0.826270	−	0.300738i	−0.105943	−	0.994372i	$-0.533786\pi$
$947$	−25.4271	−	9.25472i	−0.826270	−	0.300738i	−0.720327	+	0.693634i	$0.756008\pi$
$948$	−5.38268	+	12.7326i	−0.174821	+	0.413535i
$949$			0.501833i			0.0162902i
$950$	20.5560	+	7.24226i	0.666925	+	0.234970i
$951$	26.8921	−	13.7518i	0.872036	−	0.445934i
$952$	−18.6772	+	15.6720i	−0.605330	+	0.507933i
$953$	2.13901	−	5.87687i	0.0692892	−	0.190371i	−0.900215	−	0.435446i	$-0.856591\pi$
$953$	2.13901	−	5.87687i	0.0692892	−	0.190371i	0.969504	+	0.245076i	$0.0788128\pi$
$954$	−16.5837	−	17.0726i	−0.536917	−	0.552746i
$955$	10.5392	−	21.5806i	0.341039	−	0.698331i
$956$	−3.45803	−	9.50085i	−0.111841	−	0.307280i
$957$	−1.05840	+	20.7774i	−0.0342132	+	0.671637i
$958$	16.0340	+	27.7717i	0.518035	+	0.897263i
$959$	15.1637	−	18.0713i	0.489660	−	0.583554i
$960$	2.54370	+	2.92055i	0.0820974	+	0.0942604i
$961$	3.99964	+	6.92758i	0.129021	+	0.223470i
$962$	12.8399	+	7.41313i	0.413976	+	0.239009i
$963$	37.9221	+	10.7539i	1.22202	+	0.346541i
$964$	12.7267	−	2.24407i	0.409901	−	0.0722766i
$965$	3.90501	+	4.04787i	0.125707	+	0.130306i
$966$	6.99076	+	56.2542i	0.224924	+	1.80995i
$967$	24.9493	+	29.7334i	0.802314	+	0.956161i	0.999708	−	0.0241634i	$-0.00769218\pi$
$967$	24.9493	+	29.7334i	0.802314	+	0.956161i	−0.197394	+	0.980324i	$0.563248\pi$
$968$		−	2.57625i		−	0.0828039i
$969$	35.6266	−	29.6135i	1.14449	−	0.951321i
$970$	−14.3457	−	10.4340i	−0.460614	−	0.335014i
$971$	19.4020	−	16.2802i	0.622640	−	0.522457i	−0.275992	−	0.961160i	$-0.589006\pi$
$971$	19.4020	−	16.2802i	0.622640	−	0.522457i	0.898632	+	0.438703i	$0.144562\pi$
$972$	14.0793	−	6.69120i	0.451595	−	0.214620i
$973$	59.6442	+	10.5169i	1.91211	+	0.337156i
$974$	26.4668	−	4.66681i	0.848051	−	0.149534i
$975$	−9.88179	+	21.2162i	−0.316471	+	0.679464i
$976$	1.80026	−	3.11814i	0.0576249	−	0.0998093i
$977$	11.1102	−	6.41450i	0.355448	−	0.205218i	−0.311634	−	0.950202i	$-0.600876\pi$
$977$	11.1102	−	6.41450i	0.355448	−	0.205218i	0.667082	+	0.744984i	$0.267543\pi$
$978$	2.13747	−	9.32063i	0.0683487	−	0.298041i
$979$	−17.4467	+	20.7922i	−0.557599	+	0.664521i
$980$	19.5410	+	2.06390i	0.624214	+	0.0659289i
$981$	−5.64681	+	2.53396i	−0.180289	+	0.0809030i
$982$	−15.6442	+	5.69402i	−0.499226	+	0.181704i
$983$	−5.23194	+	0.922532i	−0.166873	+	0.0294242i	−0.256460	−	0.966555i	$-0.582556\pi$
$983$	−5.23194	+	0.922532i	−0.166873	+	0.0294242i	0.0895874	+	0.995979i	$0.471445\pi$
$984$	−3.00514	−	9.77814i	−0.0958002	−	0.311716i
$985$	7.55690	−	5.09159i	0.240783	−	0.162232i
$986$	12.8579	+	15.3234i	0.409478	+	0.487997i
$987$	66.2575	−	33.8821i	2.10900	−	1.07848i
$988$	11.7675	−	0.544661i	0.374374	−	0.0173280i
$989$		−	80.1103i		−	2.54736i
$990$	−20.9928	−	13.0473i	−0.667196	−	0.414670i
$991$	−16.7260	+	45.9543i	−0.531319	+	1.45979i	0.326184	+	0.945306i	$0.394237\pi$
$991$	−16.7260	+	45.9543i	−0.531319	+	1.45979i	−0.857503	+	0.514480i	$0.827985\pi$
$992$	1.08442	−	6.15007i	0.0344304	−	0.195265i
$993$	12.5143	+	16.5566i	0.397129	+	0.525407i
$994$	−3.35648	+	1.22166i	−0.106461	+	0.0387487i
$995$	−17.1303	−	38.5280i	−0.543066	−	1.22142i
$996$	4.32201	−	6.67670i	0.136948	−	0.211559i
$997$	13.8508	−	16.5067i	0.438659	−	0.522773i	−0.500741	−	0.865597i	$-0.666939\pi$
$997$	13.8508	−	16.5067i	0.438659	−	0.522773i	0.939400	+	0.342824i	$0.111383\pi$
$998$	0.761580	−	0.907615i	0.0241074	−	0.0287301i
$999$	10.3325	+	26.5679i	0.326907	+	0.840570i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.bf.a.89.9	✓	240
3.2	odd	2	inner	570.2.bf.a.89.25	yes	240
5.4	even	2	inner	570.2.bf.a.89.32	yes	240
15.14	odd	2	inner	570.2.bf.a.89.16	yes	240
19.3	odd	18	inner	570.2.bf.a.269.16	yes	240
57.41	even	18	inner	570.2.bf.a.269.32	yes	240
95.79	odd	18	inner	570.2.bf.a.269.25	yes	240
285.269	even	18	inner	570.2.bf.a.269.9	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.bf.a.89.9	✓	240	1.1	even	1	trivial
570.2.bf.a.89.16	yes	240	15.14	odd	2	inner
570.2.bf.a.89.25	yes	240	3.2	odd	2	inner
570.2.bf.a.89.32	yes	240	5.4	even	2	inner
570.2.bf.a.269.9	yes	240	285.269	even	18	inner
570.2.bf.a.269.16	yes	240	19.3	odd	18	inner
570.2.bf.a.269.25	yes	240	95.79	odd	18	inner
570.2.bf.a.269.32	yes	240	57.41	even	18	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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.bf (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.642788 - 0.766044i) q^{2} +(-0.213600 - 1.71883i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-2.00927 - 0.981251i) q^{5} +(-1.17940 + 1.26847i) q^{6} +(-3.44103 - 1.98668i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-2.90875 + 0.734285i) q^{9} +O(q^{10})\)	\(q+(-0.642788 - 0.766044i) q^{2} +(-0.213600 - 1.71883i) q^{3} +(-0.173648 + 0.984808i) q^{4} +(-2.00927 - 0.981251i) q^{5} +(-1.17940 + 1.26847i) q^{6} +(-3.44103 - 1.98668i) q^{7} +(0.866025 - 0.500000i) q^{8} +(-2.90875 + 0.734285i) q^{9} +(0.539849 + 2.16992i) q^{10} +(3.19095 - 1.84230i) q^{11} +(1.72981 + 0.0881164i) q^{12} +(-2.53956 + 0.924323i) q^{13} +(0.689967 + 3.91300i) q^{14} +(-1.25742 + 3.66318i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(4.70060 - 3.94427i) q^{17} +(2.43220 + 1.75624i) q^{18} +(-0.557630 + 4.32308i) q^{19} +(1.31525 - 1.80835i) q^{20} +(-2.67976 + 6.33890i) q^{21} +(-3.46239 - 1.26021i) q^{22} +(-1.43032 + 8.11177i) q^{23} +(-1.04440 - 1.38175i) q^{24} +(3.07429 + 3.94319i) q^{25} +(2.34047 + 1.35127i) q^{26} +(1.88342 + 4.84280i) q^{27} +(2.55403 - 3.04377i) q^{28} +(-2.49722 - 2.09542i) q^{29} +(3.61441 - 1.39140i) q^{30} +(-5.40828 - 3.12247i) q^{31} +(0.342020 + 0.939693i) q^{32} +(-3.84819 - 5.09119i) q^{33} +(-6.04297 - 1.06554i) q^{34} +(4.96451 + 7.36828i) q^{35} +(-0.218030 - 2.99207i) q^{36} +5.48605 q^{37} +(3.67011 - 2.35165i) q^{38} +(2.13120 + 4.16763i) q^{39} +(-2.23070 + 0.154844i) q^{40} +(5.54983 + 2.01997i) q^{41} +(6.57840 - 2.02175i) q^{42} +(-9.57801 + 1.68886i) q^{43} +(1.26021 + 3.46239i) q^{44} +(6.56497 + 1.37884i) q^{45} +(7.13337 - 4.11845i) q^{46} +(-8.28350 - 6.95068i) q^{47} +(-0.387156 + 1.68823i) q^{48} +(4.39380 + 7.61029i) q^{49} +(1.04454 - 4.88968i) q^{50} +(-7.78357 - 7.23703i) q^{51} +(-0.469291 - 2.66148i) q^{52} +(-7.81317 - 1.37767i) q^{53} +(2.49916 - 4.55568i) q^{54} +(-8.21923 + 0.570539i) q^{55} -3.97336 q^{56} +(7.54975 + 0.0350595i) q^{57} +3.25989i q^{58} +(3.14279 - 2.63711i) q^{59} +(-3.38918 - 1.87442i) q^{60} +(-0.625224 + 3.54582i) q^{61} +(1.08442 + 6.15007i) q^{62} +(11.4679 + 3.25206i) q^{63} +(0.500000 - 0.866025i) q^{64} +(6.00963 + 0.634732i) q^{65} +(-1.42651 + 6.22044i) q^{66} +(4.03846 + 3.38867i) q^{67} +(3.06810 + 5.31410i) q^{68} +(14.2483 + 0.725806i) q^{69} +(2.45331 - 8.53928i) q^{70} +(0.156103 + 0.885303i) q^{71} +(-2.15191 + 2.09028i) q^{72} +(0.0635095 - 0.174491i) q^{73} +(-3.52637 - 4.20256i) q^{74} +(6.12100 - 6.12645i) q^{75} +(-4.16057 - 1.29985i) q^{76} -14.6402 q^{77} +(1.82268 - 4.31150i) q^{78} +(-2.72968 + 7.49975i) q^{79} +(1.55248 + 1.60928i) q^{80} +(7.92165 - 4.27170i) q^{81} +(-2.01997 - 5.54983i) q^{82} +(2.29598 - 3.97675i) q^{83} +(-5.77727 - 3.73979i) q^{84} +(-13.3151 + 3.31262i) q^{85} +(7.45037 + 6.25160i) q^{86} +(-3.06826 + 4.73988i) q^{87} +(1.84230 - 3.19095i) q^{88} +(-6.92216 + 2.51946i) q^{89} +(-3.16363 - 5.91536i) q^{90} +(10.5750 + 1.86466i) q^{91} +(-7.74016 - 2.81719i) q^{92} +(-4.21178 + 9.96287i) q^{93} +10.8133i q^{94} +(5.36246 - 8.13905i) q^{95} +(1.54212 - 0.788593i) q^{96} +(-6.07708 + 5.09928i) q^{97} +(3.00554 - 8.25764i) q^{98} +(-7.92892 + 7.70185i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q+O(q^{10}) \) 240 * q	\( 240 q - 30 q^{15} + 48 q^{19} + 12 q^{25} - 48 q^{39} + 36 q^{45} - 72 q^{46} + 216 q^{49} - 180 q^{51} + 36 q^{54} + 60 q^{55} + 6 q^{60} - 72 q^{61} + 120 q^{64} - 156 q^{66} + 48 q^{79} - 120 q^{81} - 108 q^{84} - 48 q^{85} - 36 q^{90} - 24 q^{91} - 216 q^{99}+O(q^{100}) \) 240 * q - 30 * q^15 + 48 * q^19 + 12 * q^25 - 48 * q^39 + 36 * q^45 - 72 * q^46 + 216 * q^49 - 180 * q^51 + 36 * q^54 + 60 * q^55 + 6 * q^60 - 72 * q^61 + 120 * q^64 - 156 * q^66 + 48 * q^79 - 120 * q^81 - 108 * q^84 - 48 * q^85 - 36 * q^90 - 24 * q^91 - 216 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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