LMFDB - Embedded newform 1183.2.e.k.170.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1183,2,Mod(170,1183)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1183.170"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1183, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1183 = 7 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1183.e (of order $3$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [48,-1,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$9.44630255912$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			170.7
Character	$\chi$	$=$	1183.170
Dual form			1183.2.e.k.508.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.680712 + 1.17903i) q^{2} +(0.656465 + 1.13703i) q^{3} +(0.0732621 + 0.126894i) q^{4} +(-1.52933 + 2.64889i) q^{5} -1.78745 q^{6} +(-2.33513 - 1.24384i) q^{7} -2.92233 q^{8} +(0.638108 - 1.10524i) q^{9} +(-2.08207 - 3.60626i) q^{10} +(0.775465 + 1.34315i) q^{11} +(-0.0961880 + 0.166602i) q^{12} +(3.05608 - 1.90649i) q^{14} -4.01582 q^{15} +(1.84274 - 3.19172i) q^{16} +(-2.91188 - 5.04353i) q^{17} +(0.868735 + 1.50469i) q^{18} +(0.722605 - 1.25159i) q^{19} -0.448169 q^{20} +(-0.118644 - 3.47166i) q^{21} -2.11147 q^{22} +(-3.13886 + 5.43667i) q^{23} +(-1.91841 - 3.32278i) q^{24} +(-2.17773 - 3.77194i) q^{25} +5.61437 q^{27} +(-0.0132408 - 0.387440i) q^{28} -9.88196 q^{29} +(2.73362 - 4.73476i) q^{30} +(0.763337 + 1.32214i) q^{31} +(-0.413578 - 0.716337i) q^{32} +(-1.01813 + 1.76345i) q^{33} +7.92861 q^{34} +(6.86600 - 4.28325i) q^{35} +0.186996 q^{36} +(3.87574 - 6.71298i) q^{37} +(0.983772 + 1.70394i) q^{38} +(4.46922 - 7.74092i) q^{40} -7.17386 q^{41} +(4.17395 + 2.22332i) q^{42} +5.03082 q^{43} +(-0.113624 + 0.196803i) q^{44} +(1.95176 + 3.38055i) q^{45} +(-4.27333 - 7.40162i) q^{46} +(2.60922 - 4.51930i) q^{47} +4.83878 q^{48} +(3.90570 + 5.80909i) q^{49} +5.92963 q^{50} +(3.82310 - 6.62180i) q^{51} +(-3.88874 - 6.73549i) q^{53} +(-3.82177 + 6.61950i) q^{54} -4.74378 q^{55} +(6.82403 + 3.63492i) q^{56} +1.89746 q^{57} +(6.72677 - 11.6511i) q^{58} +(1.39530 + 2.41674i) q^{59} +(-0.294207 - 0.509582i) q^{60} +(-6.87860 + 11.9141i) q^{61} -2.07845 q^{62} +(-2.86481 + 1.78717i) q^{63} +8.49707 q^{64} +(-1.38611 - 2.40081i) q^{66} +(-0.341513 - 0.591518i) q^{67} +(0.426661 - 0.738999i) q^{68} -8.24222 q^{69} +(0.376298 + 11.0109i) q^{70} +0.582838 q^{71} +(-1.86476 + 3.22986i) q^{72} +(2.16244 + 3.74546i) q^{73} +(5.27653 + 9.13921i) q^{74} +(2.85921 - 4.95229i) q^{75} +0.211758 q^{76} +(-0.140151 - 4.10098i) q^{77} +(-3.20909 + 5.55831i) q^{79} +(5.63634 + 9.76242i) q^{80} +(1.77131 + 3.06800i) q^{81} +(4.88333 - 8.45818i) q^{82} -14.7890 q^{83} +(0.431839 - 0.269396i) q^{84} +17.8130 q^{85} +(-3.42454 + 5.93148i) q^{86} +(-6.48716 - 11.2361i) q^{87} +(-2.26617 - 3.92511i) q^{88} +(-1.03289 + 1.78903i) q^{89} -5.31435 q^{90} -0.919839 q^{92} +(-1.00221 + 1.73588i) q^{93} +(3.55226 + 6.15269i) q^{94} +(2.21021 + 3.82820i) q^{95} +(0.542998 - 0.940501i) q^{96} -5.78897 q^{97} +(-9.50773 + 0.650615i) q^{98} +1.97932 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - q^{2} - 23 q^{4} + 13 q^{5} - 28 q^{6} - 3 q^{7} - 26 q^{9} - 5 q^{10} - q^{11} - 5 q^{12} - 2 q^{14} - 10 q^{15} - 17 q^{16} + 5 q^{17} + 24 q^{19} - 68 q^{20} + q^{21} - 28 q^{22} - 11 q^{23}+ \cdots + 78 q^{99}+O(q^{100}) $ 48 * q - q^2 - 23 * q^4 + 13 * q^5 - 28 * q^6 - 3 * q^7 - 26 * q^9 - 5 * q^10 - q^11 - 5 * q^12 - 2 * q^14 - 10 * q^15 - 17 * q^16 + 5 * q^17 + 24 * q^19 - 68 * q^20 + q^21 - 28 * q^22 - 11 * q^23 + 32 * q^24 - 33 * q^25 - 42 * q^27 + 15 * q^28 + 8 * q^29 + 22 * q^30 + 40 * q^31 - 6 * q^32 + 24 * q^33 - 72 * q^34 + 44 * q^35 - 30 * q^36 - 4 * q^37 + 29 * q^38 + 4 * q^40 - 98 * q^41 - 9 * q^42 + 26 * q^43 + 10 * q^44 + 58 * q^45 - 10 * q^46 + 62 * q^47 + 178 * q^48 + 31 * q^49 + 46 * q^50 + 21 * q^51 + 18 * q^53 + 12 * q^54 - 28 * q^55 - 56 * q^56 + 26 * q^57 + 56 * q^58 + 79 * q^59 + 22 * q^60 - 13 * q^61 + 24 * q^62 - 22 * q^63 + 36 * q^64 + 38 * q^66 - 2 * q^67 + 12 * q^68 - 56 * q^69 - 85 * q^70 + 38 * q^71 + 81 * q^72 + 17 * q^73 - 17 * q^74 - 24 * q^75 - 116 * q^76 - 30 * q^77 + 9 * q^79 + 63 * q^80 - 16 * q^81 + 22 * q^82 - 162 * q^83 - 203 * q^84 + 68 * q^85 + 22 * q^86 - 70 * q^87 + 33 * q^88 + 72 * q^89 + 2 * q^90 - 8 * q^92 + 19 * q^93 + 30 * q^94 - 13 * q^95 + 11 * q^96 - 90 * q^97 - 81 * q^98 + 78 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1183\mathbb{Z}\right)^\times$.

$n$	$339$	$1016$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−0.680712	+	1.17903i	−0.481336	+	0.833699i	−0.999771	−	0.0214187i	$-0.993182\pi$
$2$	−0.680712	+	1.17903i	−0.481336	+	0.833699i	0.518434	+	0.855117i	$0.326515\pi$
$3$	0.656465	+	1.13703i	0.379010	+	0.656465i	0.990919	−	0.134464i	$-0.0429312\pi$
$3$	0.656465	+	1.13703i	0.379010	+	0.656465i	−0.611908	+	0.790929i	$0.709598\pi$
$4$	0.0732621	+	0.126894i	0.0366310	+	0.0634468i
$5$	−1.52933	+	2.64889i	−0.683939	+	1.18462i	0.289829	+	0.957078i	$0.406401\pi$
$5$	−1.52933	+	2.64889i	−0.683939	+	1.18462i	−0.973769	+	0.227539i	$0.926932\pi$
$6$	−1.78745			−0.729725
$7$	−2.33513	−	1.24384i	−0.882598	−	0.470129i
$7$	−2.33513	−	1.24384i	−0.882598	−	0.470129i
$8$	−2.92233			−1.03320
$9$	0.638108	−	1.10524i	0.212703	−	0.368412i
$10$	−2.08207	−	3.60626i	−0.658409	−	1.14040i
$11$	0.775465	+	1.34315i	0.233812	+	0.404973i	0.958927	−	0.283654i	$-0.0915468\pi$
$11$	0.775465	+	1.34315i	0.233812	+	0.404973i	−0.725115	+	0.688628i	$0.758213\pi$
$12$	−0.0961880	+	0.166602i	−0.0277671	+	0.0480940i
$13$		0			0
$13$		0			0
$14$	3.05608	−	1.90649i	0.816772	−	0.509530i
$15$	−4.01582			−1.03688
$16$	1.84274	−	3.19172i	0.460685	−	0.797930i
$17$	−2.91188	−	5.04353i	−0.706235	−	1.22323i	−0.966244	−	0.257629i	$-0.917059\pi$
$17$	−2.91188	−	5.04353i	−0.706235	−	1.22323i	0.260009	−	0.965606i	$-0.416274\pi$
$18$	0.868735	+	1.50469i	0.204763	+	0.354660i
$19$	0.722605	−	1.25159i	0.165777	−	0.287134i	−0.771154	−	0.636649i	$-0.780320\pi$
$19$	0.722605	−	1.25159i	0.165777	−	0.287134i	0.936931	+	0.349515i	$0.113653\pi$
$20$	−0.448169			−0.100214
$21$	−0.118644	−	3.47166i	−0.0258903	−	0.757578i
$22$	−2.11147			−0.450168
$23$	−3.13886	+	5.43667i	−0.654498	+	1.13362i	0.327521	+	0.944844i	$0.393787\pi$
$23$	−3.13886	+	5.43667i	−0.654498	+	1.13362i	−0.982019	+	0.188781i	$0.939547\pi$
$24$	−1.91841	−	3.32278i	−0.391593	−	0.678259i
$25$	−2.17773	−	3.77194i	−0.435546	−	0.754388i
$26$		0			0
$27$	5.61437			1.08049
$28$	−0.0132408	−	0.387440i	−0.00250228	−	0.0732193i
$29$	−9.88196			−1.83503			−0.917517	−	0.397698i	$-0.869809\pi$
$29$	−9.88196			−1.83503			−0.917517	+	0.397698i	$0.869809\pi$
$30$	2.73362	−	4.73476i	0.499088	−	0.864445i
$31$	0.763337	+	1.32214i	0.137099	+	0.237463i	0.926397	−	0.376547i	$-0.122889\pi$
$31$	0.763337	+	1.32214i	0.137099	+	0.237463i	−0.789298	+	0.614010i	$0.789555\pi$
$32$	−0.413578	−	0.716337i	−0.0731109	−	0.126632i
$33$	−1.01813	+	1.76345i	−0.177234	+	0.306978i
$34$	7.92861			1.35975
$35$	6.86600	−	4.28325i	1.16057	−	0.724001i
$36$	0.186996			0.0311661
$37$	3.87574	−	6.71298i	0.637168	−	1.10361i	−0.348884	−	0.937166i	$-0.613439\pi$
$37$	3.87574	−	6.71298i	0.637168	−	1.10361i	0.986051	−	0.166441i	$-0.0532275\pi$
$38$	0.983772	+	1.70394i	0.159589	+	0.276416i
$39$		0			0
$40$	4.46922	−	7.74092i	0.706646	−	1.22395i
$41$	−7.17386			−1.12037			−0.560184	−	0.828368i	$-0.689270\pi$
$41$	−7.17386			−1.12037			−0.560184	+	0.828368i	$0.689270\pi$
$42$	4.17395	+	2.22332i	0.644054	+	0.343065i
$43$	5.03082			0.767194			0.383597	−	0.923501i	$-0.374685\pi$
$43$	5.03082			0.767194			0.383597	+	0.923501i	$0.374685\pi$
$44$	−0.113624	+	0.196803i	−0.0171295	+	0.0296692i
$45$	1.95176	+	3.38055i	0.290951	+	0.503943i
$46$	−4.27333	−	7.40162i	−0.630067	−	1.09131i
$47$	2.60922	−	4.51930i	0.380594	−	0.659208i	−0.610553	−	0.791975i	$-0.709053\pi$
$47$	2.60922	−	4.51930i	0.380594	−	0.659208i	0.991147	+	0.132767i	$0.0423863\pi$
$48$	4.83878			0.698418
$49$	3.90570	+	5.80909i	0.557957	+	0.829870i
$50$	5.92963			0.838576
$51$	3.82310	−	6.62180i	0.535341	−	0.927237i
$52$		0			0
$53$	−3.88874	−	6.73549i	−0.534159	−	0.925191i	−0.999204	−	0.0399034i	$-0.987295\pi$
$53$	−3.88874	−	6.73549i	−0.534159	−	0.925191i	0.465044	−	0.885287i	$-0.346038\pi$
$54$	−3.82177	+	6.61950i	−0.520077	+	0.900800i
$55$	−4.74378			−0.639652
$56$	6.82403	+	3.63492i	0.911900	+	0.485737i
$57$	1.89746			0.251325
$58$	6.72677	−	11.6511i	0.883268	−	1.52986i
$59$	1.39530	+	2.41674i	0.181653	+	0.314632i	0.942444	−	0.334365i	$-0.108522\pi$
$59$	1.39530	+	2.41674i	0.181653	+	0.314632i	−0.760791	+	0.648997i	$0.775189\pi$
$60$	−0.294207	−	0.509582i	−0.0379820	−	0.0657867i
$61$	−6.87860	+	11.9141i	−0.880714	+	1.52544i	−0.0301651	+	0.999545i	$0.509603\pi$
$61$	−6.87860	+	11.9141i	−0.880714	+	1.52544i	−0.850549	+	0.525896i	$0.823730\pi$
$62$	−2.07845			−0.263964
$63$	−2.86481	+	1.78717i	−0.360932	+	0.225162i
$64$	8.49707			1.06213
$65$		0			0
$66$	−1.38611	−	2.40081i	−0.170618	−	0.295519i
$67$	−0.341513	−	0.591518i	−0.0417225	−	0.0722654i	0.844410	−	0.535697i	$-0.179951\pi$
$67$	−0.341513	−	0.591518i	−0.0417225	−	0.0722654i	−0.886133	+	0.463432i	$0.846618\pi$
$68$	0.426661	−	0.738999i	0.0517403	−	0.0896168i
$69$	−8.24222			−0.992246
$70$	0.376298	+	11.0109i	0.0449762	+	1.31605i
$71$	0.582838			0.0691702			0.0345851	−	0.999402i	$-0.488989\pi$
$71$	0.582838			0.0691702			0.0345851	+	0.999402i	$0.488989\pi$
$72$	−1.86476	+	3.22986i	−0.219764	+	0.380643i
$73$	2.16244	+	3.74546i	0.253095	+	0.438373i	0.964376	−	0.264534i	$-0.0852182\pi$
$73$	2.16244	+	3.74546i	0.253095	+	0.438373i	−0.711282	+	0.702907i	$0.751885\pi$
$74$	5.27653	+	9.13921i	0.613384	+	1.06241i
$75$	2.85921	−	4.95229i	0.330153	−	0.571842i
$76$	0.211758			0.0242903
$77$	−0.140151	−	4.10098i	−0.0159717	−	0.467350i
$78$		0			0
$79$	−3.20909	+	5.55831i	−0.361051	+	0.625359i	−0.988134	−	0.153594i	$-0.950915\pi$
$79$	−3.20909	+	5.55831i	−0.361051	+	0.625359i	0.627083	+	0.778952i	$0.284249\pi$
$80$	5.63634	+	9.76242i	0.630162	+	1.09147i
$81$	1.77131	+	3.06800i	0.196813	+	0.340889i
$82$	4.88333	−	8.45818i	0.539274	−	0.934050i
$83$	−14.7890			−1.62331			−0.811653	−	0.584140i	$-0.801432\pi$
$83$	−14.7890			−1.62331			−0.811653	+	0.584140i	$0.801432\pi$
$84$	0.431839	−	0.269396i	0.0471175	−	0.0293935i
$85$	17.8130			1.93209
$86$	−3.42454	+	5.93148i	−0.369278	+	0.639608i
$87$	−6.48716	−	11.2361i	−0.695496	−	1.20463i
$88$	−2.26617	−	3.92511i	−0.241574	−	0.418418i
$89$	−1.03289	+	1.78903i	−0.109487	+	0.189636i	−0.915562	−	0.402176i	$-0.868254\pi$
$89$	−1.03289	+	1.78903i	−0.109487	+	0.189636i	0.806076	+	0.591812i	$0.201587\pi$
$90$	−5.31435			−0.560182
$91$		0			0
$92$	−0.919839			−0.0958999
$93$	−1.00221	+	1.73588i	−0.103924	+	0.180002i
$94$	3.55226	+	6.15269i	0.366387	+	0.634601i
$95$	2.21021	+	3.82820i	0.226763	+	0.392765i
$96$	0.542998	−	0.940501i	0.0554195	−	0.0959894i
$97$	−5.78897			−0.587781			−0.293890	−	0.955839i	$-0.594950\pi$
$97$	−5.78897			−0.587781			−0.293890	+	0.955839i	$0.594950\pi$
$98$	−9.50773	+	0.650615i	−0.960426	+	0.0657221i
$99$	1.97932			0.198929
$100$	0.319090	−	0.552681i	0.0319090	−	0.0552681i
$101$	8.41117	+	14.5686i	0.836942	+	1.44963i	0.892439	+	0.451168i	$0.148992\pi$
$101$	8.41117	+	14.5686i	0.836942	+	1.44963i	−0.0554966	+	0.998459i	$0.517674\pi$
$102$	5.20486	+	9.01507i	0.515357	+	0.892625i
$103$	0.266398	−	0.461415i	0.0262490	−	0.0454646i	−0.852603	−	0.522560i	$-0.824977\pi$
$103$	0.266398	−	0.461415i	0.0262490	−	0.0454646i	0.878852	+	0.477095i	$0.158310\pi$
$104$		0			0
$105$	9.37747	+	4.99505i	0.915148	+	0.487467i
$106$	10.5884			1.02844
$107$	7.82744	−	13.5575i	0.756707	−	1.31066i	−0.187814	−	0.982205i	$-0.560140\pi$
$107$	7.82744	−	13.5575i	0.756707	−	1.31066i	0.944521	−	0.328450i	$-0.106526\pi$
$108$	0.411321	+	0.712428i	0.0395793	+	0.0685534i
$109$	−2.92769	−	5.07091i	−0.280422	−	0.485705i	0.691067	−	0.722791i	$-0.257141\pi$
$109$	−2.92769	−	5.07091i	−0.280422	−	0.485705i	−0.971489	+	0.237086i	$0.923808\pi$
$110$	3.22915	−	5.59305i	0.307887	−	0.533277i
$111$	10.1771			0.965972
$112$	−8.27305	+	5.16101i	−0.781730	+	0.487670i
$113$	−6.38603			−0.600747			−0.300373	−	0.953822i	$-0.597111\pi$
$113$	−6.38603			−0.600747			−0.300373	+	0.953822i	$0.597111\pi$
$114$	−1.29162	+	2.23716i	−0.120972	+	0.209529i
$115$	−9.60075	−	16.6290i	−0.895275	−	1.55066i
$116$	−0.723973	−	1.25396i	−0.0672192	−	0.116427i
$117$		0			0
$118$	−3.79920			−0.349745
$119$	0.526270	+	15.3992i	0.0482431	+	1.41165i
$120$	11.7355			1.07130
$121$	4.29731	−	7.44316i	0.390664	−	0.676650i
$122$	−9.36469	−	16.2201i	−0.847839	−	1.46850i
$123$	−4.70939	−	8.15690i	−0.424631	−	0.735483i
$124$	−0.111847	+	0.193725i	−0.0100442	+	0.0173970i
$125$	−1.97143			−0.176330
$126$	−0.157008	−	4.59423i	−0.0139874	−	0.409287i
$127$	−15.2760			−1.35552			−0.677762	−	0.735281i	$-0.737050\pi$
$127$	−15.2760			−1.35552			−0.677762	+	0.735281i	$0.737050\pi$
$128$	−4.95691	+	8.58561i	−0.438133	+	0.758868i
$129$	3.30256	+	5.72020i	0.290774	+	0.503636i
$130$		0			0
$131$	4.30125	−	7.44999i	0.375802	−	0.650909i	−0.614644	−	0.788804i	$-0.710701\pi$
$131$	4.30125	−	7.44999i	0.375802	−	0.650909i	0.990447	+	0.137896i	$0.0440339\pi$
$132$	−0.298362			−0.0259691
$133$	−3.24416	+	2.02382i	−0.281304	+	0.175487i
$134$	0.929889			0.0803301
$135$	−8.58625	+	14.8718i	−0.738987	+	1.27996i
$136$	8.50948	+	14.7389i	0.729682	+	1.26385i
$137$	4.40152	+	7.62366i	0.376047	+	0.651333i	0.990483	−	0.137634i	$-0.0439497\pi$
$137$	4.40152	+	7.62366i	0.376047	+	0.651333i	−0.614436	+	0.788967i	$0.710616\pi$
$138$	5.61058	−	9.71780i	0.477604	−	0.827234i
$139$	−9.68708			−0.821647			−0.410824	−	0.911715i	$-0.634759\pi$
$139$	−9.68708			−0.821647			−0.410824	+	0.911715i	$0.634759\pi$
$140$	1.04653	+	0.557453i	0.0884483	+	0.0471134i
$141$	6.85145			0.576996
$142$	−0.396745	+	0.687183i	−0.0332941	+	0.0576671i
$143$		0			0
$144$	−2.35174	−	4.07332i	−0.195978	−	0.339444i
$145$	15.1128	−	26.1762i	1.25505	−	2.17381i
$146$	−5.88800			−0.487295
$147$	−4.04115	+	8.25436i	−0.333309	+	0.680808i
$148$	1.13578			0.0933605
$149$	0.223722	−	0.387498i	0.0183280	−	0.0317451i	−0.856716	−	0.515789i	$-0.827499\pi$
$149$	0.223722	−	0.387498i	0.0183280	−	0.0317451i	0.875044	+	0.484043i	$0.160832\pi$
$150$	3.89259	+	6.74217i	0.317829	+	0.550496i
$151$	−7.13843	−	12.3641i	−0.580918	−	1.00618i	−0.995371	−	0.0961082i	$-0.969361\pi$
$151$	−7.13843	−	12.3641i	−0.580918	−	1.00618i	0.414453	−	0.910071i	$-0.363973\pi$
$152$	−2.11169	+	3.65755i	−0.171281	+	0.296667i
$153$	−7.43238			−0.600872
$154$	4.93057	+	2.62635i	0.397317	+	0.211637i
$155$	−4.66959			−0.375071
$156$		0			0
$157$	−3.48664	−	6.03905i	−0.278265	−	0.481968i	0.692689	−	0.721236i	$-0.256426\pi$
$157$	−3.48664	−	6.03905i	−0.278265	−	0.481968i	−0.970954	+	0.239268i	$0.923093\pi$
$158$	−4.36893	−	7.56722i	−0.347574	−	0.602015i
$159$	5.10564	−	8.84322i	0.404903	−	0.701313i
$160$	2.52999			0.200014
$161$	14.0920	−	8.79110i	1.11061	−	0.692836i
$162$	−4.82302			−0.378932
$163$	11.3057	−	19.5820i	0.885530	−	1.53378i	0.0404247	−	0.999183i	$-0.487129\pi$
$163$	11.3057	−	19.5820i	0.885530	−	1.53378i	0.845105	−	0.534600i	$-0.179538\pi$
$164$	−0.525572	−	0.910317i	−0.0410403	−	0.0710838i
$165$	−3.11413	−	5.39383i	−0.242434	−	0.419909i
$166$	10.0671	−	17.4367i	0.781356	−	1.35335i
$167$	−5.44039			−0.420990			−0.210495	−	0.977595i	$-0.567508\pi$
$167$	−5.44039			−0.420990			−0.210495	+	0.977595i	$0.567508\pi$
$168$	0.346718	+	10.1453i	0.0267498	+	0.782729i
$169$		0			0
$170$	−12.1255	+	21.0020i	−0.929984	+	1.61078i
$171$	−0.922200	−	1.59730i	−0.0705224	−	0.122148i
$172$	0.368569	+	0.638380i	0.0281031	+	0.0486760i
$173$	−9.32608	+	16.1532i	−0.709049	+	1.22811i	0.256161	+	0.966634i	$0.417542\pi$
$173$	−9.32608	+	16.1532i	−0.709049	+	1.22811i	−0.965210	+	0.261475i	$0.915791\pi$
$174$	17.6635			1.33907
$175$	0.393586	+	11.5167i	0.0297523	+	0.870584i
$176$	5.71593			0.430854
$177$	−1.83194	+	3.17301i	−0.137697	+	0.238498i
$178$	−1.40621	−	2.43562i	−0.105400	−	0.182558i
$179$	−0.719918	−	1.24693i	−0.0538092	−	0.0932002i	0.837866	−	0.545876i	$-0.183803\pi$
$179$	−0.719918	−	1.24693i	−0.0538092	−	0.0932002i	−0.891675	+	0.452676i	$0.850470\pi$
$180$	−0.285980	+	0.495332i	−0.0213157	+	0.0369199i
$181$	1.93813			0.144060			0.0720300	−	0.997402i	$-0.477052\pi$
$181$	1.93813			0.144060			0.0720300	+	0.997402i	$0.477052\pi$
$182$		0			0
$183$	−18.0622			−1.33520
$184$	9.17280	−	15.8878i	0.676228	−	1.17126i
$185$	11.8546	+	20.5328i	0.871568	+	1.50960i
$186$	−1.36443	−	2.36326i	−0.100045	−	0.173283i
$187$	4.51613	−	7.82216i	0.330252	−	0.572013i
$188$	0.764628			0.0557662
$189$	−13.1103	−	6.98340i	−0.953635	−	0.507968i
$190$	−6.01807			−0.436596
$191$	−2.56890	+	4.44947i	−0.185879	+	0.321953i	−0.943872	−	0.330310i	$-0.892847\pi$
$191$	−2.56890	+	4.44947i	−0.185879	+	0.321953i	0.757993	+	0.652263i	$0.226180\pi$
$192$	5.57803	+	9.66143i	0.402560	+	0.697254i
$193$	−4.33469	−	7.50790i	−0.312018	−	0.540431i	0.666781	−	0.745253i	$-0.267671\pi$
$193$	−4.33469	−	7.50790i	−0.312018	−	0.540431i	−0.978799	+	0.204823i	$0.934338\pi$
$194$	3.94062	−	6.82536i	0.282920	−	0.490032i
$195$		0			0
$196$	−0.450997	+	0.921195i	−0.0322140	+	0.0657996i
$197$	17.2707			1.23049			0.615243	−	0.788337i	$-0.289058\pi$
$197$	17.2707			1.23049			0.615243	+	0.788337i	$0.289058\pi$
$198$	−1.34735	+	2.33368i	−0.0957519	+	0.165847i
$199$	5.13585	+	8.89555i	0.364071	+	0.630589i	0.988627	−	0.150391i	$-0.0480534\pi$
$199$	5.13585	+	8.89555i	0.364071	+	0.630589i	−0.624556	+	0.780980i	$0.714720\pi$
$200$	6.36405	+	11.0229i	0.450006	+	0.779434i
$201$	0.448383	−	0.776622i	0.0316265	−	0.0547787i
$202$	−22.9023			−1.61140
$203$	23.0757	+	12.2916i	1.61960	+	0.862702i
$204$	1.12035			0.0784403
$205$	10.9712	−	19.0027i	0.766264	−	1.32721i
$206$	0.362681	+	0.628182i	0.0252692	+	0.0437675i
$207$	4.00587	+	6.93837i	0.278427	+	0.482250i
$208$		0			0
$209$	2.24142			0.155042
$210$	−12.2727	+	7.65611i	−0.846895	+	0.528322i
$211$	−27.7889			−1.91307			−0.956535	−	0.291618i	$-0.905806\pi$
$211$	−27.7889			−1.91307			−0.956535	+	0.291618i	$0.905806\pi$
$212$	0.569794	−	0.986912i	0.0391336	−	0.0677814i
$213$	0.382613	+	0.662705i	0.0262162	+	0.0454078i
$214$	10.6565	+	18.4575i	0.728461	+	1.26173i
$215$	−7.69382	+	13.3261i	−0.524714	+	0.908831i
$216$	−16.4070			−1.11636
$217$	−0.137960	−	4.03684i	−0.00936530	−	0.274039i
$218$	7.97167			0.539909
$219$	−2.83913	+	4.91753i	−0.191851	+	0.332296i
$220$	−0.347540	−	0.601956i	−0.0234311	−	0.0405839i
$221$		0			0
$222$	−6.92771	+	11.9991i	−0.464957	+	0.805330i
$223$	−20.2750			−1.35771			−0.678856	−	0.734271i	$-0.737524\pi$
$223$	−20.2750			−1.35771			−0.678856	+	0.734271i	$0.737524\pi$
$224$	0.0747467	+	2.18717i	0.00499423	+	0.146136i
$225$	−5.55851			−0.370567
$226$	4.34705	−	7.52930i	0.289161	−	0.500842i
$227$	0.897543	+	1.55459i	0.0595720	+	0.103182i	0.894273	−	0.447521i	$-0.147693\pi$
$227$	0.897543	+	1.55459i	0.0595720	+	0.103182i	−0.834701	+	0.550703i	$0.814360\pi$
$228$	0.139012	+	0.240776i	0.00920628	+	0.0159457i
$229$	2.40609	−	4.16747i	0.158999	−	0.275394i	−0.775509	−	0.631337i	$-0.782507\pi$
$229$	2.40609	−	4.16747i	0.158999	−	0.275394i	0.934508	+	0.355942i	$0.115840\pi$
$230$	26.1414			1.72371
$231$	4.57094	−	2.85151i	0.300746	−	0.187615i
$232$	28.8783			1.89596
$233$	−6.43889	+	11.1525i	−0.421826	+	0.730623i	−0.996118	−	0.0880267i	$-0.971944\pi$
$233$	−6.43889	+	11.1525i	−0.421826	+	0.730623i	0.574292	+	0.818650i	$0.305277\pi$
$234$		0			0
$235$	7.98074	+	13.8231i	0.520606	+	0.901717i
$236$	−0.204446	+	0.354110i	−0.0133083	+	0.0230506i
$237$	−8.42662			−0.547368
$238$	−18.5144	−	9.86196i	−1.20011	−	0.639256i
$239$	−9.97163			−0.645011			−0.322505	−	0.946568i	$-0.604525\pi$
$239$	−9.97163			−0.645011			−0.322505	+	0.946568i	$0.604525\pi$
$240$	−7.40011	+	12.8174i	−0.477675	+	0.827358i
$241$	11.7857	+	20.4134i	0.759182	+	1.31494i	0.943268	+	0.332032i	$0.107734\pi$
$241$	11.7857	+	20.4134i	0.759182	+	1.31494i	−0.184086	+	0.982910i	$0.558932\pi$
$242$	5.85046	+	10.1333i	0.376082	+	0.651393i
$243$	6.09595	−	10.5585i	0.391055	−	0.677327i
$244$	−2.01576			−0.129046
$245$	−21.3607	+	1.46172i	−1.36469	+	0.0933857i
$246$	12.8229			0.817561
$247$		0			0
$248$	−2.23072	−	3.86373i	−0.141651	−	0.245347i
$249$	−9.70847	−	16.8156i	−0.615250	−	1.06564i
$250$	1.34198	−	2.32437i	0.0848740	−	0.147006i
$251$	−12.5979			−0.795175			−0.397587	−	0.917564i	$-0.630152\pi$
$251$	−12.5979			−0.795175			−0.397587	+	0.917564i	$0.630152\pi$
$252$	−0.436662	−	0.232595i	−0.0275071	−	0.0146521i
$253$	−9.73632			−0.612117
$254$	10.3985	−	18.0108i	0.652463	−	1.13010i
$255$	11.6936	+	20.2539i	0.732281	+	1.26835i
$256$	1.74862	+	3.02870i	0.109289	+	0.189294i
$257$	2.98670	−	5.17311i	0.186305	−	0.322690i	−0.757710	−	0.652591i	$-0.773682\pi$
$257$	2.98670	−	5.17311i	0.186305	−	0.322690i	0.944015	+	0.329901i	$0.107015\pi$
$258$	−8.99237			−0.559840
$259$	−17.4003	+	10.8549i	−1.08120	+	0.674490i
$260$		0			0
$261$	−6.30575	+	10.9219i	−0.390316	+	0.676048i
$262$	5.85583	+	10.1426i	0.361774	+	0.626612i
$263$	−14.6299	−	25.3397i	−0.902118	−	1.56251i	−0.824740	−	0.565512i	$-0.808678\pi$
$263$	−14.6299	−	25.3397i	−0.902118	−	1.56251i	−0.0773783	−	0.997002i	$-0.524655\pi$
$264$	2.97532	−	5.15340i	0.183118	−	0.317170i
$265$	23.7887			1.46133
$266$	−0.177799	−	5.20259i	−0.0109016	−	0.318992i
$267$	−2.71224			−0.165986
$268$	0.0500399	−	0.0866717i	0.00305668	−	0.00529432i
$269$	−1.72211	−	2.98278i	−0.104999	−	0.181863i	0.808739	−	0.588168i	$-0.200151\pi$
$269$	−1.72211	−	2.98278i	−0.104999	−	0.181863i	−0.913738	+	0.406305i	$0.866817\pi$
$270$	−11.6895	−	20.2469i	−0.711402	−	1.23218i
$271$	−15.6138	+	27.0438i	−0.948468	+	1.64279i	−0.199814	+	0.979834i	$0.564034\pi$
$271$	−15.6138	+	27.0438i	−0.948468	+	1.64279i	−0.748654	+	0.662961i	$0.769299\pi$
$272$	−21.4634			−1.30141
$273$		0			0
$274$	−11.9847			−0.724020
$275$	3.37751	−	5.85002i	0.203671	−	0.352769i
$276$	−0.603842	−	1.04589i	−0.0363470	−	0.0629549i
$277$	−11.6182	−	20.1232i	−0.698067	−	1.20909i	−0.969136	−	0.246528i	$-0.920710\pi$
$277$	−11.6182	−	20.1232i	−0.698067	−	1.20909i	0.271069	−	0.962560i	$-0.412623\pi$
$278$	6.59411	−	11.4213i	0.395489	−	0.685006i
$279$	1.94837			0.116646
$280$	−20.0647	+	12.5171i	−1.19910	+	0.748038i
$281$	−5.30362			−0.316387			−0.158194	−	0.987408i	$-0.550567\pi$
$281$	−5.30362			−0.316387			−0.158194	+	0.987408i	$0.550567\pi$
$282$	−4.66386	+	8.07805i	−0.277729	+	0.481041i
$283$	−4.89638	−	8.48079i	−0.291060	−	0.504130i	0.683001	−	0.730418i	$-0.260675\pi$
$283$	−4.89638	−	8.48079i	−0.291060	−	0.504130i	−0.974061	+	0.226287i	$0.927341\pi$
$284$	0.0427000	+	0.0739585i	0.00253378	+	0.00438863i
$285$	−2.90185	+	5.02615i	−0.171891	+	0.297724i
$286$		0			0
$287$	16.7519	+	8.92317i	0.988835	+	0.526718i
$288$	−1.05563			−0.0622035
$289$	−8.45811	+	14.6499i	−0.497536	+	0.861757i
$290$	20.5750	+	35.6369i	1.20820	+	2.09267i
$291$	−3.80026	−	6.58224i	−0.222775	−	0.385857i
$292$	−0.316850	+	0.548800i	−0.0185423	+	0.0321161i
$293$	−24.2189			−1.41488			−0.707441	−	0.706772i	$-0.750151\pi$
$293$	−24.2189			−1.41488			−0.707441	+	0.706772i	$0.750151\pi$
$294$	−6.98126	−	10.3835i	−0.407156	−	0.605577i
$295$	−8.53555			−0.496959
$296$	−11.3262	+	19.6175i	−0.658322	+	1.14025i
$297$	4.35375	+	7.54091i	0.252630	+	0.437568i
$298$	0.304581	+	0.527549i	0.0176439	+	0.0305601i
$299$		0			0
$300$	0.837886			0.0483754
$301$	−11.7477	−	6.25756i	−0.677123	−	0.360680i
$302$	19.4369			1.11847
$303$	−11.0433	+	19.1275i	−0.634419	+	1.09885i
$304$	−2.66315	−	4.61271i	−0.152742	−	0.264557i
$305$	−21.0394	−	36.4412i	−1.20471	−	2.08662i
$306$	5.05931	−	8.76298i	0.289221	−	0.500946i
$307$	−6.52654			−0.372490			−0.186245	−	0.982503i	$-0.559632\pi$
$307$	−6.52654			−0.372490			−0.186245	+	0.982503i	$0.559632\pi$
$308$	0.510121	−	0.318231i	0.0290668	−	0.0181329i
$309$	0.699524			0.0397946
$310$	3.17865	−	5.50558i	0.180535	−	0.312696i
$311$	0.856568	+	1.48362i	0.0485715	+	0.0841283i	0.889289	−	0.457346i	$-0.151200\pi$
$311$	0.856568	+	1.48362i	0.0485715	+	0.0841283i	−0.840717	+	0.541474i	$0.817866\pi$
$312$		0			0
$313$	2.03949	−	3.53250i	0.115279	−	0.199669i	−0.802612	−	0.596501i	$-0.796557\pi$
$313$	2.03949	−	3.53250i	0.115279	−	0.199669i	0.917891	+	0.396832i	$0.129890\pi$
$314$	9.49360			0.535755
$315$	−0.352746	−	10.3217i	−0.0198750	−	0.581563i
$316$	−0.940419			−0.0529027
$317$	−0.248829	+	0.430985i	−0.0139756	+	0.0242065i	−0.872929	−	0.487848i	$-0.837782\pi$
$317$	−0.248829	+	0.430985i	−0.0139756	+	0.0242065i	0.858953	+	0.512054i	$0.171115\pi$
$318$	6.95094	+	12.0394i	0.389789	+	0.675135i
$319$	−7.66311	−	13.2729i	−0.429052	−	0.743140i
$320$	−12.9949	+	22.5078i	−0.726435	+	1.25822i
$321$	20.5538			1.14720
$322$	0.772327	+	22.5991i	0.0430401	+	1.25940i
$323$	−8.41656			−0.468310
$324$	−0.259540	+	0.449537i	−0.0144189	+	0.0249743i
$325$		0			0
$326$	15.3918	+	26.6594i	0.852475	+	1.47653i
$327$	3.84386	−	6.65775i	0.212566	−	0.368175i
$328$	20.9644			1.15756
$329$	−11.7142	+	7.30771i	−0.645824	+	0.402887i
$330$	8.47930			0.466770
$331$	−5.02718	+	8.70734i	−0.276319	+	0.478599i	−0.970467	−	0.241234i	$-0.922448\pi$
$331$	−5.02718	+	8.70734i	−0.276319	+	0.478599i	0.694148	+	0.719832i	$0.255781\pi$
$332$	−1.08347	−	1.87663i	−0.0594634	−	0.102994i
$333$	−4.94628	−	8.56721i	−0.271055	−	0.469480i
$334$	3.70334	−	6.41437i	0.202638	−	0.350979i
$335$	2.08915			0.114143
$336$	−11.2992	−	6.01869i	−0.616422	−	0.328346i
$337$	−20.4206			−1.11238			−0.556189	−	0.831056i	$-0.687737\pi$
$337$	−20.4206			−1.11238			−0.556189	+	0.831056i	$0.687737\pi$
$338$		0			0
$339$	−4.19220	−	7.26111i	−0.227689	−	0.394369i
$340$	1.30502	+	2.26035i	0.0707744	+	0.122585i
$341$	−1.18388	+	2.05055i	−0.0641109	+	0.111043i
$342$	2.51101			0.135780
$343$	−1.89474	−	18.4231i	−0.102306	−	0.994753i
$344$	−14.7017			−0.792664
$345$	12.6051	−	21.8327i	0.678636	−	1.17543i
$346$	−12.6968	−	21.9914i	−0.682582	−	1.18227i
$347$	13.6834	+	23.7003i	0.734562	+	1.27230i	0.954915	+	0.296879i	$0.0959459\pi$
$347$	13.6834	+	23.7003i	0.734562	+	1.27230i	−0.220353	+	0.975420i	$0.570721\pi$
$348$	0.950525	−	1.64636i	0.0509535	−	0.0882541i
$349$	22.2070			1.18871			0.594356	−	0.804202i	$-0.297407\pi$
$349$	22.2070			1.18871			0.594356	+	0.804202i	$0.297407\pi$
$350$	−13.8465	−	7.37554i	−0.740126	−	0.394239i
$351$		0			0
$352$	0.641430	−	1.11099i	0.0341883	−	0.0592159i
$353$	13.9253	+	24.1193i	0.741168	+	1.28374i	0.951964	+	0.306211i	$0.0990613\pi$
$353$	13.9253	+	24.1193i	0.741168	+	1.28374i	−0.210795	+	0.977530i	$0.567605\pi$
$354$	−2.49404	−	4.31981i	−0.132557	−	0.229595i
$355$	−0.891355	+	1.54387i	−0.0473082	+	0.0819402i
$356$	−0.302688			−0.0160424
$357$	−17.1639	+	10.7074i	−0.908411	+	0.566698i
$358$	1.96023			0.103601
$359$	10.4003	−	18.0138i	0.548904	−	0.950730i	−0.449446	−	0.893308i	$-0.648378\pi$
$359$	10.4003	−	18.0138i	0.548904	−	0.950730i	0.998350	−	0.0574224i	$-0.0182882\pi$
$360$	−5.70369	−	9.87908i	−0.300611	−	0.520673i
$361$	8.45568	+	14.6457i	0.445036	+	0.770825i
$362$	−1.31931	+	2.28511i	−0.0693413	+	0.120103i
$363$	11.2841			0.592263
$364$		0			0
$365$	−13.2284			−0.692406
$366$	12.2952	−	21.2959i	0.642679	−	1.11315i
$367$	7.89290	+	13.6709i	0.412006	+	0.713615i	0.995109	−	0.0987829i	$-0.0314949\pi$
$367$	7.89290	+	13.6709i	0.412006	+	0.713615i	−0.583103	+	0.812398i	$0.698162\pi$
$368$	11.5682	+	20.0368i	0.603036	+	1.04449i
$369$	−4.57770	+	7.92880i	−0.238305	+	0.412757i
$370$	−32.2783			−1.67807
$371$	0.702820	+	20.5653i	0.0364886	+	1.06769i
$372$	−0.293695			−0.0152274
$373$	−4.50500	+	7.80289i	−0.233260	+	0.404018i	−0.958766	−	0.284198i	$-0.908273\pi$
$373$	−4.50500	+	7.80289i	−0.233260	+	0.404018i	0.725506	+	0.688216i	$0.241606\pi$
$374$	6.14836	+	10.6493i	0.317924	+	0.550661i
$375$	−1.29417	−	2.24158i	−0.0668309	−	0.115754i
$376$	−7.62500	+	13.2069i	−0.393229	+	0.681093i
$377$		0			0
$378$	17.1580	−	10.7037i	0.882511	−	0.550541i
$379$	−11.6146			−0.596603			−0.298301	−	0.954472i	$-0.596420\pi$
$379$	−11.6146			−0.596603			−0.298301	+	0.954472i	$0.596420\pi$
$380$	−0.323849	+	0.560923i	−0.0166131	+	0.0287748i
$381$	−10.0281	−	17.3693i	−0.513758	−	0.889854i
$382$	−3.49737	−	6.05762i	−0.178941	−	0.309935i
$383$	2.16816	−	3.75537i	0.110788	−	0.191890i	−0.805300	−	0.592867i	$-0.797996\pi$
$383$	2.16816	−	3.75537i	0.110788	−	0.191890i	0.916088	+	0.400977i	$0.131329\pi$
$384$	−13.0161			−0.664227
$385$	11.0774	+	5.90053i	0.564555	+	0.300719i
$386$	11.8027			0.600742
$387$	3.21021	−	5.56024i	0.163184	−	0.282643i
$388$	−0.424112	−	0.734584i	−0.0215310	−	0.0372928i
$389$	−3.40867	−	5.90398i	−0.172826	−	0.299344i	0.766581	−	0.642148i	$-0.221957\pi$
$389$	−3.40867	−	5.90398i	−0.172826	−	0.299344i	−0.939407	+	0.342804i	$0.888623\pi$
$390$		0			0
$391$	36.5600			1.84892
$392$	−11.4137	−	16.9761i	−0.576481	−	0.857421i
$393$	11.2945			0.569732
$394$	−11.7564	+	20.3626i	−0.592278	+	1.02586i
$395$	−9.81555	−	17.0010i	−0.493874	−	0.855415i
$396$	0.145009	+	0.251163i	0.00728699	+	0.0126214i
$397$	−12.4137	+	21.5012i	−0.623027	+	1.07912i	0.365891	+	0.930658i	$0.380764\pi$
$397$	−12.4137	+	21.5012i	−0.623027	+	1.07912i	−0.988919	+	0.148457i	$0.952569\pi$
$398$	−13.9841			−0.700961
$399$	−4.43082	−	2.36014i	−0.221818	−	0.118155i
$400$	−16.0520			−0.802599
$401$	−5.31056	+	9.19816i	−0.265197	+	0.459334i	−0.967615	−	0.252430i	$-0.918770\pi$
$401$	−5.31056	+	9.19816i	−0.265197	+	0.459334i	0.702418	+	0.711764i	$0.252104\pi$
$402$	0.610439	+	1.05731i	0.0304459	+	0.0527339i
$403$		0			0
$404$	−1.23244	+	2.13465i	−0.0613162	+	0.106203i
$405$	−10.8357			−0.538432
$406$	−30.2001	+	18.8398i	−1.49880	+	0.935005i
$407$	12.0220			0.595909
$408$	−11.1723	+	19.3511i	−0.553114	+	0.958021i
$409$	5.33494	+	9.24039i	0.263796	+	0.456908i	0.967247	−	0.253835i	$-0.0816921\pi$
$409$	5.33494	+	9.24039i	0.263796	+	0.456908i	−0.703452	+	0.710743i	$0.748359\pi$
$410$	14.9365	+	25.8708i	0.737661	+	1.27767i
$411$	−5.77889	+	10.0093i	−0.285051	+	0.493724i
$412$	0.0780676			0.00384611
$413$	−0.252176	−	7.37894i	−0.0124088	−	0.363094i
$414$	−10.9074			−0.536068
$415$	22.6174	−	39.1744i	1.11024	−	1.92300i
$416$		0			0
$417$	−6.35923	−	11.0145i	−0.311413	−	0.539383i
$418$	−1.52576	+	2.64270i	−0.0746274	+	0.129259i
$419$	−8.54940			−0.417666			−0.208833	−	0.977951i	$-0.566966\pi$
$419$	−8.54940			−0.417666			−0.208833	+	0.977951i	$0.566966\pi$
$420$	0.0531727	+	1.55589i	0.00259456	+	0.0759197i
$421$	−0.523234			−0.0255009			−0.0127504	−	0.999919i	$-0.504059\pi$
$421$	−0.523234			−0.0255009			−0.0127504	+	0.999919i	$0.504059\pi$
$422$	18.9163	−	32.7639i	0.920830	−	1.59492i
$423$	−3.32993	−	5.76760i	−0.161907	−	0.280430i
$424$	11.3642	+	19.6833i	0.551893	+	0.955907i
$425$	−12.6826	+	21.9669i	−0.615196	+	1.06555i
$426$	−1.04180			−0.0504752
$427$	30.8817	−	19.2651i	1.49447	−	0.932302i
$428$	2.29382			0.110876
$429$		0			0
$430$	−10.4745	−	18.1424i	−0.505128	−	0.874907i
$431$	13.3251	+	23.0797i	0.641846	+	1.11171i	0.985020	+	0.172438i	$0.0551644\pi$
$431$	13.3251	+	23.0797i	0.641846	+	1.11171i	−0.343175	+	0.939272i	$0.611502\pi$
$432$	10.3458	−	17.9195i	0.497764	−	0.862153i
$433$	13.2489			0.636700			0.318350	−	0.947973i	$-0.396871\pi$
$433$	13.2489			0.636700			0.318350	+	0.947973i	$0.396871\pi$
$434$	4.85346	+	2.58527i	0.232974	+	0.124097i
$435$	39.6841			1.90271
$436$	0.428978	−	0.743012i	0.0205443	−	0.0355838i
$437$	4.53632	+	7.85713i	0.217001	+	0.375858i
$438$	−3.86527	−	6.69484i	−0.184690	−	0.319892i
$439$	3.95428	−	6.84902i	0.188728	−	0.326886i	−0.756099	−	0.654458i	$-0.772897\pi$
$439$	3.95428	−	6.84902i	0.188728	−	0.326886i	0.944826	+	0.327572i	$0.106230\pi$
$440$	13.8629			0.660888
$441$	8.91267	−	0.609895i	0.424413	−	0.0290426i
$442$		0			0
$443$	−0.370956	+	0.642514i	−0.0176246	+	0.0305268i	−0.874703	−	0.484659i	$-0.838944\pi$
$443$	−0.370956	+	0.642514i	−0.0176246	+	0.0305268i	0.857079	+	0.515186i	$0.172277\pi$
$444$	0.745599	+	1.29142i	0.0353846	+	0.0612879i
$445$	−3.15928	−	5.47204i	−0.149764	−	0.259400i
$446$	13.8014	−	23.9047i	0.653516	−	1.13192i
$447$	0.587463			0.0277860
$448$	−19.8418	−	10.5690i	−0.937437	−	0.499340i
$449$	26.1281			1.23306			0.616530	−	0.787332i	$-0.288538\pi$
$449$	26.1281			1.23306			0.616530	+	0.787332i	$0.288538\pi$
$450$	3.78374	−	6.55364i	0.178367	−	0.308941i
$451$	−5.56308	−	9.63553i	−0.261955	−	0.453720i
$452$	−0.467854	−	0.810346i	−0.0220060	−	0.0381155i
$453$	9.37226	−	16.2332i	0.440347	−	0.762704i
$454$	−2.44387			−0.114697
$455$		0			0
$456$	−5.54500			−0.259668
$457$	−1.47913	+	2.56193i	−0.0691907	+	0.119842i	−0.898545	−	0.438881i	$-0.855375\pi$
$457$	−1.47913	+	2.56193i	−0.0691907	+	0.119842i	0.829355	+	0.558723i	$0.188708\pi$
$458$	3.27571	+	5.67370i	0.153064	+	0.265114i
$459$	−16.3484	−	28.3162i	−0.763077	−	1.32169i
$460$	1.40674	−	2.43655i	0.0655897	−	0.113605i
$461$	0.916982			0.0427081			0.0213541	−	0.999772i	$-0.493202\pi$
$461$	0.916982			0.0427081			0.0213541	+	0.999772i	$0.493202\pi$
$462$	0.250514	+	7.33032i	0.0116550	+	0.341037i
$463$	−10.1773			−0.472981			−0.236490	−	0.971634i	$-0.575997\pi$
$463$	−10.1773			−0.472981			−0.236490	+	0.971634i	$0.575997\pi$
$464$	−18.2099	+	31.5404i	−0.845373	+	1.46423i
$465$	−3.06542	−	5.30947i	−0.142156	−	0.246221i
$466$	−8.76606	−	15.1833i	−0.406080	−	0.703351i
$467$	13.6339	−	23.6146i	0.630900	−	1.09275i	−0.356468	−	0.934308i	$-0.616019\pi$
$467$	13.6339	−	23.6146i	0.630900	−	1.09275i	0.987368	−	0.158444i	$-0.0506477\pi$
$468$		0			0
$469$	0.0617224	+	1.80606i	0.00285008	+	0.0833963i
$470$	−21.7304			−1.00235
$471$	4.57772	−	7.92884i	0.210930	−	0.365342i
$472$	−4.07754	−	7.06250i	−0.187684	−	0.325078i
$473$	3.90123	+	6.75713i	0.179379	+	0.310693i
$474$	5.73610	−	9.93522i	0.263468	−	0.456340i
$475$	−6.29456			−0.288814
$476$	−1.91551	+	1.19496i	−0.0877973	+	0.0547709i
$477$	−9.92573			−0.454468
$478$	6.78781	−	11.7568i	0.310467	−	0.537745i
$479$	16.7148	+	28.9509i	0.763720	+	1.32280i	0.940921	+	0.338627i	$0.109962\pi$
$479$	16.7148	+	28.9509i	0.763720	+	1.32280i	−0.177201	+	0.984175i	$0.556704\pi$
$480$	1.66085	+	2.87668i	0.0758072	+	0.131302i
$481$		0			0
$482$	−32.0906			−1.46169
$483$	19.2467	+	10.2520i	0.875754	+	0.466484i
$484$	1.25932			0.0572418
$485$	8.85327	−	15.3343i	0.402006	−	0.696296i
$486$	8.29917	+	14.3746i	0.376458	+	0.652044i
$487$	18.3164	+	31.7250i	0.829996	+	1.43760i	0.898040	+	0.439913i	$0.144991\pi$
$487$	18.3164	+	31.7250i	0.829996	+	1.43760i	−0.0680439	+	0.997682i	$0.521676\pi$
$488$	20.1015	−	34.8169i	0.909953	−	1.57609i
$489$	29.6871			1.34250
$490$	12.8171	−	26.1799i	0.579018	−	1.18269i
$491$	13.1049			0.591415			0.295708	−	0.955278i	$-0.404445\pi$
$491$	13.1049			0.591415			0.295708	+	0.955278i	$0.404445\pi$
$492$	0.690039	−	1.19518i	0.0311094	−	0.0538830i
$493$	28.7751	+	49.8399i	1.29596	+	2.24468i
$494$		0			0
$495$	−3.02705	+	5.24300i	−0.136056	+	0.235655i
$496$	5.62653			0.252639
$497$	−1.36101	−	0.724960i	−0.0610494	−	0.0325189i
$498$	26.4347			1.18457
$499$	−2.08696	+	3.61472i	−0.0934250	+	0.161817i	−0.908950	−	0.416905i	$-0.863115\pi$
$499$	−2.08696	+	3.61472i	−0.0934250	+	0.161817i	0.815525	+	0.578722i	$0.196448\pi$
$500$	−0.144431	−	0.250162i	−0.00645915	−	0.0111876i
$501$	−3.57142	−	6.18589i	−0.159559	−	0.276365i
$502$	8.57557	−	14.8533i	0.382746	−	0.662936i
$503$	18.9926			0.846838			0.423419	−	0.905934i	$-0.360830\pi$
$503$	18.9926			0.846838			0.423419	+	0.905934i	$0.360830\pi$
$504$	8.37191	−	5.22269i	0.372915	−	0.232637i
$505$	−51.4540			−2.28967
$506$	6.62763	−	11.4794i	0.294634	−	0.510321i
$507$		0			0
$508$	−1.11915	−	1.93843i	−0.0496543	−	0.0860037i
$509$	−2.12865	+	3.68694i	−0.0943509	+	0.163421i	−0.909338	−	0.416059i	$-0.863411\pi$
$509$	−2.12865	+	3.68694i	−0.0943509	+	0.163421i	0.814987	+	0.579480i	$0.196744\pi$
$510$	−31.8399			−1.40989
$511$	−0.390823	−	11.4359i	−0.0172890	−	0.505894i
$512$	−24.5889			−1.08668
$513$	4.05697	−	7.02688i	0.179120	−	0.310244i
$514$	4.06616	+	7.04280i	0.179351	+	0.310644i
$515$	0.814824	+	1.41132i	0.0359055	+	0.0621901i
$516$	−0.483905	+	0.838148i	−0.0213027	+	0.0368974i
$517$	8.09344			0.355949
$518$	−0.953638	−	27.9045i	−0.0419004	−	1.22605i
$519$	−24.4890			−1.07495
$520$		0			0
$521$	1.17914	+	2.04233i	0.0516590	+	0.0894760i	0.890699	−	0.454594i	$-0.150216\pi$
$521$	1.17914	+	2.04233i	0.0516590	+	0.0894760i	−0.839040	+	0.544070i	$0.816882\pi$
$522$	−8.58480	−	14.8693i	−0.375747	−	0.650812i
$523$	−2.78708	+	4.82736i	−0.121870	+	0.211086i	−0.920505	−	0.390730i	$-0.872223\pi$
$523$	−2.78708	+	4.82736i	−0.121870	+	0.211086i	0.798635	+	0.601816i	$0.205556\pi$
$524$	1.26048			0.0550641
$525$	−12.8365	+	8.00786i	−0.560231	+	0.349492i
$526$	39.8350			1.73689
$527$	4.44550	−	7.69982i	0.193649	−	0.335410i
$528$	3.75230	+	6.49918i	0.163298	+	0.282841i
$529$	−8.20494	−	14.2114i	−0.356736	−	0.617886i
$530$	−16.1933	+	28.0476i	−0.703391	+	1.21831i
$531$	3.56142			0.154552
$532$	−0.494484	−	0.263394i	−0.0214386	−	0.0114196i
$533$		0			0
$534$	1.84625	−	3.19780i	0.0798951	−	0.138382i
$535$	23.9416	+	41.4680i	1.03508	+	1.79282i
$536$	0.998014	+	1.72861i	0.0431076	+	0.0746646i
$537$	0.945201	−	1.63714i	0.0407884	−	0.0706477i
$538$	4.68904			0.202159
$539$	−4.77371	+	9.75067i	−0.205618	+	0.419991i
$540$	−2.51619			−0.108279
$541$	−2.32062	+	4.01943i	−0.0997712	+	0.172809i	−0.911590	−	0.411101i	$-0.865144\pi$
$541$	−2.32062	+	4.01943i	−0.0997712	+	0.172809i	0.811819	+	0.583910i	$0.198478\pi$
$542$	−21.2569	−	36.8181i	−0.913064	−	1.58147i
$543$	1.27231	+	2.20371i	0.0546002	+	0.0945703i
$544$	−2.40858	+	4.17178i	−0.103267	+	0.178864i
$545$	17.9097			0.767167
$546$		0			0
$547$	−7.82685			−0.334652			−0.167326	−	0.985902i	$-0.553513\pi$
$547$	−7.82685			−0.334652			−0.167326	+	0.985902i	$0.553513\pi$
$548$	−0.644929	+	1.11705i	−0.0275500	+	0.0477180i
$549$	8.77857	+	15.2049i	0.374660	+	0.648931i
$550$	4.59822	+	7.96435i	0.196069	+	0.339601i
$551$	−7.14075	+	12.3681i	−0.304206	+	0.526901i
$552$	24.0865			1.02519
$553$	14.4073	−	8.98779i	0.612662	−	0.382200i
$554$	31.6345			1.34402
$555$	−15.5643	+	26.9581i	−0.660667	+	1.14431i
$556$	−0.709696	−	1.22923i	−0.0300978	−	0.0521309i
$557$	17.0230	+	29.4847i	0.721288	+	1.24931i	0.960484	+	0.278336i	$0.0897829\pi$
$557$	17.0230	+	29.4847i	0.721288	+	1.24931i	−0.239196	+	0.970971i	$0.576884\pi$
$558$	−1.32628	+	2.29718i	−0.0561457	+	0.0972473i
$559$		0			0
$560$	−1.01867	−	29.8073i	−0.0430465	−	1.25959i
$561$	11.8587			0.500675
$562$	3.61024	−	6.25312i	0.152289	−	0.263772i
$563$	2.06614	+	3.57865i	0.0870772	+	0.150822i	0.906274	−	0.422690i	$-0.138914\pi$
$563$	2.06614	+	3.57865i	0.0870772	+	0.150822i	−0.819197	+	0.573512i	$0.805581\pi$
$564$	0.501951	+	0.869405i	0.0211360	+	0.0366086i
$565$	9.76637	−	16.9159i	0.410874	−	0.711655i
$566$	13.3321			0.560390
$567$	−0.320133	−	9.36744i	−0.0134443	−	0.393396i
$568$	−1.70325			−0.0714666
$569$	−5.02290	+	8.69993i	−0.210571	+	0.364720i	−0.951893	−	0.306429i	$-0.900866\pi$
$569$	−5.02290	+	8.69993i	−0.210571	+	0.364720i	0.741322	+	0.671149i	$0.234199\pi$
$570$	−3.95065	−	6.84273i	−0.165474	−	0.286610i
$571$	−5.36802	−	9.29768i	−0.224645	−	0.389096i	0.731568	−	0.681768i	$-0.238789\pi$
$571$	−5.36802	−	9.29768i	−0.224645	−	0.389096i	−0.956213	+	0.292672i	$0.905455\pi$
$572$		0			0
$573$	−6.74558			−0.281801
$574$	−21.9239	+	13.6769i	−0.915086	+	0.570862i
$575$	27.3424			1.14026
$576$	5.42205	−	9.39126i	0.225919	−	0.391303i
$577$	21.2535	+	36.8122i	0.884795	+	1.53251i	0.845948	+	0.533265i	$0.179035\pi$
$577$	21.2535	+	36.8122i	0.884795	+	1.53251i	0.0388471	+	0.999245i	$0.487631\pi$
$578$	−11.5151	−	19.9447i	−0.478964	−	0.829590i
$579$	5.69114	−	9.85735i	0.236516	−	0.409657i
$580$	4.42879			0.183895
$581$	34.5344	+	18.3952i	1.43273	+	0.763163i
$582$	10.3475			0.428918
$583$	6.03116	−	10.4463i	0.249785	−	0.432641i
$584$	−6.31937	−	10.9455i	−0.261497	−	0.452927i
$585$		0			0
$586$	16.4861	−	28.5547i	0.681034	−	1.17959i
$587$	−18.8276			−0.777098			−0.388549	−	0.921428i	$-0.627024\pi$
$587$	−18.8276			−0.777098			−0.388549	+	0.921428i	$0.627024\pi$
$588$	−1.34349	+	0.0919352i	−0.0554046	+	0.00379134i
$589$	2.20637			0.0909117
$590$	5.81025	−	10.0636i	0.239204	−	0.414314i
$591$	11.3376	+	19.6373i	0.466367	+	0.807771i
$592$	−14.2840	−	24.7406i	−0.587068	−	1.01683i
$593$	4.22588	−	7.31943i	0.173536	−	0.300573i	−0.766118	−	0.642700i	$-0.777814\pi$
$593$	4.22588	−	7.31943i	0.173536	−	0.300573i	0.939654	+	0.342127i	$0.111147\pi$
$594$	−11.8546			−0.486400
$595$	−41.5957	−	22.1566i	−1.70526	−	0.908331i
$596$	0.0655614			0.00268550
$597$	−6.74301	+	11.6792i	−0.275973	+	0.477999i
$598$		0			0
$599$	−17.3762	−	30.0965i	−0.709972	−	1.22971i	−0.964867	−	0.262739i	$-0.915374\pi$
$599$	−17.3762	−	30.0965i	−0.709972	−	1.22971i	0.254895	−	0.966969i	$-0.417959\pi$
$600$	−8.35555	+	14.4722i	−0.341114	+	0.590826i
$601$	33.2606			1.35673			0.678364	−	0.734726i	$-0.262689\pi$
$601$	33.2606			1.35673			0.678364	+	0.734726i	$0.262689\pi$
$602$	15.3746	−	9.59121i	0.626622	−	0.390908i
$603$	−0.871689			−0.0354979
$604$	1.04595	−	1.81164i	0.0425592	−	0.0737148i
$605$	13.1440	+	22.7662i	0.534381	+	0.925576i
$606$	−15.0346	−	26.0407i	−0.610738	−	1.05783i
$607$	13.3494	−	23.1219i	0.541837	−	0.938489i	−0.456962	−	0.889486i	$-0.651062\pi$
$607$	13.3494	−	23.1219i	0.541837	−	0.938489i	0.998799	−	0.0490027i	$-0.0156043\pi$
$608$	−1.19541			−0.0484804
$609$	1.17244	+	34.3068i	0.0475096	+	1.39018i
$610$	57.2870			2.31948
$611$		0			0
$612$	−0.544512	−	0.943122i	−0.0220106	−	0.0381234i
$613$	−10.5403	−	18.2563i	−0.425719	−	0.737367i	0.570768	−	0.821111i	$-0.306645\pi$
$613$	−10.5403	−	18.2563i	−0.425719	−	0.737367i	−0.996487	+	0.0837442i	$0.973312\pi$
$614$	4.44270	−	7.69498i	0.179293	−	0.310544i
$615$	28.8089			1.16169
$616$	0.409569	+	11.9844i	0.0165020	+	0.482866i
$617$	6.37659			0.256712			0.128356	−	0.991728i	$-0.459030\pi$
$617$	6.37659			0.256712			0.128356	+	0.991728i	$0.459030\pi$
$618$	−0.476175	+	0.824759i	−0.0191546	+	0.0331767i
$619$	−19.5220	−	33.8131i	−0.784656	−	1.35906i	−0.929204	−	0.369566i	$-0.879506\pi$
$619$	−19.5220	−	33.8131i	−0.784656	−	1.35906i	0.144548	−	0.989498i	$-0.453827\pi$
$620$	−0.342104	−	0.592542i	−0.0137392	−	0.0237971i
$621$	−17.6227	+	30.5235i	−0.707176	+	1.22487i
$622$	−2.33230			−0.0935169
$623$	4.63722	−	2.89285i	0.185786	−	0.115900i
$624$		0			0
$625$	13.9036	−	24.0818i	0.556145	−	0.963272i
$626$	2.77661	+	4.80924i	0.110976	+	0.192216i
$627$	1.47141	+	2.54856i	0.0587626	+	0.101780i
$628$	0.510878	−	0.884866i	0.0203862	−	0.0353100i
$629$	−45.1428			−1.79996
$630$	12.4097	+	6.61022i	0.494415	+	0.263358i
$631$	11.7857			0.469181			0.234590	−	0.972094i	$-0.424625\pi$
$631$	11.7857			0.469181			0.234590	+	0.972094i	$0.424625\pi$
$632$	9.37802	−	16.2432i	0.373038	−	0.646120i
$633$	−18.2425	−	31.5969i	−0.725073	−	1.25586i
$634$	−0.338762	−	0.586753i	−0.0134540	−	0.0233029i
$635$	23.3621	−	40.4643i	0.927097	−	1.60578i
$636$	1.49620			0.0593281
$637$		0			0
$638$	20.8655			0.826073
$639$	0.371914	−	0.644173i	0.0147127	−	0.0254831i
$640$	−15.1615	−	26.2606i	−0.599312	−	1.03804i
$641$	−0.310443	−	0.537704i	−0.0122618	−	0.0212380i	0.859829	−	0.510581i	$-0.170570\pi$
$641$	−0.310443	−	0.537704i	−0.0122618	−	0.0212380i	−0.872091	+	0.489343i	$0.837236\pi$
$642$	−13.9912	+	24.2334i	−0.552188	+	0.956418i
$643$	−6.61337			−0.260806			−0.130403	−	0.991461i	$-0.541627\pi$
$643$	−6.61337			−0.260806			−0.130403	+	0.991461i	$0.541627\pi$
$644$	2.14795	+	1.14414i	0.0846410	+	0.0450853i
$645$	−20.2029			−0.795488
$646$	5.72925	−	9.92336i	0.225414	−	0.390429i
$647$	−3.22669	−	5.58879i	−0.126854	−	0.219718i	0.795602	−	0.605820i	$-0.207155\pi$
$647$	−3.22669	−	5.58879i	−0.126854	−	0.219718i	−0.922456	+	0.386102i	$0.873821\pi$
$648$	−5.17636	−	8.96572i	−0.203347	−	0.352207i
$649$	−2.16402	+	3.74819i	−0.0849452	+	0.147129i
$650$		0			0
$651$	4.49945	−	2.80691i	0.176347	−	0.110012i
$652$	3.31311			0.129752
$653$	2.26449	−	3.92221i	0.0886164	−	0.153488i	−0.818310	−	0.574777i	$-0.805089\pi$
$653$	2.26449	−	3.92221i	0.0886164	−	0.153488i	0.906927	+	0.421289i	$0.138422\pi$
$654$	5.23312	+	9.06403i	0.204631	+	0.354431i
$655$	13.1561	+	22.7871i	0.514052	+	0.890364i
$656$	−13.2196	+	22.8970i	−0.516137	+	0.893976i
$657$	5.51949			0.215336
$658$	−0.642007	−	18.7858i	−0.0250280	−	0.732347i
$659$	−27.2666			−1.06216			−0.531078	−	0.847323i	$-0.678213\pi$
$659$	−27.2666			−1.06216			−0.531078	+	0.847323i	$0.678213\pi$
$660$	0.456295	−	0.790326i	0.0177613	−	0.0307634i
$661$	1.94515	+	3.36910i	0.0756577	+	0.131043i	0.901372	−	0.433045i	$-0.142561\pi$
$661$	1.94515	+	3.36910i	0.0756577	+	0.131043i	−0.825714	+	0.564088i	$0.809228\pi$
$662$	−6.84413	−	11.8544i	−0.266005	−	0.460734i
$663$		0			0
$664$	43.2184			1.67720
$665$	−0.399456	−	11.6885i	−0.0154902	−	0.453261i
$666$	13.4680			0.521873
$667$	31.0181	−	53.7250i	1.20103	−	2.08024i
$668$	−0.398574	−	0.690351i	−0.0154213	−	0.0267105i
$669$	−13.3098	−	23.0533i	−0.514587	−	0.891290i
$670$	−1.42211	+	2.46317i	−0.0549409	+	0.0951605i
$671$	−21.3364			−0.823684
$672$	−2.43781	+	1.52079i	−0.0940406	+	0.0586657i
$673$	−4.18325			−0.161253			−0.0806263	−	0.996744i	$-0.525692\pi$
$673$	−4.18325			−0.161253			−0.0806263	+	0.996744i	$0.525692\pi$
$674$	13.9005	−	24.0764i	0.535428	−	0.927389i
$675$	−12.2266	−	21.1771i	−0.470602	−	0.815106i
$676$		0			0
$677$	−21.7827	+	37.7287i	−0.837175	+	1.45003i	0.0550716	+	0.998482i	$0.482461\pi$
$677$	−21.7827	+	37.7287i	−0.837175	+	1.45003i	−0.892247	+	0.451548i	$0.850872\pi$
$678$	11.4147			0.438380
$679$	13.5180	+	7.20058i	0.518774	+	0.276333i
$680$	−52.0554			−1.99623
$681$	−1.17841	+	2.04107i	−0.0451568	+	0.0782138i
$682$	−1.61177	−	2.79166i	−0.0617177	−	0.106898i
$683$	−7.39970	−	12.8167i	−0.283142	−	0.490416i	0.689015	−	0.724747i	$-0.258043\pi$
$683$	−7.39970	−	12.8167i	−0.283142	−	0.490416i	−0.972157	+	0.234331i	$0.924710\pi$
$684$	0.135125	−	0.234043i	0.00516662	−	0.00894884i
$685$	−26.9256			−1.02877
$686$	23.0111	+	10.3069i	0.878568	+	0.393518i
$687$	6.31806			0.241049
$688$	9.27051	−	16.0570i	0.353435	−	0.612167i
$689$		0			0
$690$	17.1609	+	29.7236i	0.653304	+	1.13156i
$691$	−2.36594	+	4.09793i	−0.0900047	+	0.155893i	−0.907513	−	0.420024i	$-0.862022\pi$
$691$	−2.36594	+	4.09793i	−0.0900047	+	0.155893i	0.817508	+	0.575917i	$0.195355\pi$
$692$	−2.73299			−0.103893
$693$	−4.62198	−	2.46197i	−0.175575	−	0.0935224i
$694$	−37.2578			−1.41429
$695$	14.8148	−	25.6600i	0.561957	−	0.973338i
$696$	18.9576	+	32.8355i	0.718586	+	1.24463i
$697$	20.8894	+	36.1816i	0.791244	+	1.37047i
$698$	−15.1166	+	26.1826i	−0.572170	+	0.991027i
$699$	−16.9076			−0.639505
$700$	−1.43257	+	0.893684i	−0.0541459	+	0.0337781i
$701$	36.8398			1.39142			0.695709	−	0.718324i	$-0.255090\pi$
$701$	36.8398			1.39142			0.695709	+	0.718324i	$0.255090\pi$
$702$		0			0
$703$	−5.60126	−	9.70166i	−0.211255	−	0.365905i
$704$	6.58918	+	11.4128i	0.248339	+	0.430136i
$705$	−10.4782	+	18.1487i	−0.394630	+	0.683519i
$706$	−37.9164			−1.42700
$707$	−1.52017	−	44.4817i	−0.0571718	−	1.67291i
$708$	−0.536846			−0.0201759
$709$	−8.53578	+	14.7844i	−0.320568	+	0.555240i	−0.980605	−	0.195993i	$-0.937207\pi$
$709$	−8.53578	+	14.7844i	−0.320568	+	0.555240i	0.660037	+	0.751233i	$0.270540\pi$
$710$	−1.21351	−	2.10187i	−0.0455423	−	0.0788816i
$711$	4.09549	+	7.09360i	0.153593	+	0.266031i
$712$	3.01846	−	5.22812i	0.113122	−	0.195932i
$713$	−9.58405			−0.358925
$714$	−0.940684	−	27.5254i	−0.0352042	−	1.03011i
$715$		0			0
$716$	0.105485	−	0.182706i	0.00394217	−	0.00682804i
$717$	−6.54602	−	11.3380i	−0.244466	−	0.423427i
$718$	14.1592	+	24.5244i	0.528415	+	0.915241i
$719$	−11.1245	+	19.2682i	−0.414874	+	0.718582i	−0.995415	−	0.0956486i	$-0.969508\pi$
$719$	−11.1245	+	19.2682i	−0.414874	+	0.718582i	0.580542	+	0.814231i	$0.302841\pi$
$720$	14.3864			0.536148
$721$	−1.19600	+	0.746109i	−0.0445415	+	0.0277865i
$722$	−23.0235			−0.856848
$723$	−15.4738	+	26.8013i	−0.575476	+	0.996753i
$724$	0.141991	+	0.245936i	0.00527707	+	0.00914015i
$725$	21.5202	+	37.2741i	0.799242	+	1.38433i
$726$	−7.68124	+	13.3043i	−0.285078	+	0.493769i
$727$	−47.9699			−1.77910			−0.889552	−	0.456833i	$-0.848984\pi$
$727$	−47.9699			−1.77910			−0.889552	+	0.456833i	$0.848984\pi$
$728$		0			0
$729$	26.6350			0.986481
$730$	9.00473	−	15.5966i	0.333280	−	0.577258i
$731$	−14.6492	−	25.3731i	−0.541819	−	0.938458i
$732$	−1.32328	−	2.29198i	−0.0489097	−	0.0847141i
$733$	−18.9978	+	32.9052i	−0.701701	+	1.21538i	0.266168	+	0.963927i	$0.414242\pi$
$733$	−18.9978	+	32.9052i	−0.701701	+	1.21538i	−0.967869	+	0.251455i	$0.919091\pi$
$734$	−21.4912			−0.793254
$735$	−15.6846	−	23.3282i	−0.578535	−	0.860475i
$736$	5.19266			0.191404
$737$	0.529663	−	0.917403i	0.0195104	−	0.0337930i
$738$	−6.23219	−	10.7945i	−0.229410	−	0.397350i
$739$	−17.2944	−	29.9547i	−0.636184	−	1.10190i	−0.986263	−	0.165182i	$-0.947179\pi$
$739$	−17.2944	−	29.9547i	−0.636184	−	1.10190i	0.350079	−	0.936720i	$-0.386155\pi$
$740$	−1.73699	+	3.00855i	−0.0638529	+	0.110597i
$741$		0			0
$742$	−24.7254	−	13.1704i	−0.907699	−	0.483500i
$743$	25.1252			0.921752			0.460876	−	0.887464i	$-0.347535\pi$
$743$	25.1252			0.921752			0.460876	+	0.887464i	$0.347535\pi$
$744$	2.92878	−	5.07280i	0.107374	−	0.185978i
$745$	0.684292	+	1.18523i	0.0250705	+	0.0434234i
$746$	−6.13321	−	10.6230i	−0.224553	−	0.388937i
$747$	−9.43699	+	16.3453i	−0.345281	+	0.598045i
$748$	1.32344			0.0483899
$749$	−35.1416	+	21.9225i	−1.28404	+	0.801031i
$750$	3.52384			0.128672
$751$	5.29843	−	9.17715i	0.193343	−	0.334879i	−0.753013	−	0.658005i	$-0.771400\pi$
$751$	5.29843	−	9.17715i	0.193343	−	0.334879i	0.946356	+	0.323126i	$0.104734\pi$
$752$	−9.61623	−	16.6558i	−0.350668	−	0.607375i
$753$	−8.27010	−	14.3242i	−0.301379	−	0.522004i
$754$		0			0
$755$	43.6682			1.58925
$756$	−0.0743388	−	2.17523i	−0.00270368	−	0.0791125i
$757$	20.4219			0.742248			0.371124	−	0.928583i	$-0.378972\pi$
$757$	20.4219			0.742248			0.371124	+	0.928583i	$0.378972\pi$
$758$	7.90621	−	13.6940i	0.287166	−	0.497387i
$759$	−6.39155	−	11.0705i	−0.231999	−	0.401833i
$760$	−6.45896	−	11.1873i	−0.234291	−	0.405804i
$761$	4.28522	−	7.42222i	0.155339	−	0.269055i	−0.777843	−	0.628458i	$-0.783686\pi$
$761$	4.28522	−	7.42222i	0.155339	−	0.269055i	0.933182	+	0.359403i	$0.117020\pi$
$762$	27.3051			0.989160
$763$	0.529128	+	15.4829i	0.0191557	+	0.560517i
$764$	−0.752813			−0.0272358
$765$	11.3666	−	19.6875i	0.410960	−	0.711804i
$766$	2.95179	+	5.11265i	0.106653	+	0.184728i
$767$		0			0
$768$	−2.29582	+	3.97647i	−0.0828432	+	0.143489i
$769$	−14.8952			−0.537133			−0.268567	−	0.963261i	$-0.586550\pi$
$769$	−14.8952			−0.537133			−0.268567	+	0.963261i	$0.586550\pi$
$770$	−14.4974	+	9.04397i	−0.522450	+	0.325922i
$771$	7.84264			0.282446
$772$	0.635137	−	1.10009i	0.0228591	−	0.0395931i
$773$	−24.6151	−	42.6347i	−0.885345	−	1.53346i	−0.845318	−	0.534264i	$-0.820589\pi$
$773$	−24.6151	−	42.6347i	−0.885345	−	1.53346i	−0.0400272	−	0.999199i	$-0.512744\pi$
$774$	4.37046	+	7.56985i	0.157093	+	0.272093i
$775$	3.32469	−	5.75853i	0.119426	−	0.206852i
$776$	16.9173			0.607295
$777$	−23.7650	−	12.6588i	−0.852565	−	0.454132i
$778$	9.28128			0.332750
$779$	−5.18387	+	8.97872i	−0.185731	+	0.321696i
$780$		0			0
$781$	0.451971	+	0.782836i	0.0161728	+	0.0280121i
$782$	−24.8868	+	43.1053i	−0.889951	+	1.54144i
$783$	−55.4810			−1.98273
$784$	25.7382	−	1.76127i	0.919221	−	0.0629024i
$785$	21.3290			0.761264
$786$	−7.68829	+	13.3165i	−0.274232	+	0.474984i
$787$	9.44253	+	16.3549i	0.336590	+	0.582991i	0.983789	−	0.179330i	$-0.0573931\pi$
$787$	9.44253	+	16.3549i	0.336590	+	0.582991i	−0.647199	+	0.762321i	$0.724060\pi$
$788$	1.26529	+	2.19154i	0.0450740	+	0.0780705i
$789$	19.2080	−	33.2693i	0.683824	−	1.18442i
$790$	26.7263			0.950877
$791$	14.9122	+	7.94322i	0.530218	+	0.282429i
$792$	−5.78423			−0.205534
$793$		0			0
$794$	−16.9004	−	29.2723i	−0.599771	−	1.03883i
$795$	15.6165	+	27.0485i	0.553859	+	0.959312i
$796$	−0.752526	+	1.30341i	−0.0266726	+	0.0461982i
$797$	11.8478			0.419672			0.209836	−	0.977737i	$-0.432707\pi$
$797$	11.8478			0.419672			0.209836	+	0.977737i	$0.432707\pi$
$798$	5.79879	−	3.61748i	0.205275	−	0.128058i
$799$	−30.3910			−1.07515
$800$	−1.80132	+	3.11998i	−0.0636863	+	0.110308i
$801$	1.31820	+	2.28318i	0.0465762	+	0.0806723i
$802$	−7.22993	−	12.5226i	−0.255298	−	0.442188i
$803$	−3.35380	+	5.80895i	−0.118353	+	0.204993i
$804$	0.131398			0.00463404
$805$	1.73516	+	50.7728i	0.0611565	+	1.78950i
$806$		0			0
$807$	2.26101	−	3.91618i	0.0795912	−	0.137856i
$808$	−24.5802	−	42.5742i	−0.864729	−	1.49775i
$809$	11.6811	+	20.2323i	0.410686	+	0.711328i	0.994965	−	0.100224i	$-0.0319561\pi$
$809$	11.6811	+	20.2323i	0.410686	+	0.711328i	−0.584279	+	0.811553i	$0.698623\pi$
$810$	7.37601	−	12.7756i	0.259167	−	0.448890i
$811$	17.8384			0.626390			0.313195	−	0.949689i	$-0.398601\pi$
$811$	17.8384			0.626390			0.313195	+	0.949689i	$0.398601\pi$
$812$	0.130845	+	3.82867i	0.00459176	+	0.134360i
$813$	−40.9995			−1.43792
$814$	−8.18353	+	14.1743i	−0.286832	+	0.496808i
$815$	34.5804	+	59.8950i	1.21130	+	2.09803i
$816$	−14.0900	−	24.4045i	−0.493247	−	0.854329i
$817$	3.63530	−	6.29652i	0.127183	−	0.220287i
$818$	−14.5262			−0.507898
$819$		0			0
$820$	3.21510			0.112276
$821$	−13.5030	+	23.3879i	−0.471258	+	0.816242i	−0.999459	−	0.0328765i	$-0.989533\pi$
$821$	−13.5030	+	23.3879i	−0.471258	+	0.816242i	0.528202	+	0.849119i	$0.322867\pi$
$822$	−7.86751	−	13.6269i	−0.274411	−	0.475294i
$823$	24.9256	+	43.1724i	0.868852	+	1.50490i	0.863171	+	0.504912i	$0.168475\pi$
$823$	24.9256	+	43.1724i	0.868852	+	1.50490i	0.00568103	+	0.999984i	$0.498192\pi$
$824$	−0.778504	+	1.34841i	−0.0271205	+	0.0469740i
$825$	8.86886			0.308774
$826$	8.87164	+	4.72561i	0.308684	+	0.164425i
$827$	29.2002			1.01539			0.507695	−	0.861537i	$-0.330498\pi$
$827$	29.2002			1.01539			0.507695	+	0.861537i	$0.330498\pi$
$828$	−0.586956	+	1.01664i	−0.0203981	+	0.0353306i
$829$	−7.69940	−	13.3357i	−0.267411	−	0.463170i	0.700781	−	0.713376i	$-0.252835\pi$
$829$	−7.69940	−	13.3357i	−0.267411	−	0.463170i	−0.968192	+	0.250206i	$0.919501\pi$
$830$	30.7918	+	53.3330i	1.06880	+	1.85122i
$831$	15.2538	−	26.4204i	0.529149	−	0.916513i
$832$		0			0
$833$	17.9253	−	36.6139i	0.621076	−	1.26860i
$834$	17.3152			0.599577
$835$	8.32018	−	14.4110i	0.287932	−	0.498712i
$836$	0.164211	+	0.284422i	0.00567936	+	0.00983694i
$837$	4.28566	+	7.42298i	0.148134	+	0.256576i
$838$	5.81968	−	10.0800i	0.201038	−	0.348207i
$839$	−29.6007			−1.02193			−0.510966	−	0.859601i	$-0.670712\pi$
$839$	−29.6007			−1.02193			−0.510966	+	0.859601i	$0.670712\pi$
$840$	−27.4041	−	14.5972i	−0.945530	−	0.503651i
$841$	68.6530			2.36735
$842$	0.356172	−	0.616908i	0.0122745	−	0.0212600i
$843$	−3.48164	−	6.03038i	−0.119914	−	0.207697i
$844$	−2.03588	−	3.52624i	−0.0700778	−	0.121378i
$845$		0			0
$846$	9.06689			0.311726
$847$	−19.2929	+	12.0356i	−0.662912	+	0.413547i
$848$	−28.6637			−0.984317
$849$	6.42861	−	11.1347i	0.220629	−	0.382141i
$850$	−17.2664	−	29.9063i	−0.592232	−	1.02578i
$851$	24.3308	+	42.1423i	0.834051	+	1.44462i
$852$	−0.0560620	+	0.0971023i	−0.00192065	+	0.00332667i
$853$	27.5135			0.942046			0.471023	−	0.882121i	$-0.343885\pi$
$853$	27.5135			0.942046			0.471023	+	0.882121i	$0.343885\pi$
$854$	1.69250	+	49.5243i	0.0579161	+	1.69469i
$855$	5.64141			0.192932
$856$	−22.8744	+	39.6196i	−0.781829	+	1.35417i
$857$	−6.69957	−	11.6040i	−0.228853	−	0.396385i	0.728616	−	0.684923i	$-0.240164\pi$
$857$	−6.69957	−	11.6040i	−0.228853	−	0.396385i	−0.957468	+	0.288538i	$0.906831\pi$
$858$		0			0
$859$	−22.2368	+	38.5153i	−0.758710	+	1.31412i	0.184799	+	0.982776i	$0.440837\pi$
$859$	−22.2368	+	38.5153i	−0.758710	+	1.31412i	−0.943509	+	0.331347i	$0.892497\pi$
$860$	−2.25466			−0.0768833
$861$	0.851137	+	24.9052i	0.0290067	+	0.848767i
$862$	−36.2821			−1.23577
$863$	13.7777	−	23.8637i	0.468998	−	0.812328i	−0.530374	−	0.847764i	$-0.677949\pi$
$863$	13.7777	−	23.8637i	0.468998	−	0.812328i	0.999372	+	0.0354356i	$0.0112818\pi$
$864$	−2.32198	−	4.02178i	−0.0789953	−	0.136824i
$865$	−28.5254	−	49.4075i	−0.969893	−	1.67990i
$866$	−9.01867	+	15.6208i	−0.306467	+	0.530816i
$867$	−22.2098			−0.754285
$868$	0.502143	−	0.313254i	0.0170438	−	0.0106325i
$869$	−9.95415			−0.337672
$870$	−27.0135	+	46.7887i	−0.915843	+	1.58629i
$871$		0			0
$872$	8.55569	+	14.8189i	0.289732	+	0.501831i
$873$	−3.69399	+	6.39817i	−0.125023	+	0.216545i
$874$	−12.3517			−0.417803
$875$	4.60355	+	2.45215i	0.155628	+	0.0828979i
$876$	−0.832004			−0.0281108
$877$	9.72172	−	16.8385i	0.328279	−	0.568596i	−0.653891	−	0.756588i	$-0.726865\pi$
$877$	9.72172	−	16.8385i	0.328279	−	0.568596i	0.982170	+	0.187992i	$0.0601980\pi$
$878$	5.38345	+	9.32441i	0.181683	+	0.314684i
$879$	−15.8989	−	27.5376i	−0.536255	−	0.928821i
$880$	−8.74157	+	15.1408i	−0.294678	+	0.510397i
$881$	5.21331			0.175641			0.0878205	−	0.996136i	$-0.472010\pi$
$881$	5.21331			0.175641			0.0878205	+	0.996136i	$0.472010\pi$
$882$	−5.34788	+	10.9234i	−0.180072	+	0.367812i
$883$	−25.9305			−0.872632			−0.436316	−	0.899793i	$-0.643717\pi$
$883$	−25.9305			−0.872632			−0.436316	+	0.899793i	$0.643717\pi$
$884$		0			0
$885$	−5.60329	−	9.70518i	−0.188352	−	0.326236i
$886$	−0.505028	−	0.874734i	−0.0169667	−	0.0293873i
$887$	−9.76469	+	16.9129i	−0.327866	+	0.567881i	−0.982088	−	0.188422i	$-0.939663\pi$
$887$	−9.76469	+	16.9129i	−0.327866	+	0.567881i	0.654222	+	0.756303i	$0.272996\pi$
$888$	−29.7410			−0.998042
$889$	35.6715	+	19.0009i	1.19638	+	0.637271i
$890$	8.60225			0.288348
$891$	−2.74718	+	4.75826i	−0.0920341	+	0.159408i
$892$	−1.48539	−	2.57276i	−0.0497344	−	0.0861425i
$893$	−3.77087	−	6.53134i	−0.126187	−	0.218563i
$894$	−0.399893	+	0.692635i	−0.0133744	+	0.0231652i
$895$	4.40398			0.147209
$896$	22.2542	−	13.8829i	0.743461	−	0.463796i
$897$		0			0
$898$	−17.7857	+	30.8057i	−0.593516	+	1.02800i
$899$	−7.54326	−	13.0653i	−0.251582	−	0.435753i
$900$	−0.407228	−	0.705340i	−0.0135743	−	0.0235113i
$901$	−22.6471	+	39.2259i	−0.754484	+	1.30680i
$902$	15.1474			0.504354
$903$	−0.596879	−	17.4653i	−0.0198629	−	0.581209i
$904$	18.6621			0.620691
$905$	−2.96405	+	5.13388i	−0.0985283	+	0.170656i
$906$	12.7596	+	22.1003i	0.423910	+	0.734234i
$907$	13.9404	+	24.1455i	0.462883	+	0.801737i	0.999103	−	0.0423414i	$-0.0134817\pi$
$907$	13.9404	+	24.1455i	0.462883	+	0.801737i	−0.536220	+	0.844078i	$0.680148\pi$
$908$	−0.131512	+	0.227785i	−0.00436437	+	0.00755931i
$909$	21.4689			0.712079
$910$		0			0
$911$	26.1656			0.866906			0.433453	−	0.901176i	$-0.357295\pi$
$911$	26.1656			0.866906			0.433453	+	0.901176i	$0.357295\pi$
$912$	3.49653	−	6.05616i	0.115782	−	0.200540i
$913$	−11.4684	−	19.8638i	−0.379548	−	0.657396i
$914$	−2.01372	−	3.48787i	−0.0666080	−	0.115368i
$915$	27.6232	−	47.8448i	0.913195	−	1.58170i
$916$	0.705101			0.0232972
$917$	−19.3106	+	12.0466i	−0.637693	+	0.397815i
$918$	44.5142			1.46919
$919$	13.6865	−	23.7057i	0.451476	−	0.781979i	−0.547002	−	0.837131i	$-0.684231\pi$
$919$	13.6865	−	23.7057i	0.451476	−	0.781979i	0.998478	+	0.0551523i	$0.0175644\pi$
$920$	28.0566	+	48.5954i	0.924997	+	1.60214i
$921$	−4.28445	−	7.42088i	−0.141177	−	0.244526i
$922$	−0.624201	+	1.08115i	−0.0205570	+	0.0356057i
$923$		0			0
$924$	0.696715	+	0.371116i	0.0229202	+	0.0122088i
$925$	−33.7613			−1.11006
$926$	6.92783	−	11.9994i	0.227663	−	0.394323i
$927$	−0.339982	−	0.588865i	−0.0111665	−	0.0193409i
$928$	4.08696	+	7.07881i	0.134161	+	0.232373i
$929$	−4.93003	+	8.53906i	−0.161749	+	0.280158i	−0.935496	−	0.353337i	$-0.885047\pi$
$929$	−4.93003	+	8.53906i	−0.161749	+	0.280158i	0.773747	+	0.633495i	$0.218380\pi$
$930$	8.34668			0.273699
$931$	10.0929	−	0.690656i	0.330780	−	0.0226353i
$932$	−1.88691			−0.0618077
$933$	−1.12461	+	1.94789i	−0.0368182	+	0.0637710i
$934$	18.5615	+	32.1494i	0.607350	+	1.05196i
$935$	13.8133	+	23.9254i	0.451744	+	0.782444i
$936$		0			0
$937$	−48.2540			−1.57639			−0.788194	−	0.615426i	$-0.788984\pi$
$937$	−48.2540			−1.57639			−0.788194	+	0.615426i	$0.788984\pi$
$938$	−2.17141	−	1.15664i	−0.0708992	−	0.0377655i
$939$	5.35542			0.174767
$940$	−1.16937	+	2.02541i	−0.0381407	+	0.0660616i
$941$	1.21479	+	2.10407i	0.0396009	+	0.0685907i	0.885147	−	0.465312i	$-0.154058\pi$
$941$	1.21479	+	2.10407i	0.0396009	+	0.0685907i	−0.845546	+	0.533903i	$0.820725\pi$
$942$	6.23222	+	10.7945i	0.203057	+	0.351704i
$943$	22.5178	−	39.0019i	0.733279	−	1.27008i
$944$	10.2847			0.334740
$945$	38.5483	−	24.0477i	1.25398	−	0.782273i
$946$	−10.6225			−0.345366
$947$	−0.348209	+	0.603116i	−0.0113153	+	0.0195986i	−0.871628	−	0.490169i	$-0.836935\pi$
$947$	−0.348209	+	0.603116i	−0.0113153	+	0.0195986i	0.860312	+	0.509767i	$0.170269\pi$
$948$	−0.617352	−	1.06928i	−0.0200507	−	0.0347288i
$949$		0			0
$950$	4.28478	−	7.42146i	0.139017	−	0.240784i
$951$	−0.653391			−0.0211876
$952$	−1.53794	−	45.0017i	−0.0498448	−	1.45851i
$953$	34.9112			1.13088			0.565442	−	0.824788i	$-0.308706\pi$
$953$	34.9112			1.13088			0.565442	+	0.824788i	$0.308706\pi$
$954$	6.75657	−	11.7027i	0.218752	−	0.378889i
$955$	−7.85743	−	13.6095i	−0.254260	−	0.440392i
$956$	−0.730542	−	1.26534i	−0.0236274	−	0.0409239i
$957$	10.0611	−	17.4264i	0.325230	−	0.563315i
$958$	−45.5119			−1.47042
$959$	−0.795496	−	23.2771i	−0.0256879	−	0.751656i
$960$	−34.1227			−1.10131
$961$	14.3346	−	24.8283i	0.462407	−	0.800913i
$962$		0			0
$963$	−9.98950	−	17.3023i	−0.321907	−	0.557559i
$964$	−1.72689	+	2.99106i	−0.0556193	+	0.0963354i
$965$	26.5168			0.853605
$966$	−25.1889	+	15.7137i	−0.810439	+	0.505580i
$967$	12.1384			0.390345			0.195172	−	0.980769i	$-0.437473\pi$
$967$	12.1384			0.390345			0.195172	+	0.980769i	$0.437473\pi$
$968$	−12.5582	+	21.7514i	−0.403634	+	0.699115i
$969$	−5.52518	−	9.56989i	−0.177494	−	0.307429i
$970$	12.0531	+	20.8765i	0.387000	+	0.670305i
$971$	16.5605	−	28.6836i	0.531451	−	0.920501i	−0.467875	−	0.883795i	$-0.654980\pi$
$971$	16.5605	−	28.6836i	0.531451	−	0.920501i	0.999326	−	0.0367060i	$-0.0116865\pi$
$972$	1.78641			0.0572990
$973$	22.6206	+	12.0492i	0.725184	+	0.386280i
$974$	−49.8728			−1.59803
$975$		0			0
$976$	25.3509	+	43.9091i	0.811464	+	1.40550i
$977$	−21.5958	−	37.4050i	−0.690911	−	1.19669i	−0.971540	−	0.236877i	$-0.923876\pi$
$977$	−21.5958	−	37.4050i	−0.690911	−	1.19669i	0.280629	−	0.959816i	$-0.409457\pi$
$978$	−20.2084	+	35.0020i	−0.646193	+	1.11924i
$979$	−3.20389			−0.102397
$980$	−1.75041	−	2.60345i	−0.0559150	−	0.0831643i
$981$	−7.47274			−0.238586
$982$	−8.92066	+	15.4510i	−0.284670	+	0.493062i
$983$	19.5920	+	33.9343i	0.624887	+	1.08234i	0.988563	+	0.150810i	$0.0481881\pi$
$983$	19.5920	+	33.9343i	0.624887	+	1.08234i	−0.363676	+	0.931525i	$0.618479\pi$
$984$	13.7624	+	23.8371i	0.438729	+	0.759900i
$985$	−26.4127	+	45.7481i	−0.841578	+	1.45766i
$986$	−78.3502			−2.49518
$987$	−15.9990	−	8.52213i	−0.509255	−	0.271262i
$988$		0			0
$989$	−15.7911	+	27.3509i	−0.502127	+	0.869709i
$990$	−4.12109	−	7.13794i	−0.130977	−	0.226859i
$991$	−4.22865	−	7.32423i	−0.134327	−	0.232662i	0.791013	−	0.611799i	$-0.209554\pi$
$991$	−4.22865	−	7.32423i	−0.134327	−	0.232662i	−0.925340	+	0.379138i	$0.876221\pi$
$992$	0.631398	−	1.09361i	0.0200469	−	0.0347223i
$993$	−13.2007			−0.418911
$994$	1.78120	−	1.11117i	0.0564963	−	0.0352443i
$995$	−31.4177			−0.996009
$996$	1.42253	−	2.46389i	0.0450745	−	0.0780713i
$997$	14.8717	+	25.7585i	0.470990	+	0.815779i	0.999449	−	0.0331799i	$-0.0105634\pi$
$997$	14.8717	+	25.7585i	0.470990	+	0.815779i	−0.528459	+	0.848959i	$0.677230\pi$
$998$	−2.84123	−	4.92116i	−0.0899377	−	0.155777i
$999$	21.7598	−	37.6892i	0.688451	−	1.19243i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1183.2.e.k.170.7	✓	48
7.2	even	3		8281.2.a.cv.1.18		24
7.4	even	3	inner	1183.2.e.k.508.7	yes	48
7.5	odd	6		8281.2.a.cw.1.18		24
13.12	even	2		1183.2.e.l.170.18	yes	48
91.12	odd	6		8281.2.a.ct.1.7		24
91.25	even	6		1183.2.e.l.508.18	yes	48
91.51	even	6		8281.2.a.cu.1.7		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1183.2.e.k.170.7	✓	48	1.1	even	1	trivial
1183.2.e.k.508.7	yes	48	7.4	even	3	inner
1183.2.e.l.170.18	yes	48	13.12	even	2
1183.2.e.l.508.18	yes	48	91.25	even	6
8281.2.a.ct.1.7		24	91.12	odd	6
8281.2.a.cu.1.7		24	91.51	even	6
8281.2.a.cv.1.18		24	7.2	even	3
8281.2.a.cw.1.18		24	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1183 = 7 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1183.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.680712 + 1.17903i) q^{2} +(0.656465 + 1.13703i) q^{3} +(0.0732621 + 0.126894i) q^{4} +(-1.52933 + 2.64889i) q^{5} -1.78745 q^{6} +(-2.33513 - 1.24384i) q^{7} -2.92233 q^{8} +(0.638108 - 1.10524i) q^{9} +(-2.08207 - 3.60626i) q^{10} +(0.775465 + 1.34315i) q^{11} +(-0.0961880 + 0.166602i) q^{12} +(3.05608 - 1.90649i) q^{14} -4.01582 q^{15} +(1.84274 - 3.19172i) q^{16} +(-2.91188 - 5.04353i) q^{17} +(0.868735 + 1.50469i) q^{18} +(0.722605 - 1.25159i) q^{19} -0.448169 q^{20} +(-0.118644 - 3.47166i) q^{21} -2.11147 q^{22} +(-3.13886 + 5.43667i) q^{23} +(-1.91841 - 3.32278i) q^{24} +(-2.17773 - 3.77194i) q^{25} +5.61437 q^{27} +(-0.0132408 - 0.387440i) q^{28} -9.88196 q^{29} +(2.73362 - 4.73476i) q^{30} +(0.763337 + 1.32214i) q^{31} +(-0.413578 - 0.716337i) q^{32} +(-1.01813 + 1.76345i) q^{33} +7.92861 q^{34} +(6.86600 - 4.28325i) q^{35} +0.186996 q^{36} +(3.87574 - 6.71298i) q^{37} +(0.983772 + 1.70394i) q^{38} +(4.46922 - 7.74092i) q^{40} -7.17386 q^{41} +(4.17395 + 2.22332i) q^{42} +5.03082 q^{43} +(-0.113624 + 0.196803i) q^{44} +(1.95176 + 3.38055i) q^{45} +(-4.27333 - 7.40162i) q^{46} +(2.60922 - 4.51930i) q^{47} +4.83878 q^{48} +(3.90570 + 5.80909i) q^{49} +5.92963 q^{50} +(3.82310 - 6.62180i) q^{51} +(-3.88874 - 6.73549i) q^{53} +(-3.82177 + 6.61950i) q^{54} -4.74378 q^{55} +(6.82403 + 3.63492i) q^{56} +1.89746 q^{57} +(6.72677 - 11.6511i) q^{58} +(1.39530 + 2.41674i) q^{59} +(-0.294207 - 0.509582i) q^{60} +(-6.87860 + 11.9141i) q^{61} -2.07845 q^{62} +(-2.86481 + 1.78717i) q^{63} +8.49707 q^{64} +(-1.38611 - 2.40081i) q^{66} +(-0.341513 - 0.591518i) q^{67} +(0.426661 - 0.738999i) q^{68} -8.24222 q^{69} +(0.376298 + 11.0109i) q^{70} +0.582838 q^{71} +(-1.86476 + 3.22986i) q^{72} +(2.16244 + 3.74546i) q^{73} +(5.27653 + 9.13921i) q^{74} +(2.85921 - 4.95229i) q^{75} +0.211758 q^{76} +(-0.140151 - 4.10098i) q^{77} +(-3.20909 + 5.55831i) q^{79} +(5.63634 + 9.76242i) q^{80} +(1.77131 + 3.06800i) q^{81} +(4.88333 - 8.45818i) q^{82} -14.7890 q^{83} +(0.431839 - 0.269396i) q^{84} +17.8130 q^{85} +(-3.42454 + 5.93148i) q^{86} +(-6.48716 - 11.2361i) q^{87} +(-2.26617 - 3.92511i) q^{88} +(-1.03289 + 1.78903i) q^{89} -5.31435 q^{90} -0.919839 q^{92} +(-1.00221 + 1.73588i) q^{93} +(3.55226 + 6.15269i) q^{94} +(2.21021 + 3.82820i) q^{95} +(0.542998 - 0.940501i) q^{96} -5.78897 q^{97} +(-9.50773 + 0.650615i) q^{98} +1.97932 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - q^{2} - 23 q^{4} + 13 q^{5} - 28 q^{6} - 3 q^{7} - 26 q^{9} - 5 q^{10} - q^{11} - 5 q^{12} - 2 q^{14} - 10 q^{15} - 17 q^{16} + 5 q^{17} + 24 q^{19} - 68 q^{20} + q^{21} - 28 q^{22} - 11 q^{23}+ \cdots + 78 q^{99}+O(q^{100}) \) 48 * q - q^2 - 23 * q^4 + 13 * q^5 - 28 * q^6 - 3 * q^7 - 26 * q^9 - 5 * q^10 - q^11 - 5 * q^12 - 2 * q^14 - 10 * q^15 - 17 * q^16 + 5 * q^17 + 24 * q^19 - 68 * q^20 + q^21 - 28 * q^22 - 11 * q^23 + 32 * q^24 - 33 * q^25 - 42 * q^27 + 15 * q^28 + 8 * q^29 + 22 * q^30 + 40 * q^31 - 6 * q^32 + 24 * q^33 - 72 * q^34 + 44 * q^35 - 30 * q^36 - 4 * q^37 + 29 * q^38 + 4 * q^40 - 98 * q^41 - 9 * q^42 + 26 * q^43 + 10 * q^44 + 58 * q^45 - 10 * q^46 + 62 * q^47 + 178 * q^48 + 31 * q^49 + 46 * q^50 + 21 * q^51 + 18 * q^53 + 12 * q^54 - 28 * q^55 - 56 * q^56 + 26 * q^57 + 56 * q^58 + 79 * q^59 + 22 * q^60 - 13 * q^61 + 24 * q^62 - 22 * q^63 + 36 * q^64 + 38 * q^66 - 2 * q^67 + 12 * q^68 - 56 * q^69 - 85 * q^70 + 38 * q^71 + 81 * q^72 + 17 * q^73 - 17 * q^74 - 24 * q^75 - 116 * q^76 - 30 * q^77 + 9 * q^79 + 63 * q^80 - 16 * q^81 + 22 * q^82 - 162 * q^83 - 203 * q^84 + 68 * q^85 + 22 * q^86 - 70 * q^87 + 33 * q^88 + 72 * q^89 + 2 * q^90 - 8 * q^92 + 19 * q^93 + 30 * q^94 - 13 * q^95 + 11 * q^96 - 90 * q^97 - 81 * q^98 + 78 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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