LMFDB - Embedded newform 798.2.cc.b.317.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [798,2,Mod(317,798)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(798, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 6, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("798.317"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	798.cc (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [162,0,0,0,0,0,0,81] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$162$
Relative dimension:	$27$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			317.1
Character	$\chi$	$=$	798.317
Dual form			798.2.cc.b.725.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.173648 - 0.984808i) q^{2} +(-1.66333 - 0.483049i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.727990 - 2.00013i) q^{5} +(-0.186877 + 1.72194i) q^{6} +(-2.16840 - 1.51592i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.53333 + 1.60694i) q^{9} +(-2.09616 - 0.369610i) q^{10} +(-1.00279 - 0.578960i) q^{11} +(1.72823 - 0.114974i) q^{12} +(-1.22956 - 3.37819i) q^{13} +(-1.11635 + 2.39870i) q^{14} +(-2.17705 + 2.97523i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.624353 - 1.71540i) q^{17} +(1.14262 - 2.77388i) q^{18} +(-3.48100 - 2.62348i) q^{19} +2.12850i q^{20} +(2.87450 + 3.56893i) q^{21} +(-0.396032 + 1.08809i) q^{22} +(-3.58489 + 4.27231i) q^{23} +(-0.413332 - 1.68201i) q^{24} +(0.359652 + 0.301784i) q^{25} +(-3.11336 + 1.79750i) q^{26} +(-3.43753 - 3.89659i) q^{27} +(2.55611 + 0.682865i) q^{28} +(1.36177 + 1.14266i) q^{29} +(3.30807 + 1.62733i) q^{30} +3.06379i q^{31} +(-0.766044 - 0.642788i) q^{32} +(1.38830 + 1.44740i) q^{33} +(-1.79775 - 0.316993i) q^{34} +(-4.61063 + 3.23352i) q^{35} +(-2.93015 - 0.643580i) q^{36} +(0.676418 + 0.390530i) q^{37} +(-1.97915 + 3.88368i) q^{38} +(0.413333 + 6.21299i) q^{39} +(2.09616 - 0.369610i) q^{40} +(-2.19799 - 0.800003i) q^{41} +(3.01555 - 3.45057i) q^{42} +(-0.664161 - 3.76664i) q^{43} +(1.14033 + 0.201071i) q^{44} +(5.05833 - 3.89716i) q^{45} +(4.82991 + 2.78855i) q^{46} +(3.91683 + 10.7614i) q^{47} +(-1.58468 + 0.699130i) q^{48} +(2.40395 + 6.57427i) q^{49} +(0.234746 - 0.406592i) q^{50} +(-1.86713 + 2.55168i) q^{51} +(2.31082 + 2.75393i) q^{52} +(-10.1857 + 3.70729i) q^{53} +(-3.24047 + 4.06194i) q^{54} +(-1.88802 + 1.58424i) q^{55} +(0.228627 - 2.63585i) q^{56} +(4.52278 + 6.04520i) q^{57} +(0.888831 - 1.53950i) q^{58} +(3.55294 + 1.29316i) q^{59} +(1.02817 - 3.54039i) q^{60} +(1.52040 + 1.27576i) q^{61} +(3.01725 - 0.532022i) q^{62} +(-3.05728 - 7.32482i) q^{63} +(-0.500000 + 0.866025i) q^{64} -7.65195 q^{65} +(1.18433 - 1.61855i) q^{66} +(-8.70664 - 1.53522i) q^{67} +1.82549i q^{68} +(8.02658 - 5.37457i) q^{69} +(3.98503 + 3.97909i) q^{70} +(1.47553 + 8.36813i) q^{71} +(-0.124987 + 2.99740i) q^{72} +(-0.456889 - 2.59115i) q^{73} +(0.267138 - 0.733957i) q^{74} +(-0.452443 - 0.675695i) q^{75} +(4.16835 + 1.27469i) q^{76} +(1.29679 + 2.77557i) q^{77} +(6.04682 - 1.48593i) q^{78} +(0.231591 + 0.275999i) q^{79} +(-0.727990 - 2.00013i) q^{80} +(3.83549 + 8.14181i) q^{81} +(-0.406172 + 2.30352i) q^{82} +(-3.88159 - 2.24104i) q^{83} +(-3.92179 - 2.37056i) q^{84} +(-2.97650 - 2.49758i) q^{85} +(-3.59409 + 1.30814i) q^{86} +(-1.71311 - 2.55842i) q^{87} -1.15792i q^{88} +(-0.768392 + 4.35777i) q^{89} +(-4.71632 - 4.30475i) q^{90} +(-2.45490 + 9.18921i) q^{91} +(1.90748 - 5.24076i) q^{92} +(1.47996 - 5.09610i) q^{93} +(9.91775 - 5.72602i) q^{94} +(-7.78144 + 5.05261i) q^{95} +(0.963686 + 1.43920i) q^{96} +(-7.43363 - 8.85906i) q^{97} +(6.05695 - 3.50904i) q^{98} +(-1.61004 - 3.07812i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 162 q + 81 q^{8} + 15 q^{13} - 9 q^{14} + 3 q^{15} - 12 q^{17} + 18 q^{18} - 36 q^{19} - 6 q^{22} + 12 q^{25} + 9 q^{27} - 12 q^{28} - 6 q^{29} - 12 q^{33} + 6 q^{34} + 12 q^{35} - 18 q^{37} - 9 q^{39}+ \cdots + 39 q^{99}+O(q^{100}) $ 162 * q + 81 * q^8 + 15 * q^13 - 9 * q^14 + 3 * q^15 - 12 * q^17 + 18 * q^18 - 36 * q^19 - 6 * q^22 + 12 * q^25 + 9 * q^27 - 12 * q^28 - 6 * q^29 - 12 * q^33 + 6 * q^34 + 12 * q^35 - 18 * q^37 - 9 * q^39 - 9 * q^43 - 6 * q^44 + 18 * q^45 - 18 * q^46 - 12 * q^47 + 24 * q^49 - 87 * q^50 + 24 * q^51 + 12 * q^52 + 36 * q^53 + 18 * q^54 - 18 * q^57 - 24 * q^59 - 27 * q^60 - 9 * q^61 - 36 * q^62 + 6 * q^63 - 81 * q^64 + 72 * q^65 + 12 * q^66 - 63 * q^67 - 9 * q^69 + 12 * q^70 - 12 * q^71 - 51 * q^73 + 42 * q^74 - 18 * q^78 + 21 * q^79 - 12 * q^81 + 3 * q^84 - 6 * q^85 - 36 * q^86 - 84 * q^87 + 54 * q^89 + 12 * q^90 + 75 * q^91 - 66 * q^93 + 72 * q^94 - 12 * q^97 - 12 * q^98 + 39 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/798\mathbb{Z}\right)^\times$.

$n$	$115$	$211$	$533$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{18}\right)$	$-1$

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 $

$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$2$	−0.173648	−	0.984808i	−0.122788	−	0.696364i
$3$	−1.66333	−	0.483049i	−0.960323	−	0.278889i
$3$	−1.66333	−	0.483049i	−0.960323	−	0.278889i
$4$	−0.939693	+	0.342020i	−0.469846	+	0.171010i
$5$	0.727990	−	2.00013i	0.325567	−	0.894487i	−0.663652	−	0.748042i	$-0.730994\pi$
$5$	0.727990	−	2.00013i	0.325567	−	0.894487i	0.989219	−	0.146446i	$-0.0467834\pi$
$6$	−0.186877	+	1.72194i	−0.0762920	+	0.702979i
$7$	−2.16840	−	1.51592i	−0.819580	−	0.572965i
$7$	−2.16840	−	1.51592i	−0.819580	−	0.572965i
$8$	0.500000	+	0.866025i	0.176777	+	0.306186i
$9$	2.53333	+	1.60694i	0.844442	+	0.535646i
$10$	−2.09616	−	0.369610i	−0.662865	−	0.116881i
$11$	−1.00279	−	0.578960i	−0.302352	−	0.174563i	0.341147	−	0.940010i	$-0.389185\pi$
$11$	−1.00279	−	0.578960i	−0.302352	−	0.174563i	−0.643499	+	0.765447i	$0.722518\pi$
$12$	1.72823	−	0.114974i	0.498897	−	0.0331902i
$13$	−1.22956	−	3.37819i	−0.341019	−	0.936943i	−0.985100	−	0.171985i	$-0.944982\pi$
$13$	−1.22956	−	3.37819i	−0.341019	−	0.936943i	0.644080	−	0.764958i	$-0.277240\pi$
$14$	−1.11635	+	2.39870i	−0.298358	+	0.641079i
$15$	−2.17705	+	2.97523i	−0.562112	+	0.768200i
$16$	0.766044	−	0.642788i	0.191511	−	0.160697i
$17$	0.624353	−	1.71540i	0.151428	−	0.416045i	−0.840664	−	0.541557i	$-0.817835\pi$
$17$	0.624353	−	1.71540i	0.151428	−	0.416045i	0.992092	+	0.125512i	$0.0400573\pi$
$18$	1.14262	−	2.77388i	0.269318	−	0.653810i
$19$	−3.48100	−	2.62348i	−0.798596	−	0.601867i
$19$	−3.48100	−	2.62348i	−0.798596	−	0.601867i
$20$			2.12850i			0.475947i
$21$	2.87450	+	3.56893i	0.627268	+	0.778803i
$22$	−0.396032	+	1.08809i	−0.0844344	+	0.231981i
$23$	−3.58489	+	4.27231i	−0.747501	+	0.890837i	−0.996989	−	0.0775407i	$-0.975293\pi$
$23$	−3.58489	+	4.27231i	−0.747501	+	0.890837i	0.249488	+	0.968378i	$0.419738\pi$
$24$	−0.413332	−	1.68201i	−0.0843710	−	0.343339i
$25$	0.359652	+	0.301784i	0.0719304	+	0.0603568i
$26$	−3.11336	+	1.79750i	−0.610580	+	0.352519i
$27$	−3.43753	−	3.89659i	−0.661552	−	0.749899i
$28$	2.55611	+	0.682865i	0.483059	+	0.129049i
$29$	1.36177	+	1.14266i	0.252874	+	0.212186i	0.760409	−	0.649445i	$-0.224999\pi$
$29$	1.36177	+	1.14266i	0.252874	+	0.212186i	−0.507535	+	0.861631i	$0.669443\pi$
$30$	3.30807	+	1.62733i	0.603968	+	0.297109i
$31$			3.06379i			0.550274i	0.961405	+	0.275137i	$0.0887232\pi$
$31$			3.06379i			0.550274i	−0.961405	+	0.275137i	$0.911277\pi$
$32$	−0.766044	−	0.642788i	−0.135419	−	0.113630i
$33$	1.38830	+	1.44740i	0.241672	+	0.251960i
$34$	−1.79775	−	0.316993i	−0.308312	−	0.0543638i
$35$	−4.61063	+	3.23352i	−0.779338	+	0.546565i
$36$	−2.93015	−	0.643580i	−0.488359	−	0.107263i
$37$	0.676418	+	0.390530i	0.111202	+	0.0642028i	0.554570	−	0.832137i	$-0.312883\pi$
$37$	0.676418	+	0.390530i	0.111202	+	0.0642028i	−0.443367	+	0.896340i	$0.646216\pi$
$38$	−1.97915	+	3.88368i	−0.321061	+	0.630016i
$39$	0.413333	+	6.21299i	0.0661862	+	0.994874i
$40$	2.09616	−	0.369610i	0.331432	−	0.0584405i
$41$	−2.19799	−	0.800003i	−0.343269	−	0.124940i	0.164632	−	0.986355i	$-0.447356\pi$
$41$	−2.19799	−	0.800003i	−0.343269	−	0.124940i	−0.507901	+	0.861415i	$0.669578\pi$
$42$	3.01555	−	3.45057i	0.465310	−	0.532435i
$43$	−0.664161	−	3.76664i	−0.101284	−	0.574408i	−0.992640	−	0.121104i	$-0.961356\pi$
$43$	−0.664161	−	3.76664i	−0.101284	−	0.574408i	0.891356	−	0.453304i	$-0.149755\pi$
$44$	1.14033	+	0.201071i	0.171911	+	0.0303126i
$45$	5.05833	−	3.89716i	0.754051	−	0.580954i
$46$	4.82991	+	2.78855i	0.712131	+	0.411149i
$47$	3.91683	+	10.7614i	0.571328	+	1.56971i	0.802408	+	0.596775i	$0.203552\pi$
$47$	3.91683	+	10.7614i	0.571328	+	1.56971i	−0.231081	+	0.972935i	$0.574226\pi$
$48$	−1.58468	+	0.699130i	−0.228729	+	0.100911i
$49$	2.40395	+	6.57427i	0.343421	+	0.939181i
$50$	0.234746	−	0.406592i	0.0331981	−	0.0575008i
$51$	−1.86713	+	2.55168i	−0.261450	+	0.357306i
$52$	2.31082	+	2.75393i	0.320453	+	0.381901i
$53$	−10.1857	+	3.70729i	−1.39911	+	0.509235i	−0.927915	−	0.372792i	$-0.878400\pi$
$53$	−10.1857	+	3.70729i	−1.39911	+	0.509235i	−0.471198	+	0.882028i	$0.656178\pi$
$54$	−3.24047	+	4.06194i	−0.440972	+	0.552760i
$55$	−1.88802	+	1.58424i	−0.254580	+	0.213618i
$56$	0.228627	−	2.63585i	0.0305515	−	0.352231i
$57$	4.52278	+	6.04520i	0.599057	+	0.800706i
$58$	0.888831	−	1.53950i	0.116709	−	0.202146i
$59$	3.55294	+	1.29316i	0.462553	+	0.168356i	0.562776	−	0.826609i	$-0.309733\pi$
$59$	3.55294	+	1.29316i	0.462553	+	0.168356i	−0.100223	+	0.994965i	$0.531956\pi$
$60$	1.02817	−	3.54039i	0.132736	−	0.457063i
$61$	1.52040	+	1.27576i	0.194667	+	0.163345i	0.734911	−	0.678163i	$-0.237224\pi$
$61$	1.52040	+	1.27576i	0.194667	+	0.163345i	−0.540244	+	0.841508i	$0.681668\pi$
$62$	3.01725	−	0.532022i	0.383191	−	0.0675669i
$63$	−3.05728	−	7.32482i	−0.385181	−	0.922841i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	−7.65195			−0.949108
$66$	1.18433	−	1.61855i	0.145781	−	0.199229i
$67$	−8.70664	−	1.53522i	−1.06369	−	0.187556i	−0.385694	−	0.922627i	$-0.626038\pi$
$67$	−8.70664	−	1.53522i	−1.06369	−	0.187556i	−0.677991	+	0.735070i	$0.737149\pi$
$68$			1.82549i			0.221373i
$69$	8.02658	−	5.37457i	0.966287	−	0.647022i
$70$	3.98503	+	3.97909i	0.476302	+	0.475592i
$71$	1.47553	+	8.36813i	0.175113	+	0.993114i	0.938014	+	0.346599i	$0.112663\pi$
$71$	1.47553	+	8.36813i	0.175113	+	0.993114i	−0.762901	+	0.646516i	$0.776225\pi$
$72$	−0.124987	+	2.99740i	−0.0147298	+	0.353246i
$73$	−0.456889	−	2.59115i	−0.0534748	−	0.303271i	0.946326	−	0.323213i	$-0.104763\pi$
$73$	−0.456889	−	2.59115i	−0.0534748	−	0.303271i	−0.999801	+	0.0199420i	$0.993652\pi$
$74$	0.267138	−	0.733957i	0.0310542	−	0.0853207i
$75$	−0.452443	−	0.675695i	−0.0522436	−	0.0780226i
$76$	4.16835	+	1.27469i	0.478143	+	0.146217i
$77$	1.29679	+	2.77557i	0.147783	+	0.316306i
$78$	6.04682	−	1.48593i	0.684668	−	0.168248i
$79$	0.231591	+	0.275999i	0.0260560	+	0.0310523i	0.778915	−	0.627129i	$-0.215770\pi$
$79$	0.231591	+	0.275999i	0.0260560	+	0.0310523i	−0.752859	+	0.658182i	$0.771326\pi$
$80$	−0.727990	−	2.00013i	−0.0813917	−	0.223622i
$81$	3.83549	+	8.14181i	0.426166	+	0.904645i
$82$	−0.406172	+	2.30352i	−0.0448542	+	0.254381i
$83$	−3.88159	−	2.24104i	−0.426060	−	0.245986i	0.271607	−	0.962408i	$-0.412445\pi$
$83$	−3.88159	−	2.24104i	−0.426060	−	0.245986i	−0.697667	+	0.716423i	$0.745778\pi$
$84$	−3.92179	−	2.37056i	−0.427903	−	0.258649i
$85$	−2.97650	−	2.49758i	−0.322847	−	0.270901i
$86$	−3.59409	+	1.30814i	−0.387561	+	0.141061i
$87$	−1.71311	−	2.55842i	−0.183664	−	0.274291i
$88$		−	1.15792i		−	0.123435i
$89$	−0.768392	+	4.35777i	−0.0814494	+	0.461923i	0.916617	+	0.399767i	$0.130909\pi$
$89$	−0.768392	+	4.35777i	−0.0814494	+	0.461923i	−0.998066	+	0.0621562i	$0.980202\pi$
$90$	−4.71632	−	4.30475i	−0.497144	−	0.453760i
$91$	−2.45490	+	9.18921i	−0.257343	+	0.963291i
$92$	1.90748	−	5.24076i	0.198869	−	0.546387i
$93$	1.47996	−	5.09610i	0.153465	−	0.528441i
$94$	9.91775	−	5.72602i	1.02294	−	0.590593i
$95$	−7.78144	+	5.05261i	−0.798359	+	0.518386i
$96$	0.963686	+	1.43920i	0.0983558	+	0.146888i
$97$	−7.43363	−	8.85906i	−0.754771	−	0.899501i	0.242734	−	0.970093i	$-0.421956\pi$
$97$	−7.43363	−	8.85906i	−0.754771	−	0.899501i	−0.997505	+	0.0705919i	$0.977511\pi$
$98$	6.05695	−	3.50904i	0.611844	−	0.354466i
$99$	−1.61004	−	3.07812i	−0.161815	−	0.309362i
$100$	−0.441179	−	0.160576i	−0.0441179	−	0.0160576i
$101$	−1.31888	+	1.57178i	−0.131233	+	0.156398i	−0.827659	−	0.561231i	$-0.810328\pi$
$101$	−1.31888	+	1.57178i	−0.131233	+	0.156398i	0.696426	+	0.717629i	$0.254772\pi$
$102$	2.83713	+	1.39567i	0.280918	+	0.138192i
$103$		−	16.7844i		−	1.65381i	−0.562339	−	0.826907i	$-0.690098\pi$
$103$		−	16.7844i		−	1.65381i	0.562339	−	0.826907i	$-0.309902\pi$
$104$	2.31082	−	2.75393i	0.226595	−	0.270045i
$105$	9.23094	−	3.15125i	0.900848	−	0.307531i
$106$	5.41969	+	9.38719i	0.526407	+	0.911764i
$107$	−0.0853864	−	0.147894i	−0.00825461	−	0.0142974i	0.861869	−	0.507132i	$-0.169294\pi$
$107$	−0.0853864	−	0.147894i	−0.00825461	−	0.0142974i	−0.870123	+	0.492834i	$0.835961\pi$
$108$	4.56293	+	2.48589i	0.439068	+	0.239205i
$109$	1.65021	+	1.96664i	0.158061	+	0.188370i	0.839263	−	0.543726i	$-0.182987\pi$
$109$	1.65021	+	1.96664i	0.158061	+	0.188370i	−0.681202	+	0.732096i	$0.738542\pi$
$110$	1.88802	+	1.58424i	0.180016	+	0.151051i
$111$	−0.936461	−	0.976323i	−0.0888849	−	0.0926685i
$112$	−2.63551	+	0.232558i	−0.249032	+	0.0219747i
$113$	3.50712			0.329922			0.164961	−	0.986300i	$-0.447250\pi$
$113$	3.50712			0.329922			0.164961	+	0.986300i	$0.447250\pi$
$114$	5.16799	−	5.50381i	0.484026	−	0.515479i
$115$	5.93542	+	10.2805i	0.553481	+	0.958657i
$116$	−1.67046	−	0.607996i	−0.155098	−	0.0564510i
$117$	2.31367	−	10.5339i	0.213899	−	0.973860i
$118$	0.656557	−	3.72352i	0.0604409	−	0.342778i
$119$	−3.95426	+	2.77320i	−0.362487	+	0.254219i
$120$	−3.66515	−	0.397766i	−0.334581	−	0.0363109i
$121$	−4.82961	−	8.36513i	−0.439055	−	0.760466i
$122$	0.992368	−	1.71883i	0.0898448	−	0.155616i
$123$	3.26954	+	2.39241i	0.294805	+	0.215716i
$124$	−1.04788	−	2.87902i	−0.0941023	−	0.258544i
$125$	10.0821	−	5.82090i	0.901771	−	0.520638i
$126$	−6.68265	+	4.28277i	−0.595338	+	0.381540i
$127$	−6.89948	−	18.9562i	−0.612230	−	1.68209i	−0.725241	−	0.688495i	$-0.758272\pi$
$127$	−6.89948	−	18.9562i	−0.612230	−	1.68209i	0.113011	−	0.993594i	$-0.463950\pi$
$128$	0.939693	+	0.342020i	0.0830579	+	0.0302306i
$129$	−0.714756	+	6.58599i	−0.0629307	+	0.579864i
$130$	1.32875	+	7.53570i	0.116539	+	0.660925i
$131$	3.47848	−	0.613350i	0.303916	−	0.0535886i	−0.0196104	−	0.999808i	$-0.506243\pi$
$131$	3.47848	−	0.613350i	0.303916	−	0.0535886i	0.323527	+	0.946219i	$0.395131\pi$
$132$	−1.79962	−	0.885282i	−0.156636	−	0.0770539i
$133$	3.57122	+	10.9657i	0.309664	+	0.950846i
$134$			8.84096i			0.763742i
$135$	−10.2962	+	4.03884i	−0.886155	+	0.347608i
$136$	1.79775	−	0.316993i	0.154156	−	0.0271819i
$137$	2.21363	+	6.08190i	0.189123	+	0.519612i	0.997625	−	0.0688824i	$-0.0219433\pi$
$137$	2.21363	+	6.08190i	0.189123	+	0.519612i	−0.808502	+	0.588494i	$0.799721\pi$
$138$	−6.68672	−	6.97136i	−0.569212	−	0.593441i
$139$	−20.9797	+	7.63600i	−1.77948	+	0.647677i	−0.779709	+	0.626142i	$0.784633\pi$
$139$	−20.9797	+	7.63600i	−1.77948	+	0.647677i	−0.999768	+	0.0215350i	$0.993145\pi$
$140$	3.22664	−	4.61545i	0.272701	−	0.390076i
$141$	−1.31669	−	19.7918i	−0.110885	−	1.66677i
$142$	7.98478	−	2.90622i	0.670068	−	0.243885i
$143$	−0.722850	+	4.09948i	−0.0604477	+	0.342816i
$144$	2.97356	−	0.397404i	0.247797	−	0.0331170i
$145$	3.27682	−	1.89188i	0.272125	−	0.157112i
$146$	−2.47244	+	0.899896i	−0.204621	+	0.0744759i
$147$	−0.822865	−	12.0964i	−0.0678688	−	0.997694i
$148$	−0.769194	−	0.135630i	−0.0632274	−	0.0111487i
$149$	−11.6555	−	13.8905i	−0.954857	−	1.13795i	−0.990351	−	0.138584i	$-0.955745\pi$
$149$	−11.6555	−	13.8905i	−0.954857	−	1.13795i	0.0354940	−	0.999370i	$-0.488700\pi$
$150$	−0.586864	+	0.562903i	−0.0479173	+	0.0459608i
$151$	0.0662402	−	0.0382438i	0.00539055	−	0.00311223i	−0.497302	−	0.867577i	$-0.665676\pi$
$151$	0.0662402	−	0.0382438i	0.00539055	−	0.00311223i	0.502693	+	0.864465i	$0.332343\pi$
$152$	0.531498	−	4.32637i	0.0431102	−	0.350915i
$153$	4.33823	−	3.34236i	0.350725	−	0.270214i
$154$	2.50822	−	1.75906i	0.202118	−	0.141749i
$155$	6.12800	+	2.23041i	0.492213	+	0.179151i
$156$	−2.51337	−	5.69693i	−0.201231	−	0.456119i
$157$	12.4649	−	10.4593i	0.994805	−	0.834741i	0.00854898	−	0.999963i	$-0.497279\pi$
$157$	12.4649	−	10.4593i	0.994805	−	0.834741i	0.986256	+	0.165223i	$0.0528343\pi$
$158$	0.231591	−	0.275999i	0.0184244	−	0.0219573i
$159$	18.7330	−	1.24625i	1.48562	−	0.0988341i
$160$	−1.84333	+	1.06425i	−0.145728	+	0.0841363i
$161$	14.2500	−	3.82966i	1.12306	−	0.301820i
$162$	7.35209	−	5.19103i	0.577635	−	0.407846i
$163$	6.80260			0.532821			0.266410	−	0.963860i	$-0.414162\pi$
$163$	6.80260			0.532821			0.266410	+	0.963860i	$0.414162\pi$
$164$	2.33905			0.182649
$165$	3.90566	−	1.72310i	0.304055	−	0.134143i
$166$	−1.53296	+	4.21177i	−0.118981	+	0.326897i
$167$	2.57680	−	14.6138i	0.199399	−	1.13085i	−0.706615	−	0.707598i	$-0.749779\pi$
$167$	2.57680	−	14.6138i	0.199399	−	1.13085i	0.906014	−	0.423248i	$-0.139110\pi$
$168$	−1.65353	+	4.27386i	−0.127573	+	0.329735i
$169$	0.0582040	−	0.0488390i	0.00447723	−	0.00375684i
$170$	−1.94277	+	3.36498i	−0.149004	+	0.258082i
$171$	−4.60274	−	12.2399i	−0.351981	−	0.936007i
$172$	1.91237	+	3.31233i	0.145817	+	0.252563i
$173$	−3.94634	−	22.3808i	−0.300035	−	1.70158i	−0.646003	−	0.763335i	$-0.723561\pi$
$173$	−3.94634	−	22.3808i	−0.300035	−	1.70158i	0.345968	−	0.938246i	$-0.387550\pi$
$174$	−2.22207	+	2.13135i	−0.168455	+	0.161577i
$175$	−0.322389	−	1.19959i	−0.0243704	−	0.0906808i
$176$	−1.14033	+	0.201071i	−0.0859556	+	0.0151563i
$177$	−5.28504	−	3.86720i	−0.397248	−	0.290677i
$178$	4.42500			0.331667
$179$	−2.41364	+	4.18054i	−0.180404	+	0.312468i	−0.942018	−	0.335562i	$-0.891074\pi$
$179$	−2.41364	+	4.18054i	−0.180404	+	0.312468i	0.761614	+	0.648030i	$0.224407\pi$
$180$	−3.42037	+	5.39218i	−0.254939	+	0.401910i
$181$	−9.07547	+	10.8157i	−0.674574	+	0.803926i	−0.989399	−	0.145224i	$-0.953610\pi$
$181$	−9.07547	+	10.8157i	−0.674574	+	0.803926i	0.314825	+	0.949150i	$0.398054\pi$
$182$	9.47590	+	0.821912i	0.702400	+	0.0609242i
$183$	−1.91266	−	2.85644i	−0.141388	−	0.211154i
$184$	−5.49237	−	0.968453i	−0.404903	−	0.0713953i
$185$	1.27354	−	1.06863i	0.0936324	−	0.0785669i
$186$	−5.27567	−	0.572551i	−0.386831	−	0.0419815i
$187$	−1.61924	+	1.35870i	−0.118411	+	0.0993583i
$188$	−7.36122	−	8.77277i	−0.536872	−	0.639820i
$189$	1.54701	+	13.6604i	0.112528	+	0.993649i
$190$	6.32708	+	6.78585i	0.459015	+	0.492297i
$191$	0.184819	+	0.106705i	0.0133730	+	0.00772091i	0.506672	−	0.862139i	$-0.330876\pi$
$191$	0.184819	+	0.106705i	0.0133730	+	0.00772091i	−0.493299	+	0.869860i	$0.664209\pi$
$192$	1.25000	−	1.19896i	0.0902108	−	0.0865275i
$193$	−22.6603	+	3.99563i	−1.63113	+	0.287612i	−0.912896	−	0.408193i	$-0.866159\pi$
$193$	−22.6603	+	3.99563i	−1.63113	+	0.287612i	−0.718231	+	0.695804i	$0.755048\pi$
$194$	−7.43363	+	8.85906i	−0.533704	+	0.636043i
$195$	12.7277	+	3.69627i	0.911451	+	0.264695i
$196$	−4.50751	−	5.35559i	−0.321965	−	0.382542i
$197$	4.99284	+	2.88262i	0.355725	+	0.205378i	0.667204	−	0.744875i	$-0.267491\pi$
$197$	4.99284	+	2.88262i	0.355725	+	0.205378i	−0.311479	+	0.950253i	$0.600824\pi$
$198$	−2.75177	+	2.12009i	−0.195560	+	0.150668i
$199$	3.12051	−	17.6973i	0.221207	−	1.25453i	−0.648598	−	0.761131i	$-0.724644\pi$
$199$	3.12051	−	17.6973i	0.221207	−	1.25453i	0.869805	−	0.493395i	$-0.164244\pi$
$200$	−0.0815265	+	0.462360i	−0.00576479	+	0.0326938i
$201$	13.7404	+	6.75931i	0.969175	+	0.476765i
$202$	1.77692	+	1.02590i	0.125024	+	0.0721824i
$203$	−1.22068	−	4.54208i	−0.0856749	−	0.318792i
$204$	0.881800	−	3.03639i	0.0617384	−	0.212590i
$205$	−3.20023	+	3.81388i	−0.223514	+	0.266373i
$206$	−16.5294	+	2.91458i	−1.15166	+	0.203068i
$207$	−15.9470	+	5.06245i	−1.10840	+	0.351864i
$208$	−3.11336	−	1.79750i	−0.215873	−	0.124634i
$209$	1.97182	+	4.64616i	0.136394	+	0.321381i
$210$	−4.70631	−	8.54349i	−0.324767	−	0.589557i
$211$	−14.9351	−	17.7990i	−1.02818	−	1.22533i	−0.973940	−	0.226806i	$-0.927172\pi$
$211$	−14.9351	−	17.7990i	−1.02818	−	1.22533i	−0.0542374	−	0.998528i	$-0.517273\pi$
$212$	8.30345	−	6.96742i	0.570283	−	0.478525i
$213$	1.58793	−	14.6317i	0.108803	−	1.00255i
$214$	−0.130820	+	0.109771i	−0.00894264	+	0.00750376i
$215$	−8.01730	−	1.41367i	−0.546775	−	0.0964112i
$216$	1.65578	−	4.92528i	0.112662	−	0.335123i
$217$	4.64448	−	6.64354i	0.315288	−	0.450993i
$218$	1.65021	−	1.96664i	0.111766	−	0.133198i
$219$	−0.491694	+	4.53063i	−0.0332256	+	0.306152i
$220$	1.23232	−	2.13443i	0.0830828	−	0.143904i
$221$	−6.56262			−0.441450
$222$	−0.798876	+	1.09177i	−0.0536171	+	0.0732748i
$223$	−22.2974	+	3.93164i	−1.49315	+	0.263282i	−0.859818	−	0.510601i	$-0.829423\pi$
$223$	−22.2974	+	3.93164i	−1.49315	+	0.263282i	−0.633329	+	0.773883i	$0.718312\pi$
$224$	0.686677	+	2.55509i	0.0458805	+	0.170719i
$225$	0.426168	+	1.34246i	0.0284112	+	0.0894971i
$226$	−0.609005	−	3.45384i	−0.0405104	−	0.229746i
$227$	12.4389	+	21.5448i	0.825597	+	1.42998i	0.901462	+	0.432858i	$0.142495\pi$
$227$	12.4389	+	21.5448i	0.825597	+	1.42998i	−0.0758650	+	0.997118i	$0.524172\pi$
$228$	−6.31760	−	4.13375i	−0.418394	−	0.273764i
$229$	1.25492	−	2.17359i	0.0829277	−	0.143635i	−0.821579	−	0.570095i	$-0.806906\pi$
$229$	1.25492	−	2.17359i	0.0829277	−	0.143635i	0.904506	+	0.426460i	$0.140240\pi$
$230$	9.09360	−	7.63043i	0.599614	−	0.503136i
$231$	−0.816253	−	5.24310i	−0.0537055	−	0.344971i
$232$	−0.308688	+	1.75065i	−0.0202663	+	0.114936i
$233$	−9.39731	+	25.8189i	−0.615638	+	1.69145i	0.101777	+	0.994807i	$0.467547\pi$
$233$	−9.39731	+	25.8189i	−0.615638	+	1.69145i	−0.717415	+	0.696646i	$0.754675\pi$
$234$	−10.7756	−	0.449328i	−0.704425	−	0.0293735i
$235$	24.3756			1.59009
$236$	−3.78096			−0.246119
$237$	−0.251890	−	0.570947i	−0.0163620	−	0.0370870i
$238$	3.41772	+	3.41263i	0.221538	+	0.221208i
$239$	4.02825	−	2.32571i	0.260566	−	0.150438i	−0.364027	−	0.931388i	$-0.618598\pi$
$239$	4.02825	−	2.32571i	0.260566	−	0.150438i	0.624593	+	0.780951i	$0.285265\pi$
$240$	0.244723	+	3.67854i	0.0157968	+	0.237449i
$241$	−12.2113	+	14.5529i	−0.786602	+	0.937436i	−0.999212	−	0.0397015i	$-0.987359\pi$
$241$	−12.2113	+	14.5529i	−0.786602	+	0.937436i	0.212610	+	0.977137i	$0.431804\pi$
$242$	−7.39939	+	6.20883i	−0.475651	+	0.399118i
$243$	−2.44679	−	15.3952i	−0.156962	−	0.987605i
$244$	−1.86504	−	0.678820i	−0.119397	−	0.0434570i
$245$	14.8995	−	0.0222254i	0.951893	−	0.00141993i
$246$	1.78831	−	3.63531i	0.114019	−	0.231779i
$247$	−4.58251	+	14.9852i	−0.291578	+	0.953487i
$248$	−2.65332	+	1.53190i	−0.168486	+	0.0972756i
$249$	5.37383	+	5.60258i	0.340553	+	0.355049i
$250$	−7.48321	−	8.91814i	−0.473280	−	0.564033i
$251$	−11.7118	−	2.06510i	−0.739239	−	0.130348i	−0.208666	−	0.977987i	$-0.566912\pi$
$251$	−11.7118	−	2.06510i	−0.739239	−	0.130348i	−0.530573	+	0.847639i	$0.678023\pi$
$252$	5.37814	+	5.83743i	0.338791	+	0.367724i
$253$	6.06838	−	2.20871i	0.381516	−	0.138860i
$254$	−17.4701	+	10.0864i	−1.09617	+	0.632875i
$255$	3.74445	+	5.59210i	0.234486	+	0.350191i
$256$	0.173648	−	0.984808i	0.0108530	−	0.0615505i
$257$	8.80441	−	3.20454i	0.549204	−	0.199894i	−0.0524887	−	0.998622i	$-0.516715\pi$
$257$	8.80441	−	3.20454i	0.549204	−	0.199894i	0.601693	+	0.798728i	$0.294493\pi$
$258$	6.61005	−	0.439748i	0.411524	−	0.0273775i
$259$	−0.874734	−	1.87223i	−0.0543533	−	0.116334i
$260$	7.19048	−	2.61712i	0.445935	−	0.162307i
$261$	1.61362	+	5.08301i	0.0998805	+	0.314630i
$262$	−1.20806	−	3.31913i	−0.0746344	−	0.205056i
$263$	−11.5775	+	2.04142i	−0.713899	+	0.125880i	−0.518790	−	0.854902i	$-0.673617\pi$
$263$	−11.5775	+	2.04142i	−0.713899	+	0.125880i	−0.195109	+	0.980782i	$0.562506\pi$
$264$	−0.559333	+	1.92600i	−0.0344245	+	0.118537i
$265$			23.0716i			1.41728i
$266$	10.1790	−	5.42114i	0.624112	−	0.332391i
$267$	3.38311	−	6.87723i	0.207043	−	0.420880i
$268$	8.70664	−	1.53522i	0.531843	−	0.0937782i
$269$	−2.50682	−	14.2169i	−0.152843	−	0.866818i	−0.960731	−	0.277481i	$-0.910500\pi$
$269$	−2.50682	−	14.2169i	−0.152843	−	0.866818i	0.807888	−	0.589337i	$-0.200611\pi$
$270$	5.76539	+	9.43843i	0.350871	+	0.574405i
$271$	26.5051	+	9.64705i	1.61007	+	0.586017i	0.981454	−	0.191700i	$-0.0614001\pi$
$271$	26.5051	+	9.64705i	1.61007	+	0.586017i	0.628614	+	0.777717i	$0.283622\pi$
$272$	−0.624353	−	1.71540i	−0.0378570	−	0.104011i
$273$	8.52214	−	14.0988i	0.515784	−	0.853301i
$274$	5.60511	−	3.23611i	0.338617	−	0.195501i
$275$	−0.185934	−	0.510850i	−0.0112122	−	0.0308054i
$276$	−5.70431	+	7.79570i	−0.343359	+	0.469246i
$277$	1.70343	−	2.95042i	0.102349	−	0.177274i	−0.810303	−	0.586011i	$-0.800697\pi$
$277$	1.70343	−	2.95042i	0.102349	−	0.177274i	0.912652	+	0.408737i	$0.134031\pi$
$278$	11.1631	+	19.3350i	0.669517	+	1.15964i
$279$	−4.92333	+	7.76159i	−0.294752	+	0.464674i
$280$	−5.10563	−	2.37616i	−0.305120	−	0.142003i
$281$	−3.24252	+	18.3893i	−0.193433	+	1.09701i	0.721200	+	0.692727i	$0.243591\pi$
$281$	−3.24252	+	18.3893i	−0.193433	+	1.09701i	−0.914633	+	0.404285i	$0.867520\pi$
$282$	−19.2624	+	4.73349i	−1.14706	+	0.281875i
$283$	2.10440	+	0.765940i	0.125094	+	0.0455304i	0.403809	−	0.914844i	$-0.367686\pi$
$283$	2.10440	+	0.765940i	0.125094	+	0.0455304i	−0.278715	+	0.960374i	$0.589908\pi$
$284$	−4.24861	−	7.35881i	−0.252109	−	0.436665i
$285$	15.3838	−	4.64533i	0.911255	−	0.275166i
$286$	4.16272			0.246147
$287$	3.55339	+	5.06672i	0.209750	+	0.299079i
$288$	−0.907720	−	2.85938i	−0.0534879	−	0.168490i
$289$	10.4700	+	8.78536i	0.615882	+	0.516786i
$290$	−2.43215	−	2.89852i	−0.142821	−	0.170207i
$291$	8.08521	+	18.3263i	0.473964	+	1.07431i
$292$	1.31556	+	2.27862i	0.0769873	+	0.133346i
$293$	−11.0218	−	19.0903i	−0.643899	−	1.11527i	−0.984555	−	0.175078i	$-0.943982\pi$
$293$	−11.0218	−	19.0903i	−0.643899	−	1.11527i	0.340655	−	0.940188i	$-0.389351\pi$
$294$	−11.7697	+	2.91088i	−0.686425	+	0.169766i
$295$	5.17300	−	6.16495i	0.301184	−	0.358937i
$296$			0.781060i			0.0453982i
$297$	1.19114	+	5.89765i	0.0691170	+	0.342216i
$298$	−11.6555	+	13.8905i	−0.675186	+	0.804655i
$299$	18.8405	+	6.85739i	1.08958	+	0.396573i
$300$	0.656259	+	0.480201i	0.0378891	+	0.0277244i
$301$	−4.26977	+	9.17442i	−0.246106	+	0.528805i
$302$	−0.0491653	−	0.0585929i	−0.00282914	−	0.00337164i
$303$	2.95297	−	1.97730i	0.169644	−	0.113593i
$304$	−4.35294	+	0.227844i	−0.249658	+	0.0130677i
$305$	3.65853	−	2.11225i	0.209487	−	0.120947i
$306$	−4.04491	−	3.69193i	−0.231232	−	0.211053i
$307$	5.11390	−	14.0503i	0.291865	−	0.801894i	−0.703928	−	0.710271i	$-0.748572\pi$
$307$	5.11390	−	14.0503i	0.291865	−	0.801894i	0.995794	−	0.0916228i	$-0.0292054\pi$
$308$	−2.16789	−	2.16466i	−0.123527	−	0.123343i
$309$	−8.10768	+	27.9179i	−0.461230	+	1.58820i
$310$	1.13241	−	6.42221i	0.0643165	−	0.364757i
$311$		−	3.35640i		−	0.190324i	−0.995462	−	0.0951621i	$-0.969663\pi$
$311$		−	3.35640i		−	0.190324i	0.995462	−	0.0951621i	$-0.0303369\pi$
$312$	−5.17394	+	3.46445i	−0.292917	+	0.196136i
$313$	13.5070	−	4.91613i	0.763459	−	0.277876i	0.0692012	−	0.997603i	$-0.477955\pi$
$313$	13.5070	−	4.91613i	0.763459	−	0.277876i	0.694258	+	0.719726i	$0.255733\pi$
$314$	−12.4649	−	10.4593i	−0.703434	−	0.590251i
$315$	−16.8763	+	0.782573i	−0.950872	+	0.0440930i
$316$	−0.312021	−	0.180145i	−0.0175526	−	0.0101340i
$317$	1.24627	−	7.06795i	0.0699975	−	0.396975i	−0.929599	−	0.368572i	$-0.879847\pi$
$317$	1.24627	−	7.06795i	0.0699975	−	0.396975i	0.999597	−	0.0284031i	$-0.00904220\pi$
$318$	−4.48026	−	18.2320i	−0.251241	−	1.02240i
$319$	−0.704011	−	1.93426i	−0.0394171	−	0.108297i
$320$	1.36817	+	1.63052i	0.0764832	+	0.0911491i
$321$	0.0705858	+	0.287241i	0.00393971	+	0.0160323i
$322$	−6.24597	−	13.3685i	−0.348074	−	0.744996i
$323$	−6.67368	+	4.33332i	−0.371333	+	0.241112i
$324$	−6.38884	−	6.33898i	−0.354936	−	0.352166i
$325$	0.577270	−	1.58604i	0.0320212	−	0.0879775i
$326$	−1.18126	−	6.69926i	−0.0654239	−	0.371037i
$327$	−1.79486	−	4.06831i	−0.0992558	−	0.224978i
$328$	−0.406172	−	2.30352i	−0.0224271	−	0.127190i
$329$	7.82019	−	29.2726i	0.431141	−	1.61385i
$330$	−2.37513	−	3.54711i	−0.130747	−	0.195262i
$331$			27.3623i			1.50397i	0.659183	+	0.751983i	$0.270902\pi$
$331$			27.3623i			1.50397i	−0.659183	+	0.751983i	$0.729098\pi$
$332$	4.41398	+	0.778304i	0.242249	+	0.0427150i
$333$	1.08603	+	2.07630i	0.0595141	+	0.113781i
$334$	−14.8392			−0.811965
$335$	−9.40898	+	16.2968i	−0.514068	+	0.890391i
$336$	4.49606	+	0.886261i	0.245280	+	0.0483495i
$337$	−2.21575	+	0.390696i	−0.120700	+	0.0212826i	−0.233672	−	0.972316i	$-0.575074\pi$
$337$	−2.21575	+	0.390696i	−0.120700	+	0.0212826i	0.112972	+	0.993598i	$0.463963\pi$
$338$	−0.0582040	−	0.0488390i	−0.00316588	−	0.00265649i
$339$	−5.83349	−	1.69411i	−0.316832	−	0.0920115i
$340$	3.65122	+	1.32894i	0.198015	+	0.0720716i
$341$	1.77382	−	3.07234i	0.0960575	−	0.166376i
$342$	−11.2547	+	6.65825i	−0.608583	+	0.360037i
$343$	4.75336	−	17.8999i	0.256657	−	0.966503i
$344$	2.92993	−	2.45850i	0.157971	−	0.132554i
$345$	−4.90660	−	19.9669i	−0.264162	−	1.07498i
$346$	−21.3555	+	7.77277i	−1.14808	+	0.417867i
$347$	−3.27129	−	3.89857i	−0.175612	−	0.209286i	0.671058	−	0.741405i	$-0.265840\pi$
$347$	−3.27129	−	3.89857i	−0.175612	−	0.209286i	−0.846670	+	0.532119i	$0.821396\pi$
$348$	2.48483	+	1.81821i	0.133201	+	0.0974663i
$349$	16.1361	−	27.9486i	0.863747	−	1.49605i	−0.00453819	−	0.999990i	$-0.501445\pi$
$349$	16.1361	−	27.9486i	0.863747	−	1.49605i	0.868286	−	0.496065i	$-0.165222\pi$
$350$	−1.12539	+	0.525799i	−0.0601545	+	0.0281051i
$351$	−8.93679	+	16.4037i	−0.477010	+	0.875566i
$352$	0.396032	+	1.08809i	0.0211086	+	0.0579954i
$353$	−4.07353	−	2.35186i	−0.216812	−	0.125177i	0.387661	−	0.921802i	$-0.373283\pi$
$353$	−4.07353	−	2.35186i	−0.216812	−	0.125177i	−0.604473	+	0.796625i	$0.706616\pi$
$354$	−2.89071	+	5.87629i	−0.153640	+	0.312321i
$355$	17.8116	+	3.14066i	0.945339	+	0.166689i
$356$	−0.768392	−	4.35777i	−0.0407247	−	0.230961i
$357$	7.91683	−	2.70264i	0.419003	−	0.143039i
$358$	4.53615	+	1.65102i	0.239743	+	0.0872594i
$359$	25.1222	−	4.42972i	1.32590	−	0.233792i	0.534539	−	0.845144i	$-0.320485\pi$
$359$	25.1222	−	4.42972i	1.32590	−	0.233792i	0.791359	+	0.611352i	$0.209374\pi$
$360$	5.90421	+	2.43206i	0.311179	+	0.128181i
$361$	5.23473	+	18.2647i	0.275512	+	0.961298i
$362$	12.2273	+	7.05946i	0.642655	+	0.371037i
$363$	3.99246	+	16.2469i	0.209550	+	0.852741i
$364$	−0.836046	−	9.47466i	−0.0438207	−	0.496607i
$365$	−5.51525	−	0.972488i	−0.288681	−	0.0509023i
$366$	−2.48091	+	2.37962i	−0.129680	+	0.124385i
$367$	19.3445	+	16.2319i	1.00977	+	0.847301i	0.988308	−	0.152469i	$-0.0487224\pi$
$367$	19.3445	+	16.2319i	1.00977	+	0.847301i	0.0214654	+	0.999770i	$0.493167\pi$
$368$			5.57710i			0.290726i
$369$	−4.28267	−	5.55871i	−0.222947	−	0.289375i
$370$	−1.27354	−	1.06863i	−0.0662081	−	0.0555552i
$371$	27.7067	+	7.40183i	1.43846	+	0.384284i
$372$	0.352258	+	5.29494i	0.0182637	+	0.274530i
$373$	4.49469	−	2.59501i	0.232726	−	0.134365i	−0.379103	−	0.925355i	$-0.623767\pi$
$373$	4.49469	−	2.59501i	0.232726	−	0.134365i	0.611829	+	0.790990i	$0.290434\pi$
$374$	1.61924	+	1.35870i	0.0837290	+	0.0702570i
$375$	−19.5816	+	4.81193i	−1.01119	+	0.248487i
$376$	−7.36122	+	8.77277i	−0.379626	+	0.452421i
$377$	2.18575	−	6.00529i	0.112572	−	0.309288i
$378$	13.1842	−	3.89561i	0.678124	−	0.200369i
$379$			18.4070i			0.945502i	0.881196	+	0.472751i	$0.156739\pi$
$379$			18.4070i			0.945502i	−0.881196	+	0.472751i	$0.843261\pi$
$380$	5.58407	−	7.40931i	0.286457	−	0.380089i
$381$	2.31935	+	34.8631i	0.118824	+	1.78609i
$382$	0.0729906	−	0.200540i	0.00373452	−	0.0102605i
$383$	−0.327328	+	0.274661i	−0.0167257	+	0.0140345i	−0.651112	−	0.758982i	$-0.725697\pi$
$383$	−0.327328	+	0.274661i	−0.0167257	+	0.0140345i	0.634386	+	0.773016i	$0.281253\pi$
$384$	−1.39781	−	1.02281i	−0.0713315	−	0.0521950i
$385$	6.49557	−	0.573171i	0.331045	−	0.0292115i
$386$	7.86985	+	21.6222i	0.400565	+	1.10054i
$387$	4.37023	−	10.6094i	0.222151	−	0.539306i
$388$	10.0153	+	5.78234i	0.508450	+	0.293554i
$389$	28.6615	+	5.05380i	1.45320	+	0.256238i	0.843813	−	0.536637i	$-0.180305\pi$
$389$	28.6615	+	5.05380i	1.45320	+	0.256238i	0.609385	+	0.792875i	$0.291417\pi$
$390$	1.42997	−	13.1762i	0.0724094	−	0.667203i
$391$	5.09046	+	8.81694i	0.257436	+	0.445892i
$392$	−4.49151	+	5.36902i	−0.226855	+	0.271176i
$393$	−6.08214	−	0.660074i	−0.306803	−	0.0332964i
$394$	1.97183	−	5.41755i	0.0993393	−	0.272932i
$395$	0.720630	−	0.262288i	0.0362588	−	0.0131971i
$396$	2.56572	+	2.34182i	0.128932	+	0.117681i
$397$	0.200305	+	1.13598i	0.0100530	+	0.0570134i	0.989422	−	0.145069i	$-0.0463403\pi$
$397$	0.200305	+	1.13598i	0.0100530	+	0.0570134i	−0.979369	+	0.202082i	$0.935229\pi$
$398$	−17.9703			−0.900769
$399$	−0.643152	−	19.9646i	−0.0321979	−	0.999482i
$400$	0.469492			0.0234746
$401$	−4.71219	−	26.7242i	−0.235316	−	1.33454i	−0.841948	−	0.539559i	$-0.818591\pi$
$401$	−4.71219	−	26.7242i	−0.235316	−	1.33454i	0.606632	−	0.794983i	$-0.292520\pi$
$402$	4.27062	−	14.7054i	0.212999	−	0.733440i
$403$	10.3501	−	3.76713i	0.515575	−	0.187654i
$404$	0.701760	−	1.92807i	0.0349139	−	0.0959251i
$405$	19.0769	−	1.74435i	0.947939	−	0.0866774i
$406$	−4.26111	+	1.99086i	−0.211475	+	0.0988046i
$407$	−0.452203	−	0.783239i	−0.0224149	−	0.0388237i
$408$	−3.14338	−	0.341141i	−0.155620	−	0.0168890i
$409$	−31.7393	−	5.59649i	−1.56941	−	0.276729i	−0.679779	−	0.733417i	$-0.737924\pi$
$409$	−31.7393	−	5.59649i	−1.56941	−	0.276729i	−0.889627	+	0.456689i	$0.849035\pi$
$410$	4.31166	+	2.48934i	0.212938	+	0.122940i
$411$	−0.744139	−	11.1855i	−0.0367057	−	0.551739i
$412$	5.74059	+	15.7722i	0.282819	+	0.777038i
$413$	−5.74387	−	8.19009i	−0.282637	−	0.403008i
$414$	7.75471	+	14.8257i	0.381123	+	0.728642i
$415$	−7.30813	+	6.13225i	−0.358742	+	0.301020i
$416$	−1.22956	+	3.37819i	−0.0602842	+	0.165630i
$417$	38.5848	−	2.56693i	1.88950	−	0.125703i
$418$	4.23317	−	2.74866i	0.207051	−	0.134441i
$419$		−	27.2303i		−	1.33029i	−0.746716	−	0.665143i	$-0.768371\pi$
$419$		−	27.2303i		−	1.33029i	0.746716	−	0.665143i	$-0.231629\pi$
$420$	−7.59645	+	6.11838i	−0.370669	+	0.298546i
$421$	−1.59493	+	4.38204i	−0.0777322	+	0.213568i	−0.972472	−	0.233021i	$-0.925139\pi$
$421$	−1.59493	+	4.38204i	−0.0777322	+	0.213568i	0.894740	+	0.446588i	$0.147361\pi$
$422$	−14.9351	+	17.7990i	−0.727031	+	0.866442i
$423$	−7.37030	+	33.5562i	−0.358356	+	1.63156i
$424$	−8.30345	−	6.96742i	−0.403251	−	0.338368i
$425$	0.742229	−	0.428526i	0.0360034	−	0.0207866i
$426$	−14.6852	+	0.976962i	−0.711498	+	0.0473340i
$427$	−1.36287	−	5.07118i	−0.0659540	−	0.245411i
$428$	0.130820	+	0.109771i	0.00632340	+	0.00530596i
$429$	3.18259	−	6.46962i	0.153657	−	0.312356i
$430$			8.14098i			0.392593i
$431$	−31.4856	−	26.4196i	−1.51661	−	1.27259i	−0.849449	−	0.527671i	$-0.823065\pi$
$431$	−31.4856	−	26.4196i	−1.51661	−	1.27259i	−0.667160	−	0.744915i	$-0.732490\pi$
$432$	−5.13798	−	0.775363i	−0.247201	−	0.0373047i
$433$	4.37944	+	0.772213i	0.210462	+	0.0371102i	0.277885	−	0.960614i	$-0.410367\pi$
$433$	4.37944	+	0.772213i	0.210462	+	0.0371102i	−0.0674228	+	0.997724i	$0.521478\pi$
$434$	−7.34912	−	3.42028i	−0.352769	−	0.164179i
$435$	−6.36431	+	1.56394i	−0.305145	+	0.0749854i
$436$	−2.22332	−	1.28364i	−0.106478	−	0.0614750i
$437$	23.6873	−	5.46702i	1.13312	−	0.261523i
$438$	4.54718	−	0.302511i	0.217273	−	0.0144545i
$439$	−15.9817	+	2.81801i	−0.762766	+	0.134496i	−0.541481	−	0.840713i	$-0.682136\pi$
$439$	−15.9817	+	2.81801i	−0.762766	+	0.134496i	−0.221285	+	0.975209i	$0.571025\pi$
$440$	−2.31600	−	0.842954i	−0.110411	−	0.0401863i
$441$	−4.47446	+	20.5178i	−0.213070	+	0.977037i
$442$	1.13959	+	6.46292i	0.0542047	+	0.307410i
$443$	1.05381	+	0.185816i	0.0500681	+	0.00882836i	0.198626	−	0.980075i	$-0.436352\pi$
$443$	1.05381	+	0.185816i	0.0500681	+	0.00882836i	−0.148558	+	0.988904i	$0.547463\pi$
$444$	1.21391	+	0.597155i	0.0576095	+	0.0283397i
$445$	8.15675	+	4.70930i	0.386667	+	0.223242i
$446$	7.74382	+	21.2760i	0.366681	+	1.00745i
$447$	12.6772	+	28.7347i	0.599609	+	1.35910i
$448$	2.39703	−	1.11993i	0.113249	−	0.0529118i
$449$	−17.9875	+	31.1553i	−0.848883	+	1.47031i	0.0333225	+	0.999445i	$0.489391\pi$
$449$	−17.9875	+	31.1553i	−0.848883	+	1.47031i	−0.882206	+	0.470864i	$0.843942\pi$
$450$	1.24806	−	0.652808i	0.0588340	−	0.0307737i
$451$	1.74095	+	2.07478i	0.0819782	+	0.0976978i
$452$	−3.29561	+	1.19951i	−0.155013	+	0.0564200i
$453$	−0.128653	+	0.0316147i	−0.00604464	+	0.00148539i
$454$	19.0575	−	15.9911i	0.894411	−	0.750500i
$455$	16.5925	+	11.5998i	0.777869	+	0.543806i
$456$	−2.97391	+	6.93944i	−0.139266	+	0.324969i
$457$	7.55406	−	13.0840i	0.353364	−	0.612045i	−0.633472	−	0.773765i	$-0.718371\pi$
$457$	7.55406	−	13.0840i	0.353364	−	0.612045i	0.986837	+	0.161721i	$0.0517043\pi$
$458$	−2.35849	−	0.858419i	−0.110205	−	0.0401113i
$459$	−8.83043	+	3.46387i	−0.412169	+	0.161680i
$460$	−9.09360	−	7.63043i	−0.423991	−	0.355771i
$461$	−41.2507	+	7.27361i	−1.92124	+	0.338766i	−0.998869	−	0.0475461i	$-0.984860\pi$
$461$	−41.2507	+	7.27361i	−1.92124	+	0.338766i	−0.922368	+	0.386312i	$0.873749\pi$
$462$	−5.02171	+	1.71431i	−0.233631	+	0.0797568i
$463$	−18.7985	+	32.5599i	−0.873639	+	1.51319i	−0.0154327	+	0.999881i	$0.504913\pi$
$463$	−18.7985	+	32.5599i	−0.873639	+	1.51319i	−0.858206	+	0.513306i	$0.828421\pi$
$464$	1.77766			0.0825259
$465$	−9.11548	−	6.67003i	−0.422720	−	0.309315i
$466$	27.0585	+	4.77114i	1.25346	+	0.221019i
$467$			30.2200i			1.39841i	0.714919	+	0.699207i	$0.246463\pi$
$467$			30.2200i			1.39841i	−0.714919	+	0.699207i	$0.753537\pi$
$468$	1.42867	+	10.6900i	0.0660402	+	0.494143i
$469$	16.5522	+	16.5276i	0.764312	+	0.763172i
$470$	−4.23279	−	24.0053i	−0.195244	−	1.10728i
$471$	−25.7855	+	11.3761i	−1.18813	+	0.524181i
$472$	0.656557	+	3.72352i	0.0302205	+	0.171389i
$473$	−1.51472	+	4.16167i	−0.0696471	+	0.191354i
$474$	−0.518532	+	0.347207i	−0.0238170	+	0.0159478i
$475$	−0.460226	−	1.99405i	−0.0211166	−	0.0914932i
$476$	2.76730	−	3.95839i	0.126839	−	0.181433i
$477$	−31.7611	−	6.97602i	−1.45424	−	0.319410i
$478$	−2.98988	−	3.56320i	−0.136754	−	0.162977i
$479$	2.52967	+	6.95022i	0.115584	+	0.317564i	0.983973	−	0.178320i	$-0.0570663\pi$
$479$	2.52967	+	6.95022i	0.115584	+	0.317564i	−0.868389	+	0.495884i	$0.834844\pi$
$480$	3.58016	−	0.879776i	0.163411	−	0.0401561i
$481$	0.487589	−	2.76525i	0.0222321	−	0.126085i
$482$	16.4523	+	9.49874i	0.749382	+	0.432656i
$483$	−25.5523	−	0.513449i	−1.16267	−	0.0233627i
$484$	7.39939	+	6.20883i	0.336336	+	0.282219i
$485$	−23.1309	+	8.41896i	−1.05032	+	0.382285i
$486$	−14.7365	+	5.08297i	−0.668460	+	0.230568i
$487$		−	35.0898i		−	1.59007i	−0.606564	−	0.795035i	$-0.707453\pi$
$487$		−	35.0898i		−	1.59007i	0.606564	−	0.795035i	$-0.292547\pi$
$488$	−0.344646	+	1.95458i	−0.0156014	+	0.0884798i
$489$	−11.3150	−	3.28599i	−0.511680	−	0.148598i
$490$	−2.60915	−	14.6693i	−0.117870	−	0.662690i
$491$	8.19523	−	22.5162i	0.369845	−	1.01614i	−0.605575	−	0.795788i	$-0.707057\pi$
$491$	8.19523	−	22.5162i	0.369845	−	1.01614i	0.975420	−	0.220353i	$-0.0707211\pi$
$492$	−3.89061	−	1.12988i	−0.175402	−	0.0509388i
$493$	2.81034	−	1.62255i	0.126571	−	0.0730759i
$494$	15.5533	+	1.91073i	0.699777	+	0.0859680i
$495$	−7.32874	+	0.979456i	−0.329402	+	0.0440233i
$496$	1.96937	+	2.34700i	0.0884273	+	0.105384i
$497$	9.48591	−	20.3823i	0.425501	−	0.914270i
$498$	4.58431	−	6.26507i	0.205428	−	0.280744i
$499$	−5.68393	−	2.06878i	−0.254448	−	0.0926113i	0.211647	−	0.977346i	$-0.432117\pi$
$499$	−5.68393	−	2.06878i	−0.254448	−	0.0926113i	−0.466095	+	0.884735i	$0.654339\pi$
$500$	−7.48321	+	8.91814i	−0.334659	+	0.398831i
$501$	−11.3452	+	23.0628i	−0.506867	+	1.03037i
$502$			11.8924i			0.530785i
$503$	−20.2845	+	24.1741i	−0.904440	+	1.07787i	0.0921823	+	0.995742i	$0.470616\pi$
$503$	−20.2845	+	24.1741i	−0.904440	+	1.07787i	−0.996622	+	0.0821270i	$0.973829\pi$
$504$	4.81484	−	6.31009i	0.214470	−	0.281074i
$505$	2.18364	+	3.78217i	0.0971706	+	0.168304i
$506$	−3.22892	−	5.59265i	−0.143543	−	0.248624i
$507$	−0.120404	+	0.0531199i	−0.00534733	+	0.00235914i
$508$	12.9668	+	15.4532i	0.575308	+	0.685626i
$509$	6.14714	+	5.15806i	0.272467	+	0.228627i	0.768775	−	0.639520i	$-0.220867\pi$
$509$	6.14714	+	5.15806i	0.272467	+	0.228627i	−0.496308	+	0.868147i	$0.665311\pi$
$510$	4.85692	−	4.65862i	0.215068	−	0.206287i
$511$	−2.93726	+	6.31126i	−0.129937	+	0.279194i
$512$	−1.00000			−0.0441942
$513$	1.74341	+	22.5823i	0.0769735	+	0.997033i
$514$	−4.68473	−	8.11419i	−0.206635	−	0.357902i
$515$	−33.5710	−	12.2188i	−1.47932	−	0.538427i
$516$	−1.58089	−	6.43327i	−0.0695948	−	0.283209i
$517$	2.30267	−	13.0591i	0.101271	−	0.574338i
$518$	−1.69189	+	1.18655i	−0.0743372	+	0.0521341i
$519$	−4.24697	+	39.1329i	−0.186421	+	1.71774i
$520$	−3.82598	−	6.62678i	−0.167780	−	0.290604i
$521$	−13.6701	+	23.6774i	−0.598899	+	1.03732i	0.394084	+	0.919074i	$0.371062\pi$
$521$	−13.6701	+	23.6774i	−0.598899	+	1.03732i	−0.992984	+	0.118250i	$0.962272\pi$
$522$	4.72558	−	2.47176i	0.206833	−	0.108186i
$523$	−9.83352	−	27.0174i	−0.429990	−	1.18139i	−0.945819	−	0.324696i	$-0.894738\pi$
$523$	−9.83352	−	27.0174i	−0.429990	−	1.18139i	0.515829	−	0.856692i	$-0.327484\pi$
$524$	−3.05892	+	1.76607i	−0.133630	+	0.0771512i
$525$	−0.0432233	+	2.15105i	−0.00188642	+	0.0938795i
$526$	4.02082	+	11.0471i	0.175316	+	0.481677i
$527$	5.25562	+	1.91289i	0.228938	+	0.0833268i
$528$	1.99387	+	0.216388i	0.0867721	+	0.00941709i
$529$	−1.40725	−	7.98091i	−0.0611848	−	0.346996i
$530$	22.7211	−	4.00635i	0.986942	−	0.174025i
$531$	6.92272	+	8.98536i	0.300420	+	0.389932i
$532$	−7.10634	−	9.08295i	−0.308099	−	0.393796i
$533$			8.40889i			0.364230i
$534$	−7.36022	−	2.13749i	−0.318508	−	0.0924983i
$535$	−0.357967	+	0.0631193i	−0.0154763	+	0.00272889i
$536$	−3.02378	−	8.30778i	−0.130608	−	0.358841i
$537$	6.03408	−	5.78771i	0.260390	−	0.249758i
$538$	−13.5656	+	4.93747i	−0.584854	+	0.212869i
$539$	1.39559	−	7.98440i	0.0601122	−	0.343912i
$540$	8.29389	−	7.31677i	0.356912	−	0.314864i
$541$	−5.74998	+	2.09282i	−0.247211	+	0.0899774i	−0.462654	−	0.886539i	$-0.653103\pi$
$541$	−5.74998	+	2.09282i	−0.247211	+	0.0899774i	0.215443	+	0.976516i	$0.430880\pi$
$542$	4.89794	−	27.7776i	0.210384	−	1.19315i
$543$	20.3200	−	13.6062i	0.872015	−	0.583898i
$544$	−1.58092	+	0.912744i	−0.0677813	+	0.0391336i
$545$	5.13489	−	1.86895i	0.219954	−	0.0800568i
$546$	−15.3645	−	5.94443i	−0.657540	−	0.254398i
$547$	7.55832	+	1.33273i	0.323170	+	0.0569836i	0.332880	−	0.942969i	$-0.391980\pi$
$547$	7.55832	+	1.33273i	0.323170	+	0.0569836i	−0.00970968	+	0.999953i	$0.503091\pi$
$548$	−4.16026	−	4.95801i	−0.177718	−	0.211796i
$549$	1.80159	+	5.67511i	0.0768898	+	0.242208i
$550$	−0.470802	+	0.271817i	−0.0200751	+	0.0115903i
$551$	−1.74257	−	7.55016i	−0.0742362	−	0.321648i
$552$	8.66781	+	4.26394i	0.368926	+	0.181485i
$553$	−0.0837886	−	0.949551i	−0.00356305	−	0.0403790i
$554$	−3.20139	−	1.16521i	−0.136014	−	0.0495051i
$555$	−2.63451	+	1.16229i	−0.111829	+	0.0493366i
$556$	17.1028	−	14.3510i	0.725322	−	0.608617i
$557$	21.4918	−	25.6129i	0.910637	−	1.08526i	−0.0854025	−	0.996347i	$-0.527218\pi$
$557$	21.4918	−	25.6129i	0.910637	−	1.08526i	0.996040	−	0.0889087i	$-0.0283379\pi$
$558$	8.49860	+	3.50075i	0.359775	+	0.148199i
$559$	−11.9078	+	6.87499i	−0.503647	+	0.290781i
$560$	−1.45348	+	5.44068i	−0.0614206	+	0.229911i
$561$	3.34965	−	1.47780i	0.141422	−	0.0623928i
$562$	18.6730			0.787671
$563$	−0.0338512			−0.00142666			−0.000713328	−	1.00000i	$-0.500227\pi$
$563$	−0.0338512			−0.00142666			−0.000713328		1.00000i	$0.500227\pi$
$564$	8.00646	+	18.1478i	0.337133	+	0.764161i
$565$	2.55315	−	7.01471i	0.107412	−	0.295111i
$566$	0.388878	−	2.20544i	0.0163457	−	0.0927013i
$567$	4.02546	−	23.4690i	0.169054	−	0.985607i
$568$	−6.50925	+	5.46191i	−0.273122	+	0.229177i
$569$	16.3755	−	28.3632i	0.686497	−	1.18905i	−0.286466	−	0.958090i	$-0.592481\pi$
$569$	16.3755	−	28.3632i	0.686497	−	1.18905i	0.972964	−	0.230958i	$-0.0741860\pi$
$570$	−7.24612	−	14.3434i	−0.303506	−	0.600778i
$571$	3.79175	+	6.56751i	0.158680	+	0.274842i	0.934393	−	0.356244i	$-0.115943\pi$
$571$	3.79175	+	6.56751i	0.158680	+	0.274842i	−0.775713	+	0.631086i	$0.782610\pi$
$572$	−0.722850	−	4.09948i	−0.0302239	−	0.171408i
$573$	−0.255870	−	0.266762i	−0.0106891	−	0.0111441i
$574$	4.37270	−	4.37923i	0.182513	−	0.182786i
$575$	−2.57863	+	0.454681i	−0.107536	+	0.0189615i
$576$	−2.65831	+	1.39046i	−0.110763	+	0.0579357i
$577$	−35.9505			−1.49664			−0.748319	−	0.663339i	$-0.769139\pi$
$577$	−35.9505			−1.49664			−0.748319	+	0.663339i	$0.769139\pi$
$578$	6.83380	−	11.8365i	0.284249	−	0.492333i
$579$	39.6217	+	4.30001i	1.64662	+	0.178702i
$580$	−2.43215	+	2.89852i	−0.100989	+	0.120355i
$581$	5.01961	+	10.7437i	0.208249	+	0.445722i
$582$	16.6439	−	11.1447i	0.689913	−	0.461963i
$583$	12.3605	+	2.17948i	0.511918	+	0.0902650i
$584$	2.01555	−	1.69125i	0.0834042	−	0.0699845i
$585$	−19.3849	−	12.2962i	−0.801467	−	0.508386i
$586$	−16.8864	+	14.1693i	−0.697569	+	0.585330i
$587$	−8.44592	−	10.0655i	−0.348601	−	0.415446i	0.563043	−	0.826428i	$-0.309631\pi$
$587$	−8.44592	−	10.0655i	−0.348601	−	0.415446i	−0.911644	+	0.410982i	$0.865186\pi$
$588$	4.91045	+	11.0855i	0.202504	+	0.457157i
$589$	8.03779	−	10.6651i	0.331192	−	0.439446i
$590$	−6.96957	−	4.02388i	−0.286933	−	0.165661i
$591$	−6.91230	−	7.20653i	−0.284334	−	0.296437i
$592$	0.769194	−	0.135630i	0.0316137	−	0.00557435i
$593$	−23.7416	+	28.2941i	−0.974949	+	1.16190i	0.0118467	+	0.999930i	$0.496229\pi$
$593$	−23.7416	+	28.2941i	−0.974949	+	1.16190i	−0.986796	+	0.161969i	$0.948215\pi$
$594$	5.60121	−	2.19716i	0.229820	−	0.0901506i
$595$	2.66811	+	9.92792i	0.109382	+	0.407005i
$596$	15.7034	+	9.06638i	0.643237	+	0.371373i
$597$	−13.7391	+	27.9290i	−0.562303	+	1.14306i
$598$	3.48159	−	19.7451i	0.142373	−	0.807436i
$599$	6.60147	−	37.4388i	0.269729	−	1.52971i	−0.485494	−	0.874240i	$-0.661360\pi$
$599$	6.60147	−	37.4388i	0.269729	−	1.52971i	0.755223	−	0.655468i	$-0.227529\pi$
$600$	0.358948	−	0.729675i	0.0146540	−	0.0297889i
$601$	−22.2162	−	12.8265i	−0.906218	−	0.523205i	−0.0270058	−	0.999635i	$-0.508597\pi$
$601$	−22.2162	−	12.8265i	−0.906218	−	0.523205i	−0.879212	+	0.476430i	$0.841931\pi$
$602$	9.77648	+	2.61179i	0.398460	+	0.106448i
$603$	−19.5898	−	17.8802i	−0.797757	−	0.728140i
$604$	−0.0491653	+	0.0585929i	−0.00200051	+	0.00238411i
$605$	−20.2473	+	3.57014i	−0.823169	+	0.145147i
$606$	−2.46004	−	2.56476i	−0.0999322	−	0.104186i
$607$	−14.9316	−	8.62074i	−0.606054	−	0.349905i	0.165366	−	0.986232i	$-0.447120\pi$
$607$	−14.9316	−	8.62074i	−0.606054	−	0.349905i	−0.771419	+	0.636327i	$0.780453\pi$
$608$	0.980262	+	4.24724i	0.0397549	+	0.172249i
$609$	−0.163658	+	8.14462i	−0.00663177	+	0.330037i
$610$	−2.71546	−	3.23616i	−0.109946	−	0.131028i
$611$	31.5381	−	26.4636i	1.27589	−	1.07060i
$612$	−2.93345	+	4.62456i	−0.118578	+	0.186937i
$613$	−16.7312	+	14.0392i	−0.675768	+	0.567036i	−0.914766	−	0.403984i	$-0.867625\pi$
$613$	−16.7312	+	14.0392i	−0.675768	+	0.567036i	0.238999	+	0.971020i	$0.423181\pi$
$614$	−14.7249	−	2.59639i	−0.594248	−	0.104782i
$615$	7.16533	−	4.79788i	0.288934	−	0.193469i
$616$	−1.75532	+	2.51084i	−0.0707238	+	0.101165i
$617$	25.8350	−	30.7890i	1.04008	−	1.23952i	0.0697913	−	0.997562i	$-0.477767\pi$
$617$	25.8350	−	30.7890i	1.04008	−	1.23952i	0.970287	−	0.241956i	$-0.0777889\pi$
$618$	28.9017	+	3.13660i	1.16260	+	0.126173i
$619$	−8.66597	+	15.0099i	−0.348315	+	0.603299i	−0.985950	−	0.167039i	$-0.946579\pi$
$619$	−8.66597	+	15.0099i	−0.348315	+	0.603299i	0.637635	+	0.770338i	$0.279913\pi$
$620$	−6.52128			−0.261901
$621$	28.9706	−	0.717311i	1.16255	−	0.0287847i
$622$	−3.30541	+	0.582833i	−0.132535	+	0.0233695i
$623$	8.27223	−	8.28458i	0.331420	−	0.331915i
$624$	4.31026	+	4.49374i	0.172549	+	0.179894i
$625$	−3.89530	−	22.0913i	−0.155812	−	0.883653i
$626$	−7.18691	−	12.4481i	−0.287247	−	0.497526i
$627$	−1.03546	−	8.68057i	−0.0413524	−	0.346669i
$628$	−8.13587	+	14.0917i	−0.324657	+	0.562322i
$629$	1.09224	−	0.916497i	0.0435504	−	0.0365431i
$630$	3.70122	+	16.4840i	0.147460	+	0.656739i
$631$	8.56714	−	48.5867i	0.341053	−	1.93421i	−0.0153739	−	0.999882i	$-0.504894\pi$
$631$	8.56714	−	48.5867i	0.341053	−	1.93421i	0.356426	−	0.934323i	$-0.383995\pi$
$632$	−0.123227	+	0.338563i	−0.00490170	+	0.0134673i
$633$	16.2443	+	36.8200i	0.645651	+	1.46346i
$634$	−7.17698			−0.285034
$635$	−42.9377			−1.70393
$636$	−17.1770	+	7.57814i	−0.681112	+	0.300493i
$637$	19.2534	−	16.2045i	0.762846	−	0.642045i
$638$	−1.78262	+	1.02920i	−0.0705746	+	0.0407462i
$639$	−9.70909	+	23.5703i	−0.384086	+	0.932426i
$640$	1.36817	−	1.63052i	0.0540818	−	0.0644522i
$641$	−13.7249	+	11.5165i	−0.542100	+	0.454876i	−0.872255	−	0.489050i	$-0.837343\pi$
$641$	−13.7249	+	11.5165i	−0.542100	+	0.454876i	0.330155	+	0.943927i	$0.392899\pi$
$642$	0.270621	−	0.119392i	0.0106805	−	0.00471204i
$643$	3.21390	+	1.16976i	0.126744	+	0.0461310i	0.404613	−	0.914488i	$-0.367406\pi$
$643$	3.21390	+	1.16976i	0.126744	+	0.0461310i	−0.277870	+	0.960619i	$0.589628\pi$
$644$	−12.0808	+	8.47249i	−0.476049	+	0.333863i
$645$	12.6525	+	6.22414i	0.498193	+	0.245075i
$646$	5.42636	+	5.81982i	0.213497	+	0.228978i
$647$	31.2367	−	18.0345i	1.22804	−	0.709011i	0.261423	−	0.965224i	$-0.415808\pi$
$647$	31.2367	−	18.0345i	1.22804	−	0.709011i	0.966620	+	0.256213i	$0.0824749\pi$
$648$	−5.13327	+	7.39254i	−0.201654	+	0.290406i
$649$	−2.81416	−	3.35378i	−0.110465	−	0.131647i
$650$	−1.66218	−	0.293088i	−0.0651962	−	0.0114958i
$651$	−10.9345	+	8.80689i	−0.428555	+	0.345169i
$652$	−6.39235	+	2.32663i	−0.250344	+	0.0911177i
$653$	−18.3489	+	10.5938i	−0.718049	+	0.414566i	−0.814034	−	0.580817i	$-0.802733\pi$
$653$	−18.3489	+	10.5938i	−0.718049	+	0.414566i	0.0959849	+	0.995383i	$0.469400\pi$
$654$	−3.69483	+	2.47404i	−0.144479	+	0.0967427i
$655$	1.30551	−	7.40394i	0.0510107	−	0.289296i
$656$	−2.19799	+	0.800003i	−0.0858171	+	0.0312349i
$657$	3.00637	−	7.29841i	0.117290	−	0.284738i
$658$	−30.1859	−	2.61824i	−1.17677	−	0.102070i
$659$	34.0621	−	12.3976i	1.32687	−	0.482941i	0.421216	−	0.906960i	$-0.361603\pi$
$659$	34.0621	−	12.3976i	1.32687	−	0.482941i	0.905653	+	0.424019i	$0.139381\pi$
$660$	−3.08078	+	2.95500i	−0.119919	+	0.115023i
$661$	0.654392	+	1.79793i	0.0254529	+	0.0699312i	0.951768	−	0.306818i	$-0.0992642\pi$
$661$	0.654392	+	1.79793i	0.0254529	+	0.0699312i	−0.926315	+	0.376749i	$0.877042\pi$
$662$	26.9466	−	4.75140i	1.04731	−	0.184669i
$663$	10.9158	+	3.17007i	0.423935	+	0.123115i
$664$		−	4.48207i		−	0.173938i
$665$	24.5327	+	0.839979i	0.951336	+	0.0325730i
$666$	1.85617	−	1.43008i	0.0719252	−	0.0554144i
$667$	−9.76357	+	1.72158i	−0.378047	+	0.0666599i
$668$	2.57680	+	14.6138i	0.0996994	+	0.565423i
$669$	38.9872	+	4.23115i	1.50733	+	0.163586i
$670$	17.6831	+	6.43612i	0.683158	+	0.248649i
$671$	−0.786019	−	2.15957i	−0.0303439	−	0.0833693i
$672$	0.0920639	−	4.58165i	0.00355144	−	0.176741i
$673$	−6.60440	+	3.81305i	−0.254581	+	0.146982i	−0.621860	−	0.783128i	$-0.713623\pi$
$673$	−6.60440	+	3.81305i	−0.254581	+	0.146982i	0.367279	+	0.930111i	$0.380289\pi$
$674$	0.769521	+	2.11424i	0.0296409	+	0.0814376i
$675$	−0.0603848	−	2.43881i	−0.00232421	−	0.0938697i
$676$	−0.0379900	+	0.0658006i	−0.00146115	+	0.00253079i
$677$	18.8989	+	32.7339i	0.726344	+	1.25807i	0.958418	+	0.285367i	$0.0921156\pi$
$677$	18.8989	+	32.7339i	0.726344	+	1.25807i	−0.232074	+	0.972698i	$0.574551\pi$
$678$	−0.655398	+	6.03905i	−0.0251704	+	0.231928i
$679$	2.68946	+	30.4788i	0.103212	+	1.16967i
$680$	0.674718	−	3.82652i	0.0258743	−	0.146740i
$681$	−10.2828	−	41.8446i	−0.394036	−	1.60349i
$682$	−3.33368	−	1.21336i	−0.127653	−	0.0464620i
$683$	−10.2162	−	17.6950i	−0.390913	−	0.677081i	0.601658	−	0.798754i	$-0.294507\pi$
$683$	−10.2162	−	17.6950i	−0.390913	−	0.677081i	−0.992570	+	0.121674i	$0.961174\pi$
$684$	8.51145	+	9.92750i	0.325443	+	0.379587i
$685$	13.7761			0.526358
$686$	−18.4533	−	1.57286i	−0.704552	−	0.0600521i
$687$	−3.13730	+	3.00921i	−0.119696	+	0.114808i
$688$	−2.92993	−	2.45850i	−0.111702	−	0.0937295i
$689$	25.0479	+	29.8509i	0.954248	+	1.13723i
$690$	−18.8115	+	8.29927i	−0.716142	+	0.315948i
$691$	−3.82862	−	6.63136i	−0.145648	−	0.252269i	0.783967	−	0.620803i	$-0.213193\pi$
$691$	−3.82862	−	6.63136i	−0.145648	−	0.252269i	−0.929614	+	0.368534i	$0.879860\pi$
$692$	11.3630	+	19.6813i	0.431958	+	0.748173i
$693$	−1.17498	+	9.11529i	−0.0446337	+	0.346261i
$694$	−3.27129	+	3.89857i	−0.124176	+	0.147988i
$695$			47.5212i			1.80258i
$696$	1.35910	−	2.76280i	0.0515166	−	0.104724i
$697$	−2.74465	+	3.27094i	−0.103961	+	0.123896i
$698$	−30.3260	−	11.0378i	−1.14786	−	0.417786i
$699$	28.1026	−	38.4060i	1.06294	−	1.45265i
$700$	0.713232	+	1.01699i	0.0269577	+	0.0384385i
$701$	20.2591	+	24.1439i	0.765177	+	0.911902i	0.998163	−	0.0605779i	$-0.0192944\pi$
$701$	20.2591	+	24.1439i	0.765177	+	0.911902i	−0.232987	+	0.972480i	$0.574850\pi$
$702$	17.7064	+	5.95254i	0.668284	+	0.224664i
$703$	−1.33006	−	3.13400i	−0.0501643	−	0.118201i
$704$	1.00279	−	0.578960i	0.0377940	−	0.0218204i
$705$	−40.5447	−	11.7746i	−1.52700	−	0.443458i
$706$	−1.60876	+	4.42004i	−0.0605467	+	0.166351i
$707$	5.24255	−	1.40893i	0.197167	−	0.0529883i
$708$	6.28898	+	1.82639i	0.236354	+	0.0686399i
$709$	1.03196	−	5.85253i	0.0387560	−	0.219796i	−0.959279	−	0.282462i	$-0.908849\pi$
$709$	1.03196	−	5.85253i	0.0387560	−	0.219796i	0.998035	+	0.0626654i	$0.0199601\pi$
$710$		−	18.0863i		−	0.678768i
$711$	0.143181	+	1.07135i	0.00536971	+	0.0401787i
$712$	−4.15814	+	1.51344i	−0.155833	+	0.0567185i
$713$	−13.0895	−	10.9834i	−0.490204	−	0.411330i
$714$	−4.03633	−	7.32725i	−0.151056	−	0.274215i
$715$	7.67329	+	4.43018i	0.286965	+	0.165679i
$716$	0.838247	−	4.75394i	0.0313268	−	0.177663i
$717$	−7.82374	+	1.92258i	−0.292183	+	0.0718001i
$718$	−8.72484	−	23.9713i	−0.325608	−	0.894601i
$719$	−10.7892	−	12.8581i	−0.402370	−	0.479526i	0.526371	−	0.850255i	$-0.323552\pi$
$719$	−10.7892	−	12.8581i	−0.402370	−	0.479526i	−0.928741	+	0.370729i	$0.879108\pi$
$720$	1.36986	−	6.23683i	0.0510517	−	0.232433i
$721$	−25.4438	+	36.3953i	−0.947578	+	1.35543i
$722$	17.0782	−	8.32683i	0.635584	−	0.309892i
$723$	27.3413	−	18.3076i	1.01683	−	0.680867i
$724$	4.82895	−	13.2674i	0.179467	−	0.493081i
$725$	0.144927	+	0.821919i	0.00538244	+	0.0305253i
$726$	15.3068	−	6.75305i	0.568088	−	0.250629i
$727$	−4.74349	−	26.9017i	−0.175926	−	0.997727i	−0.937069	−	0.349143i	$-0.886473\pi$
$727$	−4.74349	−	26.9017i	−0.175926	−	0.997727i	0.761143	−	0.648584i	$-0.224638\pi$
$728$	−9.18554	+	2.46860i	−0.340439	+	0.0914925i
$729$	−3.36684	+	26.7893i	−0.124698	+	0.992195i
$730$			5.60033i			0.207278i
$731$	−6.87596	−	1.21242i	−0.254317	−	0.0448429i
$732$	2.77428	+	2.03001i	0.102540	+	0.0750312i
$733$	−15.1627			−0.560046			−0.280023	−	0.959993i	$-0.590342\pi$
$733$	−15.1627			−0.560046			−0.280023	+	0.959993i	$0.590342\pi$
$734$	12.6262	−	21.8692i	0.466042	−	0.807209i
$735$	−24.7935	−	7.16021i	−0.914521	−	0.264108i
$736$	5.49237	−	0.968453i	0.202451	−	0.0356977i
$737$	7.84209	+	6.58030i	0.288867	+	0.242388i
$738$	−4.73058	+	5.18287i	−0.174135	+	0.190784i
$739$	19.6443	+	7.14993i	0.722626	+	0.263014i	0.677040	−	0.735946i	$-0.263262\pi$
$739$	19.6443	+	7.14993i	0.722626	+	0.263014i	0.0455860	+	0.998960i	$0.485484\pi$
$740$	−0.831243	+	1.43976i	−0.0305571	+	0.0529265i
$741$	14.8608	−	22.7118i	0.545926	−	0.834338i
$742$	2.47817	−	28.5711i	0.0909765	−	1.04888i
$743$	37.5261	−	31.4881i	1.37670	−	1.15519i	0.406284	−	0.913747i	$-0.366824\pi$
$743$	37.5261	−	31.4881i	1.37670	−	1.15519i	0.970416	−	0.241441i	$-0.0776200\pi$
$744$	5.15333	−	1.26636i	0.188930	−	0.0464271i
$745$	−36.2680	+	13.2005i	−1.32876	+	0.483627i
$746$	−3.33608	−	3.97579i	−0.122143	−	0.145564i
$747$	−6.23212	−	11.9148i	−0.228021	−	0.435938i
$748$	1.05688	−	1.83058i	0.0386435	−	0.0669326i
$749$	−0.0390432	+	0.450132i	−0.00142661	+	0.0164475i
$750$	8.13914	+	18.4486i	0.297199	+	0.673646i
$751$	1.73539	+	4.76794i	0.0633252	+	0.173985i	0.967320	−	0.253559i	$-0.0816012\pi$
$751$	1.73539	+	4.76794i	0.0633252	+	0.173985i	−0.903995	+	0.427544i	$0.859379\pi$
$752$	9.91775	+	5.72602i	0.361663	+	0.208806i
$753$	18.4830	+	9.09229i	0.673556	+	0.331341i
$754$	−6.29360	−	1.10973i	−0.229200	−	0.0404141i
$755$	−0.0282706	−	0.160330i	−0.00102887	−	0.00583502i
$756$	−6.12585	−	12.3075i	−0.222795	−	0.447619i
$757$	−29.5025	−	10.7380i	−1.07229	−	0.390280i	−0.255255	−	0.966874i	$-0.582159\pi$
$757$	−29.5025	−	10.7380i	−1.07229	−	0.390280i	−0.817031	+	0.576594i	$0.804382\pi$
$758$	18.1273	−	3.19633i	0.658414	−	0.116096i
$759$	−11.1606	+	0.742485i	−0.405105	+	0.0269505i
$760$	−8.26641	−	4.21262i	−0.299854	−	0.152808i
$761$	−1.73696	−	1.00283i	−0.0629647	−	0.0363527i	0.468187	−	0.883629i	$-0.344907\pi$
$761$	−1.73696	−	1.00283i	−0.0629647	−	0.0363527i	−0.531152	+	0.847277i	$0.678241\pi$
$762$	33.9307	−	8.33803i	1.22918	−	0.302055i
$763$	−0.597040	−	6.76607i	−0.0216143	−	0.244948i
$764$	−0.210168	−	0.0370583i	−0.00760361	−	0.00134072i
$765$	−3.52699	−	11.1102i	−0.127519	−	0.401692i
$766$	0.327328	+	0.274661i	0.0118268	+	0.00992390i
$767$		−	13.5925i		−	0.490798i
$768$	−0.764545	+	1.55418i	−0.0275881	+	0.0560816i
$769$	0.602944	+	0.505930i	0.0217427	+	0.0182443i	0.653594	−	0.756845i	$-0.273260\pi$
$769$	0.602944	+	0.505930i	0.0217427	+	0.0182443i	−0.631852	+	0.775089i	$0.717705\pi$
$770$	−1.69241	−	6.29735i	−0.0609901	−	0.226941i
$771$	−16.1926	+	1.07725i	−0.583162	+	0.0387961i
$772$	19.9272	−	11.5050i	0.717195	−	0.414072i
$773$	35.0885	+	29.4428i	1.26205	+	1.05898i	0.995461	+	0.0951709i	$0.0303397\pi$
$773$	35.0885	+	29.4428i	1.26205	+	1.05898i	0.266585	+	0.963811i	$0.414105\pi$
$774$	−11.2071	−	2.46153i	−0.402831	−	0.0884780i
$775$	−0.924604	+	1.10190i	−0.0332127	+	0.0395814i
$776$	3.95535	−	10.8672i	0.141989	−	0.390111i
$777$	0.550593	+	3.53667i	0.0197524	+	0.126877i
$778$		−	29.1037i		−	1.04342i
$779$	5.55242	+	8.55119i	0.198936	+	0.306378i
$780$	−13.2243	+	0.879778i	−0.473507	+	0.0315011i
$781$	3.36517	−	9.24574i	0.120415	−	0.330839i
$782$	7.79904	−	6.54417i	0.278893	−	0.234019i
$783$	−0.228638	−	9.23417i	−0.00817085	−	0.330002i
$784$	6.06739	+	3.49095i	0.216693	+	0.124677i
$785$	−11.8457	−	32.5457i	−0.422790	−	1.16160i
$786$	0.406106	+	6.10436i	0.0144853	+	0.217735i
$787$	−25.9523	−	14.9836i	−0.925099	−	0.534106i	−0.0398406	−	0.999206i	$-0.512685\pi$
$787$	−25.9523	−	14.9836i	−0.925099	−	0.534106i	−0.885258	+	0.465100i	$0.846018\pi$
$788$	−5.67765	−	1.00112i	−0.202258	−	0.0356635i
$789$	20.2433	+	2.19694i	0.720680	+	0.0782131i
$790$	−0.383439	−	0.664137i	−0.0136422	−	0.0236289i
$791$	−7.60485	−	5.31653i	−0.270397	−	0.189034i
$792$	1.86071	−	2.93339i	0.0661174	−	0.104234i
$793$	2.44036	−	6.70482i	0.0866596	−	0.238095i
$794$	1.08394	−	0.394523i	0.0384677	−	0.0140011i
$795$	11.1447	−	38.3757i	0.395263	−	1.36105i
$796$	3.12051	+	17.6973i	0.110603	+	0.627263i
$797$	−28.0836			−0.994771			−0.497386	−	0.867530i	$-0.665707\pi$
$797$	−28.0836			−0.994771			−0.497386	+	0.867530i	$0.665707\pi$
$798$	−19.5496	+	4.10020i	−0.692050	+	0.145146i
$799$	20.9055			0.739585
$800$	−0.0815265	−	0.462360i	−0.00288240	−	0.0163469i
$801$	−8.94926	+	9.80490i	−0.316207	+	0.346439i
$802$	−25.4999	+	9.28121i	−0.900433	+	0.327731i
$803$	−1.04201	+	2.86289i	−0.0367717	+	0.101029i
$804$	−15.2236	−	1.65217i	−0.536895	−	0.0582674i
$805$	2.71399	−	31.2898i	0.0956556	−	1.10282i
$806$	−5.50717	−	9.53870i	−0.193982	−	0.335986i
$807$	−2.69778	+	24.8583i	−0.0949665	+	0.875052i
$808$	−2.02064	−	0.356293i	−0.0710858	−	0.0125343i
$809$	−14.0505	−	8.11208i	−0.493990	−	0.285205i	0.232238	−	0.972659i	$-0.425395\pi$
$809$	−14.0505	−	8.11208i	−0.493990	−	0.285205i	−0.726228	+	0.687453i	$0.758729\pi$
$810$	−5.03052	−	18.4842i	−0.176754	−	0.649468i
$811$	−11.7876	−	32.3862i	−0.413919	−	1.13723i	−0.955089	−	0.296320i	$-0.904241\pi$
$811$	−11.7876	−	32.3862i	−0.413919	−	1.13723i	0.541170	−	0.840913i	$-0.317982\pi$
$812$	2.70055	+	3.85066i	0.0947706	+	0.135132i
$813$	−39.4266	−	28.8495i	−1.38275	−	1.01180i
$814$	−0.692815	+	0.581341i	−0.0242832	+	0.0203760i
$815$	4.95222	−	13.6061i	0.173469	−	0.476602i
$816$	0.209884	+	3.15486i	0.00734741	+	0.110442i
$817$	−7.56976	+	14.8541i	−0.264832	+	0.519679i
$818$			32.2289i			1.12686i
$819$	−20.9856	+	19.3344i	−0.733295	+	0.675599i
$820$	1.70281	−	4.67842i	0.0594646	−	0.163378i
$821$	16.2716	−	19.3917i	0.567882	−	0.676776i	−0.403312	−	0.915062i	$-0.632141\pi$
$821$	16.2716	−	19.3917i	0.567882	−	0.676776i	0.971195	+	0.238286i	$0.0765857\pi$
$822$	−10.8863	+	2.67517i	−0.379705	+	0.0933074i
$823$	5.73379	+	4.81122i	0.199867	+	0.167709i	0.737228	−	0.675644i	$-0.236134\pi$
$823$	5.73379	+	4.81122i	0.199867	+	0.167709i	−0.537361	+	0.843352i	$0.680579\pi$
$824$	14.5357	−	8.39219i	0.506375	−	0.292356i
$825$	0.0625040	+	0.939527i	0.00217611	+	0.0327101i
$826$	−7.06825	+	7.07880i	−0.245936	+	0.246303i
$827$	4.69751	+	3.94168i	0.163348	+	0.137065i	0.720798	−	0.693145i	$-0.243776\pi$
$827$	4.69751	+	3.94168i	0.163348	+	0.137065i	−0.557450	+	0.830211i	$0.688220\pi$
$828$	13.2539	−	10.2113i	0.460603	−	0.354869i
$829$		−	27.7404i		−	0.963465i	−0.876318	−	0.481732i	$-0.840008\pi$
$829$		−	27.7404i		−	0.963465i	0.876318	−	0.481732i	$-0.159992\pi$
$830$	7.30813	+	6.13225i	0.253669	+	0.212853i
$831$	−4.25856	+	4.08468i	−0.147728	+	0.141696i
$832$	3.54038	+	0.624265i	0.122741	+	0.0216425i
$833$	12.7784	−	0.0190614i	0.442745	−	0.000660438i
$834$	−9.22811	−	37.5528i	−0.319543	−	1.30035i
$835$	−27.3536	−	15.7926i	−0.946610	−	0.546526i
$836$	−3.44198	−	3.69156i	−0.119043	−	0.127675i
$837$	11.9384	−	10.5319i	0.412650	−	0.364035i
$838$	−26.8166	+	4.72848i	−0.926363	+	0.163343i
$839$	33.0082	+	12.0140i	1.13957	+	0.414769i	0.841758	−	0.539855i	$-0.181521\pi$
$839$	33.0082	+	12.0140i	1.13957	+	0.414769i	0.297812	+	0.954625i	$0.403743\pi$
$840$	7.34454	+	6.41860i	0.253411	+	0.221463i
$841$	−4.48705	−	25.4474i	−0.154726	−	0.877495i
$842$	4.59242	+	0.809768i	0.158265	+	0.0279065i
$843$	14.2763	−	29.0211i	0.491702	−	0.999540i
$844$	20.1221	+	11.6175i	0.692630	+	0.399890i
$845$	−0.0553126	−	0.151970i	−0.00190281	−	0.00522793i
$846$	34.3263	+	1.43135i	1.18016	+	0.0492110i
$847$	−2.20835	+	25.4603i	−0.0758799	+	0.874826i
$848$	−5.41969	+	9.38719i	−0.186113	+	0.322357i
$849$	−3.13033	−	2.29054i	−0.107433	−	0.0786111i
$850$	−0.550903	−	0.656540i	−0.0188958	−	0.0225191i
$851$	−4.09335	+	1.48986i	−0.140318	+	0.0510716i
$852$	3.51217	+	14.2924i	0.120325	+	0.489650i
$853$	25.1716	−	21.1215i	0.861859	−	0.723186i	−0.100508	−	0.994936i	$-0.532047\pi$
$853$	25.1716	−	21.1215i	0.861859	−	0.723186i	0.962368	+	0.271750i	$0.0876025\pi$
$854$	−4.75747	+	2.22277i	−0.162797	+	0.0760615i
$855$	−27.8322	+	0.295600i	−0.951840	+	0.0101093i
$856$	0.0853864	−	0.147894i	0.00291845	−	0.00505490i
$857$	−5.53371	−	2.01411i	−0.189028	−	0.0688005i	0.245772	−	0.969328i	$-0.420959\pi$
$857$	−5.53371	−	2.01411i	−0.189028	−	0.0688005i	−0.434800	+	0.900527i	$0.643181\pi$
$858$	−6.92398	−	2.01080i	−0.236381	−	0.0686476i
$859$	11.6011	+	9.73450i	0.395825	+	0.332137i	0.818877	−	0.573969i	$-0.194597\pi$
$859$	11.6011	+	9.73450i	0.395825	+	0.332137i	−0.423052	+	0.906105i	$0.639041\pi$
$860$	8.01730	−	1.41367i	0.273388	−	0.0482056i
$861$	−3.46298	−	10.1441i	−0.118018	−	0.345709i
$862$	−20.5508	+	35.5950i	−0.699962	+	1.21237i
$863$	−34.8388			−1.18592			−0.592962	−	0.805230i	$-0.702042\pi$
$863$	−34.8388			−1.18592			−0.592962	+	0.805230i	$0.702042\pi$
$864$	0.128617	+	5.19456i	0.00437565	+	0.176723i
$865$	−47.6375	−	8.39978i	−1.61972	−	0.285601i
$866$		−	4.44700i		−	0.151115i
$867$	−13.1713	−	19.6705i	−0.447320	−	0.668044i
$868$	−2.09216	+	7.83139i	−0.0710124	+	0.265815i
$869$	−0.0724440	−	0.410850i	−0.00245749	−	0.0139371i
$870$	2.64533	+	5.99604i	0.0896852	+	0.203285i
$871$	5.51910	+	31.3004i	0.187008	+	1.06057i
$872$	−0.878058	+	2.41244i	−0.0297348	+	0.0816957i
$873$	−4.59585	−	34.3883i	−0.155546	−	1.16387i
$874$	−9.49722	−	22.3781i	−0.321248	−	0.756951i
$875$	−30.6861	−	2.66163i	−1.03738	−	0.0899794i
$876$	−1.08752	−	4.42557i	−0.0367441	−	0.149526i
$877$	12.3157	+	14.6773i	0.415873	+	0.495618i	0.932792	−	0.360416i	$-0.117365\pi$
$877$	12.3157	+	14.6773i	0.415873	+	0.495618i	−0.516918	+	0.856035i	$0.672921\pi$
$878$	5.55039	+	15.2496i	0.187317	+	0.514649i
$879$	9.11130	+	37.0775i	0.307317	+	1.25059i
$880$	−0.427979	+	2.42719i	−0.0144272	+	0.0818206i
$881$	19.4756	+	11.2442i	0.656149	+	0.378828i	0.790808	−	0.612064i	$-0.209661\pi$
$881$	19.4756	+	11.2442i	0.656149	+	0.378828i	−0.134659	+	0.990892i	$0.542994\pi$
$882$	20.9830	+	0.843609i	0.706536	+	0.0284058i
$883$	41.9672	+	35.2146i	1.41231	+	1.18507i	0.955312	+	0.295598i	$0.0955189\pi$
$883$	41.9672	+	35.2146i	1.41231	+	1.18507i	0.456996	+	0.889469i	$0.348926\pi$
$884$	6.16685	−	2.24455i	0.207414	−	0.0754924i
$885$	−11.5824	+	7.75552i	−0.389337	+	0.260699i
$886$		−	1.07007i		−	0.0359497i
$887$	3.31372	−	18.7930i	0.111264	−	0.631008i	−0.877269	−	0.480000i	$-0.840637\pi$
$887$	3.31372	−	18.7930i	0.111264	−	0.631008i	0.988532	−	0.151008i	$-0.0482521\pi$
$888$	0.377291	−	1.29916i	0.0126610	−	0.0435970i
$889$	−13.7752	+	51.5637i	−0.462007	+	1.72939i
$890$	3.22135	−	8.85059i	0.107980	−	0.296672i
$891$	0.867596	−	10.3851i	0.0290655	−	0.347914i
$892$	19.6080	−	11.3207i	0.656526	−	0.379045i
$893$	14.5978	−	47.7361i	0.488496	−	1.59743i
$894$	26.0967	−	17.4743i	0.872806	−	0.584427i
$895$	6.60454	+	7.87099i	0.220766	+	0.263098i
$896$	−1.51916	−	2.16614i	−0.0507515	−	0.0723657i
$897$	−28.0255	−	20.5070i	−0.935745	−	0.684709i
$898$	33.8055	+	12.3042i	1.12810	+	0.410596i
$899$	−3.50087	+	4.17218i	−0.116761	+	0.139150i
$900$	−0.859614	−	1.11574i	−0.0286538	−	0.0371913i
$901$			19.7872i			0.659206i
$902$	1.74095	−	2.07478i	0.0579673	−	0.0690828i
$903$	11.5337	−	13.1976i	0.383819	−	0.439188i
$904$	1.75356	+	3.03725i	0.0583225	+	0.101018i
$905$	15.0261	+	26.0259i	0.499483	+	0.865130i
$906$	0.0534748	+	0.121208i	0.00177658	+	0.00402688i
$907$	34.1881	+	40.7438i	1.13520	+	1.35287i	0.927121	+	0.374761i	$0.122275\pi$
$907$	34.1881	+	40.7438i	1.13520	+	1.35287i	0.208075	+	0.978113i	$0.433280\pi$
$908$	−19.0575	−	15.9911i	−0.632444	−	0.530684i
$909$	−5.86690	+	1.86247i	−0.194593	+	0.0617742i
$910$	8.54229	−	18.3547i	0.283174	−	0.608453i
$911$	−35.6137			−1.17993			−0.589967	−	0.807427i	$-0.700859\pi$
$911$	−35.6137			−1.17993			−0.589967	+	0.807427i	$0.700859\pi$
$912$	7.35043	+	1.72370i	0.243397	+	0.0570776i
$913$	2.59494	+	4.49457i	0.0858801	+	0.148749i
$914$	−14.1970	−	5.16728i	−0.469595	−	0.170919i
$915$	−7.10567	+	1.74612i	−0.234906	+	0.0577251i
$916$	−0.435831	+	2.47172i	−0.0144002	+	0.0816679i
$917$	−8.47254	−	3.94312i	−0.279788	−	0.130213i
$918$	4.94463	+	8.09478i	0.163197	+	0.267168i
$919$	12.9182	+	22.3749i	0.426131	+	0.738081i	0.996525	−	0.0832901i	$-0.0265428\pi$
$919$	12.9182	+	22.3749i	0.426131	+	0.738081i	−0.570394	+	0.821371i	$0.693209\pi$
$920$	−5.93542	+	10.2805i	−0.195685	+	0.338937i
$921$	−15.2931	+	20.9000i	−0.503924	+	0.688679i
$922$	14.3262	+	39.3610i	0.471809	+	1.29628i
$923$	26.4549	−	15.2738i	0.870774	−	0.502742i
$924$	2.56027	+	4.64773i	0.0842268	+	0.152899i
$925$	0.125419	+	0.344587i	0.00412377	+	0.0113300i
$926$	35.3296	+	12.8589i	1.16100	+	0.422570i
$927$	26.9715	−	42.5203i	0.885859	−	1.39655i
$928$	−0.308688	−	1.75065i	−0.0101332	−	0.0574681i
$929$	−52.4631	+	9.25067i	−1.72126	+	0.303505i	−0.945039	−	0.326957i	$-0.893977\pi$
$929$	−52.4631	+	9.25067i	−1.72126	+	0.303505i	−0.776220	+	0.630462i	$0.782866\pi$
$930$	−4.98581	+	10.1352i	−0.163491	+	0.332348i
$931$	8.87930	−	29.1917i	0.291007	−	0.956721i
$932$		−	27.4759i		−	0.900003i
$933$	−1.62131	+	5.58280i	−0.0530792	+	0.182773i
$934$	29.7609	−	5.24765i	0.973806	−	0.171708i
$935$	1.53880	+	4.22782i	0.0503242	+	0.138265i
$936$	10.2795	−	3.26325i	0.335995	−	0.106663i
$937$	−6.15552	+	2.24042i	−0.201092	+	0.0731915i	−0.440603	−	0.897702i	$-0.645235\pi$
$937$	−6.15552	+	2.24042i	−0.201092	+	0.0731915i	0.239511	+	0.970894i	$0.423013\pi$
$938$	13.4022	−	19.1708i	0.437598	−	0.625948i
$939$	−24.8413	+	1.65262i	−0.810664	+	0.0539312i
$940$	−22.9056	+	8.33696i	−0.747099	+	0.271922i
$941$	3.33597	−	18.9192i	0.108749	−	0.616748i	−0.880907	−	0.473290i	$-0.843066\pi$
$941$	3.33597	−	18.9192i	0.108749	−	0.616748i	0.989656	−	0.143459i	$-0.0458225\pi$
$942$	15.6808	+	23.4184i	0.510910	+	0.763011i
$943$	11.2974	−	6.52256i	0.367894	−	0.212404i
$944$	3.55294	−	1.29316i	0.115638	−	0.0420889i
$945$	28.4489	+	6.85041i	0.925442	+	0.222844i
$946$	4.36147	+	0.769046i	0.141804	+	0.0250038i
$947$	−3.82336	−	4.55651i	−0.124243	−	0.148067i	0.700337	−	0.713812i	$-0.253033\pi$
$947$	−3.82336	−	4.55651i	−0.124243	−	0.148067i	−0.824580	+	0.565745i	$0.808588\pi$
$948$	0.431975	+	0.450363i	0.0140299	+	0.0146271i
$949$	−8.19162	+	4.72944i	−0.265911	+	0.153524i
$950$	−1.88384	+	0.799497i	−0.0611198	+	0.0259391i
$951$	−5.48712	+	11.1543i	−0.177932	+	0.361703i
$952$	−4.37879	−	2.03789i	−0.141917	−	0.0660484i
$953$	48.4128	+	17.6208i	1.56824	+	0.570794i	0.972606	−	0.232460i	$-0.0746774\pi$
$953$	48.4128	+	17.6208i	1.56824	+	0.570794i	0.595637	+	0.803254i	$0.296900\pi$
$954$	−1.35478	+	32.4899i	−0.0438627	+	1.05190i
$955$	0.347971	−	0.291982i	0.0112601	−	0.00944831i
$956$	−2.98988	+	3.56320i	−0.0966995	+	0.115242i
$957$	0.236662	+	3.55737i	0.00765020	+	0.114994i
$958$	6.40536	−	3.69814i	0.206948	−	0.119481i
$959$	4.41965	−	16.5437i	0.142718	−	0.534224i
$960$	−1.48810	−	3.37299i	−0.0480281	−	0.108863i
$961$	21.6132			0.697199
$962$	−2.80791			−0.0905307
$963$	0.0213444	−	0.511873i	0.000687812	−	0.0164949i
$964$	6.49752	−	17.8518i	0.209271	−	0.574968i
$965$	−8.50469	+	48.2325i	−0.273776	+	1.55266i
$966$	3.93146	+	25.2533i	0.126493	+	0.812511i
$967$	−3.84288	+	3.22456i	−0.123579	+	0.103695i	−0.702483	−	0.711701i	$-0.747925\pi$
$967$	−3.84288	+	3.22456i	−0.123579	+	0.103695i	0.578904	+	0.815396i	$0.303481\pi$
$968$	4.82961	−	8.36513i	0.155230	−	0.268865i
$969$	13.1937	−	3.98402i	0.423844	−	0.127985i
$970$	12.3077	+	21.3176i	0.395176	+	0.684466i
$971$	−2.61042	−	14.8044i	−0.0837723	−	0.475096i	−0.997615	−	0.0690274i	$-0.978010\pi$
$971$	−2.61042	−	14.8044i	−0.0837723	−	0.475096i	0.913842	−	0.406069i	$-0.133101\pi$
$972$	7.56471	+	13.6299i	0.242638	+	0.437180i
$973$	57.0681	+	15.2457i	1.82952	+	0.488756i
$974$	−34.5567	+	6.09327i	−1.10727	+	0.195241i
$975$	−1.72632	+	2.35925i	−0.0552866	+	0.0755565i
$976$	1.98474			0.0635299
$977$	−3.49551	+	6.05439i	−0.111831	+	0.193697i	−0.916509	−	0.400015i	$-0.869005\pi$
$977$	−3.49551	+	6.05439i	−0.111831	+	0.193697i	0.804677	+	0.593712i	$0.202338\pi$
$978$	−1.27125	+	11.7137i	−0.0406500	+	0.374562i
$979$	3.29351	−	3.92505i	0.105261	−	0.125445i
$980$	−13.9933	+	5.11681i	−0.447000	+	0.163450i
$981$	1.02024	+	7.63394i	0.0325739	+	0.243733i
$982$	−23.5972	−	4.16083i	−0.753017	−	0.132777i
$983$	−28.5486	+	23.9551i	−0.910559	+	0.764050i	−0.972225	−	0.234047i	$-0.924803\pi$
$983$	−28.5486	+	23.9551i	−0.910559	+	0.764050i	0.0616659	+	0.998097i	$0.480359\pi$
$984$	−0.437114	+	4.02771i	−0.0139347	+	0.128399i
$985$	9.40037	−	7.88784i	0.299521	−	0.251328i
$986$	−2.08591	−	2.48589i	−0.0664289	−	0.0791669i
$987$	−27.1477	+	44.9125i	−0.864120	+	1.42958i
$988$	−0.819098	−	15.6488i	−0.0260590	−	0.497855i
$989$	18.4732	+	10.6655i	0.587413	+	0.339143i
$990$	2.23720	+	7.04732i	0.0711028	+	0.223978i
$991$	15.4538	−	2.72492i	0.490905	−	0.0865598i	0.0772844	−	0.997009i	$-0.475375\pi$
$991$	15.4538	−	2.72492i	0.490905	−	0.0865598i	0.413621	+	0.910449i	$0.364264\pi$
$992$	1.96937	−	2.34700i	0.0625275	−	0.0745174i
$993$	13.2173	−	45.5124i	0.419439	−	1.44429i
$994$	−21.7198	−	5.80245i	−0.688911	−	0.184043i
$995$	−33.1252	−	19.1249i	−1.05014	−	0.606299i
$996$	−6.96594	−	3.42674i	−0.220724	−	0.108581i
$997$	6.55612	−	37.1816i	0.207634	−	1.17755i	−0.685606	−	0.727973i	$-0.740463\pi$
$997$	6.55612	−	37.1816i	0.207634	−	1.17755i	0.893240	−	0.449580i	$-0.148426\pi$
$998$	−1.05035	+	5.95682i	−0.0332482	+	0.188560i
$999$	−0.803468	−	3.97818i	−0.0254206	−	0.125864i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.cc.b.317.1	yes	162
3.2	odd	2		798.2.cc.a.317.5	yes	162
7.4	even	3		798.2.bu.b.431.17	yes	162
19.3	odd	18		798.2.bu.a.611.23	yes	162
21.11	odd	6		798.2.bu.a.431.23	✓	162
57.41	even	18		798.2.bu.b.611.17	yes	162
133.60	odd	18		798.2.cc.a.725.5	yes	162
399.326	even	18	inner	798.2.cc.b.725.1	yes	162

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.bu.a.431.23	✓	162	21.11	odd	6
798.2.bu.a.611.23	yes	162	19.3	odd	18
798.2.bu.b.431.17	yes	162	7.4	even	3
798.2.bu.b.611.17	yes	162	57.41	even	18
798.2.cc.a.317.5	yes	162	3.2	odd	2
798.2.cc.a.725.5	yes	162	133.60	odd	18
798.2.cc.b.317.1	yes	162	1.1	even	1	trivial
798.2.cc.b.725.1	yes	162	399.326	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.cc (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.173648 - 0.984808i) q^{2} +(-1.66333 - 0.483049i) q^{3} +(-0.939693 + 0.342020i) q^{4} +(0.727990 - 2.00013i) q^{5} +(-0.186877 + 1.72194i) q^{6} +(-2.16840 - 1.51592i) q^{7} +(0.500000 + 0.866025i) q^{8} +(2.53333 + 1.60694i) q^{9} +(-2.09616 - 0.369610i) q^{10} +(-1.00279 - 0.578960i) q^{11} +(1.72823 - 0.114974i) q^{12} +(-1.22956 - 3.37819i) q^{13} +(-1.11635 + 2.39870i) q^{14} +(-2.17705 + 2.97523i) q^{15} +(0.766044 - 0.642788i) q^{16} +(0.624353 - 1.71540i) q^{17} +(1.14262 - 2.77388i) q^{18} +(-3.48100 - 2.62348i) q^{19} +2.12850i q^{20} +(2.87450 + 3.56893i) q^{21} +(-0.396032 + 1.08809i) q^{22} +(-3.58489 + 4.27231i) q^{23} +(-0.413332 - 1.68201i) q^{24} +(0.359652 + 0.301784i) q^{25} +(-3.11336 + 1.79750i) q^{26} +(-3.43753 - 3.89659i) q^{27} +(2.55611 + 0.682865i) q^{28} +(1.36177 + 1.14266i) q^{29} +(3.30807 + 1.62733i) q^{30} +3.06379i q^{31} +(-0.766044 - 0.642788i) q^{32} +(1.38830 + 1.44740i) q^{33} +(-1.79775 - 0.316993i) q^{34} +(-4.61063 + 3.23352i) q^{35} +(-2.93015 - 0.643580i) q^{36} +(0.676418 + 0.390530i) q^{37} +(-1.97915 + 3.88368i) q^{38} +(0.413333 + 6.21299i) q^{39} +(2.09616 - 0.369610i) q^{40} +(-2.19799 - 0.800003i) q^{41} +(3.01555 - 3.45057i) q^{42} +(-0.664161 - 3.76664i) q^{43} +(1.14033 + 0.201071i) q^{44} +(5.05833 - 3.89716i) q^{45} +(4.82991 + 2.78855i) q^{46} +(3.91683 + 10.7614i) q^{47} +(-1.58468 + 0.699130i) q^{48} +(2.40395 + 6.57427i) q^{49} +(0.234746 - 0.406592i) q^{50} +(-1.86713 + 2.55168i) q^{51} +(2.31082 + 2.75393i) q^{52} +(-10.1857 + 3.70729i) q^{53} +(-3.24047 + 4.06194i) q^{54} +(-1.88802 + 1.58424i) q^{55} +(0.228627 - 2.63585i) q^{56} +(4.52278 + 6.04520i) q^{57} +(0.888831 - 1.53950i) q^{58} +(3.55294 + 1.29316i) q^{59} +(1.02817 - 3.54039i) q^{60} +(1.52040 + 1.27576i) q^{61} +(3.01725 - 0.532022i) q^{62} +(-3.05728 - 7.32482i) q^{63} +(-0.500000 + 0.866025i) q^{64} -7.65195 q^{65} +(1.18433 - 1.61855i) q^{66} +(-8.70664 - 1.53522i) q^{67} +1.82549i q^{68} +(8.02658 - 5.37457i) q^{69} +(3.98503 + 3.97909i) q^{70} +(1.47553 + 8.36813i) q^{71} +(-0.124987 + 2.99740i) q^{72} +(-0.456889 - 2.59115i) q^{73} +(0.267138 - 0.733957i) q^{74} +(-0.452443 - 0.675695i) q^{75} +(4.16835 + 1.27469i) q^{76} +(1.29679 + 2.77557i) q^{77} +(6.04682 - 1.48593i) q^{78} +(0.231591 + 0.275999i) q^{79} +(-0.727990 - 2.00013i) q^{80} +(3.83549 + 8.14181i) q^{81} +(-0.406172 + 2.30352i) q^{82} +(-3.88159 - 2.24104i) q^{83} +(-3.92179 - 2.37056i) q^{84} +(-2.97650 - 2.49758i) q^{85} +(-3.59409 + 1.30814i) q^{86} +(-1.71311 - 2.55842i) q^{87} -1.15792i q^{88} +(-0.768392 + 4.35777i) q^{89} +(-4.71632 - 4.30475i) q^{90} +(-2.45490 + 9.18921i) q^{91} +(1.90748 - 5.24076i) q^{92} +(1.47996 - 5.09610i) q^{93} +(9.91775 - 5.72602i) q^{94} +(-7.78144 + 5.05261i) q^{95} +(0.963686 + 1.43920i) q^{96} +(-7.43363 - 8.85906i) q^{97} +(6.05695 - 3.50904i) q^{98} +(-1.61004 - 3.07812i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 162 q + 81 q^{8} + 15 q^{13} - 9 q^{14} + 3 q^{15} - 12 q^{17} + 18 q^{18} - 36 q^{19} - 6 q^{22} + 12 q^{25} + 9 q^{27} - 12 q^{28} - 6 q^{29} - 12 q^{33} + 6 q^{34} + 12 q^{35} - 18 q^{37} - 9 q^{39}+ \cdots + 39 q^{99}+O(q^{100}) \) 162 * q + 81 * q^8 + 15 * q^13 - 9 * q^14 + 3 * q^15 - 12 * q^17 + 18 * q^18 - 36 * q^19 - 6 * q^22 + 12 * q^25 + 9 * q^27 - 12 * q^28 - 6 * q^29 - 12 * q^33 + 6 * q^34 + 12 * q^35 - 18 * q^37 - 9 * q^39 - 9 * q^43 - 6 * q^44 + 18 * q^45 - 18 * q^46 - 12 * q^47 + 24 * q^49 - 87 * q^50 + 24 * q^51 + 12 * q^52 + 36 * q^53 + 18 * q^54 - 18 * q^57 - 24 * q^59 - 27 * q^60 - 9 * q^61 - 36 * q^62 + 6 * q^63 - 81 * q^64 + 72 * q^65 + 12 * q^66 - 63 * q^67 - 9 * q^69 + 12 * q^70 - 12 * q^71 - 51 * q^73 + 42 * q^74 - 18 * q^78 + 21 * q^79 - 12 * q^81 + 3 * q^84 - 6 * q^85 - 36 * q^86 - 84 * q^87 + 54 * q^89 + 12 * q^90 + 75 * q^91 - 66 * q^93 + 72 * q^94 - 12 * q^97 - 12 * q^98 + 39 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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