LMFDB - Embedded newform 666.2.k.a.175.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [666,2,Mod(175,666)] 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("666.175"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(666, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 666 = 2 \cdot 3^{2} \cdot 37 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	666.k (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$5.31803677462$
Analytic rank:	$0$
Dimension:	$76$
Relative dimension:	$38$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			175.8
Character	$\chi$	$=$	666.175
Dual form			666.2.k.a.529.27

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.00000i q^{2} +(-0.428312 - 1.67826i) q^{3} -1.00000 q^{4} +3.91841i q^{5} +(-1.67826 + 0.428312i) q^{6} +(1.32775 - 2.29973i) q^{7} +1.00000i q^{8} +(-2.63310 + 1.43763i) q^{9} +3.91841 q^{10} +(-2.18085 - 3.77734i) q^{11} +(0.428312 + 1.67826i) q^{12} -0.461777i q^{13} +(-2.29973 - 1.32775i) q^{14} +(6.57611 - 1.67830i) q^{15} +1.00000 q^{16} +(-6.41857 - 3.70577i) q^{17} +(1.43763 + 2.63310i) q^{18} +(1.39047 - 0.802790i) q^{19} -3.91841i q^{20} +(-4.42823 - 1.24331i) q^{21} +(-3.77734 + 2.18085i) q^{22} +(-6.08873 - 3.51533i) q^{23} +(1.67826 - 0.428312i) q^{24} -10.3540 q^{25} -0.461777 q^{26} +(3.54051 + 3.80326i) q^{27} +(-1.32775 + 2.29973i) q^{28} +(0.308516 - 0.178122i) q^{29} +(-1.67830 - 6.57611i) q^{30} +(-5.51273 - 3.18278i) q^{31} -1.00000i q^{32} +(-5.40527 + 5.27791i) q^{33} +(-3.70577 + 6.41857i) q^{34} +(9.01130 + 5.20267i) q^{35} +(2.63310 - 1.43763i) q^{36} +(5.47923 - 2.64159i) q^{37} +(-0.802790 - 1.39047i) q^{38} +(-0.774981 + 0.197785i) q^{39} -3.91841 q^{40} +2.16157 q^{41} +(-1.24331 + 4.42823i) q^{42} +(6.88938 - 3.97758i) q^{43} +(2.18085 + 3.77734i) q^{44} +(-5.63325 - 10.3176i) q^{45} +(-3.51533 + 6.08873i) q^{46} +(-0.387540 - 0.671238i) q^{47} +(-0.428312 - 1.67826i) q^{48} +(-0.0258395 - 0.0447554i) q^{49} +10.3540i q^{50} +(-3.47008 + 12.3592i) q^{51} +0.461777i q^{52} +(-4.95540 + 8.58300i) q^{53} +(3.80326 - 3.54051i) q^{54} +(14.8012 - 8.54547i) q^{55} +(2.29973 + 1.32775i) q^{56} +(-1.94284 - 1.98973i) q^{57} +(-0.178122 - 0.308516i) q^{58} +(-4.54130 + 2.62192i) q^{59} +(-6.57611 + 1.67830i) q^{60} +(-11.1092 - 6.41390i) q^{61} +(-3.18278 + 5.51273i) q^{62} +(-0.189923 + 7.96424i) q^{63} -1.00000 q^{64} +1.80943 q^{65} +(5.27791 + 5.40527i) q^{66} +6.00043 q^{67} +(6.41857 + 3.70577i) q^{68} +(-3.29175 + 11.7241i) q^{69} +(5.20267 - 9.01130i) q^{70} +(2.49449 + 4.32057i) q^{71} +(-1.43763 - 2.63310i) q^{72} +9.49852 q^{73} +(-2.64159 - 5.47923i) q^{74} +(4.43473 + 17.3766i) q^{75} +(-1.39047 + 0.802790i) q^{76} -11.5825 q^{77} +(0.197785 + 0.774981i) q^{78} +(-4.66224 - 2.69175i) q^{79} +3.91841i q^{80} +(4.86641 - 7.57087i) q^{81} -2.16157i q^{82} +4.36378 q^{83} +(4.42823 + 1.24331i) q^{84} +(14.5207 - 25.1506i) q^{85} +(-3.97758 - 6.88938i) q^{86} +(-0.431076 - 0.441478i) q^{87} +(3.77734 - 2.18085i) q^{88} +(9.46098 + 5.46230i) q^{89} +(-10.3176 + 5.63325i) q^{90} +(-1.06196 - 0.613125i) q^{91} +(6.08873 + 3.51533i) q^{92} +(-2.98035 + 10.6150i) q^{93} +(-0.671238 + 0.387540i) q^{94} +(3.14566 + 5.44845i) q^{95} +(-1.67826 + 0.428312i) q^{96} +(-15.8486 + 9.15019i) q^{97} +(-0.0447554 + 0.0258395i) q^{98} +(11.1728 + 6.81085i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 76 q + 4 q^{3} - 76 q^{4} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{12} + 12 q^{15} + 76 q^{16} + 6 q^{21} + 12 q^{23} - 100 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} + 18 q^{29} - 12 q^{30} + 6 q^{31} - 32 q^{33}+ \cdots - 76 q^{99}+O(q^{100}) $ 76 * q + 4 * q^3 - 76 * q^4 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^12 + 12 * q^15 + 76 * q^16 + 6 * q^21 + 12 * q^23 - 100 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 + 18 * q^29 - 12 * q^30 + 6 * q^31 - 32 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 24 * q^39 + 72 * q^41 + 6 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^45 - 20 * q^47 + 4 * q^48 - 36 * q^49 - 18 * q^51 + 14 * q^53 + 36 * q^54 + 42 * q^57 - 6 * q^59 - 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 + 32 * q^65 + 40 * q^67 + 6 * q^69 + 2 * q^71 + 28 * q^73 - 2 * q^74 - 78 * q^75 - 24 * q^77 - 2 * q^78 + 6 * q^79 - 28 * q^81 - 64 * q^83 - 6 * q^84 - 12 * q^85 + 4 * q^86 - 78 * q^87 + 60 * q^89 - 16 * q^90 + 42 * q^91 - 12 * q^92 + 6 * q^93 - 14 * q^95 - 12 * q^97 - 24 * q^98 - 76 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/666\mathbb{Z}\right)^\times$.

$n$	$371$	$631$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{6}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

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

$2$		−	1.00000i		−	0.707107i
$2$		−	1.00000i		−	0.707107i
$3$	−0.428312	−	1.67826i	−0.247286	−	0.968943i
$3$	−0.428312	−	1.67826i	−0.247286	−	0.968943i
$4$	−1.00000			−0.500000
$5$			3.91841i			1.75237i	0.481976	+	0.876184i	$0.339919\pi$
$5$			3.91841i			1.75237i	−0.481976	+	0.876184i	$0.660081\pi$
$6$	−1.67826	+	0.428312i	−0.685146	+	0.174858i
$7$	1.32775	−	2.29973i	0.501842	−	0.869216i	−0.498155	−	0.867088i	$-0.665989\pi$
$7$	1.32775	−	2.29973i	0.501842	−	0.869216i	0.999998	−	0.00212860i	$-0.000677554\pi$
$8$			1.00000i			0.353553i
$9$	−2.63310	+	1.43763i	−0.877699	+	0.479212i
$10$	3.91841			1.23911
$11$	−2.18085	−	3.77734i	−0.657551	−	1.13891i	−0.981248	−	0.192750i	$-0.938259\pi$
$11$	−2.18085	−	3.77734i	−0.657551	−	1.13891i	0.323697	−	0.946161i	$-0.395074\pi$
$12$	0.428312	+	1.67826i	0.123643	+	0.484471i
$13$		−	0.461777i		−	0.128074i	−0.997948	−	0.0640370i	$-0.979602\pi$
$13$		−	0.461777i		−	0.128074i	0.997948	−	0.0640370i	$-0.0203976\pi$
$14$	−2.29973	−	1.32775i	−0.614629	−	0.354856i
$15$	6.57611	−	1.67830i	1.69794	−	0.433336i
$16$	1.00000			0.250000
$17$	−6.41857	−	3.70577i	−1.55673	−	0.898780i	−0.997566	−	0.0697246i	$-0.977788\pi$
$17$	−6.41857	−	3.70577i	−1.55673	−	0.898780i	−0.559166	−	0.829055i	$-0.688879\pi$
$18$	1.43763	+	2.63310i	0.338854	+	0.620627i
$19$	1.39047	−	0.802790i	0.318996	−	0.184173i	−0.331949	−	0.943297i	$-0.607706\pi$
$19$	1.39047	−	0.802790i	0.318996	−	0.184173i	0.650945	+	0.759125i	$0.274373\pi$
$20$		−	3.91841i		−	0.876184i
$21$	−4.42823	−	1.24331i	−0.966319	−	0.271311i
$22$	−3.77734	+	2.18085i	−0.805332	+	0.464959i
$23$	−6.08873	−	3.51533i	−1.26959	−	0.732997i	−0.294678	−	0.955597i	$-0.595212\pi$
$23$	−6.08873	−	3.51533i	−1.26959	−	0.732997i	−0.974910	+	0.222600i	$0.928546\pi$
$24$	1.67826	−	0.428312i	0.342573	−	0.0874288i
$25$	−10.3540			−2.07079
$26$	−0.461777			−0.0905620
$27$	3.54051	+	3.80326i	0.681371	+	0.731938i
$28$	−1.32775	+	2.29973i	−0.250921	+	0.434608i
$29$	0.308516	−	0.178122i	0.0572901	−	0.0330764i	−0.471081	−	0.882090i	$-0.656136\pi$
$29$	0.308516	−	0.178122i	0.0572901	−	0.0330764i	0.528371	+	0.849013i	$0.322803\pi$
$30$	−1.67830	−	6.57611i	−0.306415	−	1.20063i
$31$	−5.51273	−	3.18278i	−0.990115	−	0.571643i	−0.0848066	−	0.996397i	$-0.527027\pi$
$31$	−5.51273	−	3.18278i	−0.990115	−	0.571643i	−0.905309	+	0.424754i	$0.860361\pi$
$32$		−	1.00000i		−	0.176777i
$33$	−5.40527	+	5.27791i	−0.940937	+	0.918766i
$34$	−3.70577	+	6.41857i	−0.635533	+	1.10078i
$35$	9.01130	+	5.20267i	1.52319	+	0.879413i
$36$	2.63310	−	1.43763i	0.438850	−	0.239606i
$37$	5.47923	−	2.64159i	0.900781	−	0.434274i
$37$	5.47923	−	2.64159i	0.900781	−	0.434274i
$38$	−0.802790	−	1.39047i	−0.130230	−	0.225565i
$39$	−0.774981	+	0.197785i	−0.124096	+	0.0316709i
$40$	−3.91841			−0.619556
$41$	2.16157			0.337581			0.168790	−	0.985652i	$-0.446014\pi$
$41$	2.16157			0.337581			0.168790	+	0.985652i	$0.446014\pi$
$42$	−1.24331	+	4.42823i	−0.191846	+	0.683291i
$43$	6.88938	−	3.97758i	1.05062	−	0.606576i	0.127797	−	0.991800i	$-0.459209\pi$
$43$	6.88938	−	3.97758i	1.05062	−	0.606576i	0.922823	+	0.385224i	$0.125876\pi$
$44$	2.18085	+	3.77734i	0.328775	+	0.569456i
$45$	−5.63325	−	10.3176i	−0.839755	−	1.53805i
$46$	−3.51533	+	6.08873i	−0.518307	+	0.897734i
$47$	−0.387540	−	0.671238i	−0.0565285	−	0.0979102i	0.836376	−	0.548156i	$-0.184670\pi$
$47$	−0.387540	−	0.671238i	−0.0565285	−	0.0979102i	−0.892905	+	0.450245i	$0.851337\pi$
$48$	−0.428312	−	1.67826i	−0.0618215	−	0.242236i
$49$	−0.0258395	−	0.0447554i	−0.00369136	−	0.00639363i
$50$			10.3540i			1.46427i
$51$	−3.47008	+	12.3592i	−0.485908	+	1.73064i
$52$			0.461777i			0.0640370i
$53$	−4.95540	+	8.58300i	−0.680676	+	1.17897i	0.294098	+	0.955775i	$0.404981\pi$
$53$	−4.95540	+	8.58300i	−0.680676	+	1.17897i	−0.974775	+	0.223191i	$0.928353\pi$
$54$	3.80326	−	3.54051i	0.517558	−	0.481802i
$55$	14.8012	−	8.54547i	1.99579	−	1.15227i
$56$	2.29973	+	1.32775i	0.307314	+	0.177428i
$57$	−1.94284	−	1.98973i	−0.257336	−	0.263546i
$58$	−0.178122	−	0.308516i	−0.0233886	−	0.0405102i
$59$	−4.54130	+	2.62192i	−0.591227	+	0.341345i	−0.765582	−	0.643338i	$-0.777549\pi$
$59$	−4.54130	+	2.62192i	−0.591227	+	0.341345i	0.174356	+	0.984683i	$0.444216\pi$
$60$	−6.57611	+	1.67830i	−0.848972	+	0.216668i
$61$	−11.1092	−	6.41390i	−1.42239	−	0.821215i	−0.425884	−	0.904778i	$-0.640037\pi$
$61$	−11.1092	−	6.41390i	−1.42239	−	0.821215i	−0.996503	+	0.0835625i	$0.973370\pi$
$62$	−3.18278	+	5.51273i	−0.404213	+	0.700117i
$63$	−0.189923	+	7.96424i	−0.0239281	+	1.00340i
$64$	−1.00000			−0.125000
$65$	1.80943			0.224433
$66$	5.27791	+	5.40527i	0.649665	+	0.665343i
$67$	6.00043			0.733069			0.366535	−	0.930404i	$-0.380544\pi$
$67$	6.00043			0.733069			0.366535	+	0.930404i	$0.380544\pi$
$68$	6.41857	+	3.70577i	0.778366	+	0.449390i
$69$	−3.29175	+	11.7241i	−0.396281	+	1.41142i
$70$	5.20267	−	9.01130i	0.621839	−	1.07706i
$71$	2.49449	+	4.32057i	0.296041	+	0.512758i	0.975226	−	0.221209i	$-0.0710002\pi$
$71$	2.49449	+	4.32057i	0.296041	+	0.512758i	−0.679186	+	0.733967i	$0.737667\pi$
$72$	−1.43763	−	2.63310i	−0.169427	−	0.310314i
$73$	9.49852			1.11172			0.555859	−	0.831277i	$-0.312389\pi$
$73$	9.49852			1.11172			0.555859	+	0.831277i	$0.312389\pi$
$74$	−2.64159	−	5.47923i	−0.307078	−	0.636948i
$75$	4.43473	+	17.3766i	0.512078	+	2.00648i
$76$	−1.39047	+	0.802790i	−0.159498	+	0.0920863i
$77$	−11.5825			−1.31995
$78$	0.197785	+	0.774981i	0.0223947	+	0.0877493i
$79$	−4.66224	−	2.69175i	−0.524543	−	0.302845i	0.214248	−	0.976779i	$-0.431270\pi$
$79$	−4.66224	−	2.69175i	−0.524543	−	0.302845i	−0.738792	+	0.673934i	$0.764603\pi$
$80$			3.91841i			0.438092i
$81$	4.86641	−	7.57087i	0.540712	−	0.841208i
$82$		−	2.16157i		−	0.238706i
$83$	4.36378			0.478987			0.239493	−	0.970898i	$-0.423019\pi$
$83$	4.36378			0.478987			0.239493	+	0.970898i	$0.423019\pi$
$84$	4.42823	+	1.24331i	0.483160	+	0.135656i
$85$	14.5207	−	25.1506i	1.57499	−	2.72797i
$86$	−3.97758	−	6.88938i	−0.428914	−	0.742901i
$87$	−0.431076	−	0.441478i	−0.0462162	−	0.0473314i
$88$	3.77734	−	2.18085i	0.402666	−	0.232479i
$89$	9.46098	+	5.46230i	1.00286	+	0.579002i	0.909094	−	0.416592i	$-0.136776\pi$
$89$	9.46098	+	5.46230i	1.00286	+	0.579002i	0.0937679	+	0.995594i	$0.470109\pi$
$90$	−10.3176	+	5.63325i	−1.08757	+	0.593797i
$91$	−1.06196	−	0.613125i	−0.111324	−	0.0642729i
$92$	6.08873	+	3.51533i	0.634794	+	0.366498i
$93$	−2.98035	+	10.6150i	−0.309048	+	1.10072i
$94$	−0.671238	+	0.387540i	−0.0692330	+	0.0399717i
$95$	3.14566	+	5.44845i	0.322738	+	0.558999i
$96$	−1.67826	+	0.428312i	−0.171286	+	0.0437144i
$97$	−15.8486	+	9.15019i	−1.60918	+	0.929061i	−0.619628	+	0.784896i	$0.712717\pi$
$97$	−15.8486	+	9.15019i	−1.60918	+	0.929061i	−0.989554	+	0.144166i	$0.953950\pi$
$98$	−0.0447554	+	0.0258395i	−0.00452098	+	0.00261019i
$99$	11.1728	+	6.81085i	1.12291	+	0.684516i
$100$	10.3540			1.03540
$101$	−4.48699	−	7.77169i	−0.446472	−	0.773312i	0.551682	−	0.834055i	$-0.313986\pi$
$101$	−4.48699	−	7.77169i	−0.446472	−	0.773312i	−0.998153	+	0.0607430i	$0.980653\pi$
$102$	12.3592	+	3.47008i	1.22375	+	0.343589i
$103$	−3.68693	−	2.12865i	−0.363284	−	0.209742i	0.307237	−	0.951633i	$-0.400596\pi$
$103$	−3.68693	−	2.12865i	−0.363284	−	0.209742i	−0.670520	+	0.741891i	$0.733929\pi$
$104$	0.461777			0.0452810
$105$	4.87179	−	17.3516i	0.475438	−	1.69335i
$106$	8.58300	+	4.95540i	0.833655	+	0.481311i
$107$	−3.28559	−	5.69081i	−0.317630	−	0.550151i	0.662363	−	0.749183i	$-0.269554\pi$
$107$	−3.28559	−	5.69081i	−0.317630	−	0.550151i	−0.979993	+	0.199032i	$0.936220\pi$
$108$	−3.54051	−	3.80326i	−0.340686	−	0.365969i
$109$	−7.68337	−	4.43600i	−0.735934	−	0.424892i	0.0846552	−	0.996410i	$-0.473021\pi$
$109$	−7.68337	−	4.43600i	−0.735934	−	0.424892i	−0.820589	+	0.571519i	$0.806354\pi$
$110$	−8.54547	−	14.8012i	−0.814779	−	1.41124i
$111$	−6.78009	−	8.06415i	−0.643537	−	0.765415i
$112$	1.32775	−	2.29973i	0.125461	−	0.217304i
$113$	14.7814	−	8.53402i	1.39051	−	0.802813i	0.397141	−	0.917758i	$-0.370002\pi$
$113$	14.7814	−	8.53402i	1.39051	−	0.802813i	0.993372	+	0.114944i	$0.0366690\pi$
$114$	−1.98973	+	1.94284i	−0.186355	+	0.181964i
$115$	13.7745	−	23.8582i	1.28448	−	2.22479i
$116$	−0.308516	+	0.178122i	−0.0286450	+	0.0165382i
$117$	0.663867	+	1.21590i	0.0613745	+	0.112410i
$118$	2.62192	+	4.54130i	0.241367	+	0.418060i
$119$	−17.0445	+	9.84066i	−1.56247	+	0.902092i
$120$	1.67830	+	6.57611i	0.153207	+	0.600314i
$121$	−4.01220	+	6.94934i	−0.364746	+	0.631758i
$122$	−6.41390	+	11.1092i	−0.580687	+	1.00578i
$123$	−0.925826	−	3.62767i	−0.0834789	−	0.327096i
$124$	5.51273	+	3.18278i	0.495058	+	0.285822i
$125$		−	20.9791i		−	1.87643i
$126$	7.96424	+	0.189923i	0.709510	+	0.0169197i
$127$	0.256760	−	0.444722i	0.0227838	−	0.0394627i	−0.854409	−	0.519602i	$-0.826080\pi$
$127$	0.256760	−	0.444722i	0.0227838	−	0.0394627i	0.877193	+	0.480139i	$0.159414\pi$
$128$			1.00000i			0.0883883i
$129$	−9.62621	−	9.85851i	−0.847541	−	0.867993i
$130$		−	1.80943i		−	0.158698i
$131$	−5.92982	+	3.42358i	−0.518091	+	0.299120i	−0.736153	−	0.676815i	$-0.763360\pi$
$131$	−5.92982	+	3.42358i	−0.518091	+	0.299120i	0.218062	+	0.975935i	$0.430026\pi$
$132$	5.40527	−	5.27791i	0.470468	−	0.459383i
$133$		−	4.26362i		−	0.369702i
$134$		−	6.00043i		−	0.518358i
$135$	−14.9028	+	13.8732i	−1.28262	+	1.19401i
$136$	3.70577	−	6.41857i	0.317767	−	0.550388i
$137$	9.89734	+	17.1427i	0.845587	+	1.46460i	0.885111	+	0.465380i	$0.154082\pi$
$137$	9.89734	+	17.1427i	0.845587	+	1.46460i	−0.0395241	+	0.999219i	$0.512584\pi$
$138$	11.7241	+	3.29175i	0.998023	+	0.280213i
$139$	−6.95612	−	12.0483i	−0.590010	−	1.02193i	−0.994230	−	0.107266i	$-0.965790\pi$
$139$	−6.95612	−	12.0483i	−0.590010	−	1.02193i	0.404220	−	0.914662i	$-0.367543\pi$
$140$	−9.01130	−	5.20267i	−0.761594	−	0.439706i
$141$	−0.960523	+	0.937891i	−0.0808907	+	0.0789847i
$142$	4.32057	−	2.49449i	0.362575	−	0.209333i
$143$	−1.74429	+	1.00707i	−0.145865	+	0.0842151i
$144$	−2.63310	+	1.43763i	−0.219425	+	0.119803i
$145$	0.697956	+	1.20890i	0.0579621	+	0.100393i
$146$		−	9.49852i		−	0.786103i
$147$	−0.0640437	+	0.0625347i	−0.00528224	+	0.00515777i
$148$	−5.47923	+	2.64159i	−0.450390	+	0.217137i
$149$	10.6364	−	18.4228i	0.871369	−	1.50925i	0.0107871	−	0.999942i	$-0.496566\pi$
$149$	10.6364	−	18.4228i	0.871369	−	1.50925i	0.860581	−	0.509313i	$-0.170100\pi$
$150$	17.3766	−	4.43473i	1.41880	−	0.362094i
$151$	6.23687	−	10.8026i	0.507549	−	0.879101i	−0.492413	−	0.870362i	$-0.663885\pi$
$151$	6.23687	−	10.8026i	0.507549	−	0.879101i	0.999962	−	0.00873896i	$-0.00278173\pi$
$152$	0.802790	+	1.39047i	0.0651149	+	0.112782i
$153$	22.2283	+	0.530078i	1.79705	+	0.0428542i
$154$			11.5825i			0.933343i
$155$	12.4714	−	21.6012i	1.00173	−	1.73505i
$156$	0.774981	−	0.197785i	0.0620481	−	0.0158354i
$157$	7.56450	+	13.1021i	0.603713	+	1.04566i	0.992253	+	0.124230i	$0.0396460\pi$
$157$	7.56450	+	13.1021i	0.603713	+	1.04566i	−0.388541	+	0.921432i	$0.627021\pi$
$158$	−2.69175	+	4.66224i	−0.214144	+	0.370908i
$159$	16.5269	+	4.64024i	1.31067	+	0.367995i
$160$	3.91841			0.309778
$161$	−16.1686	+	9.33495i	−1.27427	+	0.735697i
$162$	−7.57087	−	4.86641i	−0.594824	−	0.382341i
$163$	−1.95922	−	1.13116i	−0.153458	−	0.0885991i	0.421305	−	0.906919i	$-0.361572\pi$
$163$	−1.95922	−	1.13116i	−0.153458	−	0.0885991i	−0.574763	+	0.818320i	$0.694906\pi$
$164$	−2.16157			−0.168790
$165$	−20.6810	−	21.1801i	−1.61002	−	1.64887i
$166$		−	4.36378i		−	0.338695i
$167$		−	7.76224i		−	0.600660i	−0.953835	−	0.300330i	$-0.902903\pi$
$167$		−	7.76224i		−	0.600660i	0.953835	−	0.300330i	$-0.0970969\pi$
$168$	1.24331	−	4.42823i	0.0959231	−	0.341645i
$169$	12.7868			0.983597
$170$	−25.1506	−	14.5207i	−1.92897	−	1.11369i
$171$	−2.50713	+	4.11282i	−0.191725	+	0.314515i
$172$	−6.88938	+	3.97758i	−0.525310	+	0.303288i
$173$	−3.68122			−0.279878			−0.139939	−	0.990160i	$-0.544691\pi$
$173$	−3.68122			−0.279878			−0.139939	+	0.990160i	$0.544691\pi$
$174$	−0.441478	+	0.431076i	−0.0334684	+	0.0326798i
$175$	−13.7475	+	23.8113i	−1.03921	+	1.79997i
$176$	−2.18085	−	3.77734i	−0.164388	−	0.284728i
$177$	6.34535	+	6.49847i	0.476946	+	0.488455i
$178$	5.46230	−	9.46098i	0.409417	−	0.709130i
$179$		−	11.0546i		−	0.826261i	−0.910672	−	0.413130i	$-0.864435\pi$
$179$		−	11.0546i		−	0.826261i	0.910672	−	0.413130i	$-0.135565\pi$
$180$	5.63325	+	10.3176i	0.419878	+	0.769026i
$181$	−1.06814	−	1.85007i	−0.0793940	−	0.137514i	0.823595	−	0.567179i	$-0.191965\pi$
$181$	−1.06814	−	1.85007i	−0.0793940	−	0.137514i	−0.902989	+	0.429664i	$0.858632\pi$
$182$	−0.613125	+	1.06196i	−0.0454478	+	0.0787179i
$183$	−6.00597	+	21.3912i	−0.443974	+	1.58129i
$184$	3.51533	−	6.08873i	0.259153	−	0.448867i
$185$	10.3508	+	21.4699i	0.761009	+	1.57850i
$186$	10.6150	+	2.98035i	0.778330	+	0.218530i
$187$			32.3269i			2.36397i
$188$	0.387540	+	0.671238i	0.0282642	+	0.0489551i
$189$	13.4474	−	3.09244i	0.978153	−	0.224942i
$190$	5.44845	−	3.14566i	0.395272	−	0.228210i
$191$	−22.2509	+	12.8465i	−1.61002	+	0.929543i	−0.620651	+	0.784087i	$0.713132\pi$
$191$	−22.2509	+	12.8465i	−1.61002	+	0.929543i	−0.989365	+	0.145456i	$0.953535\pi$
$192$	0.428312	+	1.67826i	0.0309107	+	0.121118i
$193$	18.6420	+	10.7630i	1.34188	+	0.774737i	0.987084	−	0.160205i	$-0.0512157\pi$
$193$	18.6420	+	10.7630i	1.34188	+	0.774737i	0.354800	+	0.934942i	$0.384549\pi$
$194$	9.15019	+	15.8486i	0.656946	+	1.13786i
$195$	−0.775002	−	3.03670i	−0.0554990	−	0.217462i
$196$	0.0258395	+	0.0447554i	0.00184568	+	0.00319681i
$197$	8.46276	−	14.6579i	0.602946	−	1.04433i	−0.389426	−	0.921058i	$-0.627327\pi$
$197$	8.46276	−	14.6579i	0.602946	−	1.04433i	0.992372	−	0.123276i	$-0.0393400\pi$
$198$	6.81085	−	11.1728i	0.484026	−	0.794018i
$199$			8.90407i			0.631193i	0.948894	+	0.315596i	$0.102205\pi$
$199$			8.90407i			0.631193i	−0.948894	+	0.315596i	$0.897795\pi$
$200$		−	10.3540i		−	0.732137i
$201$	−2.57005	−	10.0703i	−0.181278	−	0.710302i
$202$	−7.77169	+	4.48699i	−0.546814	+	0.315703i
$203$		−	0.946006i		−	0.0663966i
$204$	3.47008	−	12.3592i	0.242954	−	0.865320i
$205$			8.46993i			0.591566i
$206$	−2.12865	+	3.68693i	−0.148310	+	0.256880i
$207$	21.0860	+	0.502837i	1.46558	+	0.0349496i
$208$		−	0.461777i		−	0.0320185i
$209$	−6.06482	−	3.50153i	−0.419513	−	0.242206i
$210$	−17.3516	−	4.87179i	−1.19738	−	0.336185i
$211$	−6.29398	+	10.9015i	−0.433295	+	0.750490i	−0.997155	−	0.0753812i	$-0.975983\pi$
$211$	−6.29398	+	10.9015i	−0.433295	+	0.750490i	0.563859	+	0.825871i	$0.309316\pi$
$212$	4.95540	−	8.58300i	0.340338	−	0.589483i
$213$	6.18262	−	6.03694i	0.423626	−	0.413644i
$214$	−5.69081	+	3.28559i	−0.389016	+	0.224598i
$215$	15.5858	+	26.9954i	1.06294	+	1.84107i
$216$	−3.80326	+	3.54051i	−0.258779	+	0.240901i
$217$	−14.6391	+	8.45186i	−0.993764	+	0.573750i
$218$	−4.43600	+	7.68337i	−0.300444	+	0.520384i
$219$	−4.06833	−	15.9410i	−0.274912	−	1.07719i
$220$	−14.8012	+	8.54547i	−0.997896	+	0.576136i
$221$	−1.71124	+	2.96395i	−0.115110	+	0.199377i
$222$	−8.06415	+	6.78009i	−0.541230	+	0.455050i
$223$	4.71308	+	8.16330i	0.315611	+	0.546655i	0.979567	−	0.201117i	$-0.0644571\pi$
$223$	4.71308	+	8.16330i	0.315611	+	0.546655i	−0.663956	+	0.747772i	$0.731124\pi$
$224$	−2.29973	−	1.32775i	−0.153657	−	0.0887140i
$225$	27.2630	−	14.8852i	1.81754	−	0.992349i
$226$	−8.53402	−	14.7814i	−0.567675	−	0.983241i
$227$	13.6938	+	7.90612i	0.908890	+	0.524748i	0.880074	−	0.474837i	$-0.157493\pi$
$227$	13.6938	+	7.90612i	0.908890	+	0.524748i	0.0288161	+	0.999585i	$0.490826\pi$
$228$	1.94284	+	1.98973i	0.128668	+	0.131773i
$229$	4.52821			0.299232			0.149616	−	0.988744i	$-0.452196\pi$
$229$	4.52821			0.299232			0.149616	+	0.988744i	$0.452196\pi$
$230$	−23.8582	−	13.7745i	−1.57316	−	0.908265i
$231$	4.96092	+	19.4384i	0.326404	+	1.27895i
$232$	0.178122	+	0.308516i	0.0116943	+	0.0202551i
$233$	5.74250			0.376203			0.188102	−	0.982150i	$-0.439767\pi$
$233$	5.74250			0.376203			0.188102	+	0.982150i	$0.439767\pi$
$234$	1.21590	−	0.663867i	0.0794862	−	0.0433983i
$235$	2.63019	−	1.51854i	0.171575	−	0.0990587i
$236$	4.54130	−	2.62192i	0.295613	−	0.170672i
$237$	−2.52055	+	8.97735i	−0.163727	+	0.583142i
$238$	9.84066	+	17.0445i	0.637875	+	1.10483i
$239$	16.6162	−	9.59339i	1.07482	−	0.620545i	0.145322	−	0.989384i	$-0.453578\pi$
$239$	16.6162	−	9.59339i	1.07482	−	0.620545i	0.929493	+	0.368840i	$0.120245\pi$
$240$	6.57611	−	1.67830i	0.424486	−	0.108334i
$241$	2.00410	+	1.15706i	0.129095	+	0.0745331i	0.563157	−	0.826350i	$-0.309587\pi$
$241$	2.00410	+	1.15706i	0.129095	+	0.0745331i	−0.434062	+	0.900883i	$0.642920\pi$
$242$	6.94934	+	4.01220i	0.446721	+	0.257914i
$243$	−14.7902	−	4.92440i	−0.948792	−	0.315900i
$244$	11.1092	+	6.41390i	0.711193	+	0.410608i
$245$	0.175370	−	0.101250i	0.0112040	−	0.00646863i
$246$	−3.62767	+	0.925826i	−0.231292	+	0.0590285i
$247$	−0.370710	−	0.642089i	−0.0235877	−	0.0408551i
$248$	3.18278	−	5.51273i	0.202106	−	0.350059i
$249$	−1.86906	−	7.32355i	−0.118447	−	0.464111i
$250$	−20.9791			−1.32683
$251$			2.52904i			0.159632i	0.996810	+	0.0798159i	$0.0254332\pi$
$251$			2.52904i			0.159632i	−0.996810	+	0.0798159i	$0.974567\pi$
$252$	0.189923	−	7.96424i	0.0119640	−	0.501700i
$253$			30.6656i			1.92793i
$254$	−0.444722	−	0.256760i	−0.0279044	−	0.0161106i
$255$	−48.4286	−	13.5972i	−3.03272	−	0.851490i
$256$	1.00000			0.0625000
$257$	−1.75065	+	1.01074i	−0.109202	+	0.0630481i	−0.553606	−	0.832778i	$-0.686749\pi$
$257$	−1.75065	+	1.01074i	−0.109202	+	0.0630481i	0.444404	+	0.895826i	$0.353415\pi$
$258$	−9.85851	+	9.62621i	−0.613764	+	0.599302i
$259$	1.20012	−	16.1081i	0.0745715	−	1.00091i
$260$	−1.80943			−0.112216
$261$	−0.556280	+	0.912547i	−0.0344328	+	0.0564852i
$262$	3.42358	+	5.92982i	0.211510	+	0.366346i
$263$	−6.05447	+	10.4867i	−0.373335	+	0.646635i	−0.990076	−	0.140531i	$-0.955119\pi$
$263$	−6.05447	+	10.4867i	−0.373335	+	0.646635i	0.616741	+	0.787166i	$0.288452\pi$
$264$	−5.27791	−	5.40527i	−0.324833	−	0.332671i
$265$	−33.6318	−	19.4173i	−2.06598	−	1.19280i
$266$	−4.26362			−0.261419
$267$	5.11490	−	18.2175i	0.313027	−	1.11489i
$268$	−6.00043			−0.366535
$269$	−10.5042			−0.640451			−0.320225	−	0.947341i	$-0.603759\pi$
$269$	−10.5042			−0.640451			−0.320225	+	0.947341i	$0.603759\pi$
$270$	13.8732	+	14.9028i	0.844295	+	0.906953i
$271$	9.91679	−	17.1764i	0.602402	−	1.04339i	−0.390054	−	0.920792i	$-0.627544\pi$
$271$	9.91679	−	17.1764i	0.602402	−	1.04339i	0.992456	−	0.122599i	$-0.0391229\pi$
$272$	−6.41857	−	3.70577i	−0.389183	−	0.224695i
$273$	−0.574130	+	2.04486i	−0.0347479	+	0.123760i
$274$	17.1427	−	9.89734i	1.03563	−	0.597920i
$275$	22.5805	+	39.1105i	1.36165	+	2.35845i
$276$	3.29175	−	11.7241i	0.198140	−	0.705709i
$277$	−7.67758	−	4.43265i	−0.461301	−	0.266332i	0.251290	−	0.967912i	$-0.419145\pi$
$277$	−7.67758	−	4.43265i	−0.461301	−	0.266332i	−0.712591	+	0.701580i	$0.752479\pi$
$278$	−12.0483	+	6.95612i	−0.722612	+	0.417200i
$279$	19.0912	+	0.455268i	1.14296	+	0.0272562i
$280$	−5.20267	+	9.01130i	−0.310919	+	0.538528i
$281$		−	18.9590i		−	1.13100i	−0.824750	−	0.565498i	$-0.808684\pi$
$281$		−	18.9590i		−	1.13100i	0.824750	−	0.565498i	$-0.191316\pi$
$282$	0.937891	+	0.960523i	0.0558506	+	0.0571983i
$283$		−	6.19810i		−	0.368439i	−0.982885	−	0.184219i	$-0.941024\pi$
$283$		−	6.19810i		−	0.368439i	0.982885	−	0.184219i	$-0.0589757\pi$
$284$	−2.49449	−	4.32057i	−0.148020	−	0.256379i
$285$	7.79658	−	7.61287i	0.461829	−	0.450947i
$286$	1.00707	+	1.74429i	0.0595491	+	0.103142i
$287$	2.87003	−	4.97103i	0.169412	−	0.293431i
$288$	1.43763	+	2.63310i	0.0847135	+	0.155157i
$289$	18.9654	+	32.8490i	1.11561	+	1.93230i
$290$	1.20890	−	0.697956i	0.0709888	−	0.0409854i
$291$	22.1445	+	22.6789i	1.29814	+	1.32946i
$292$	−9.49852			−0.555859
$293$	4.47942			0.261690			0.130845	−	0.991403i	$-0.458231\pi$
$293$	4.47942			0.261690			0.130845	+	0.991403i	$0.458231\pi$
$294$	0.0625347	+	0.0640437i	0.00364710	+	0.00373510i
$295$	−10.2738	−	17.7947i	−0.598162	−	1.03605i
$296$	2.64159	+	5.47923i	0.153539	+	0.318474i
$297$	6.64490	−	21.6680i	0.385576	−	1.25731i
$298$	−18.4228	−	10.6364i	−1.06720	−	0.616151i
$299$	−1.62330	+	2.81164i	−0.0938778	+	0.162601i
$300$	−4.43473	−	17.3766i	−0.256039	−	1.00324i
$301$		−	21.1250i		−	1.21762i
$302$	−10.8026	−	6.23687i	−0.621618	−	0.358891i
$303$	−11.1211	+	10.8590i	−0.638889	+	0.623835i
$304$	1.39047	−	0.802790i	0.0797491	−	0.0460432i
$305$	25.1323	−	43.5304i	1.43907	−	2.49255i
$306$	0.530078	−	22.2283i	0.0303025	−	1.27071i
$307$	−12.3755			−0.706307			−0.353153	−	0.935565i	$-0.614891\pi$
$307$	−12.3755			−0.706307			−0.353153	+	0.935565i	$0.614891\pi$
$308$	11.5825			0.659973
$309$	−1.99327	+	7.09934i	−0.113393	+	0.403867i
$310$	−21.6012	−	12.4714i	−1.22686	−	0.708330i
$311$	−2.08207	+	1.20208i	−0.118063	+	0.0681640i	−0.557869	−	0.829929i	$-0.688381\pi$
$311$	−2.08207	+	1.20208i	−0.118063	+	0.0681640i	0.439805	+	0.898093i	$0.355047\pi$
$312$	−0.197785	−	0.774981i	−0.0111973	−	0.0438747i
$313$		−	26.7017i		−	1.50927i	−0.656146	−	0.754634i	$-0.727814\pi$
$313$		−	26.7017i		−	1.50927i	0.656146	−	0.754634i	$-0.272186\pi$
$314$	13.1021	−	7.56450i	0.739394	−	0.426890i
$315$	−31.2072	−	0.744197i	−1.75833	−	0.0419308i
$316$	4.66224	+	2.69175i	0.262272	+	0.151423i
$317$	−26.8781			−1.50963			−0.754813	−	0.655940i	$-0.772273\pi$
$317$	−26.8781			−1.50963			−0.754813	+	0.655940i	$0.772273\pi$
$318$	4.64024	−	16.5269i	0.260212	−	0.926785i
$319$	−1.34566	−	0.776915i	−0.0753422	−	0.0434989i
$320$		−	3.91841i		−	0.219046i
$321$	−8.14339	+	7.95151i	−0.454520	+	0.443810i
$322$	9.33495	+	16.1686i	0.520217	+	0.901042i
$323$	−11.8998			−0.662123
$324$	−4.86641	+	7.57087i	−0.270356	+	0.420604i
$325$			4.78123i			0.265215i
$326$	−1.13116	+	1.95922i	−0.0626490	+	0.108511i
$327$	−4.15387	+	14.7947i	−0.229709	+	0.818147i
$328$			2.16157i			0.119353i
$329$	−2.05822			−0.113474
$330$	−21.1801	+	20.6810i	−1.16593	+	1.13845i
$331$		−	10.9561i		−	0.602202i	−0.953592	−	0.301101i	$-0.902646\pi$
$331$		−	10.9561i		−	0.602202i	0.953592	−	0.301101i	$-0.0973542\pi$
$332$	−4.36378			−0.239493
$333$	−10.6297	+	14.8327i	−0.582505	+	0.812827i
$334$	−7.76224			−0.424731
$335$			23.5122i			1.28461i
$336$	−4.42823	−	1.24331i	−0.241580	−	0.0678279i
$337$	−10.3582			−0.564247			−0.282123	−	0.959378i	$-0.591039\pi$
$337$	−10.3582			−0.564247			−0.282123	+	0.959378i	$0.591039\pi$
$338$		−	12.7868i		−	0.695508i
$339$	−20.6533	−	21.1517i	−1.12173	−	1.14880i
$340$	−14.5207	+	25.1506i	−0.787497	+	1.36398i
$341$			27.7646i			1.50354i
$342$	4.11282	+	2.50713i	0.222396	+	0.135570i
$343$	18.4513			0.996275
$344$	3.97758	+	6.88938i	0.214457	+	0.371450i
$345$	−45.9399	−	12.8985i	−2.47332	−	0.694430i
$346$			3.68122i			0.197904i
$347$	−5.57571	−	3.21914i	−0.299320	−	0.172812i	0.342818	−	0.939402i	$-0.388619\pi$
$347$	−5.57571	−	3.21914i	−0.299320	−	0.172812i	−0.642137	+	0.766590i	$0.721952\pi$
$348$	0.431076	+	0.441478i	0.0231081	+	0.0236657i
$349$	25.0833			1.34268			0.671339	−	0.741151i	$-0.265720\pi$
$349$	25.0833			1.34268			0.671339	+	0.741151i	$0.265720\pi$
$350$	23.8113	+	13.7475i	1.27277	+	0.734834i
$351$	1.75626	−	1.63493i	0.0937422	−	0.0872659i
$352$	−3.77734	+	2.18085i	−0.201333	+	0.116240i
$353$			9.45016i			0.502981i	0.967860	+	0.251491i	$0.0809208\pi$
$353$			9.45016i			0.502981i	−0.967860	+	0.251491i	$0.919079\pi$
$354$	6.49847	−	6.34535i	0.345390	−	0.337251i
$355$	−16.9298	+	9.77443i	−0.898541	+	0.518773i
$356$	−9.46098	−	5.46230i	−0.501431	−	0.289501i
$357$	23.8155	+	24.3902i	1.26045	+	1.29087i
$358$	−11.0546			−0.584255
$359$	14.0543			0.741760			0.370880	−	0.928681i	$-0.379056\pi$
$359$	14.0543			0.741760			0.370880	+	0.928681i	$0.379056\pi$
$360$	10.3176	−	5.63325i	0.543784	−	0.296898i
$361$	−8.21106	+	14.2220i	−0.432161	+	0.748525i
$362$	−1.85007	+	1.06814i	−0.0972374	+	0.0561400i
$363$	13.3813	+	3.75703i	0.702334	+	0.197193i
$364$	1.06196	+	0.613125i	0.0556620	+	0.0321365i
$365$			37.2191i			1.94814i
$366$	21.3912	+	6.00597i	1.11814	+	0.313937i
$367$	2.07124	−	3.58749i	0.108118	−	0.187266i	−0.806890	−	0.590702i	$-0.798851\pi$
$367$	2.07124	−	3.58749i	0.108118	−	0.187266i	0.915008	+	0.403436i	$0.132184\pi$
$368$	−6.08873	−	3.51533i	−0.317397	−	0.183249i
$369$	−5.69163	+	3.10755i	−0.296294	+	0.161773i
$370$	21.4699	−	10.3508i	1.11617	−	0.538114i
$371$	13.1591	+	22.7922i	0.683184	+	1.18331i
$372$	2.98035	−	10.6150i	0.154524	−	0.550362i
$373$	20.0520			1.03825			0.519126	−	0.854698i	$-0.326257\pi$
$373$	20.0520			1.03825			0.519126	+	0.854698i	$0.326257\pi$
$374$	32.3269			1.67158
$375$	−35.2083	+	8.98559i	−1.81815	+	0.464014i
$376$	0.671238	−	0.387540i	0.0346165	−	0.0199858i
$377$	−0.0822527	−	0.142466i	−0.00423623	−	0.00733737i
$378$	−3.09244	−	13.4474i	−0.159058	−	0.691659i
$379$	−8.75436	+	15.1630i	−0.449681	+	0.778871i	−0.998365	−	0.0571590i	$-0.981796\pi$
$379$	−8.75436	+	15.1630i	−0.449681	+	0.778871i	0.548684	+	0.836030i	$0.315129\pi$
$380$	−3.14566	−	5.44845i	−0.161369	−	0.279500i
$381$	−0.856332	−	0.240431i	−0.0438712	−	0.0123176i
$382$	12.8465	+	22.2509i	0.657286	+	1.13845i
$383$		−	9.06920i		−	0.463414i	−0.972786	−	0.231707i	$-0.925569\pi$
$383$		−	9.06920i		−	0.463414i	0.972786	−	0.231707i	$-0.0744311\pi$
$384$	1.67826	−	0.428312i	0.0856432	−	0.0218572i
$385$		−	45.3850i		−	2.31303i
$386$	10.7630	−	18.6420i	0.547822	−	0.948855i
$387$	−12.4221	+	20.3778i	−0.631451	+	1.03586i
$388$	15.8486	−	9.15019i	0.804591	−	0.464531i
$389$	−17.0240	−	9.82882i	−0.863152	−	0.498341i	0.00191468	−	0.999998i	$-0.499391\pi$
$389$	−17.0240	−	9.82882i	−0.863152	−	0.498341i	−0.865066	+	0.501657i	$0.832724\pi$
$390$	−3.03670	+	0.775002i	−0.153769	+	0.0392438i
$391$	26.0540	+	45.1268i	1.31761	+	2.28216i
$392$	0.0447554	−	0.0258395i	0.00226049	−	0.00130509i
$393$	8.28547	+	8.48541i	0.417947	+	0.428032i
$394$	−14.6579	−	8.46276i	−0.738455	−	0.426347i
$395$	10.5474	−	18.2686i	0.530696	−	0.919193i
$396$	−11.1728	−	6.81085i	−0.561456	−	0.342258i
$397$	−15.0638			−0.756031			−0.378015	−	0.925799i	$-0.623393\pi$
$397$	−15.0638			−0.756031			−0.378015	+	0.925799i	$0.623393\pi$
$398$	8.90407			0.446321
$399$	−7.15545	+	1.82616i	−0.358220	+	0.0914222i
$400$	−10.3540			−0.517699
$401$	−26.8767	−	15.5173i	−1.34216	−	0.774895i	−0.355034	−	0.934854i	$-0.615531\pi$
$401$	−26.8767	−	15.5173i	−1.34216	−	0.774895i	−0.987124	+	0.159959i	$0.948864\pi$
$402$	−10.0703	+	2.57005i	−0.502259	+	0.128183i
$403$	−1.46973	+	2.54565i	−0.0732126	+	0.126808i
$404$	4.48699	+	7.77169i	0.223236	+	0.386656i
$405$	29.6658	+	19.0686i	1.47411	+	0.947527i
$406$	−0.946006			−0.0469495
$407$	−21.9276	−	14.9360i	−1.08691	−	0.740352i
$408$	−12.3592	−	3.47008i	−0.611874	−	0.171794i
$409$	−10.2428	+	5.91368i	−0.506473	+	0.292413i	−0.731383	−	0.681967i	$-0.761125\pi$
$409$	−10.2428	+	5.91368i	−0.506473	+	0.292413i	0.224909	+	0.974380i	$0.427791\pi$
$410$	8.46993			0.418300
$411$	24.5307	−	23.9527i	1.21001	−	1.18150i
$412$	3.68693	+	2.12865i	0.181642	+	0.104871i
$413$			13.9250i			0.685205i
$414$	0.502837	−	21.0860i	0.0247131	−	1.03632i
$415$			17.0991i			0.839362i
$416$	−0.461777			−0.0226405
$417$	−17.2408	+	16.8346i	−0.844288	+	0.824394i
$418$	−3.50153	+	6.06482i	−0.171265	+	0.296640i
$419$	−6.17091	−	10.6883i	−0.301468	−	0.522159i	0.675000	−	0.737817i	$-0.264143\pi$
$419$	−6.17091	−	10.6883i	−0.301468	−	0.522159i	−0.976469	+	0.215659i	$0.930810\pi$
$420$	−4.87179	+	17.3516i	−0.237719	+	0.846674i
$421$	−1.57301	+	0.908176i	−0.0766637	+	0.0442618i	−0.537842	−	0.843046i	$-0.680760\pi$
$421$	−1.57301	+	0.908176i	−0.0766637	+	0.0442618i	0.461178	+	0.887308i	$0.347427\pi$
$422$	10.9015	+	6.29398i	0.530676	+	0.306386i
$423$	1.98543	+	1.21030i	0.0965347	+	0.0588466i
$424$	−8.58300	−	4.95540i	−0.416827	−	0.240655i
$425$	66.4577	+	38.3694i	3.22367	+	1.86119i
$426$	−6.03694	−	6.18262i	−0.292491	−	0.299549i
$427$	−29.5005	+	17.0321i	−1.42763	+	0.824241i
$428$	3.28559	+	5.69081i	0.158815	+	0.275076i
$429$	2.43722	+	2.49603i	0.117670	+	0.120509i
$430$	26.9954	−	15.5858i	1.30184	−	0.751615i
$431$	−0.0443855	+	0.0256260i	−0.00213798	+	0.00123436i	−0.501069	−	0.865408i	$-0.667060\pi$
$431$	−0.0443855	+	0.0256260i	−0.00213798	+	0.00123436i	0.498931	+	0.866642i	$0.333726\pi$
$432$	3.54051	+	3.80326i	0.170343	+	0.182984i
$433$	−24.5557			−1.18007			−0.590036	−	0.807377i	$-0.700886\pi$
$433$	−24.5557			−1.18007			−0.590036	+	0.807377i	$0.700886\pi$
$434$	8.45186	+	14.6391i	0.405702	+	0.702697i
$435$	1.72990	−	1.68913i	0.0829421	−	0.0809878i
$436$	7.68337	+	4.43600i	0.367967	+	0.212446i
$437$	−11.2883			−0.539992
$438$	−15.9410	+	4.06833i	−0.761689	+	0.194392i
$439$	−18.2075	−	10.5121i	−0.868998	−	0.501716i	−0.00198314	−	0.999998i	$-0.500631\pi$
$439$	−18.2075	−	10.5121i	−0.868998	−	0.501716i	−0.867015	+	0.498282i	$0.833965\pi$
$440$	8.54547	+	14.8012i	0.407389	+	0.705619i
$441$	0.132380	+	0.0806975i	0.00630381	+	0.00384274i
$442$	2.96395	+	1.71124i	0.140981	+	0.0813953i
$443$	1.68557	+	2.91950i	0.0800841	+	0.138710i	0.903286	−	0.429039i	$-0.141148\pi$
$443$	1.68557	+	2.91950i	0.0800841	+	0.138710i	−0.823202	+	0.567749i	$0.807814\pi$
$444$	6.78009	+	8.06415i	0.321769	+	0.382707i
$445$	−21.4035	+	37.0720i	−1.01463	+	1.75738i
$446$	8.16330	−	4.71308i	0.386543	−	0.223171i
$447$	−35.4739	−	9.95993i	−1.67786	−	0.471089i
$448$	−1.32775	+	2.29973i	−0.0627303	+	0.108652i
$449$	21.4579	−	12.3887i	1.01266	−	0.584661i	0.100692	−	0.994918i	$-0.467894\pi$
$449$	21.4579	−	12.3887i	1.01266	−	0.584661i	0.911970	+	0.410257i	$0.134561\pi$
$450$	−14.8852	−	27.2630i	−0.701697	−	1.28519i
$451$	−4.71406	−	8.16499i	−0.221976	−	0.384474i
$452$	−14.7814	+	8.53402i	−0.695257	+	0.401407i
$453$	−20.8008	−	5.84020i	−0.977308	−	0.274397i
$454$	7.90612	−	13.6938i	0.371053	−	0.642682i
$455$	2.40248	−	4.16121i	0.112630	−	0.195081i
$456$	1.98973	−	1.94284i	0.0931775	−	0.0909820i
$457$	9.06793	+	5.23537i	0.424180	+	0.244900i	0.696864	−	0.717203i	$-0.254578\pi$
$457$	9.06793	+	5.23537i	0.424180	+	0.244900i	−0.272684	+	0.962104i	$0.587911\pi$
$458$		−	4.52821i		−	0.211589i
$459$	−8.63102	−	37.5318i	−0.402862	−	1.75183i
$460$	−13.7745	+	23.8582i	−0.642240	+	1.11239i
$461$			8.32195i			0.387592i	0.981042	+	0.193796i	$0.0620799\pi$
$461$			8.32195i			0.387592i	−0.981042	+	0.193796i	$0.937920\pi$
$462$	19.4384	−	4.96092i	0.904356	−	0.230803i
$463$		−	30.2037i		−	1.40368i	−0.712333	−	0.701842i	$-0.752361\pi$
$463$		−	30.2037i		−	1.40368i	0.712333	−	0.701842i	$-0.247639\pi$
$464$	0.308516	−	0.178122i	0.0143225	−	0.00826911i
$465$	−41.5940	−	11.6783i	−1.92887	−	0.541566i
$466$		−	5.74250i		−	0.266016i
$467$			1.55229i			0.0718315i	0.999355	+	0.0359157i	$0.0114348\pi$
$467$			1.55229i			0.0718315i	−0.999355	+	0.0359157i	$0.988565\pi$
$468$	−0.663867	−	1.21590i	−0.0306873	−	0.0562052i
$469$	7.96707	−	13.7994i	0.367885	−	0.637196i
$470$	−1.51854	−	2.63019i	−0.0700451	−	0.121322i
$471$	18.7487	−	18.3070i	0.863896	−	0.843541i
$472$	−2.62192	−	4.54130i	−0.120684	−	0.209030i
$473$	−30.0494	−	17.3490i	−1.38167	−	0.797709i
$474$	8.97735	+	2.52055i	0.412343	+	0.115773i
$475$	−14.3969	+	8.31207i	−0.660576	+	0.381384i
$476$	17.0445	−	9.84066i	0.781234	−	0.451046i
$477$	0.708827	−	29.7239i	0.0324550	−	1.36097i
$478$	−9.59339	−	16.6162i	−0.438791	−	0.760009i
$479$			23.6661i			1.08133i	0.841237	+	0.540666i	$0.181828\pi$
$479$			23.6661i			1.08133i	−0.841237	+	0.540666i	$0.818172\pi$
$480$	−1.67830	−	6.57611i	−0.0766037	−	0.300157i
$481$	−1.21982	−	2.53019i	−0.0556192	−	0.115367i
$482$	1.15706	−	2.00410i	0.0527029	−	0.0912840i
$483$	22.5917	+	23.1368i	1.02796	+	1.05276i
$484$	4.01220	−	6.94934i	0.182373	−	0.315879i
$485$	−35.8543	−	62.1014i	−1.62806	−	2.81988i
$486$	−4.92440	+	14.7902i	−0.223375	+	0.670897i
$487$			7.84363i			0.355429i	0.984082	+	0.177714i	$0.0568703\pi$
$487$			7.84363i			0.355429i	−0.984082	+	0.177714i	$0.943130\pi$
$488$	6.41390	−	11.1092i	0.290343	−	0.502890i
$489$	−1.05922	+	3.77257i	−0.0478994	+	0.170601i
$490$	−0.101250	−	0.175370i	−0.00457401	−	0.00792242i
$491$	15.1938	−	26.3164i	0.685687	−	1.18764i	−0.287534	−	0.957770i	$-0.592835\pi$
$491$	15.1938	−	26.3164i	0.685687	−	1.18764i	0.973221	−	0.229873i	$-0.0738312\pi$
$492$	0.925826	+	3.62767i	0.0417395	+	0.163548i
$493$	−2.64031			−0.118914
$494$	−0.642089	+	0.370710i	−0.0288889	+	0.0166790i
$495$	−26.6877	+	43.7798i	−1.19952	+	1.96775i
$496$	−5.51273	−	3.18278i	−0.247529	−	0.142911i
$497$	13.2482			0.594263
$498$	−7.32355	+	1.86906i	−0.328176	+	0.0837545i
$499$		−	42.4988i		−	1.90251i	−0.308409	−	0.951254i	$-0.599796\pi$
$499$		−	42.4988i		−	1.90251i	0.308409	−	0.951254i	$-0.400204\pi$
$500$			20.9791i			0.938214i
$501$	−13.0270	+	3.32466i	−0.582005	+	0.148535i
$502$	2.52904			0.112877
$503$	−25.9998	−	15.0110i	−1.15928	−	0.669308i	−0.208145	−	0.978098i	$-0.566743\pi$
$503$	−25.9998	−	15.0110i	−1.15928	−	0.669308i	−0.951130	+	0.308790i	$0.900076\pi$
$504$	−7.96424	−	0.189923i	−0.354755	−	0.00845985i
$505$	30.4527	−	17.5819i	1.35513	−	0.782383i
$506$	30.6656			1.36325
$507$	−5.47672	−	21.4595i	−0.243230	−	0.953049i
$508$	−0.256760	+	0.444722i	−0.0113919	+	0.0197314i
$509$	−5.75276	−	9.96407i	−0.254987	−	0.441650i	0.709905	−	0.704297i	$-0.248738\pi$
$509$	−5.75276	−	9.96407i	−0.254987	−	0.441650i	−0.964892	+	0.262647i	$0.915404\pi$
$510$	−13.5972	+	48.4286i	−0.602094	+	2.14446i
$511$	12.6117	−	21.8440i	0.557907	−	0.966323i
$512$		−	1.00000i		−	0.0441942i
$513$	7.97620	+	2.44605i	0.352158	+	0.107996i
$514$	1.01074	+	1.75065i	0.0445817	+	0.0772178i
$515$	8.34093	−	14.4469i	0.367545	−	0.636607i
$516$	9.62621	+	9.85851i	0.423770	+	0.433997i
$517$	−1.69033	+	2.92774i	−0.0743407	+	0.128762i
$518$	−16.1081	−	1.20012i	−0.707751	−	0.0527300i
$519$	1.57671	+	6.17804i	0.0692099	+	0.271186i
$520$			1.80943i			0.0793490i
$521$	17.0605	+	29.5496i	0.747432	+	1.29459i	0.949050	+	0.315126i	$0.102047\pi$
$521$	17.0605	+	29.5496i	0.747432	+	1.29459i	−0.201617	+	0.979464i	$0.564620\pi$
$522$	0.912547	+	0.556280i	0.0399411	+	0.0243477i
$523$	21.8128	−	12.5936i	0.953806	−	0.550680i	0.0595446	−	0.998226i	$-0.481035\pi$
$523$	21.8128	−	12.5936i	0.953806	−	0.550680i	0.894261	+	0.447546i	$0.147702\pi$
$524$	5.92982	−	3.42358i	0.259046	−	0.149560i
$525$	45.8498	+	12.8731i	2.00105	+	0.561830i
$526$	10.4867	+	6.05447i	0.457240	+	0.263988i
$527$	23.5892	+	40.8578i	1.02756	+	1.77979i
$528$	−5.40527	+	5.27791i	−0.235234	+	0.229691i
$529$	13.2151	+	22.8892i	0.574568	+	0.995182i
$530$	−19.4173	+	33.6318i	−0.843434	+	1.46087i
$531$	8.18832	−	13.4325i	0.355343	−	0.582921i
$532$			4.26362i			0.184851i
$533$		−	0.998164i		−	0.0432353i
$534$	−18.2175	−	5.11490i	−0.788349	−	0.221343i
$535$	22.2989	−	12.8743i	0.964068	−	0.556605i
$536$			6.00043i			0.259179i
$537$	−18.5525	+	4.73482i	−0.800599	+	0.204323i
$538$			10.5042i			0.452867i
$539$	−0.112704	+	0.195209i	−0.00485452	+	0.00840827i
$540$	14.9028	−	13.8732i	0.641312	−	0.597007i
$541$		−	13.2237i		−	0.568533i	−0.958745	−	0.284266i	$-0.908250\pi$
$541$		−	13.2237i		−	0.568533i	0.958745	−	0.284266i	$-0.0917500\pi$
$542$	−17.1764	−	9.91679i	−0.737789	−	0.425963i
$543$	−2.64739	+	2.58502i	−0.113611	+	0.110934i
$544$	−3.70577	+	6.41857i	−0.158883	+	0.275194i
$545$	17.3821	−	30.1066i	0.744567	−	1.28963i
$546$	2.04486	+	0.574130i	0.0875118	+	0.0245705i
$547$	−29.1243	+	16.8149i	−1.24527	+	0.718955i	−0.970161	−	0.242460i	$-0.922046\pi$
$547$	−29.1243	+	16.8149i	−1.24527	+	0.718955i	−0.275105	+	0.961414i	$0.588712\pi$
$548$	−9.89734	−	17.1427i	−0.422793	−	0.732300i
$549$	38.4724	+	0.917452i	1.64196	+	0.0391559i
$550$	39.1105	−	22.5805i	1.66768	−	0.962834i
$551$	0.285989	−	0.495348i	0.0121835	−	0.0211025i
$552$	−11.7241	−	3.29175i	−0.499011	−	0.140106i
$553$	−12.3806	+	7.14793i	−0.526476	+	0.303961i
$554$	−4.43265	+	7.67758i	−0.188325	+	0.326189i
$555$	31.5987	−	26.5672i	1.34129	−	1.12771i
$556$	6.95612	+	12.0483i	0.295005	+	0.510964i
$557$	−33.8443	−	19.5400i	−1.43403	−	0.827937i	−0.436605	−	0.899653i	$-0.643819\pi$
$557$	−33.8443	−	19.5400i	−1.43403	−	0.827937i	−0.997425	+	0.0717161i	$0.977152\pi$
$558$	0.455268	−	19.0912i	0.0192730	−	0.808196i
$559$	−1.83676	−	3.18136i	−0.0776866	−	0.134557i
$560$	9.01130	+	5.20267i	0.380797	+	0.219853i
$561$	54.2528	−	13.8460i	2.29055	−	0.584577i
$562$	−18.9590			−0.799735
$563$	26.9060	+	15.5342i	1.13395	+	0.654688i	0.944926	−	0.327284i	$-0.106133\pi$
$563$	26.9060	+	15.5342i	1.13395	+	0.654688i	0.189027	+	0.981972i	$0.439467\pi$
$564$	0.960523	−	0.937891i	0.0404453	−	0.0394923i
$565$	33.4398	+	57.9195i	1.40682	+	2.43669i
$566$	−6.19810			−0.260526
$567$	−10.9496	−	21.2437i	−0.459839	−	0.892150i
$568$	−4.32057	+	2.49449i	−0.181287	+	0.104666i
$569$	13.6308	−	7.86973i	0.571431	−	0.329916i	−0.186289	−	0.982495i	$-0.559646\pi$
$569$	13.6308	−	7.86973i	0.571431	−	0.329916i	0.757721	+	0.652579i	$0.226313\pi$
$570$	−7.61287	−	7.79658i	−0.318868	−	0.326563i
$571$	5.04900	+	8.74513i	0.211294	+	0.365972i	0.952120	−	0.305725i	$-0.0988989\pi$
$571$	5.04900	+	8.74513i	0.211294	+	0.365972i	−0.740826	+	0.671697i	$0.765566\pi$
$572$	1.74429	−	1.00707i	0.0729324	−	0.0421076i
$573$	31.0901	+	31.8404i	1.29881	+	1.33015i
$574$	−4.97103	−	2.87003i	−0.207487	−	0.119793i
$575$	63.0425	+	36.3976i	2.62906	+	1.51789i
$576$	2.63310	−	1.43763i	0.109712	−	0.0599015i
$577$	−2.16105	−	1.24768i	−0.0899658	−	0.0519418i	0.454342	−	0.890827i	$-0.349874\pi$
$577$	−2.16105	−	1.24768i	−0.0899658	−	0.0519418i	−0.544308	+	0.838885i	$0.683208\pi$
$578$	32.8490	−	18.9654i	1.36634	−	0.788856i
$579$	10.0785	−	35.8961i	0.418847	−	1.49179i
$580$	−0.697956	−	1.20890i	−0.0289810	−	0.0501967i
$581$	5.79401	−	10.0355i	0.240376	−	0.416343i
$582$	22.6789	−	22.1445i	0.940071	−	0.917920i
$583$	43.2279			1.79032
$584$			9.49852i			0.393052i
$585$	−4.76442	+	2.60131i	−0.196984	+	0.107551i
$586$		−	4.47942i		−	0.185043i
$587$	32.5693	+	18.8039i	1.34428	+	0.776121i	0.987432	−	0.158042i	$-0.0505181\pi$
$587$	32.5693	+	18.8039i	1.34428	+	0.776121i	0.356848	+	0.934163i	$0.383851\pi$
$588$	0.0640437	−	0.0625347i	0.00264112	−	0.00257889i
$589$	−10.2204			−0.421124
$590$	−17.7947	+	10.2738i	−0.732596	+	0.422964i
$591$	−28.2245	−	7.92452i	−1.16100	−	0.325971i
$592$	5.47923	−	2.64159i	0.225195	−	0.108569i
$593$	−14.8591			−0.610189			−0.305095	−	0.952322i	$-0.598688\pi$
$593$	−14.8591			−0.610189			−0.305095	+	0.952322i	$0.598688\pi$
$594$	−21.6680	−	6.64490i	−0.889051	−	0.272644i
$595$	−38.5598	−	66.7875i	−1.58080	−	2.73802i
$596$	−10.6364	+	18.4228i	−0.435684	+	0.754627i
$597$	14.9433	−	3.81372i	0.611589	−	0.156085i
$598$	2.81164	+	1.62330i	0.114976	+	0.0663816i
$599$	18.4163			0.752471			0.376235	−	0.926524i	$-0.377218\pi$
$599$	18.4163			0.752471			0.376235	+	0.926524i	$0.377218\pi$
$600$	−17.3766	+	4.43473i	−0.709398	+	0.181047i
$601$	−23.5750			−0.961646			−0.480823	−	0.876818i	$-0.659662\pi$
$601$	−23.5750			−0.961646			−0.480823	+	0.876818i	$0.659662\pi$
$602$	−21.1250			−0.860989
$603$	−15.7997	+	8.62643i	−0.643414	+	0.351295i
$604$	−6.23687	+	10.8026i	−0.253775	+	0.439550i
$605$	−27.2304	−	15.7215i	−1.10707	−	0.639169i
$606$	10.8590	+	11.1211i	0.441118	+	0.451762i
$607$	−25.9334	+	14.9727i	−1.05261	+	0.607722i	−0.923378	−	0.383893i	$-0.874583\pi$
$607$	−25.9334	+	14.9727i	−1.05261	+	0.607722i	−0.129228	+	0.991615i	$0.541250\pi$
$608$	−0.802790	−	1.39047i	−0.0325574	−	0.0563911i
$609$	−1.58764	+	0.405186i	−0.0643345	+	0.0164189i
$610$	−43.5304	−	25.1323i	−1.76250	−	1.01758i
$611$	−0.309963	+	0.178957i	−0.0125397	+	0.00723983i
$612$	−22.2283	−	0.530078i	−0.898525	−	0.0214271i
$613$	−2.56711	+	4.44637i	−0.103685	+	0.179587i	−0.913200	−	0.407512i	$-0.866397\pi$
$613$	−2.56711	+	4.44637i	−0.103685	+	0.179587i	0.809515	+	0.587099i	$0.199730\pi$
$614$			12.3755i			0.499434i
$615$	14.2147	−	3.62777i	0.573193	−	0.146286i
$616$		−	11.5825i		−	0.466672i
$617$	2.92609	+	5.06813i	0.117800	+	0.204035i	0.918895	−	0.394501i	$-0.129083\pi$
$617$	2.92609	+	5.06813i	0.117800	+	0.204035i	−0.801096	+	0.598536i	$0.795749\pi$
$618$	7.09934	+	1.99327i	0.285577	+	0.0801809i
$619$	16.3796	+	28.3703i	0.658353	+	1.14030i	0.981042	+	0.193795i	$0.0620798\pi$
$619$	16.3796	+	28.3703i	0.658353	+	1.14030i	−0.322689	+	0.946505i	$0.604587\pi$
$620$	−12.4714	+	21.6012i	−0.500865	+	0.867523i
$621$	−8.18748	−	35.6031i	−0.328552	−	1.42870i
$622$	1.20208	+	2.08207i	0.0481992	+	0.0834835i
$623$	25.1236	−	14.5051i	1.00656	−	0.581136i
$624$	−0.774981	+	0.197785i	−0.0310241	+	0.00791772i
$625$	30.4349			1.21740
$626$	−26.7017			−1.06721
$627$	−3.27883	+	11.6781i	−0.130944	+	0.466378i
$628$	−7.56450	−	13.1021i	−0.301856	−	0.522831i
$629$	−44.9580	−	3.34954i	−1.79259	−	0.133555i
$630$	−0.744197	+	31.2072i	−0.0296495	+	1.24332i
$631$	15.9034	+	9.18183i	0.633104	+	0.365523i	0.781953	−	0.623337i	$-0.214224\pi$
$631$	15.9034	+	9.18183i	0.633104	+	0.365523i	−0.148849	+	0.988860i	$0.547557\pi$
$632$	2.69175	−	4.66224i	0.107072	−	0.185454i
$633$	20.9913	+	5.89368i	0.834329	+	0.234253i
$634$			26.8781i			1.06747i
$635$	1.74261	+	1.00609i	0.0691532	+	0.0399256i
$636$	−16.5269	−	4.64024i	−0.655336	−	0.183997i
$637$	−0.0206670	+	0.0119321i	−0.000818857	+	0.000472767i
$638$	−0.776915	+	1.34566i	−0.0307583	+	0.0532750i
$639$	−12.7796	−	7.79034i	−0.505554	−	0.308181i
$640$	−3.91841			−0.154889
$641$	−20.6116			−0.814108			−0.407054	−	0.913404i	$-0.633444\pi$
$641$	−20.6116			−0.814108			−0.407054	+	0.913404i	$0.633444\pi$
$642$	7.95151	+	8.14339i	0.313821	+	0.321394i
$643$	36.7853	+	21.2380i	1.45067	+	0.837544i	0.998519	−	0.0543980i	$-0.0173240\pi$
$643$	36.7853	+	21.2380i	1.45067	+	0.837544i	0.452150	+	0.891942i	$0.350657\pi$
$644$	16.1686	−	9.33495i	0.637133	−	0.367849i
$645$	38.6297	−	37.7195i	1.52104	−	1.48520i
$646$			11.8998i			0.468192i
$647$	−29.1064	+	16.8046i	−1.14429	+	0.660657i	−0.947490	−	0.319787i	$-0.896389\pi$
$647$	−29.1064	+	16.8046i	−1.14429	+	0.660657i	−0.196801	+	0.980443i	$0.563055\pi$
$648$	7.57087	+	4.86641i	0.297412	+	0.191171i
$649$	19.8078	+	11.4360i	0.777523	+	0.448903i
$650$	4.78123			0.187535
$651$	20.4545	+	20.9481i	0.801674	+	0.821020i
$652$	1.95922	+	1.13116i	0.0767290	+	0.0442995i
$653$		−	41.4024i		−	1.62020i	−0.586291	−	0.810101i	$-0.699412\pi$
$653$		−	41.4024i		−	1.62020i	0.586291	−	0.810101i	$-0.300588\pi$
$654$	14.7947	+	4.15387i	0.578518	+	0.162429i
$655$	−13.4150	−	23.2355i	−0.524168	−	0.907886i
$656$	2.16157			0.0843952
$657$	−25.0105	+	13.6554i	−0.975754	+	0.532748i
$658$			2.05822i			0.0802379i
$659$	18.1895	−	31.5052i	0.708564	−	1.22727i	−0.256826	−	0.966458i	$-0.582677\pi$
$659$	18.1895	−	31.5052i	0.708564	−	1.22727i	0.965390	−	0.260811i	$-0.0839899\pi$
$660$	20.6810	+	21.1801i	0.805008	+	0.824434i
$661$		−	29.7325i		−	1.15646i	−0.815874	−	0.578230i	$-0.803744\pi$
$661$		−	29.7325i		−	1.15646i	0.815874	−	0.578230i	$-0.196256\pi$
$662$	−10.9561			−0.425821
$663$	5.70722	+	1.60240i	0.221650	+	0.0622322i
$664$			4.36378i			0.169347i
$665$	16.7066			0.647855
$666$	14.8327	+	10.6297i	0.574755	+	0.411893i
$667$	−2.50463			−0.0969797
$668$			7.76224i			0.300330i
$669$	11.6815	−	11.4062i	0.451631	−	0.440989i
$670$	23.5122			0.908355
$671$			55.9510i			2.15996i
$672$	−1.24331	+	4.42823i	−0.0479615	+	0.170823i
$673$	−5.36532	+	9.29301i	−0.206818	+	0.358219i	−0.950710	−	0.310080i	$-0.899644\pi$
$673$	−5.36532	+	9.29301i	−0.206818	+	0.358219i	0.743892	+	0.668299i	$0.232977\pi$
$674$			10.3582i			0.398983i
$675$	−36.6583	−	39.3789i	−1.41098	−	1.51569i
$676$	−12.7868			−0.491799
$677$	−14.3325	−	24.8246i	−0.550842	−	0.954086i	−0.998214	−	0.0597382i	$-0.980973\pi$
$677$	−14.3325	−	24.8246i	−0.550842	−	0.954086i	0.447372	−	0.894348i	$-0.352360\pi$
$678$	−21.1517	+	20.6533i	−0.812326	+	0.793186i
$679$			48.5967i			1.86497i
$680$	25.1506	+	14.5207i	0.964483	+	0.556844i
$681$	7.40329	−	26.3680i	0.283695	−	1.01042i
$682$	27.7646			1.06316
$683$	1.20559	+	0.696050i	0.0461308	+	0.0266336i	0.522888	−	0.852401i	$-0.324855\pi$
$683$	1.20559	+	0.696050i	0.0461308	+	0.0266336i	−0.476757	+	0.879035i	$0.658188\pi$
$684$	2.50713	−	4.11282i	0.0958626	−	0.157257i
$685$	−67.1722	+	38.7819i	−2.56652	+	1.48178i
$686$		−	18.4513i		−	0.704473i
$687$	−1.93948	−	7.59950i	−0.0739959	−	0.289939i
$688$	6.88938	−	3.97758i	0.262655	−	0.151644i
$689$	3.96344	+	2.28829i	0.150995	+	0.0871769i
$690$	−12.8985	+	45.9399i	−0.491036	+	1.74890i
$691$	−4.11701			−0.156619			−0.0783093	−	0.996929i	$-0.524952\pi$
$691$	−4.11701			−0.156619			−0.0783093	+	0.996929i	$0.524952\pi$
$692$	3.68122			0.139939
$693$	30.4978	−	16.6514i	1.15852	−	0.632534i
$694$	−3.21914	+	5.57571i	−0.122197	+	0.211651i
$695$	47.2104	−	27.2570i	1.79079	−	1.03392i
$696$	0.441478	−	0.431076i	0.0167342	−	0.0163399i
$697$	−13.8742	−	8.01027i	−0.525523	−	0.303411i
$698$		−	25.0833i		−	0.949416i
$699$	−2.45958	−	9.63739i	−0.0930298	−	0.364520i
$700$	13.7475	−	23.8113i	0.519606	−	0.899984i
$701$	−27.3071	−	15.7658i	−1.03137	−	0.595464i	−0.113996	−	0.993481i	$-0.536365\pi$
$701$	−27.3071	−	15.7658i	−1.03137	−	0.595464i	−0.917378	+	0.398017i	$0.869699\pi$
$702$	−1.63493	−	1.75626i	−0.0617063	−	0.0662857i
$703$	5.49809	−	8.07173i	0.207364	−	0.304431i
$704$	2.18085	+	3.77734i	0.0821938	+	0.142364i
$705$	−3.67505	−	3.76373i	−0.138410	−	0.141750i
$706$	9.45016			0.355661
$707$	−23.8304			−0.896234
$708$	−6.34535	−	6.49847i	−0.238473	−	0.244227i
$709$	−18.6360	+	10.7595i	−0.699890	+	0.404082i	−0.807306	−	0.590132i	$-0.799076\pi$
$709$	−18.6360	+	10.7595i	−0.699890	+	0.404082i	0.107416	+	0.994214i	$0.465742\pi$
$710$	9.77443	+	16.9298i	0.366828	+	0.635364i
$711$	16.1459	+	0.385031i	0.605518	+	0.0144398i
$712$	−5.46230	+	9.46098i	−0.204708	+	0.354565i
$713$	22.3770	+	38.7581i	0.838025	+	1.45150i
$714$	24.3902	−	23.8155i	0.912781	−	0.891274i
$715$	−3.94610	−	6.83485i	−0.147576	−	0.255609i
$716$			11.0546i			0.413130i
$717$	−23.2171	−	23.7774i	−0.867059	−	0.887982i
$718$		−	14.0543i		−	0.524504i
$719$	0.902453	−	1.56309i	0.0336558	−	0.0582936i	−0.848707	−	0.528864i	$-0.822618\pi$
$719$	0.902453	−	1.56309i	0.0336558	−	0.0582936i	0.882363	+	0.470570i	$0.155952\pi$
$720$	−5.63325	−	10.3176i	−0.209939	−	0.384513i
$721$	−9.79063	+	5.65263i	−0.364622	+	0.210515i
$722$	14.2220	+	8.21106i	0.529287	+	0.305584i
$723$	1.08348	−	3.85897i	0.0402949	−	0.143517i
$724$	1.06814	+	1.85007i	0.0396970	+	0.0687572i
$725$	−3.19437	+	1.84427i	−0.118636	+	0.0684945i
$726$	3.75703	−	13.3813i	0.139436	−	0.496625i
$727$	−39.2053	−	22.6352i	−1.45404	−	0.839493i	−0.455336	−	0.890319i	$-0.650481\pi$
$727$	−39.2053	−	22.6352i	−1.45404	−	0.839493i	−0.998707	+	0.0508269i	$0.983814\pi$
$728$	0.613125	−	1.06196i	0.0227239	−	0.0393590i
$729$	−1.92959	+	26.9310i	−0.0714665	+	0.997443i
$730$	37.2191			1.37754
$731$	−58.9600			−2.18071
$732$	6.00597	−	21.3912i	0.221987	−	0.790643i
$733$	0.690135			0.0254907			0.0127454	−	0.999919i	$-0.495943\pi$
$733$	0.690135			0.0254907			0.0127454	+	0.999919i	$0.495943\pi$
$734$	−3.58749	−	2.07124i	−0.132417	−	0.0764509i
$735$	−0.245037	−	0.250950i	−0.00903832	−	0.00925642i
$736$	−3.51533	+	6.08873i	−0.129577	+	0.224433i
$737$	−13.0860	−	22.6657i	−0.482030	−	0.834901i
$738$	3.10755	+	5.69163i	0.114390	+	0.209512i
$739$	−42.3798			−1.55897			−0.779484	−	0.626422i	$-0.784519\pi$
$739$	−42.3798			−1.55897			−0.779484	+	0.626422i	$0.784519\pi$
$740$	−10.3508	−	21.4699i	−0.380504	−	0.789250i
$741$	−0.918811	+	0.897161i	−0.0337534	+	0.0329580i
$742$	22.7922	−	13.1591i	0.836727	−	0.483084i
$743$	37.1402			1.36254			0.681270	−	0.732032i	$-0.261428\pi$
$743$	37.1402			1.36254			0.681270	+	0.732032i	$0.261428\pi$
$744$	−10.6150	−	2.98035i	−0.389165	−	0.109265i
$745$	72.1882	+	41.6779i	2.64477	+	1.52696i
$746$		−	20.0520i		−	0.734155i
$747$	−11.4903	+	6.27352i	−0.420407	+	0.229536i
$748$		−	32.3269i		−	1.18199i
$749$	−17.4498			−0.637601
$750$	8.98559	+	35.2083i	0.328107	+	1.28563i
$751$	−14.9895	+	25.9625i	−0.546973	+	0.947385i	0.451507	+	0.892268i	$0.350887\pi$
$751$	−14.9895	+	25.9625i	−0.546973	+	0.947385i	−0.998480	+	0.0551177i	$0.982447\pi$
$752$	−0.387540	−	0.671238i	−0.0141321	−	0.0244775i
$753$	4.24438	−	1.08322i	0.154674	−	0.0394747i
$754$	−0.142466	+	0.0822527i	−0.00518830	+	0.00299547i
$755$	42.3290	+	24.4386i	1.54051	+	0.889413i
$756$	−13.4474	+	3.09244i	−0.489077	+	0.112471i
$757$	11.7903	+	6.80713i	0.428525	+	0.247409i	0.698718	−	0.715397i	$-0.253754\pi$
$757$	11.7903	+	6.80713i	0.428525	+	0.247409i	−0.270193	+	0.962806i	$0.587087\pi$
$758$	15.1630	+	8.75436i	0.550745	+	0.317973i
$759$	51.4648	−	13.1344i	1.86805	−	0.476750i
$760$	−5.44845	+	3.14566i	−0.197636	+	0.114105i
$761$	−19.4733	−	33.7287i	−0.705906	−	1.22267i	−0.966364	−	0.257180i	$-0.917207\pi$
$761$	−19.4733	−	33.7287i	−0.705906	−	1.22267i	0.260458	−	0.965485i	$-0.416127\pi$
$762$	−0.240431	+	0.856332i	−0.00870988	+	0.0310216i
$763$	−20.4032	+	11.7798i	−0.738645	+	0.426457i
$764$	22.2509	−	12.8465i	0.805008	−	0.464771i
$765$	−2.07706	+	87.0996i	−0.0750964	+	3.14909i
$766$	−9.06920			−0.327684
$767$	1.21074	+	2.09707i	0.0437174	+	0.0757207i
$768$	−0.428312	−	1.67826i	−0.0154554	−	0.0605589i
$769$	−16.4911	−	9.52117i	−0.594686	−	0.343342i	0.172262	−	0.985051i	$-0.444892\pi$
$769$	−16.4911	−	9.52117i	−0.594686	−	0.343342i	−0.766948	+	0.641709i	$0.778226\pi$
$770$	−45.3850			−1.63556
$771$	2.44610	+	2.50513i	0.0880942	+	0.0902200i
$772$	−18.6420	−	10.7630i	−0.670942	−	0.387368i
$773$	20.0236	+	34.6818i	0.720198	+	1.24742i	0.960920	+	0.276825i	$0.0892823\pi$
$773$	20.0236	+	34.6818i	0.720198	+	1.24742i	−0.240723	+	0.970594i	$0.577384\pi$
$774$	20.3778	+	12.4221i	0.732464	+	0.446503i
$775$	57.0787	+	32.9544i	2.05033	+	1.18376i
$776$	−9.15019	−	15.8486i	−0.328473	−	0.568932i
$777$	−27.5476	+	4.88520i	−0.988265	+	0.175256i
$778$	−9.82882	+	17.0240i	−0.352380	+	0.610340i
$779$	3.00561	−	1.73529i	0.107687	−	0.0621731i
$780$	0.775002	+	3.03670i	0.0277495	+	0.108731i
$781$	10.8802	−	18.8450i	0.389324	−	0.674329i
$782$	45.1268	−	26.0540i	1.61373	−	0.931688i
$783$	1.76975	+	0.542726i	0.0632457	+	0.0193954i
$784$	−0.0258395	−	0.0447554i	−0.000922841	−	0.00159841i
$785$	−51.3395	+	29.6409i	−1.83238	+	1.05793i
$786$	8.48541	−	8.28547i	0.302665	−	0.295533i
$787$	21.8698	−	37.8797i	0.779576	−	1.35027i	−0.152610	−	0.988286i	$-0.548768\pi$
$787$	21.8698	−	37.8797i	0.779576	−	1.35027i	0.932186	−	0.361979i	$-0.117899\pi$
$788$	−8.46276	+	14.6579i	−0.301473	+	0.522167i
$789$	20.1925	+	5.66941i	0.718873	+	0.201836i
$790$	−18.2686	−	10.5474i	−0.649968	−	0.375259i
$791$		−	45.3242i		−	1.61154i
$792$	−6.81085	+	11.1728i	−0.242013	+	0.397009i
$793$	−2.96179	+	5.12997i	−0.105176	+	0.182171i
$794$			15.0638i			0.534595i
$795$	−18.1824	+	64.7594i	−0.644862	+	2.29678i
$796$		−	8.90407i		−	0.315596i
$797$	7.08847	−	4.09253i	0.251087	−	0.144965i	−0.369175	−	0.929360i	$-0.620360\pi$
$797$	7.08847	−	4.09253i	0.251087	−	0.144965i	0.620262	+	0.784395i	$0.287026\pi$
$798$	1.82616	+	7.15545i	0.0646453	+	0.253300i
$799$			5.74452i			0.203227i
$800$			10.3540i			0.366068i
$801$	−32.7645	−	0.781334i	−1.15768	−	0.0276071i
$802$	−15.5173	+	26.8767i	−0.547933	+	0.949049i
$803$	−20.7148	−	35.8792i	−0.731011	−	1.26615i
$804$	2.57005	+	10.0703i	0.0906388	+	0.355151i
$805$	−36.5782	−	63.3553i	−1.28921	−	2.23298i
$806$	2.54565	+	1.46973i	0.0896668	+	0.0517691i
$807$	4.49906	+	17.6287i	0.158374	+	0.620560i
$808$	7.77169	−	4.48699i	0.273407	−	0.157852i
$809$	11.4095	−	6.58729i	0.401138	−	0.231597i	−0.285837	−	0.958278i	$-0.592272\pi$
$809$	11.4095	−	6.58729i	0.401138	−	0.231597i	0.686975	+	0.726681i	$0.258938\pi$
$810$	19.0686	−	29.6658i	0.670003	−	1.04235i
$811$	17.2840	+	29.9368i	0.606924	+	1.05122i	0.991744	+	0.128231i	$0.0409300\pi$
$811$	17.2840	+	29.9368i	0.606924	+	1.05122i	−0.384820	+	0.922991i	$0.625737\pi$
$812$			0.946006i			0.0331983i
$813$	−33.0739	−	9.28608i	−1.15995	−	0.325677i
$814$	−14.9360	+	21.9276i	−0.523508	+	0.768561i
$815$	4.43234	−	7.67704i	0.155258	−	0.268915i
$816$	−3.47008	+	12.3592i	−0.121477	+	0.432660i
$817$	6.38633	−	11.0614i	0.223429	−	0.386991i
$818$	5.91368	+	10.2428i	0.206767	+	0.358131i
$819$	3.67770	+	0.0877022i	0.128509	+	0.00306456i
$820$		−	8.46993i		−	0.295783i
$821$	−0.319825	+	0.553954i	−0.0111620	+	0.0193331i	−0.871552	−	0.490302i	$-0.836886\pi$
$821$	−0.319825	+	0.553954i	−0.0111620	+	0.0193331i	0.860390	+	0.509635i	$0.170220\pi$
$822$	−23.9527	−	24.5307i	−0.835446	−	0.855607i
$823$	−18.6686	−	32.3350i	−0.650747	−	1.12713i	−0.982942	−	0.183916i	$-0.941122\pi$
$823$	−18.6686	−	32.3350i	−0.650747	−	1.12713i	0.332195	−	0.943211i	$-0.392211\pi$
$824$	2.12865	−	3.68693i	0.0741550	−	0.128440i
$825$	55.9660	−	54.6473i	1.94849	−	1.90257i
$826$	13.9250			0.484513
$827$	−1.92716	+	1.11265i	−0.0670141	+	0.0386906i	−0.533133	−	0.846032i	$-0.678985\pi$
$827$	−1.92716	+	1.11265i	−0.0670141	+	0.0386906i	0.466119	+	0.884722i	$0.345652\pi$
$828$	−21.0860	−	0.502837i	−0.732788	−	0.0174748i
$829$	19.2586	+	11.1190i	0.668879	+	0.386177i	0.795652	−	0.605754i	$-0.207129\pi$
$829$	19.2586	+	11.1190i	0.668879	+	0.386177i	−0.126773	+	0.991932i	$0.540462\pi$
$830$	17.0991			0.593518
$831$	−4.15074	+	14.7835i	−0.143987	+	0.512834i
$832$			0.461777i			0.0160092i
$833$			0.383021i			0.0132709i
$834$	16.8346	+	17.2408i	0.582935	+	0.597002i
$835$	30.4157			1.05258
$836$	6.06482	+	3.50153i	0.209756	+	0.121103i
$837$	−7.41294	−	32.2350i	−0.256229	−	1.11420i
$838$	−10.6883	+	6.17091i	−0.369222	+	0.213170i
$839$	28.8056			0.994481			0.497240	−	0.867613i	$-0.334347\pi$
$839$	28.8056			0.994481			0.497240	+	0.867613i	$0.334347\pi$
$840$	17.3516	+	4.87179i	0.598689	+	0.168093i
$841$	−14.4365	+	25.0048i	−0.497812	+	0.862236i
$842$	0.908176	+	1.57301i	0.0312978	+	0.0542094i
$843$	−31.8180	+	8.12034i	−1.09587	+	0.279679i
$844$	6.29398	−	10.9015i	0.216648	−	0.375245i
$845$			50.1038i			1.72362i
$846$	1.21030	−	1.98543i	0.0416108	−	0.0682604i
$847$	10.6544	+	18.4540i	0.366090	+	0.634086i
$848$	−4.95540	+	8.58300i	−0.170169	+	0.294742i
$849$	−10.4020	+	2.65472i	−0.356996	+	0.0911098i
$850$	38.3694	−	66.4577i	1.31606	−	2.27948i
$851$	−42.6476	−	3.17741i	−1.46194	−	0.108920i
$852$	−6.18262	+	6.03694i	−0.211813	+	0.206822i
$853$			28.8037i			0.986218i	0.869967	+	0.493109i	$0.164140\pi$
$853$			28.8037i			0.986218i	−0.869967	+	0.493109i	$0.835860\pi$
$854$	17.0321	+	29.5005i	0.582826	+	1.00949i
$855$	−16.1157	−	9.82399i	−0.551146	−	0.335973i
$856$	5.69081	−	3.28559i	0.194508	−	0.112299i
$857$	43.0720	−	24.8676i	1.47131	−	0.849461i	0.471830	−	0.881690i	$-0.343594\pi$
$857$	43.0720	−	24.8676i	1.47131	−	0.849461i	0.999481	+	0.0322283i	$0.0102604\pi$
$858$	2.49603	−	2.43722i	0.0852131	−	0.0832052i
$859$	19.4870	+	11.2508i	0.664889	+	0.383874i	0.794137	−	0.607738i	$-0.207923\pi$
$859$	19.4870	+	11.2508i	0.664889	+	0.383874i	−0.129248	+	0.991612i	$0.541256\pi$
$860$	−15.5858	−	26.9954i	−0.531472	−	0.920537i
$861$	−9.57193	−	2.68749i	−0.326211	−	0.0915895i
$862$	0.0256260	+	0.0443855i	0.000872825	+	0.00151178i
$863$	6.45679	−	11.1835i	0.219792	−	0.380690i	−0.734952	−	0.678119i	$-0.762796\pi$
$863$	6.45679	−	11.1835i	0.219792	−	0.380690i	0.954744	+	0.297428i	$0.0961289\pi$
$864$	3.80326	−	3.54051i	0.129390	−	0.120451i
$865$		−	14.4246i		−	0.490450i
$866$			24.5557i			0.834436i
$867$	47.0060	−	45.8984i	1.59641	−	1.55879i
$868$	14.6391	−	8.45186i	0.496882	−	0.286875i
$869$			23.4812i			0.796544i
$870$	−1.68913	−	1.72990i	−0.0572670	−	0.0586489i
$871$		−	2.77086i		−	0.0938871i
$872$	4.43600	−	7.68337i	0.150222	−	0.260192i
$873$	28.5763	−	46.8779i	0.967161	−	1.58658i
$874$			11.2883i			0.381832i
$875$	−48.2463	−	27.8550i	−1.63102	−	0.941670i
$876$	4.06833	+	15.9410i	0.137456	+	0.538595i
$877$	−6.84875	+	11.8624i	−0.231266	+	0.400564i	−0.958181	−	0.286163i	$-0.907620\pi$
$877$	−6.84875	+	11.8624i	−0.231266	+	0.400564i	0.726915	+	0.686727i	$0.240953\pi$
$878$	−10.5121	+	18.2075i	−0.354767	+	0.614475i
$879$	−1.91859	−	7.51762i	−0.0647123	−	0.253563i
$880$	14.8012	−	8.54547i	0.498948	−	0.288068i
$881$	7.65560	+	13.2599i	0.257924	+	0.446737i	0.965686	−	0.259714i	$-0.0836283\pi$
$881$	7.65560	+	13.2599i	0.257924	+	0.446737i	−0.707762	+	0.706451i	$0.750295\pi$
$882$	0.0806975	−	0.132380i	0.00271723	−	0.00445746i
$883$	19.5217	−	11.2708i	0.656957	−	0.379294i	−0.134160	−	0.990960i	$-0.542833\pi$
$883$	19.5217	−	11.2708i	0.656957	−	0.379294i	0.791116	+	0.611666i	$0.209500\pi$
$884$	1.71124	−	2.96395i	0.0575552	−	0.0996885i
$885$	−25.4637	+	24.8637i	−0.855953	+	0.835784i
$886$	2.91950	−	1.68557i	0.0980825	−	0.0566280i
$887$	1.54504	−	2.67609i	0.0518775	−	0.0898545i	−0.838921	−	0.544254i	$-0.816813\pi$
$887$	1.54504	−	2.67609i	0.0518775	−	0.0898545i	0.890798	+	0.454399i	$0.150146\pi$
$888$	8.06415	−	6.78009i	0.270615	−	0.227525i
$889$	−0.681827	−	1.18096i	−0.0228678	−	0.0396081i
$890$	37.0720	+	21.4035i	1.24266	+	0.717449i
$891$	−39.2107	−	1.87118i	−1.31361	−	0.0626868i
$892$	−4.71308	−	8.16330i	−0.157806	−	0.273327i
$893$	−1.07773	−	0.622226i	−0.0360648	−	0.0208220i
$894$	−9.95993	+	35.4739i	−0.333110	+	1.18642i
$895$	43.3166			1.44791
$896$	2.29973	+	1.32775i	0.0768286	+	0.0443570i
$897$	5.41393	+	1.52006i	0.180766	+	0.0507532i
$898$	−12.3887	−	21.4579i	−0.413418	−	0.716060i
$899$	−2.26769			−0.0756317
$900$	−27.2630	+	14.8852i	−0.908768	+	0.496175i
$901$	63.6132	−	36.7271i	2.11926	−	1.22356i
$902$	−8.16499	+	4.71406i	−0.271864	+	0.156961i
$903$	−35.4531	+	9.04806i	−1.17981	+	0.301101i
$904$	8.53402	+	14.7814i	0.283837	+	0.491621i
$905$	7.24933	−	4.18540i	0.240976	−	0.139128i
$906$	−5.84020	+	20.8008i	−0.194028	+	0.691061i
$907$	−3.02706	−	1.74767i	−0.100512	−	0.0580305i	0.448902	−	0.893581i	$-0.351815\pi$
$907$	−3.02706	−	1.74767i	−0.100512	−	0.0580305i	−0.549413	+	0.835551i	$0.685149\pi$
$908$	−13.6938	−	7.90612i	−0.454445	−	0.262374i
$909$	22.9875	+	14.0130i	0.762448	+	0.464781i
$910$	−4.16121	−	2.40248i	−0.137943	−	0.0796413i
$911$	−41.6113	+	24.0243i	−1.37864	+	0.795961i	−0.991996	−	0.126266i	$-0.959701\pi$
$911$	−41.6113	+	24.0243i	−1.37864	+	0.795961i	−0.386648	+	0.922227i	$0.626367\pi$
$912$	−1.94284	−	1.98973i	−0.0643340	−	0.0658865i
$913$	−9.51674	−	16.4835i	−0.314958	−	0.545524i
$914$	5.23537	−	9.06793i	0.173171	−	0.299941i
$915$	−83.8197	−	23.5339i	−2.77100	−	0.778007i
$916$	−4.52821			−0.149616
$917$			18.1827i			0.600444i
$918$	−37.5318	+	8.63102i	−1.23873	+	0.284866i
$919$		−	17.5865i		−	0.580126i	−0.957007	−	0.290063i	$-0.906324\pi$
$919$		−	17.5865i		−	0.580126i	0.957007	−	0.290063i	$-0.0936763\pi$
$920$	23.8582	+	13.7745i	0.786580	+	0.454132i
$921$	5.30057	+	20.7693i	0.174660	+	0.684371i
$922$	8.32195			0.274069
$923$	1.99514	−	1.15190i	0.0656709	−	0.0379151i
$924$	−4.96092	−	19.4384i	−0.163202	−	0.639476i
$925$	−56.7319	+	27.3509i	−1.86533	+	0.899293i
$926$	−30.2037			−0.992554
$927$	12.7683	+	0.304485i	0.419365	+	0.0100006i
$928$	−0.178122	−	0.308516i	−0.00584714	−	0.0101275i
$929$	6.78312	−	11.7487i	0.222547	−	0.385463i	−0.733034	−	0.680192i	$-0.761896\pi$
$929$	6.78312	−	11.7487i	0.222547	−	0.385463i	0.955581	+	0.294730i	$0.0952296\pi$
$930$	−11.6783	+	41.5940i	−0.382945	+	1.36392i
$931$	−0.0718584	−	0.0414874i	−0.00235506	−	0.00135970i
$932$	−5.74250			−0.188102
$933$	2.90918	+	2.97939i	0.0952424	+	0.0975407i
$934$	1.55229			0.0507925
$935$	−126.670			−4.14255
$936$	−1.21590	+	0.663867i	−0.0397431	+	0.0216992i
$937$	0.704475	−	1.22019i	0.0230142	−	0.0398618i	−0.854289	−	0.519798i	$-0.826007\pi$
$937$	0.704475	−	1.22019i	0.0230142	−	0.0398618i	0.877303	+	0.479937i	$0.159340\pi$
$938$	−13.7994	−	7.96707i	−0.450565	−	0.260134i
$939$	−44.8123	+	11.4366i	−1.46239	+	0.373221i
$940$	−2.63019	+	1.51854i	−0.0857874	+	0.0495294i
$941$	−13.3886	−	23.1898i	−0.436457	−	0.755966i	0.560956	−	0.827845i	$-0.310434\pi$
$941$	−13.3886	−	23.1898i	−0.436457	−	0.755966i	−0.997413	+	0.0718798i	$0.977100\pi$
$942$	−18.3070	−	18.7487i	−0.596473	−	0.610867i
$943$	−13.1612	−	7.59863i	−0.428588	−	0.247445i
$944$	−4.54130	+	2.62192i	−0.147807	+	0.0853362i
$945$	12.1174	+	52.6924i	0.394181	+	1.71409i
$946$	−17.3490	+	30.0494i	−0.564065	+	0.976990i
$947$			8.58718i			0.279046i	0.990219	+	0.139523i	$0.0445569\pi$
$947$			8.58718i			0.279046i	−0.990219	+	0.139523i	$0.955443\pi$
$948$	2.52055	−	8.97735i	0.0818637	−	0.291571i
$949$		−	4.38620i		−	0.142382i
$950$	8.31207	+	14.3969i	0.269679	+	0.467098i
$951$	11.5122	+	45.1085i	0.373309	+	1.46274i
$952$	−9.84066	−	17.0445i	−0.318938	−	0.552416i
$953$	−4.43696	+	7.68503i	−0.143727	+	0.248943i	−0.928897	−	0.370337i	$-0.879242\pi$
$953$	−4.43696	+	7.68503i	−0.143727	+	0.248943i	0.785170	+	0.619280i	$0.212575\pi$
$954$	−29.7239	−	0.708827i	−0.962348	−	0.0229491i
$955$	−50.3381	−	87.1881i	−1.62890	−	2.82134i
$956$	−16.6162	+	9.59339i	−0.537408	+	0.310272i
$957$	−0.727503	+	2.59112i	−0.0235168	+	0.0837590i
$958$	23.6661			0.764618
$959$	52.5648			1.69740
$960$	−6.57611	+	1.67830i	−0.212243	+	0.0541670i
$961$	4.76012	+	8.24477i	0.153552	+	0.265960i
$962$	−2.53019	+	1.21982i	−0.0815765	+	0.0393287i
$963$	16.8326	+	10.2610i	0.542422	+	0.330655i
$964$	−2.00410	−	1.15706i	−0.0645476	−	0.0372666i
$965$	−42.1739	+	73.0473i	−1.35762	+	2.35147i
$966$	23.1368	−	22.5917i	0.744415	−	0.726875i
$967$		−	1.77165i		−	0.0569725i	−0.999594	−	0.0284863i	$-0.990931\pi$
$967$		−	1.77165i		−	0.0569725i	0.999594	−	0.0284863i	$-0.00906869\pi$
$968$	−6.94934	−	4.01220i	−0.223360	−	0.128957i
$969$	5.09683	+	19.9709i	0.163734	+	0.641559i
$970$	−62.1014	+	35.8543i	−1.99396	+	1.15121i
$971$	23.0626	−	39.9456i	0.740114	−	1.28192i	−0.212329	−	0.977198i	$-0.568105\pi$
$971$	23.0626	−	39.9456i	0.740114	−	1.28192i	0.952443	−	0.304717i	$-0.0985619\pi$
$972$	14.7902	+	4.92440i	0.474396	+	0.157950i
$973$	−36.9439			−1.18437
$974$	7.84363			0.251326
$975$	8.02413	−	2.04786i	0.256978	−	0.0655839i
$976$	−11.1092	−	6.41390i	−0.355597	−	0.205304i
$977$	−32.5249	+	18.7783i	−1.04056	+	0.600770i	−0.919993	−	0.391935i	$-0.871806\pi$
$977$	−32.5249	+	18.7783i	−1.04056	+	0.600770i	−0.120571	+	0.992705i	$0.538472\pi$
$978$	3.77257	+	1.05922i	0.120633	+	0.0338700i
$979$		−	47.6498i		−	1.52289i
$980$	−0.175370	+	0.101250i	−0.00560200	+	0.00323431i
$981$	26.6084	+	0.634531i	0.849542	+	0.0202590i
$982$	−26.3164	−	15.1938i	−0.839791	−	0.484854i
$983$	−39.4639			−1.25870			−0.629351	−	0.777121i	$-0.716679\pi$
$983$	−39.4639			−1.25870			−0.629351	+	0.777121i	$0.716679\pi$
$984$	3.62767	−	0.925826i	0.115646	−	0.0295143i
$985$	57.4358	+	33.1606i	1.83006	+	1.05658i
$986$			2.64031i			0.0840847i
$987$	0.881561	+	3.45423i	0.0280604	+	0.109949i
$988$	0.370710	+	0.642089i	0.0117939	+	0.0204276i
$989$	−55.9301			−1.77847
$990$	43.7798	+	26.6877i	1.39141	+	0.848191i
$991$		−	15.6665i		−	0.497663i	−0.968547	−	0.248831i	$-0.919953\pi$
$991$		−	15.6665i		−	0.497663i	0.968547	−	0.248831i	$-0.0800465\pi$
$992$	−3.18278	+	5.51273i	−0.101053	+	0.175029i
$993$	−18.3872	+	4.69263i	−0.583499	+	0.148916i
$994$		−	13.2482i		−	0.420208i
$995$	−34.8898			−1.10608
$996$	1.86906	+	7.32355i	0.0592234	+	0.232055i
$997$			17.4828i			0.553687i	0.960915	+	0.276844i	$0.0892884\pi$
$997$			17.4828i			0.553687i	−0.960915	+	0.276844i	$0.910712\pi$
$998$	−42.4988			−1.34528
$999$	29.4459	+	11.4864i	0.931628	+	0.363414i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	666.2.k.a.175.8	✓	76
3.2	odd	2		1998.2.k.a.1063.38		76
9.2	odd	6		1998.2.t.a.397.38		76
9.7	even	3		666.2.t.a.619.6	yes	76
37.11	even	6		666.2.t.a.85.6	yes	76
111.11	odd	6		1998.2.t.a.307.38		76
333.11	odd	6		1998.2.k.a.1639.1		76
333.196	even	6	inner	666.2.k.a.529.27	yes	76

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
666.2.k.a.175.8	✓	76	1.1	even	1	trivial
666.2.k.a.529.27	yes	76	333.196	even	6	inner
666.2.t.a.85.6	yes	76	37.11	even	6
666.2.t.a.619.6	yes	76	9.7	even	3
1998.2.k.a.1063.38		76	3.2	odd	2
1998.2.k.a.1639.1		76	333.11	odd	6
1998.2.t.a.307.38		76	111.11	odd	6
1998.2.t.a.397.38		76	9.2	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:	\( N \)	\(=\)	\( 666 = 2 \cdot 3^{2} \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	666.k (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-1.00000i q^{2} +(-0.428312 - 1.67826i) q^{3} -1.00000 q^{4} +3.91841i q^{5} +(-1.67826 + 0.428312i) q^{6} +(1.32775 - 2.29973i) q^{7} +1.00000i q^{8} +(-2.63310 + 1.43763i) q^{9} +3.91841 q^{10} +(-2.18085 - 3.77734i) q^{11} +(0.428312 + 1.67826i) q^{12} -0.461777i q^{13} +(-2.29973 - 1.32775i) q^{14} +(6.57611 - 1.67830i) q^{15} +1.00000 q^{16} +(-6.41857 - 3.70577i) q^{17} +(1.43763 + 2.63310i) q^{18} +(1.39047 - 0.802790i) q^{19} -3.91841i q^{20} +(-4.42823 - 1.24331i) q^{21} +(-3.77734 + 2.18085i) q^{22} +(-6.08873 - 3.51533i) q^{23} +(1.67826 - 0.428312i) q^{24} -10.3540 q^{25} -0.461777 q^{26} +(3.54051 + 3.80326i) q^{27} +(-1.32775 + 2.29973i) q^{28} +(0.308516 - 0.178122i) q^{29} +(-1.67830 - 6.57611i) q^{30} +(-5.51273 - 3.18278i) q^{31} -1.00000i q^{32} +(-5.40527 + 5.27791i) q^{33} +(-3.70577 + 6.41857i) q^{34} +(9.01130 + 5.20267i) q^{35} +(2.63310 - 1.43763i) q^{36} +(5.47923 - 2.64159i) q^{37} +(-0.802790 - 1.39047i) q^{38} +(-0.774981 + 0.197785i) q^{39} -3.91841 q^{40} +2.16157 q^{41} +(-1.24331 + 4.42823i) q^{42} +(6.88938 - 3.97758i) q^{43} +(2.18085 + 3.77734i) q^{44} +(-5.63325 - 10.3176i) q^{45} +(-3.51533 + 6.08873i) q^{46} +(-0.387540 - 0.671238i) q^{47} +(-0.428312 - 1.67826i) q^{48} +(-0.0258395 - 0.0447554i) q^{49} +10.3540i q^{50} +(-3.47008 + 12.3592i) q^{51} +0.461777i q^{52} +(-4.95540 + 8.58300i) q^{53} +(3.80326 - 3.54051i) q^{54} +(14.8012 - 8.54547i) q^{55} +(2.29973 + 1.32775i) q^{56} +(-1.94284 - 1.98973i) q^{57} +(-0.178122 - 0.308516i) q^{58} +(-4.54130 + 2.62192i) q^{59} +(-6.57611 + 1.67830i) q^{60} +(-11.1092 - 6.41390i) q^{61} +(-3.18278 + 5.51273i) q^{62} +(-0.189923 + 7.96424i) q^{63} -1.00000 q^{64} +1.80943 q^{65} +(5.27791 + 5.40527i) q^{66} +6.00043 q^{67} +(6.41857 + 3.70577i) q^{68} +(-3.29175 + 11.7241i) q^{69} +(5.20267 - 9.01130i) q^{70} +(2.49449 + 4.32057i) q^{71} +(-1.43763 - 2.63310i) q^{72} +9.49852 q^{73} +(-2.64159 - 5.47923i) q^{74} +(4.43473 + 17.3766i) q^{75} +(-1.39047 + 0.802790i) q^{76} -11.5825 q^{77} +(0.197785 + 0.774981i) q^{78} +(-4.66224 - 2.69175i) q^{79} +3.91841i q^{80} +(4.86641 - 7.57087i) q^{81} -2.16157i q^{82} +4.36378 q^{83} +(4.42823 + 1.24331i) q^{84} +(14.5207 - 25.1506i) q^{85} +(-3.97758 - 6.88938i) q^{86} +(-0.431076 - 0.441478i) q^{87} +(3.77734 - 2.18085i) q^{88} +(9.46098 + 5.46230i) q^{89} +(-10.3176 + 5.63325i) q^{90} +(-1.06196 - 0.613125i) q^{91} +(6.08873 + 3.51533i) q^{92} +(-2.98035 + 10.6150i) q^{93} +(-0.671238 + 0.387540i) q^{94} +(3.14566 + 5.44845i) q^{95} +(-1.67826 + 0.428312i) q^{96} +(-15.8486 + 9.15019i) q^{97} +(-0.0447554 + 0.0258395i) q^{98} +(11.1728 + 6.81085i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 76 q + 4 q^{3} - 76 q^{4} - 2 q^{7} - 4 q^{9} - 4 q^{11} - 4 q^{12} + 12 q^{15} + 76 q^{16} + 6 q^{21} + 12 q^{23} - 100 q^{25} - 24 q^{26} + 4 q^{27} + 2 q^{28} + 18 q^{29} - 12 q^{30} + 6 q^{31} - 32 q^{33}+ \cdots - 76 q^{99}+O(q^{100}) \) 76 * q + 4 * q^3 - 76 * q^4 - 2 * q^7 - 4 * q^9 - 4 * q^11 - 4 * q^12 + 12 * q^15 + 76 * q^16 + 6 * q^21 + 12 * q^23 - 100 * q^25 - 24 * q^26 + 4 * q^27 + 2 * q^28 + 18 * q^29 - 12 * q^30 + 6 * q^31 - 32 * q^33 - 18 * q^35 + 4 * q^36 + 10 * q^37 + 12 * q^38 + 24 * q^39 + 72 * q^41 + 6 * q^42 + 6 * q^43 + 4 * q^44 + 12 * q^45 - 20 * q^47 + 4 * q^48 - 36 * q^49 - 18 * q^51 + 14 * q^53 + 36 * q^54 + 42 * q^57 - 6 * q^59 - 12 * q^60 - 16 * q^62 + 46 * q^63 - 76 * q^64 + 32 * q^65 + 40 * q^67 + 6 * q^69 + 2 * q^71 + 28 * q^73 - 2 * q^74 - 78 * q^75 - 24 * q^77 - 2 * q^78 + 6 * q^79 - 28 * q^81 - 64 * q^83 - 6 * q^84 - 12 * q^85 + 4 * q^86 - 78 * q^87 + 60 * q^89 - 16 * q^90 + 42 * q^91 - 12 * q^92 + 6 * q^93 - 14 * q^95 - 12 * q^97 - 24 * q^98 - 76 * q^99

Introduction

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