LMFDB - Embedded newform 546.2.bu.b.71.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(71,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 5]))

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

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

chi := DirichletCharacter("546.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bu (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			71.4
Character	$\chi$	$=$	546.71
Dual form			546.2.bu.b.323.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.965926 + 0.258819i) q^{2} +(-0.186842 + 1.72194i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.04268 - 2.04268i) q^{5} +(-0.265197 - 1.71163i) q^{6} +(-0.258819 + 0.965926i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.93018 - 0.643461i) q^{9} +O(q^{10})$	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.186842 + 1.72194i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.04268 - 2.04268i) q^{5} +(-0.265197 - 1.71163i) q^{6} +(-0.258819 + 0.965926i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.93018 - 0.643461i) q^{9} +(2.50176 + 1.44439i) q^{10} +(0.446430 + 1.66610i) q^{11} +(0.699162 + 1.58467i) q^{12} +(3.02199 + 1.96661i) q^{13} -1.00000i q^{14} +(3.89903 - 3.13572i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.47565 - 6.02001i) q^{17} +(2.99688 - 0.136851i) q^{18} +(-5.79151 - 1.55183i) q^{19} +(-2.79035 - 0.747671i) q^{20} +(-1.61491 - 0.626147i) q^{21} +(-0.862436 - 1.49378i) q^{22} +(3.94076 - 6.82559i) q^{23} +(-1.08548 - 1.34972i) q^{24} +3.34505i q^{25} +(-3.42802 - 1.11745i) q^{26} +(1.65548 - 4.92538i) q^{27} +(0.258819 + 0.965926i) q^{28} +(-2.64980 - 1.52986i) q^{29} +(-2.95459 + 4.03801i) q^{30} +(5.66232 - 5.66232i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-2.95234 + 0.457430i) q^{33} +(4.91531 + 4.91531i) q^{34} +(2.50176 - 1.44439i) q^{35} +(-2.85934 + 0.907836i) q^{36} +(-5.75540 + 1.54215i) q^{37} +5.99581 q^{38} +(-3.95103 + 4.83625i) q^{39} +2.88878 q^{40} +(3.05005 - 0.817259i) q^{41} +(1.72194 + 0.186842i) q^{42} +(9.94067 - 5.73925i) q^{43} +(1.21967 + 1.21967i) q^{44} +(4.67103 + 7.29979i) q^{45} +(-2.03989 + 7.61296i) q^{46} +(-2.12290 + 2.12290i) q^{47} +(1.39783 + 1.02278i) q^{48} +(-0.866025 - 0.500000i) q^{49} +(-0.865763 - 3.23107i) q^{50} +(11.0155 - 4.86009i) q^{51} +(3.60043 + 0.192141i) q^{52} +1.27079i q^{53} +(-0.324292 + 5.18602i) q^{54} +(2.49139 - 4.31521i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(3.75426 - 9.68270i) q^{57} +(2.95546 + 0.791914i) q^{58} +(-2.54856 - 0.682885i) q^{59} +(1.80880 - 4.66513i) q^{60} +(-2.57403 - 4.45834i) q^{61} +(-4.00386 + 6.93490i) q^{62} +(1.37992 - 2.66380i) q^{63} -1.00000i q^{64} +(-2.15580 - 10.1901i) q^{65} +(2.73335 - 1.20597i) q^{66} +(0.346835 + 1.29441i) q^{67} +(-6.02001 - 3.47565i) q^{68} +(11.0170 + 8.06107i) q^{69} +(-2.04268 + 2.04268i) q^{70} +(-2.86989 + 10.7106i) q^{71} +(2.52695 - 1.61695i) q^{72} +(-6.64934 - 6.64934i) q^{73} +(5.16015 - 2.97921i) q^{74} +(-5.75999 - 0.624995i) q^{75} +(-5.79151 + 1.55183i) q^{76} -1.72487 q^{77} +(2.56469 - 5.69407i) q^{78} -8.40565 q^{79} +(-2.79035 + 0.747671i) q^{80} +(8.17191 + 3.77092i) q^{81} +(-2.73460 + 1.57882i) q^{82} +(-10.1535 - 10.1535i) q^{83} +(-1.71163 + 0.265197i) q^{84} +(-5.19729 + 19.3966i) q^{85} +(-8.11652 + 8.11652i) q^{86} +(3.12943 - 4.27696i) q^{87} +(-1.49378 - 0.862436i) q^{88} +(0.857755 + 3.20119i) q^{89} +(-6.40119 - 5.84211i) q^{90} +(-2.68175 + 2.41002i) q^{91} -7.88152i q^{92} +(8.69224 + 10.8082i) q^{93} +(1.50112 - 2.60001i) q^{94} +(8.66029 + 15.0001i) q^{95} +(-1.61491 - 0.626147i) q^{96} +(-8.03620 - 2.15329i) q^{97} +(0.965926 + 0.258819i) q^{98} +(-0.236050 - 5.16923i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{6} - 24 q^{9}+O(q^{10}) $ 56 * q + 8 * q^6 - 24 * q^9	$ 56 q + 8 q^{6} - 24 q^{9} + 24 q^{10} + 8 q^{11} + 24 q^{13} + 4 q^{15} + 28 q^{16} - 4 q^{17} - 8 q^{18} + 8 q^{19} + 4 q^{21} - 8 q^{23} - 8 q^{24} - 4 q^{26} - 24 q^{27} - 8 q^{30} - 8 q^{31} + 8 q^{33} - 24 q^{34} + 24 q^{35} - 12 q^{36} - 8 q^{37} - 20 q^{39} - 28 q^{41} + 8 q^{44} + 72 q^{45} - 20 q^{46} + 64 q^{50} + 16 q^{54} + 8 q^{55} - 28 q^{56} + 4 q^{58} - 8 q^{59} + 20 q^{60} + 8 q^{61} - 32 q^{62} - 16 q^{63} - 24 q^{65} + 32 q^{66} - 16 q^{69} - 112 q^{71} + 8 q^{73} + 48 q^{74} + 40 q^{75} + 8 q^{76} + 16 q^{79} + 12 q^{81} - 4 q^{83} - 4 q^{84} + 32 q^{85} - 16 q^{86} - 144 q^{87} + 88 q^{89} - 8 q^{90} - 8 q^{91} + 52 q^{93} - 8 q^{94} - 48 q^{95} + 4 q^{96} - 64 q^{97} + 56 q^{99}+O(q^{100}) $ 56 * q + 8 * q^6 - 24 * q^9 + 24 * q^10 + 8 * q^11 + 24 * q^13 + 4 * q^15 + 28 * q^16 - 4 * q^17 - 8 * q^18 + 8 * q^19 + 4 * q^21 - 8 * q^23 - 8 * q^24 - 4 * q^26 - 24 * q^27 - 8 * q^30 - 8 * q^31 + 8 * q^33 - 24 * q^34 + 24 * q^35 - 12 * q^36 - 8 * q^37 - 20 * q^39 - 28 * q^41 + 8 * q^44 + 72 * q^45 - 20 * q^46 + 64 * q^50 + 16 * q^54 + 8 * q^55 - 28 * q^56 + 4 * q^58 - 8 * q^59 + 20 * q^60 + 8 * q^61 - 32 * q^62 - 16 * q^63 - 24 * q^65 + 32 * q^66 - 16 * q^69 - 112 * q^71 + 8 * q^73 + 48 * q^74 + 40 * q^75 + 8 * q^76 + 16 * q^79 + 12 * q^81 - 4 * q^83 - 4 * q^84 + 32 * q^85 - 16 * q^86 - 144 * q^87 + 88 * q^89 - 8 * q^90 - 8 * q^91 + 52 * q^93 - 8 * q^94 - 48 * q^95 + 4 * q^96 - 64 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{12}\right)$

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 $

$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$2$	−0.965926	+	0.258819i	−0.683013	+	0.183013i
$3$	−0.186842	+	1.72194i	−0.107873	+	0.994165i
$3$	−0.186842	+	1.72194i	−0.107873	+	0.994165i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	−2.04268	−	2.04268i	−0.913513	−	0.913513i	0.0830341	−	0.996547i	$-0.473539\pi$
$5$	−2.04268	−	2.04268i	−0.913513	−	0.913513i	−0.996547	+	0.0830341i	$0.973539\pi$
$6$	−0.265197	−	1.71163i	−0.108266	−	0.698769i
$7$	−0.258819	+	0.965926i	−0.0978244	+	0.365086i
$7$	−0.258819	+	0.965926i	−0.0978244	+	0.365086i
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	−2.93018	−	0.643461i	−0.976727	−	0.214487i
$10$	2.50176	+	1.44439i	0.791125	+	0.456756i
$11$	0.446430	+	1.66610i	0.134604	+	0.502348i	0.999999	+	0.00125826i	$0.000400515\pi$
$11$	0.446430	+	1.66610i	0.134604	+	0.502348i	−0.865396	+	0.501089i	$0.832933\pi$
$12$	0.699162	+	1.58467i	0.201831	+	0.457454i
$13$	3.02199	+	1.96661i	0.838150	+	0.545440i
$13$	3.02199	+	1.96661i	0.838150	+	0.545440i
$14$		−	1.00000i		−	0.267261i
$15$	3.89903	−	3.13572i	1.00673	−	0.809639i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−3.47565	−	6.02001i	−0.842969	−	1.46007i	−0.887373	−	0.461052i	$-0.847472\pi$
$17$	−3.47565	−	6.02001i	−0.842969	−	1.46007i	0.0444037	−	0.999014i	$-0.485861\pi$
$18$	2.99688	−	0.136851i	0.706371	−	0.0322560i
$19$	−5.79151	−	1.55183i	−1.32866	−	0.356014i	−0.476446	−	0.879204i	$-0.658075\pi$
$19$	−5.79151	−	1.55183i	−1.32866	−	0.356014i	−0.852216	+	0.523190i	$0.824742\pi$
$20$	−2.79035	−	0.747671i	−0.623941	−	0.167184i
$21$	−1.61491	−	0.626147i	−0.352403	−	0.136636i
$22$	−0.862436	−	1.49378i	−0.183872	−	0.318476i
$23$	3.94076	−	6.82559i	0.821705	−	1.42323i	−0.0827070	−	0.996574i	$-0.526357\pi$
$23$	3.94076	−	6.82559i	0.821705	−	1.42323i	0.904412	−	0.426661i	$-0.140310\pi$
$24$	−1.08548	−	1.34972i	−0.221573	−	0.275509i
$25$			3.34505i			0.669010i
$26$	−3.42802	−	1.11745i	−0.672289	−	0.219151i
$27$	1.65548	−	4.92538i	0.318598	−	0.947890i
$28$	0.258819	+	0.965926i	0.0489122	+	0.182543i
$29$	−2.64980	−	1.52986i	−0.492055	−	0.284088i	0.233372	−	0.972388i	$-0.425024\pi$
$29$	−2.64980	−	1.52986i	−0.492055	−	0.284088i	−0.725427	+	0.688300i	$0.758357\pi$
$30$	−2.95459	+	4.03801i	−0.539432	+	0.737237i
$31$	5.66232	−	5.66232i	1.01698	−	1.01698i	0.0171293	−	0.999853i	$-0.494547\pi$
$31$	5.66232	−	5.66232i	1.01698	−	1.01698i	0.999853	−	0.0171293i	$-0.00545269\pi$
$32$	−0.258819	+	0.965926i	−0.0457532	+	0.170753i
$33$	−2.95234	+	0.457430i	−0.513936	+	0.0796284i
$34$	4.91531	+	4.91531i	0.842969	+	0.842969i
$35$	2.50176	−	1.44439i	0.422874	−	0.244146i
$36$	−2.85934	+	0.907836i	−0.476557	+	0.151306i
$37$	−5.75540	+	1.54215i	−0.946182	+	0.253529i	−0.698741	−	0.715375i	$-0.746256\pi$
$37$	−5.75540	+	1.54215i	−0.946182	+	0.253529i	−0.247440	+	0.968903i	$0.579589\pi$
$38$	5.99581			0.972648
$39$	−3.95103	+	4.83625i	−0.632671	+	0.774421i
$40$	2.88878			0.456756
$41$	3.05005	−	0.817259i	0.476338	−	0.127634i	−0.0126588	−	0.999920i	$-0.504030\pi$
$41$	3.05005	−	0.817259i	0.476338	−	0.127634i	0.488997	+	0.872285i	$0.337363\pi$
$42$	1.72194	+	0.186842i	0.265702	+	0.0288303i
$43$	9.94067	−	5.73925i	1.51594	−	0.875227i	0.516113	−	0.856520i	$-0.327378\pi$
$43$	9.94067	−	5.73925i	1.51594	−	0.875227i	0.999825	−	0.0187068i	$-0.00595491\pi$
$44$	1.21967	+	1.21967i	0.183872	+	0.183872i
$45$	4.67103	+	7.29979i	0.696316	+	1.08819i
$46$	−2.03989	+	7.61296i	−0.300765	+	1.12247i
$47$	−2.12290	+	2.12290i	−0.309657	+	0.309657i	−0.844776	−	0.535120i	$-0.820267\pi$
$47$	−2.12290	+	2.12290i	−0.309657	+	0.309657i	0.535120	+	0.844776i	$0.320267\pi$
$48$	1.39783	+	1.02278i	0.201759	+	0.147626i
$49$	−0.866025	−	0.500000i	−0.123718	−	0.0714286i
$50$	−0.865763	−	3.23107i	−0.122437	−	0.456943i
$51$	11.0155	−	4.86009i	1.54248	−	0.680549i
$52$	3.60043	+	0.192141i	0.499290	+	0.0266452i
$53$			1.27079i			0.174557i	0.996184	+	0.0872783i	$0.0278169\pi$
$53$			1.27079i			0.174557i	−0.996184	+	0.0872783i	$0.972183\pi$
$54$	−0.324292	+	5.18602i	−0.0441306	+	0.705728i
$55$	2.49139	−	4.31521i	0.335939	−	0.581863i
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$	3.75426	−	9.68270i	0.497263	−	1.28251i
$58$	2.95546	+	0.791914i	0.388072	+	0.103983i
$59$	−2.54856	−	0.682885i	−0.331795	−	0.0889041i	0.0890758	−	0.996025i	$-0.471609\pi$
$59$	−2.54856	−	0.682885i	−0.331795	−	0.0889041i	−0.420871	+	0.907121i	$0.638275\pi$
$60$	1.80880	−	4.66513i	0.233515	−	0.602265i
$61$	−2.57403	−	4.45834i	−0.329570	−	0.570833i	0.652856	−	0.757482i	$-0.273571\pi$
$61$	−2.57403	−	4.45834i	−0.329570	−	0.570833i	−0.982427	+	0.186649i	$0.940237\pi$
$62$	−4.00386	+	6.93490i	−0.508491	+	0.880733i
$63$	1.37992	−	2.66380i	0.173854	−	0.335607i
$64$		−	1.00000i		−	0.125000i
$65$	−2.15580	−	10.1901i	−0.267394	−	1.26393i
$66$	2.73335	−	1.20597i	0.336452	−	0.148444i
$67$	0.346835	+	1.29441i	0.0423727	+	0.158137i	0.983871	−	0.178882i	$-0.0572480\pi$
$67$	0.346835	+	1.29441i	0.0423727	+	0.158137i	−0.941498	+	0.337019i	$0.890581\pi$
$68$	−6.02001	−	3.47565i	−0.730033	−	0.421485i
$69$	11.0170	+	8.06107i	1.32629	+	0.970439i
$70$	−2.04268	+	2.04268i	−0.244146	+	0.244146i
$71$	−2.86989	+	10.7106i	−0.340593	+	1.27111i	0.557084	+	0.830456i	$0.311920\pi$
$71$	−2.86989	+	10.7106i	−0.340593	+	1.27111i	−0.897677	+	0.440654i	$0.854747\pi$
$72$	2.52695	−	1.61695i	0.297803	−	0.190560i
$73$	−6.64934	−	6.64934i	−0.778246	−	0.778246i	0.201286	−	0.979532i	$-0.435488\pi$
$73$	−6.64934	−	6.64934i	−0.778246	−	0.778246i	−0.979532	+	0.201286i	$0.935488\pi$
$74$	5.16015	−	2.97921i	0.599855	−	0.346327i
$75$	−5.75999	−	0.624995i	−0.665106	−	0.0721682i
$76$	−5.79151	+	1.55183i	−0.664331	+	0.178007i
$77$	−1.72487			−0.196567
$78$	2.56469	−	5.69407i	0.290394	−	0.644726i
$79$	−8.40565			−0.945710			−0.472855	−	0.881140i	$-0.656777\pi$
$79$	−8.40565			−0.945710			−0.472855	+	0.881140i	$0.656777\pi$
$80$	−2.79035	+	0.747671i	−0.311970	+	0.0835922i
$81$	8.17191	+	3.77092i	0.907991	+	0.418991i
$82$	−2.73460	+	1.57882i	−0.301986	+	0.174352i
$83$	−10.1535	−	10.1535i	−1.11449	−	1.11449i	−0.992535	−	0.121957i	$-0.961083\pi$
$83$	−10.1535	−	10.1535i	−1.11449	−	1.11449i	−0.121957	−	0.992535i	$-0.538917\pi$
$84$	−1.71163	+	0.265197i	−0.186754	+	0.0289353i
$85$	−5.19729	+	19.3966i	−0.563725	+	2.10385i
$86$	−8.11652	+	8.11652i	−0.875227	+	0.875227i
$87$	3.12943	−	4.27696i	0.335510	−	0.458538i
$88$	−1.49378	−	0.862436i	−0.159238	−	0.0919360i
$89$	0.857755	+	3.20119i	0.0909219	+	0.339325i	0.996370	−	0.0851326i	$-0.0271314\pi$
$89$	0.857755	+	3.20119i	0.0909219	+	0.339325i	−0.905448	+	0.424458i	$0.860465\pi$
$90$	−6.40119	−	5.84211i	−0.674745	−	0.615812i
$91$	−2.68175	+	2.41002i	−0.281124	+	0.252639i
$92$		−	7.88152i		−	0.821705i
$93$	8.69224	+	10.8082i	0.901343	+	1.12075i
$94$	1.50112	−	2.60001i	0.154828	−	0.268170i
$95$	8.66029	+	15.0001i	0.888527	+	1.53897i
$96$	−1.61491	−	0.626147i	−0.164821	−	0.0639059i
$97$	−8.03620	−	2.15329i	−0.815952	−	0.218634i	−0.173376	−	0.984856i	$-0.555468\pi$
$97$	−8.03620	−	2.15329i	−0.815952	−	0.218634i	−0.642576	+	0.766222i	$0.722134\pi$
$98$	0.965926	+	0.258819i	0.0975732	+	0.0261447i
$99$	−0.236050	−	5.16923i	−0.0237239	−	0.519527i
$100$	1.67253	+	2.89690i	0.167253	+	0.289690i
$101$	−3.11520	+	5.39568i	−0.309974	+	0.536890i	−0.978356	−	0.206928i	$-0.933654\pi$
$101$	−3.11520	+	5.39568i	−0.309974	+	0.536890i	0.668383	+	0.743818i	$0.266987\pi$
$102$	−9.38228	+	7.54551i	−0.928984	+	0.747117i
$103$		−	14.8902i		−	1.46718i	−0.679594	−	0.733588i	$-0.737844\pi$
$103$		−	14.8902i		−	1.46718i	0.679594	−	0.733588i	$-0.262156\pi$
$104$	−3.52748	+	0.746265i	−0.345897	+	0.0731773i
$105$	2.01973	+	4.57776i	0.197105	+	0.446743i
$106$	−0.328905	−	1.22749i	−0.0319461	−	0.119224i
$107$	13.3846	+	7.72758i	1.29393	+	0.747053i	0.979349	−	0.202176i	$-0.0648012\pi$
$107$	13.3846	+	7.72758i	1.29393	+	0.747053i	0.314585	+	0.949229i	$0.398135\pi$
$108$	−1.02900	−	5.09325i	−0.0990155	−	0.490098i
$109$	6.00151	−	6.00151i	0.574840	−	0.574840i	−0.358637	−	0.933477i	$-0.616758\pi$
$109$	6.00151	−	6.00151i	0.574840	−	0.574840i	0.933477	+	0.358637i	$0.116758\pi$
$110$	−1.28964	+	4.81299i	−0.122962	+	0.458901i
$111$	−1.58016	−	10.1986i	−0.149982	−	0.968009i
$112$	0.707107	+	0.707107i	0.0668153	+	0.0668153i
$113$	−9.12535	+	5.26853i	−0.858441	+	0.495621i	−0.863490	−	0.504366i	$-0.831726\pi$
$113$	−9.12535	+	5.26853i	−0.858441	+	0.495621i	0.00504883	+	0.999987i	$0.498393\pi$
$114$	−1.12027	+	10.3244i	−0.104923	+	0.966973i
$115$	−21.9922	+	5.89278i	−2.05078	+	0.549505i
$116$	−3.05972			−0.284088
$117$	−7.58954	−	7.70707i	−0.701653	−	0.712518i
$118$	2.63847			0.242891
$119$	6.71444	−	1.79913i	0.615512	−	0.164926i
$120$	−0.539744	+	4.97432i	−0.0492717	+	0.454091i
$121$	6.94970	−	4.01241i	0.631790	−	0.364764i
$122$	3.64022	+	3.64022i	0.329570	+	0.329570i
$123$	0.837398	+	5.40472i	0.0755056	+	0.487327i
$124$	2.07255	−	7.73487i	0.186121	−	0.694612i
$125$	−3.38052	+	3.38052i	−0.302363	+	0.302363i
$126$	−0.643461	+	2.93018i	−0.0573241	+	0.261041i
$127$	−18.1226	−	10.4631i	−1.60812	−	0.928448i	−0.989791	−	0.142528i	$-0.954477\pi$
$127$	−18.1226	−	10.4631i	−1.60812	−	0.928448i	−0.618329	−	0.785920i	$-0.712190\pi$
$128$	0.258819	+	0.965926i	0.0228766	+	0.0853766i
$129$	8.02533	+	18.1896i	0.706591	+	1.60151i
$130$	4.71973	+	9.28492i	0.413948	+	0.814342i
$131$		−	7.19779i		−	0.628874i	−0.949278	−	0.314437i	$-0.898184\pi$
$131$		−	7.19779i		−	0.628874i	0.949278	−	0.314437i	$-0.101816\pi$
$132$	−2.32809	+	1.87232i	−0.202634	+	0.162964i
$133$	2.99790	−	5.19252i	0.259951	−	0.450249i
$134$	−0.670034	−	1.16053i	−0.0578821	−	0.100255i
$135$	−13.4426	+	6.67934i	−1.15695	+	0.574866i
$136$	6.71444	+	1.79913i	0.575759	+	0.154274i
$137$	1.74850	+	0.468509i	0.149384	+	0.0400274i	0.332736	−	0.943020i	$-0.392028\pi$
$137$	1.74850	+	0.468509i	0.149384	+	0.0400274i	−0.183352	+	0.983047i	$0.558695\pi$
$138$	−12.7280	−	4.93499i	−1.08348	−	0.420094i
$139$	7.89222	+	13.6697i	0.669409	+	1.15945i	0.978070	+	0.208278i	$0.0667860\pi$
$139$	7.89222	+	13.6697i	0.669409	+	1.15945i	−0.308660	+	0.951172i	$0.599881\pi$
$140$	1.44439	−	2.50176i	0.122073	−	0.211437i
$141$	−3.25887	−	4.05216i	−0.274446	−	0.341253i
$142$		−	11.0884i		−	0.930517i
$143$	−1.92746	+	5.91289i	−0.161183	+	0.494461i
$144$	−2.02234	+	2.21588i	−0.168529	+	0.184657i
$145$	2.28767	+	8.53769i	0.189980	+	0.709016i
$146$	8.14374	+	4.70179i	0.673981	+	0.389123i
$147$	1.02278	−	1.39783i	0.0843576	−	0.115291i
$148$	−4.21324	+	4.21324i	−0.346327	+	0.346327i
$149$	−5.03455	+	18.7892i	−0.412446	+	1.53927i	0.377451	+	0.926030i	$0.376801\pi$
$149$	−5.03455	+	18.7892i	−0.412446	+	1.53927i	−0.789897	+	0.613240i	$0.789866\pi$
$150$	5.72548	−	0.887097i	0.467484	−	0.0724312i
$151$	5.01991	+	5.01991i	0.408514	+	0.408514i	0.881220	−	0.472706i	$-0.156723\pi$
$151$	5.01991	+	5.01991i	0.408514	+	0.408514i	−0.472706	+	0.881220i	$0.656723\pi$
$152$	5.19252	−	2.99790i	0.421169	−	0.243162i
$153$	6.31065	+	19.8761i	0.510186	+	1.60689i
$154$	1.66610	−	0.446430i	0.134258	−	0.0359743i
$155$	−23.1326			−1.85805
$156$	−1.00357	+	6.16383i	−0.0803495	+	0.493502i
$157$	7.53131			0.601064			0.300532	−	0.953772i	$-0.402836\pi$
$157$	7.53131			0.601064			0.300532	+	0.953772i	$0.402836\pi$
$158$	8.11924	−	2.17554i	0.645932	−	0.173077i
$159$	−2.18823	−	0.237437i	−0.173538	−	0.0188299i
$160$	2.50176	−	1.44439i	0.197781	−	0.114189i
$161$	5.57307	+	5.57307i	0.439220	+	0.439220i
$162$	−8.86945	−	1.52738i	−0.696850	−	0.120002i
$163$	−0.397736	+	1.48437i	−0.0311531	+	0.116265i	−0.979751	−	0.200217i	$-0.935835\pi$
$163$	−0.397736	+	1.48437i	−0.0311531	+	0.116265i	0.948598	+	0.316482i	$0.102502\pi$
$164$	2.23279	−	2.23279i	0.174352	−	0.174352i
$165$	6.96506	+	5.09629i	0.542229	+	0.396746i
$166$	12.4355	+	7.17962i	0.965179	+	0.557246i
$167$	−1.88138	−	7.02139i	−0.145585	−	0.543331i	−0.999729	−	0.0232939i	$-0.992585\pi$
$167$	−1.88138	−	7.02139i	−0.145585	−	0.543331i	0.854143	−	0.520037i	$-0.174082\pi$
$168$	1.58467	−	0.699162i	0.122260	−	0.0539415i
$169$	5.26487	+	11.8862i	0.404990	+	0.914321i
$170$		−	20.0808i		−	1.54013i
$171$	15.9716	+	8.27375i	1.22138	+	0.632709i
$172$	5.73925	−	9.94067i	0.437614	−	0.757969i
$173$	−7.09523	−	12.2893i	−0.539440	−	0.934338i	−0.998934	−	0.0461571i	$-0.985303\pi$
$173$	−7.09523	−	12.2893i	−0.539440	−	0.934338i	0.459494	−	0.888181i	$-0.348031\pi$
$174$	−1.91584	+	4.94118i	−0.145239	+	0.374590i
$175$	−3.23107	−	0.865763i	−0.244246	−	0.0654455i
$176$	1.66610	+	0.446430i	0.125587	+	0.0336509i
$177$	1.65207	−	4.26089i	0.124177	−	0.320268i
$178$	−1.65706	−	2.87011i	−0.124202	−	0.215124i
$179$	2.69411	−	4.66633i	0.201367	−	0.348778i	−0.747602	−	0.664147i	$-0.768795\pi$
$179$	2.69411	−	4.66633i	0.201367	−	0.348778i	0.948969	+	0.315369i	$0.102128\pi$
$180$	7.69512	+	3.98629i	0.573561	+	0.297121i
$181$			14.2323i			1.05788i	0.848659	+	0.528940i	$0.177410\pi$
$181$			14.2323i			1.05788i	−0.848659	+	0.528940i	$0.822590\pi$
$182$	1.96661	−	3.02199i	0.145775	−	0.224005i
$183$	8.15795	−	3.59932i	0.603053	−	0.266070i
$184$	2.03989	+	7.61296i	0.150382	+	0.561235i
$185$	14.9065	+	8.60629i	1.09595	+	0.632747i
$186$	−11.1934	−	8.19016i	−0.820741	−	0.600531i
$187$	8.47829	−	8.47829i	0.619994	−	0.619994i
$188$	−0.777035	+	2.89993i	−0.0566711	+	0.211499i
$189$	4.32908	+	2.87386i	0.314894	+	0.209042i
$190$	−12.2475	−	12.2475i	−0.888527	−	0.888527i
$191$	−0.744908	+	0.430073i	−0.0538996	+	0.0311190i	−0.526708	−	0.850046i	$-0.676574\pi$
$191$	−0.744908	+	0.430073i	−0.0538996	+	0.0311190i	0.472808	+	0.881165i	$0.343240\pi$
$192$	1.72194	+	0.186842i	0.124271	+	0.0134841i
$193$	1.78606	−	0.478574i	0.128564	−	0.0344485i	−0.193963	−	0.981009i	$-0.562134\pi$
$193$	1.78606	−	0.478574i	0.128564	−	0.0344485i	0.322527	+	0.946560i	$0.395468\pi$
$194$	8.31968			0.597318
$195$	17.9496	−	1.80823i	1.28540	−	0.129490i
$196$	−1.00000			−0.0714286
$197$	−12.9669	+	3.47446i	−0.923852	+	0.247545i	−0.689231	−	0.724542i	$-0.742051\pi$
$197$	−12.9669	+	3.47446i	−0.923852	+	0.247545i	−0.234621	+	0.972087i	$0.575385\pi$
$198$	1.56590	+	4.93200i	0.111284	+	0.350502i
$199$	−20.7346	+	11.9711i	−1.46984	+	0.848610i	−0.999427	−	0.0338395i	$-0.989226\pi$
$199$	−20.7346	+	11.9711i	−1.46984	+	0.848610i	−0.470408	+	0.882449i	$0.655893\pi$
$200$	−2.36531	−	2.36531i	−0.167253	−	0.167253i
$201$	−2.29370	+	0.355382i	−0.161785	+	0.0250667i
$202$	1.61254	−	6.01810i	0.113458	−	0.423432i
$203$	2.16355	−	2.16355i	0.151851	−	0.151851i
$204$	7.10966	−	9.71671i	0.497776	−	0.680306i
$205$	−7.89967	−	4.56088i	−0.551737	−	0.318545i
$206$	3.85387	+	14.3828i	0.268512	+	1.00210i
$207$	−15.9391	+	17.4645i	−1.10785	+	1.21387i
$208$	3.21413	−	1.63382i	0.222860	−	0.113285i
$209$		−	10.3420i		−	0.715371i
$210$	−3.13572	−	3.89903i	−0.216385	−	0.269059i
$211$	−1.46282	+	2.53368i	−0.100705	+	0.174426i	−0.911975	−	0.410245i	$-0.865443\pi$
$211$	−1.46282	+	2.53368i	−0.100705	+	0.174426i	0.811270	+	0.584671i	$0.198776\pi$
$212$	0.635396	+	1.10054i	0.0436391	+	0.0755852i
$213$	−17.9068	−	6.94296i	−1.22695	−	0.475724i
$214$	−14.9285	−	4.00009i	−1.02049	−	0.273441i
$215$	−32.0290	−	8.58214i	−2.18436	−	0.585297i
$216$	2.31217	+	4.65337i	0.157323	+	0.316622i
$217$	4.00386	+	6.93490i	0.271800	+	0.470771i
$218$	−4.24371	+	7.35032i	−0.287420	+	0.497826i
$219$	12.6922	−	10.2074i	0.857657	−	0.689753i
$220$		−	4.98278i		−	0.335939i
$221$	1.33563	−	25.0277i	0.0898442	−	1.68354i
$222$	4.16591	+	9.44213i	0.279597	+	0.633714i
$223$	−4.11651	−	15.3630i	−0.275662	−	1.02878i	−0.955397	−	0.295325i	$-0.904572\pi$
$223$	−4.11651	−	15.3630i	−0.275662	−	1.02878i	0.679735	−	0.733458i	$-0.262095\pi$
$224$	−0.866025	−	0.500000i	−0.0578638	−	0.0334077i
$225$	2.15241	−	9.80161i	0.143494	−	0.653440i
$226$	7.45082	−	7.45082i	0.495621	−	0.495621i
$227$	3.35272	−	12.5125i	0.222528	−	0.830484i	−0.760852	−	0.648925i	$-0.775219\pi$
$227$	3.35272	−	12.5125i	0.222528	−	0.830484i	0.983380	−	0.181559i	$-0.0581144\pi$
$228$	−1.59007	−	10.2626i	−0.105305	−	0.679657i
$229$	−9.74834	−	9.74834i	−0.644189	−	0.644189i	0.307394	−	0.951582i	$-0.400543\pi$
$229$	−9.74834	−	9.74834i	−0.644189	−	0.644189i	−0.951582	+	0.307394i	$0.900543\pi$
$230$	19.7176	−	11.3840i	1.30014	−	0.750638i
$231$	0.322278	−	2.97013i	0.0212043	−	0.195420i
$232$	2.95546	−	0.791914i	0.194036	−	0.0519917i
$233$	17.7198			1.16086			0.580430	−	0.814310i	$-0.302885\pi$
$233$	17.7198			1.16086			0.580430	+	0.814310i	$0.302885\pi$
$234$	9.32567	+	5.48014i	0.609638	+	0.358248i
$235$	8.67279			0.565750
$236$	−2.54856	+	0.682885i	−0.165897	+	0.0444521i
$237$	1.57053	−	14.4741i	0.102017	−	0.940191i
$238$	−6.02001	+	3.47565i	−0.390219	+	0.225293i
$239$	3.93333	+	3.93333i	0.254426	+	0.254426i	0.822782	−	0.568357i	$-0.192421\pi$
$239$	3.93333	+	3.93333i	0.254426	+	0.254426i	−0.568357	+	0.822782i	$0.692421\pi$
$240$	−0.766095	−	4.94452i	−0.0494512	−	0.319167i
$241$	2.28012	−	8.50951i	0.146875	−	0.548146i	−0.852790	−	0.522255i	$-0.825091\pi$
$241$	2.28012	−	8.50951i	0.146875	−	0.548146i	0.999665	−	0.0258910i	$-0.00824227\pi$
$242$	−5.67440	+	5.67440i	−0.364764	+	0.364764i
$243$	−8.02016	+	13.3670i	−0.514493	+	0.857494i
$244$	−4.45834	−	2.57403i	−0.285416	−	0.164785i
$245$	0.747671	+	2.79035i	0.0477670	+	0.178269i
$246$	−2.20771	−	5.00382i	−0.140758	−	0.319032i
$247$	−14.4500	−	16.0793i	−0.919434	−	1.02310i
$248$			8.00773i			0.508491i
$249$	19.3809	−	15.5867i	1.22821	−	0.987766i
$250$	2.39039	−	4.14028i	0.151182	−	0.261854i
$251$	−1.15656	−	2.00322i	−0.0730013	−	0.126442i	0.827214	−	0.561887i	$-0.189924\pi$
$251$	−1.15656	−	2.00322i	−0.0730013	−	0.126442i	−0.900215	+	0.435445i	$0.856591\pi$
$252$	−0.136851	−	2.99688i	−0.00862078	−	0.188786i
$253$	13.1314	+	3.51854i	0.825563	+	0.221209i
$254$	20.2131	+	5.41609i	1.26828	+	0.339836i
$255$	−32.4287	−	12.5735i	−2.03076	−	0.787385i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−4.19256	+	7.26172i	−0.261525	+	0.452974i	−0.966647	−	0.256112i	$-0.917559\pi$
$257$	−4.19256	+	7.26172i	−0.261525	+	0.452974i	0.705123	+	0.709085i	$0.250892\pi$
$258$	−12.4597	−	15.4927i	−0.775707	−	0.964533i
$259$		−	5.95843i		−	0.370239i
$260$	−6.96203	−	7.74699i	−0.431767	−	0.480448i
$261$	6.77998	+	6.18781i	0.419670	+	0.383016i
$262$	1.86293	+	6.95253i	0.115092	+	0.429529i
$263$	−1.44442	−	0.833937i	−0.0890669	−	0.0514228i	0.454805	−	0.890591i	$-0.349709\pi$
$263$	−1.44442	−	0.833937i	−0.0890669	−	0.0514228i	−0.543872	+	0.839168i	$0.683042\pi$
$264$	1.76417	−	2.41107i	0.108577	−	0.148391i
$265$	2.59581	−	2.59581i	0.159460	−	0.159460i
$266$	−1.55183	+	5.79151i	−0.0951488	+	0.355100i
$267$	−5.67253	+	0.878892i	−0.347153	+	0.0537873i
$268$	0.947571	+	0.947571i	0.0578821	+	0.0578821i
$269$	17.3350	−	10.0084i	1.05693	−	0.610222i	0.132352	−	0.991203i	$-0.457747\pi$
$269$	17.3350	−	10.0084i	1.05693	−	0.610222i	0.924583	+	0.380981i	$0.124414\pi$
$270$	11.2558	−	9.93094i	0.685006	−	0.604378i
$271$	19.9354	−	5.34166i	1.21099	−	0.324483i	0.403838	−	0.914831i	$-0.367676\pi$
$271$	19.9354	−	5.34166i	1.21099	−	0.324483i	0.807149	+	0.590348i	$0.201009\pi$
$272$	−6.95130			−0.421485
$273$	−3.64886	−	5.06812i	−0.220839	−	0.306736i
$274$	−1.81018			−0.109357
$275$	−5.57319	+	1.49333i	−0.336076	+	0.0900512i
$276$	13.5715	+	1.47259i	0.816910	+	0.0886398i
$277$	6.91279	−	3.99110i	0.415349	−	0.239802i	−0.277736	−	0.960657i	$-0.589584\pi$
$277$	6.91279	−	3.99110i	0.415349	−	0.239802i	0.693086	+	0.720855i	$0.256251\pi$
$278$	−11.1613	−	11.1613i	−0.669409	−	0.669409i
$279$	−20.2351	+	12.9481i	−1.21144	+	0.775184i
$280$	−0.747671	+	2.79035i	−0.0446819	+	0.166755i
$281$	11.4207	−	11.4207i	0.681299	−	0.681299i	−0.278994	−	0.960293i	$-0.590001\pi$
$281$	11.4207	−	11.4207i	0.681299	−	0.681299i	0.960293	+	0.278994i	$0.0900008\pi$
$282$	4.19660	+	3.07063i	0.249904	+	0.182853i
$283$	7.14047	+	4.12255i	0.424457	+	0.245060i	0.696982	−	0.717088i	$-0.254526\pi$
$283$	7.14047	+	4.12255i	0.424457	+	0.245060i	−0.272525	+	0.962149i	$0.587859\pi$
$284$	2.86989	+	10.7106i	0.170296	+	0.635555i
$285$	−27.4474	+	12.1099i	−1.62584	+	0.717328i
$286$	0.331419	−	6.21028i	0.0195972	−	0.367221i
$287$			3.15765i			0.186390i
$288$	1.37992	−	2.66380i	0.0813127	−	0.156966i
$289$	−15.6603	+	27.1245i	−0.921195	+	1.59556i
$290$	−4.41943	−	7.65468i	−0.259518	−	0.449498i
$291$	5.20934	−	13.4356i	0.305377	−	0.787606i
$292$	−9.08317	−	2.43383i	−0.531552	−	0.142429i
$293$	14.2375	+	3.81492i	0.831763	+	0.222870i	0.649483	−	0.760376i	$-0.274985\pi$
$293$	14.2375	+	3.81492i	0.831763	+	0.222870i	0.182280	+	0.983247i	$0.441652\pi$
$294$	−0.626147	+	1.61491i	−0.0365176	+	0.0941836i
$295$	3.81098	+	6.60080i	0.221884	+	0.384314i
$296$	2.97921	−	5.16015i	0.173163	−	0.299928i
$297$	8.94523	+	0.559363i	0.519055	+	0.0324575i
$298$		−	19.4520i		−	1.12682i
$299$	25.3322	−	12.8769i	1.46500	−	0.744693i
$300$	−5.30080	+	2.33873i	−0.306042	+	0.135027i
$301$	2.97085	+	11.0874i	0.171237	+	0.639066i
$302$	−6.14811	−	3.54961i	−0.353784	−	0.204257i
$303$	−8.70901	−	6.37233i	−0.500319	−	0.366081i
$304$	−4.23968	+	4.23968i	−0.243162	+	0.243162i
$305$	−3.84905	+	14.3649i	−0.220396	+	0.822529i
$306$	−11.2399	−	17.5656i	−0.642545	−	1.00416i
$307$	7.53860	+	7.53860i	0.430250	+	0.430250i	0.888713	−	0.458463i	$-0.151600\pi$
$307$	7.53860	+	7.53860i	0.430250	+	0.430250i	−0.458463	+	0.888713i	$0.651600\pi$
$308$	−1.49378	+	0.862436i	−0.0851162	+	0.0491418i
$309$	25.6401	+	2.78211i	1.45861	+	0.158269i
$310$	22.3443	−	5.98715i	1.26907	−	0.340047i
$311$	−13.1987			−0.748432			−0.374216	−	0.927342i	$-0.622088\pi$
$311$	−13.1987			−0.748432			−0.374216	+	0.927342i	$0.622088\pi$
$312$	−0.625948	−	6.21355i	−0.0354373	−	0.351773i
$313$	−19.2373			−1.08736			−0.543679	−	0.839293i	$-0.682969\pi$
$313$	−19.2373			−1.08736			−0.543679	+	0.839293i	$0.682969\pi$
$314$	−7.27469	+	1.94925i	−0.410534	+	0.110002i
$315$	−8.26001	+	2.62254i	−0.465399	+	0.147763i
$316$	−7.27951	+	4.20283i	−0.409504	+	0.236427i
$317$	4.57322	+	4.57322i	0.256858	+	0.256858i	0.823775	−	0.566917i	$-0.191864\pi$
$317$	4.57322	+	4.57322i	0.256858	+	0.256858i	−0.566917	+	0.823775i	$0.691864\pi$
$318$	2.17512	−	0.337010i	0.121975	−	0.0188986i
$319$	1.36595	−	5.09780i	0.0764786	−	0.285422i
$320$	−2.04268	+	2.04268i	−0.114189	+	0.114189i
$321$	−15.8073	+	21.6036i	−0.882275	+	1.20580i
$322$	−6.82559	−	3.94076i	−0.380375	−	0.219610i
$323$	10.7872	+	40.2585i	0.600218	+	2.24004i
$324$	8.96254	−	0.820249i	0.497919	−	0.0455694i
$325$	−6.57842	+	10.1087i	−0.364905	+	0.560731i
$326$		−	1.53673i		−	0.0851118i
$327$	9.21293	+	11.4556i	0.509476	+	0.633496i
$328$	−1.57882	+	2.73460i	−0.0871760	+	0.150993i
$329$	−1.50112	−	2.60001i	−0.0827592	−	0.143343i
$330$	−8.04674	−	3.11995i	−0.442959	−	0.171748i
$331$	22.8621	+	6.12587i	1.25661	+	0.336708i	0.824888	−	0.565297i	$-0.191238\pi$
$331$	22.8621	+	6.12587i	1.25661	+	0.336708i	0.431725	+	0.902005i	$0.357905\pi$
$332$	−13.8700	−	3.71644i	−0.761213	−	0.203966i
$333$	17.8567	−	0.815414i	0.978540	−	0.0446844i
$334$	3.63454	+	6.29521i	0.198873	+	0.344458i
$335$	1.93558	−	3.35253i	0.105752	−	0.183168i
$336$	−1.34972	+	1.08548i	−0.0736330	+	0.0592179i
$337$		−	29.0006i		−	1.57976i	−0.613260	−	0.789881i	$-0.710142\pi$
$337$		−	29.0006i		−	1.57976i	0.613260	−	0.789881i	$-0.289858\pi$
$338$	−8.16184	−	10.1185i	−0.443946	−	0.550375i
$339$	−7.36711	−	16.6977i	−0.400126	−	0.906896i
$340$	5.19729	+	19.3966i	0.281863	+	1.05193i
$341$	11.9618	+	6.90615i	0.647768	+	0.373989i
$342$	−17.5688	−	3.85807i	−0.950012	−	0.208621i
$343$	0.707107	−	0.707107i	0.0381802	−	0.0381802i
$344$	−2.97085	+	11.0874i	−0.160178	+	0.597791i
$345$	−6.03799	−	38.9703i	−0.325074	−	2.09809i
$346$	10.0342	+	10.0342i	0.539440	+	0.539440i
$347$	10.5525	−	6.09249i	0.566488	−	0.327062i	−0.189257	−	0.981928i	$-0.560608\pi$
$347$	10.5525	−	6.09249i	0.566488	−	0.327062i	0.755745	+	0.654865i	$0.227275\pi$
$348$	0.571683	−	5.26867i	0.0306454	−	0.282430i
$349$	−28.0558	+	7.51754i	−1.50179	+	0.402404i	−0.913700	−	0.406388i	$-0.866788\pi$
$349$	−28.0558	+	7.51754i	−1.50179	+	0.402404i	−0.588094	+	0.808793i	$0.700121\pi$
$350$	3.34505			0.178801
$351$	14.6892	−	11.6288i	0.784050	−	0.620697i
$352$	−1.72487			−0.0919360
$353$	8.58425	−	2.30014i	0.456894	−	0.122424i	−0.0230296	−	0.999735i	$-0.507331\pi$
$353$	8.58425	−	2.30014i	0.456894	−	0.122424i	0.479923	+	0.877310i	$0.340665\pi$
$354$	−0.492975	+	4.54329i	−0.0262013	+	0.241473i
$355$	27.7405	−	16.0160i	1.47231	−	0.850039i
$356$	2.34343	+	2.34343i	0.124202	+	0.124202i
$357$	1.84346	+	11.8980i	0.0975664	+	0.629711i
$358$	−1.39457	+	5.20462i	−0.0737055	+	0.275073i
$359$	13.6176	−	13.6176i	0.718709	−	0.718709i	−0.249632	−	0.968341i	$-0.580310\pi$
$359$	13.6176	−	13.6176i	0.718709	−	0.718709i	0.968341	+	0.249632i	$0.0803096\pi$
$360$	−8.46465	−	1.85882i	−0.446126	−	0.0979683i
$361$	14.6789	+	8.47486i	0.772573	+	0.446045i
$362$	−3.68360	−	13.7474i	−0.193606	−	0.722546i
$363$	5.61065	+	12.7167i	0.294483	+	0.667452i
$364$	−1.11745	+	3.42802i	−0.0585705	+	0.179677i
$365$			27.1649i			1.42188i
$366$	−6.94840	+	5.58811i	−0.363199	+	0.292095i
$367$	−9.81631	+	17.0024i	−0.512407	+	0.887516i	0.487489	+	0.873129i	$0.337913\pi$
$367$	−9.81631	+	17.0024i	−0.512407	+	0.887516i	−0.999897	+	0.0143866i	$0.995420\pi$
$368$	−3.94076	−	6.82559i	−0.205426	−	0.355809i
$369$	−9.46308	+	0.432126i	−0.492628	+	0.0224956i
$370$	−16.6261	−	4.45494i	−0.864349	−	0.231602i
$371$	−1.22749	−	0.328905i	−0.0637281	−	0.0170759i
$372$	12.9318	+	5.01401i	0.670481	+	0.259965i
$373$	7.66469	+	13.2756i	0.396863	+	0.687386i	0.993337	−	0.115246i	$-0.0367656\pi$
$373$	7.66469	+	13.2756i	0.396863	+	0.687386i	−0.596474	+	0.802632i	$0.703432\pi$
$374$	−5.99505	+	10.3837i	−0.309997	+	0.536930i
$375$	−5.18945	−	6.45269i	−0.267982	−	0.333216i
$376$		−	3.00223i		−	0.154828i
$377$	−4.99902	−	9.83435i	−0.257463	−	0.506495i
$378$	−4.92538	−	1.65548i	−0.253334	−	0.0851489i
$379$	−2.11146	−	7.88009i	−0.108459	−	0.404773i	0.890256	−	0.455461i	$-0.150525\pi$
$379$	−2.11146	−	7.88009i	−0.108459	−	0.404773i	−0.998715	+	0.0506876i	$0.983859\pi$
$380$	15.0001	+	8.66029i	0.769487	+	0.444263i
$381$	21.4029	−	29.2511i	1.09650	−	1.49858i
$382$	0.608215	−	0.608215i	0.0311190	−	0.0311190i
$383$	6.84818	−	25.5578i	0.349926	−	1.30594i	−0.536826	−	0.843693i	$-0.680377\pi$
$383$	6.84818	−	25.5578i	0.349926	−	1.30594i	0.886751	−	0.462247i	$-0.152957\pi$
$384$	−1.71163	+	0.265197i	−0.0873462	+	0.0135333i
$385$	3.52335	+	3.52335i	0.179567	+	0.179567i
$386$	−1.60134	+	0.924534i	−0.0815060	+	0.0470575i
$387$	−32.8209	+	10.4206i	−1.66838	+	0.529709i
$388$	−8.03620	+	2.15329i	−0.407976	+	0.109317i
$389$	−15.4625			−0.783981			−0.391990	−	0.919969i	$-0.628213\pi$
$389$	−15.4625			−0.783981			−0.391990	+	0.919969i	$0.628213\pi$
$390$	−16.8700	+	6.39230i	−0.854243	+	0.323687i
$391$	−54.7868			−2.77069
$392$	0.965926	−	0.258819i	0.0487866	−	0.0130723i
$393$	12.3942	+	1.34485i	0.625204	+	0.0678386i
$394$	11.6258	−	6.71215i	0.585698	−	0.338153i
$395$	17.1700	+	17.1700i	0.863918	+	0.863918i
$396$	−2.78904	−	4.35866i	−0.140155	−	0.219031i
$397$	−6.10106	+	22.7694i	−0.306203	+	1.14277i	0.625701	+	0.780063i	$0.284813\pi$
$397$	−6.10106	+	22.7694i	−0.306203	+	1.14277i	−0.931905	+	0.362703i	$0.881854\pi$
$398$	16.9297	−	16.9297i	0.848610	−	0.848610i
$399$	8.38110	+	6.13240i	0.419580	+	0.307004i
$400$	2.89690	+	1.67253i	0.144845	+	0.0836263i
$401$	−2.88110	−	10.7524i	−0.143875	−	0.536949i	−0.999803	−	0.0198538i	$-0.993680\pi$
$401$	−2.88110	−	10.7524i	−0.143875	−	0.536949i	0.855928	−	0.517095i	$-0.172987\pi$
$402$	2.12356	−	0.936925i	0.105914	−	0.0467296i
$403$	28.2471	−	5.97589i	1.40709	−	0.297680i
$404$			6.23039i			0.309974i
$405$	−8.98982	−	24.3953i	−0.446708	−	1.21221i
$406$	−1.52986	+	2.64980i	−0.0759257	+	0.131507i
$407$	−5.13876	−	8.90060i	−0.254719	−	0.441186i
$408$	−4.35254	+	11.2257i	−0.215483	+	0.555757i
$409$	−18.5711	−	4.97612i	−0.918283	−	0.246053i	−0.231432	−	0.972851i	$-0.574341\pi$
$409$	−18.5711	−	4.97612i	−0.918283	−	0.246053i	−0.686851	+	0.726798i	$0.741008\pi$
$410$	8.81094	+	2.36088i	0.435141	+	0.116596i
$411$	−1.13344	+	2.92328i	−0.0559084	+	0.144195i
$412$	−7.44511	−	12.8953i	−0.366794	−	0.635306i
$413$	1.31923	−	2.28498i	0.0649152	−	0.112436i
$414$	10.8759	−	20.9948i	0.534520	−	1.03184i
$415$			41.4807i			2.03621i
$416$	−2.68175	+	2.41002i	−0.131484	+	0.118161i
$417$	−25.0131	+	11.0359i	−1.22490	+	0.540430i
$418$	2.67671	+	9.98961i	0.130922	+	0.488608i
$419$	15.9960	+	9.23531i	0.781457	+	0.451174i	0.836946	−	0.547285i	$-0.184339\pi$
$419$	15.9960	+	9.23531i	0.781457	+	0.451174i	−0.0554894	+	0.998459i	$0.517672\pi$
$420$	4.03801	+	2.95459i	0.197035	+	0.144169i
$421$	20.9699	−	20.9699i	1.02201	−	1.02201i	0.0222576	−	0.999752i	$-0.492915\pi$
$421$	20.9699	−	20.9699i	1.02201	−	1.02201i	0.999752	−	0.0222576i	$-0.00708540\pi$
$422$	0.757212	−	2.82595i	0.0368605	−	0.137565i
$423$	7.58648	−	4.85447i	0.368867	−	0.236033i
$424$	−0.898585	−	0.898585i	−0.0436391	−	0.0436391i
$425$	20.1372	−	11.6262i	0.976799	−	0.563955i
$426$	19.0936	+	2.07177i	0.925087	+	0.100378i
$427$	4.97264	−	1.33241i	0.240643	−	0.0644800i
$428$	15.4552			0.747053
$429$	−9.82153	−	4.42376i	−0.474188	−	0.213581i
$430$	33.1589			1.59906
$431$	9.63530	−	2.58177i	0.464116	−	0.124360i	−0.0191808	−	0.999816i	$-0.506106\pi$
$431$	9.63530	−	2.58177i	0.464116	−	0.124360i	0.483297	+	0.875456i	$0.339439\pi$
$432$	−3.43776	−	3.89638i	−0.165399	−	0.187465i
$433$	22.5884	−	13.0414i	1.08553	−	0.626731i	0.153148	−	0.988203i	$-0.451059\pi$
$433$	22.5884	−	13.0414i	1.08553	−	0.626731i	0.932383	+	0.361472i	$0.117726\pi$
$434$	−5.66232	−	5.66232i	−0.271800	−	0.271800i
$435$	−15.1289	+	2.34404i	−0.725373	+	0.112388i
$436$	2.19670	−	8.19821i	0.105203	−	0.392623i
$437$	−33.4151	+	33.4151i	−1.59846	+	1.59846i
$438$	−9.61781	+	13.1446i	−0.459557	+	0.628072i
$439$	13.7683	+	7.94912i	0.657125	+	0.379391i	0.791180	−	0.611583i	$-0.209467\pi$
$439$	13.7683	+	7.94912i	0.657125	+	0.379391i	−0.134056	+	0.990974i	$0.542800\pi$
$440$	1.28964	+	4.81299i	0.0614810	+	0.229450i
$441$	2.21588	+	2.02234i	0.105518	+	0.0963021i
$442$	5.18752	+	24.5206i	0.246745	+	1.16632i
$443$		−	5.40463i		−	0.256782i	−0.991724	−	0.128391i	$-0.959019\pi$
$443$		−	5.40463i		−	0.256782i	0.991724	−	0.128391i	$-0.0409812\pi$
$444$	−6.46776	−	8.04218i	−0.306946	−	0.381665i
$445$	4.78687	−	8.29111i	0.226919	−	0.393036i
$446$	7.95248	+	13.7741i	0.376561	+	0.652222i
$447$	−31.4133	−	12.1798i	−1.48580	−	0.576085i
$448$	0.965926	+	0.258819i	0.0456357	+	0.0122281i
$449$	−16.3882	−	4.39121i	−0.773407	−	0.207234i	−0.149531	−	0.988757i	$-0.547776\pi$
$449$	−16.3882	−	4.39121i	−0.773407	−	0.207234i	−0.623876	+	0.781523i	$0.714443\pi$
$450$	0.457772	+	10.0247i	0.0215796	+	0.472569i
$451$	2.72327	+	4.71684i	0.128234	+	0.222107i
$452$	−5.26853	+	9.12535i	−0.247811	+	0.429221i
$453$	−9.58193	+	7.70608i	−0.450198	+	0.362063i
$454$			12.9539i			0.607957i
$455$	10.4008	+	0.555053i	0.487599	+	0.0260213i
$456$	4.19204	+	9.50136i	0.196310	+	0.444942i
$457$	0.0705509	+	0.263300i	0.00330023	+	0.0123166i	0.967556	−	0.252655i	$-0.0813039\pi$
$457$	0.0705509	+	0.263300i	0.00330023	+	0.0123166i	−0.964256	+	0.264972i	$0.914637\pi$
$458$	11.9392	+	6.89312i	0.557884	+	0.322094i
$459$	−35.4047	+	7.15289i	−1.65255	+	0.333868i
$460$	−16.0994	+	16.0994i	−0.750638	+	0.750638i
$461$	−5.91669	+	22.0814i	−0.275568	+	1.02843i	0.679892	+	0.733312i	$0.262027\pi$
$461$	−5.91669	+	22.0814i	−0.275568	+	1.02843i	−0.955460	+	0.295121i	$0.904640\pi$
$462$	0.457430	+	2.95234i	0.0212816	+	0.137355i
$463$	−4.23145	−	4.23145i	−0.196652	−	0.196652i	0.601911	−	0.798563i	$-0.294406\pi$
$463$	−4.23145	−	4.23145i	−0.196652	−	0.196652i	−0.798563	+	0.601911i	$0.794406\pi$
$464$	−2.64980	+	1.52986i	−0.123014	+	0.0710220i
$465$	4.32213	−	39.8330i	0.200434	−	1.84721i
$466$	−17.1160	+	4.58621i	−0.792882	+	0.212452i
$467$	11.2748			0.521735			0.260868	−	0.965375i	$-0.415991\pi$
$467$	11.2748			0.521735			0.260868	+	0.965375i	$0.415991\pi$
$468$	−10.4263	−	2.87974i	−0.481954	−	0.133116i
$469$	−1.34007			−0.0618786
$470$	−8.37727	+	2.24468i	−0.386415	+	0.103539i
$471$	−1.40716	+	12.9685i	−0.0648386	+	0.597557i
$472$	2.28498	−	1.31923i	0.105175	−	0.0607226i
$473$	14.0000	+	14.0000i	0.643719	+	0.643719i
$474$	2.22915	+	14.3873i	0.102388	+	0.660833i
$475$	5.19095	−	19.3729i	0.238177	−	0.888889i
$476$	4.91531	−	4.91531i	0.225293	−	0.225293i
$477$	0.817705	−	3.72365i	0.0374401	−	0.170494i
$478$	−4.81732	−	2.78128i	−0.220339	−	0.127213i
$479$	0.236062	+	0.880996i	0.0107860	+	0.0402538i	0.971109	−	0.238636i	$-0.0767003\pi$
$479$	0.236062	+	0.880996i	0.0107860	+	0.0402538i	−0.960323	+	0.278890i	$0.910034\pi$
$480$	2.01973	+	4.57776i	0.0921875	+	0.208945i
$481$	−20.4256	−	6.65826i	−0.931327	−	0.303591i
$482$			8.80969i			0.401270i
$483$	−10.6378	+	8.55524i	−0.484037	+	0.389277i
$484$	4.01241	−	6.94970i	0.182382	−	0.315895i
$485$	12.0169	+	20.8138i	0.545658	+	0.945107i
$486$	4.28724	−	14.9873i	0.194473	−	0.679838i
$487$	−7.04569	−	1.88789i	−0.319271	−	0.0855483i	0.0956247	−	0.995417i	$-0.469515\pi$
$487$	−7.04569	−	1.88789i	−0.319271	−	0.0855483i	−0.414895	+	0.909869i	$0.636182\pi$
$488$	4.97264	+	1.33241i	0.225101	+	0.0603156i
$489$	−2.48169	−	0.962221i	−0.112226	−	0.0435131i
$490$	−1.44439	−	2.50176i	−0.0652509	−	0.113018i
$491$	−16.7764	+	29.0576i	−0.757109	+	1.31135i	0.187209	+	0.982320i	$0.440056\pi$
$491$	−16.7764	+	29.0576i	−0.757109	+	1.31135i	−0.944319	+	0.329032i	$0.893278\pi$
$492$	3.42757	+	4.26193i	0.154527	+	0.192142i
$493$			21.2691i			0.957910i
$494$	18.1193	+	11.7914i	0.815225	+	0.530522i
$495$	−10.0769	+	11.0412i	−0.452922	+	0.496267i
$496$	−2.07255	−	7.73487i	−0.0930604	−	0.347306i
$497$	−9.60283	−	5.54420i	−0.430746	−	0.248691i
$498$	−14.6864	+	20.0717i	−0.658111	+	0.899435i
$499$	4.17983	−	4.17983i	0.187115	−	0.187115i	−0.607333	−	0.794448i	$-0.707760\pi$
$499$	4.17983	−	4.17983i	0.187115	−	0.187115i	0.794448	+	0.607333i	$0.207760\pi$
$500$	−1.23736	+	4.61788i	−0.0553363	+	0.206518i
$501$	12.4420	−	1.92774i	0.555866	−	0.0861249i
$502$	1.63562	+	1.63562i	0.0730013	+	0.0730013i
$503$	34.3630	−	19.8395i	1.53217	−	0.884599i	0.532909	−	0.846173i	$-0.321099\pi$
$503$	34.3630	−	19.8395i	1.53217	−	0.884599i	0.999261	−	0.0384265i	$-0.0122345\pi$
$504$	0.907836	+	2.85934i	0.0404382	+	0.127365i
$505$	17.3850	−	4.65829i	0.773621	−	0.207291i
$506$	−13.5946			−0.604354
$507$	−21.4510	+	6.84497i	−0.952673	+	0.303996i
$508$	−20.9262			−0.928448
$509$	−7.78615	+	2.08629i	−0.345115	+	0.0924733i	−0.427213	−	0.904151i	$-0.640505\pi$
$509$	−7.78615	+	2.08629i	−0.345115	+	0.0924733i	0.0820981	+	0.996624i	$0.473838\pi$
$510$	34.5780	+	3.75193i	1.53114	+	0.166138i
$511$	8.14374	−	4.70179i	0.360258	−	0.207995i
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−17.2311	+	25.9563i	−0.760771	+	1.14600i
$514$	2.17023	−	8.09940i	0.0957246	−	0.357249i
$515$	−30.4159	+	30.4159i	−1.34028	+	1.34028i
$516$	16.0449	+	11.7400i	0.706339	+	0.516824i
$517$	−4.48468	−	2.58923i	−0.197236	−	0.113874i
$518$	1.54215	+	5.75540i	0.0677584	+	0.252878i
$519$	22.4872	−	9.92143i	0.987077	−	0.435503i
$520$	8.72987	+	5.68111i	0.382830	+	0.249133i
$521$		−	14.4268i		−	0.632049i	−0.948751	−	0.316024i	$-0.897652\pi$
$521$		−	14.4268i		−	0.632049i	0.948751	−	0.316024i	$-0.102348\pi$
$522$	−8.15048	−	4.22218i	−0.356737	−	0.184800i
$523$	−3.76733	+	6.52521i	−0.164734	+	0.285328i	−0.936561	−	0.350505i	$-0.886010\pi$
$523$	−3.76733	+	6.52521i	−0.164734	+	0.285328i	0.771827	+	0.635833i	$0.219343\pi$
$524$	−3.59890	−	6.23347i	−0.157219	−	0.272310i
$525$	2.09449	−	5.40196i	0.0914112	−	0.235761i
$526$	1.61104	+	0.431678i	0.0702448	+	0.0188220i
$527$	−53.7674	−	14.4069i	−2.34215	−	0.627576i
$528$	−1.08002	+	2.78552i	−0.0470020	+	0.121224i
$529$	−19.5591	−	33.8774i	−0.850398	−	1.47293i
$530$	−1.83552	+	3.17921i	−0.0797298	+	0.138096i
$531$	7.02834	+	3.64088i	0.305004	+	0.158001i
$532$		−	5.99581i		−	0.259951i
$533$	10.8245	+	3.52852i	0.468860	+	0.152837i
$534$	5.25177	−	2.31710i	0.227266	−	0.100271i
$535$	−11.5554	−	43.1253i	−0.499583	−	1.86447i
$536$	−1.16053	−	0.670034i	−0.0501274	−	0.0289411i
$537$	7.53179	+	5.51097i	0.325021	+	0.237816i
$538$	−14.1540	+	14.1540i	−0.610222	+	0.610222i
$539$	0.446430	−	1.66610i	0.0192291	−	0.0717639i
$540$	−8.30194	+	12.5058i	−0.357259	+	0.538162i
$541$	−11.0227	−	11.0227i	−0.473903	−	0.473903i	0.429272	−	0.903175i	$-0.358770\pi$
$541$	−11.0227	−	11.0227i	−0.473903	−	0.473903i	−0.903175	+	0.429272i	$0.858770\pi$
$542$	−17.8736	+	10.3193i	−0.767735	+	0.443252i
$543$	−24.5073	−	2.65919i	−1.05171	−	0.114117i
$544$	6.71444	−	1.79913i	0.287879	−	0.0771371i
$545$	−24.5183			−1.05025
$546$	4.83625	+	3.95103i	0.206973	+	0.169088i
$547$	21.0958			0.901990			0.450995	−	0.892527i	$-0.351069\pi$
$547$	21.0958			0.901990			0.450995	+	0.892527i	$0.351069\pi$
$548$	1.74850	−	0.468509i	0.0746922	−	0.0200137i
$549$	4.67359	+	14.7200i	0.199464	+	0.628236i
$550$	4.99678	−	2.88489i	0.213063	−	0.123012i
$551$	12.9722	+	12.9722i	0.552636	+	0.552636i
$552$	−13.4902	+	2.09015i	−0.574182	+	0.0889628i
$553$	2.17554	−	8.11924i	0.0925135	−	0.345265i
$554$	−5.64427	+	5.64427i	−0.239802	+	0.239802i
$555$	−17.6047	+	24.0602i	−0.747278	+	1.02130i
$556$	13.6697	+	7.89222i	0.579725	+	0.334705i
$557$	−5.57264	−	20.7974i	−0.236120	−	0.881213i	−0.977641	−	0.210283i	$-0.932562\pi$
$557$	−5.57264	−	20.7974i	−0.236120	−	0.881213i	0.741520	−	0.670931i	$-0.234105\pi$
$558$	16.1944	−	17.7442i	0.685563	−	0.751170i
$559$	41.3275	+	2.20549i	1.74797	+	0.0932823i
$560$		−	2.88878i		−	0.122073i
$561$	13.0150	+	16.1832i	0.549495	+	0.683256i
$562$	−8.07562	+	13.9874i	−0.340650	+	0.590022i
$563$	−12.5256	−	21.6950i	−0.527891	−	0.914333i	−0.999471	−	0.0325105i	$-0.989650\pi$
$563$	−12.5256	−	21.6950i	−0.527891	−	0.914333i	0.471581	−	0.881823i	$-0.343684\pi$
$564$	−4.84834	−	1.87984i	−0.204152	−	0.0791555i
$565$	29.4020	+	7.87825i	1.23695	+	0.331441i
$566$	−7.96416	−	2.13399i	−0.334759	−	0.0896983i
$567$	−5.75747	+	6.91748i	−0.241791	+	0.290507i
$568$	−5.54420	−	9.60283i	−0.232629	−	0.402926i
$569$	11.3432	−	19.6469i	0.475530	−	0.823642i	−0.524077	−	0.851671i	$-0.675590\pi$
$569$	11.3432	−	19.6469i	0.475530	−	0.823642i	0.999607	+	0.0280285i	$0.00892293\pi$
$570$	23.3778	−	18.8012i	0.979190	−	0.787494i
$571$		−	7.57683i		−	0.317080i	−0.987353	−	0.158540i	$-0.949321\pi$
$571$		−	7.57683i		−	0.317080i	0.987353	−	0.158540i	$-0.0506787\pi$
$572$	1.28721	+	6.08444i	0.0538210	+	0.254403i
$573$	−0.601381	−	1.36304i	−0.0251231	−	0.0569420i
$574$	−0.817259	−	3.05005i	−0.0341118	−	0.127307i
$575$	22.8320	+	13.1820i	0.952159	+	0.549729i
$576$	−0.643461	+	2.93018i	−0.0268109	+	0.122091i
$577$	5.29010	−	5.29010i	0.220230	−	0.220230i	−0.588366	−	0.808595i	$-0.700228\pi$
$577$	5.29010	−	5.29010i	0.220230	−	0.220230i	0.808595	+	0.588366i	$0.200228\pi$
$578$	8.10637	−	30.2534i	0.337181	−	1.25838i
$579$	0.490367	+	3.16492i	0.0203789	+	0.131529i
$580$	6.25002	+	6.25002i	0.259518	+	0.259518i
$581$	12.4355	−	7.17962i	0.515910	−	0.297861i
$582$	−1.55446	+	14.3260i	−0.0644346	+	0.593833i
$583$	−2.11726	+	0.567319i	−0.0876881	+	0.0234959i
$584$	9.40359			0.389123
$585$	−0.240064	+	31.2460i	−0.00992542	+	1.29186i
$586$	−14.7397			−0.608893
$587$	6.00016	−	1.60774i	0.247653	−	0.0663585i	−0.132857	−	0.991135i	$-0.542415\pi$
$587$	6.00016	−	1.60774i	0.247653	−	0.0663585i	0.380510	+	0.924777i	$0.375748\pi$
$588$	0.186842	−	1.72194i	0.00770522	−	0.0710118i
$589$	−41.5803	+	24.0064i	−1.71329	+	0.989167i
$590$	−5.38953	−	5.38953i	−0.221884	−	0.221884i
$591$	−3.56008	−	22.9774i	−0.146442	−	0.945164i
$592$	−1.54215	+	5.75540i	−0.0633822	+	0.236545i
$593$	−30.4769	+	30.4769i	−1.25154	+	1.25154i	−0.296504	+	0.955032i	$0.595821\pi$
$593$	−30.4769	+	30.4769i	−1.25154	+	1.25154i	−0.955032	+	0.296504i	$0.904179\pi$
$594$	−8.78520	+	1.77489i	−0.360461	+	0.0728247i
$595$	−17.3905	−	10.0404i	−0.712940	−	0.411616i
$596$	5.03455	+	18.7892i	0.206223	+	0.769635i
$597$	−16.7395	−	37.9405i	−0.685102	−	1.55280i
$598$	−21.1363	+	18.9946i	−0.864326	+	0.776748i
$599$			16.8196i			0.687229i	0.939111	+	0.343614i	$0.111651\pi$
$599$			16.8196i			0.687229i	−0.939111	+	0.343614i	$0.888349\pi$
$600$	4.51487	−	3.63099i	0.184319	−	0.148235i
$601$	−18.5605	+	32.1476i	−0.757097	+	1.31133i	0.187229	+	0.982316i	$0.440049\pi$
$601$	−18.5605	+	32.1476i	−0.757097	+	1.31133i	−0.944325	+	0.329013i	$0.893284\pi$
$602$	−5.73925	−	9.94067i	−0.233914	−	0.405151i
$603$	−0.183389	−	4.01602i	−0.00746818	−	0.163545i
$604$	6.85732	+	1.83741i	0.279021	+	0.0747633i
$605$	−22.3920	−	5.99993i	−0.910365	−	0.243932i
$606$	10.0615	+	3.90114i	0.408722	+	0.158473i
$607$	−6.76372	−	11.7151i	−0.274531	−	0.475502i	0.695486	−	0.718540i	$-0.255189\pi$
$607$	−6.76372	−	11.7151i	−0.274531	−	0.475502i	−0.970017	+	0.243038i	$0.921856\pi$
$608$	2.99790	−	5.19252i	0.121581	−	0.210585i
$609$	3.32127	+	4.12975i	0.134585	+	0.167346i
$610$		−	14.8716i		−	0.602133i
$611$	−10.5903	+	2.24046i	−0.428438	+	0.0906394i
$612$	15.4033	+	14.0579i	0.622640	+	0.568258i
$613$	−6.63090	−	24.7468i	−0.267819	−	0.999515i	−0.960502	−	0.278273i	$-0.910238\pi$
$613$	−6.63090	−	24.7468i	−0.267819	−	0.999515i	0.692683	−	0.721242i	$-0.256429\pi$
$614$	−9.23286	−	5.33059i	−0.372608	−	0.215125i
$615$	9.32956	−	12.7506i	0.376204	−	0.514155i
$616$	1.21967	−	1.21967i	0.0491418	−	0.0491418i
$617$	3.63391	−	13.5620i	0.146296	−	0.545984i	−0.853398	−	0.521259i	$-0.825462\pi$
$617$	3.63391	−	13.5620i	0.146296	−	0.545984i	0.999694	−	0.0247245i	$-0.00787085\pi$
$618$	−25.4865	+	3.94884i	−1.02522	+	0.158845i
$619$	−2.26075	−	2.26075i	−0.0908673	−	0.0908673i	0.660212	−	0.751079i	$-0.270466\pi$
$619$	−2.26075	−	2.26075i	−0.0908673	−	0.0908673i	−0.751079	+	0.660212i	$0.770466\pi$
$620$	−20.0334	+	11.5663i	−0.804560	+	0.464513i
$621$	−27.0948	−	30.7094i	−1.08728	−	1.23233i
$622$	12.7490	−	3.41609i	0.511188	−	0.136973i
$623$	−3.31411			−0.132777
$624$	2.21280	+	5.83982i	0.0885831	+	0.233780i
$625$	30.5359			1.22144
$626$	18.5818	−	4.97899i	0.742679	−	0.199000i
$627$	17.8083	+	1.93232i	0.711197	+	0.0771693i
$628$	6.52231	−	3.76566i	0.260268	−	0.150266i
$629$	29.2875	+	29.2875i	1.16777	+	1.16777i
$630$	7.29979	−	4.67103i	0.290831	−	0.186098i
$631$	−5.21129	+	19.4488i	−0.207458	+	0.774245i	0.781228	+	0.624246i	$0.214594\pi$
$631$	−5.21129	+	19.4488i	−0.207458	+	0.774245i	−0.988686	+	0.149999i	$0.952073\pi$
$632$	5.94369	−	5.94369i	0.236427	−	0.236427i
$633$	−4.08954	−	2.99229i	−0.162545	−	0.118933i
$634$	−5.60103	−	3.23376i	−0.222445	−	0.128429i
$635$	15.6459	+	58.3913i	0.620888	+	2.31719i
$636$	−2.01378	+	0.888489i	−0.0798516	+	0.0352309i
$637$	−1.63382	−	3.21413i	−0.0647341	−	0.127349i
$638$			5.27763i			0.208943i
$639$	15.3011	−	29.5372i	0.605303	−	1.16847i
$640$	1.44439	−	2.50176i	0.0570945	−	0.0988906i
$641$	6.54052	+	11.3285i	0.258335	+	0.447449i	0.965796	−	0.259303i	$-0.0834928\pi$
$641$	6.54052	+	11.3285i	0.258335	+	0.447449i	−0.707461	+	0.706752i	$0.750159\pi$
$642$	9.67720	−	24.9587i	0.381929	−	0.985042i
$643$	37.5442	+	10.0599i	1.48060	+	0.396726i	0.906551	−	0.422096i	$-0.138705\pi$
$643$	37.5442	+	10.0599i	1.48060	+	0.396726i	0.574049	+	0.818821i	$0.305372\pi$
$644$	7.61296	+	2.03989i	0.299993	+	0.0803828i
$645$	20.7623	−	53.5486i	0.817515	−	2.10848i
$646$	−20.8393	−	36.0948i	−0.819913	−	1.42013i
$647$	14.4953	−	25.1065i	0.569868	−	0.987040i	−0.426711	−	0.904388i	$-0.640328\pi$
$647$	14.4953	−	25.1065i	0.569868	−	0.987040i	0.996578	−	0.0826520i	$-0.0263390\pi$
$648$	−8.44486	+	3.11198i	−0.331745	+	0.122250i
$649$		−	4.55102i		−	0.178643i
$650$	3.73794	−	11.4669i	0.146614	−	0.449769i
$651$	−12.6896	+	5.59870i	−0.497344	+	0.219430i
$652$	0.397736	+	1.48437i	0.0155765	+	0.0581324i
$653$	34.2471	+	19.7726i	1.34019	+	0.773761i	0.986835	−	0.161728i	$-0.0517066\pi$
$653$	34.2471	+	19.7726i	1.34019	+	0.773761i	0.353358	+	0.935488i	$0.385040\pi$
$654$	−11.8639	−	8.68077i	−0.463916	−	0.339445i
$655$	−14.7028	+	14.7028i	−0.574484	+	0.574484i
$656$	0.817259	−	3.05005i	0.0319086	−	0.119085i
$657$	15.2052	+	23.7624i	0.593210	+	0.927058i
$658$	2.12290	+	2.12290i	0.0827592	+	0.0827592i
$659$	43.6509	−	25.2019i	1.70040	−	0.981726i	0.755050	−	0.655667i	$-0.227613\pi$
$659$	43.6509	−	25.2019i	1.70040	−	0.981726i	0.945350	−	0.326059i	$-0.105721\pi$
$660$	8.58006	+	0.930990i	0.333978	+	0.0362387i
$661$	−31.1518	+	8.34711i	−1.21167	+	0.324665i	−0.807415	−	0.589984i	$-0.799134\pi$
$661$	−31.1518	+	8.34711i	−1.21167	+	0.324665i	−0.404250	+	0.914648i	$0.632468\pi$
$662$	−23.6686			−0.919905
$663$	42.8467	+	6.97609i	1.66403	+	0.270929i
$664$	14.3592			0.557246
$665$	−16.7304	+	4.48289i	−0.648777	+	0.173839i
$666$	−17.0372	+	5.40928i	−0.660177	+	0.209605i
$667$	−20.8844	+	12.0576i	−0.808648	+	0.466873i
$668$	−5.14001	−	5.14001i	−0.198873	−	0.198873i
$669$	27.2234	−	4.21794i	1.05252	−	0.163075i
$670$	−1.00193	+	3.73926i	−0.0387080	+	0.144460i
$671$	6.27892	−	6.27892i	0.242395	−	0.242395i
$672$	1.02278	−	1.39783i	0.0394546	−	0.0539223i
$673$	−14.3618	−	8.29182i	−0.553609	−	0.319626i	0.196968	−	0.980410i	$-0.436891\pi$
$673$	−14.3618	−	8.29182i	−0.553609	−	0.319626i	−0.750576	+	0.660784i	$0.770224\pi$
$674$	7.50590	+	28.0124i	0.289117	+	1.07900i
$675$	16.4757	+	5.53768i	0.634148	+	0.213145i
$676$	10.5026	+	7.66130i	0.403946	+	0.294665i
$677$		−	43.7323i		−	1.68077i	−0.541991	−	0.840384i	$-0.682329\pi$
$677$		−	43.7323i		−	1.68077i	0.541991	−	0.840384i	$-0.317671\pi$
$678$	11.4378	+	14.2220i	0.439265	+	0.546193i
$679$	4.15984	−	7.20506i	0.159640	−	0.276505i
$680$	−10.0404	−	17.3905i	−0.385032	−	0.666894i
$681$	20.9194	+	8.11104i	0.801633	+	0.310816i
$682$	−13.3417	−	3.57489i	−0.510879	−	0.136890i
$683$	−4.92584	−	1.31987i	−0.188482	−	0.0505036i	0.163343	−	0.986569i	$-0.447772\pi$
$683$	−4.92584	−	1.31987i	−0.188482	−	0.0505036i	−0.351825	+	0.936066i	$0.614439\pi$
$684$	17.9687	−	0.820530i	0.687050	−	0.0313737i
$685$	−2.61461	−	4.52863i	−0.0998990	−	0.173030i
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$	18.6075	−	14.9647i	0.709920	−	0.570939i
$688$		−	11.4785i		−	0.437614i
$689$	−2.49915	+	3.84032i	−0.0952102	+	0.146305i
$690$	15.9185	+	36.0797i	0.606007	+	1.37353i
$691$	−0.776008	−	2.89610i	−0.0295207	−	0.110173i	0.949593	−	0.313484i	$-0.101496\pi$
$691$	−0.776008	−	2.89610i	−0.0295207	−	0.110173i	−0.979114	+	0.203311i	$0.934830\pi$
$692$	−12.2893	−	7.09523i	−0.467169	−	0.269720i
$693$	5.05419	+	1.10989i	0.191993	+	0.0421612i
$694$	−8.61608	+	8.61608i	−0.327062	+	0.327062i
$695$	11.8016	−	44.0441i	0.447659	−	1.67069i
$696$	0.811428	+	5.23711i	0.0307571	+	0.198512i
$697$	−15.5208	−	15.5208i	−0.587893	−	0.587893i
$698$	25.1542	−	14.5228i	0.952099	−	0.549695i
$699$	−3.31079	+	30.5124i	−0.125225	+	1.15409i
$700$	−3.23107	+	0.865763i	−0.122123	+	0.0327228i
$701$	−24.6775			−0.932055			−0.466027	−	0.884770i	$-0.654315\pi$
$701$	−24.6775			−0.932055			−0.466027	+	0.884770i	$0.654315\pi$
$702$	−11.1789	+	15.0344i	−0.421921	+	0.567435i
$703$	35.7256			1.34742
$704$	1.66610	−	0.446430i	0.0627934	−	0.0168255i
$705$	−1.62044	+	14.9341i	−0.0610292	+	0.562449i
$706$	−7.69643	+	4.44354i	−0.289659	+	0.167235i
$707$	−4.40555	−	4.40555i	−0.165688	−	0.165688i
$708$	−0.699713	−	4.51607i	−0.0262968	−	0.169724i
$709$	−5.45655	+	20.3641i	−0.204925	+	0.764791i	0.784547	+	0.620069i	$0.212895\pi$
$709$	−5.45655	+	20.3641i	−0.204925	+	0.764791i	−0.989472	+	0.144722i	$0.953771\pi$
$710$	−22.6500	+	22.6500i	−0.850039	+	0.850039i
$711$	24.6301	+	5.40871i	0.923700	+	0.202843i
$712$	−2.87011	−	1.65706i	−0.107562	−	0.0621008i
$713$	−16.3349	−	60.9625i	−0.611745	−	2.28306i
$714$	−4.86009	−	11.0155i	−0.181884	−	0.412245i
$715$	16.0153	−	8.14093i	0.598938	−	0.304454i
$716$		−	5.38822i		−	0.201367i
$717$	−7.50788	+	6.03806i	−0.280387	+	0.225496i
$718$	−9.62909	+	16.6781i	−0.359355	+	0.622420i
$719$	4.85123	+	8.40257i	0.180920	+	0.313363i	0.942194	−	0.335067i	$-0.108759\pi$
$719$	4.85123	+	8.40257i	0.180920	+	0.313363i	−0.761274	+	0.648430i	$0.775426\pi$
$720$	8.65732	−	0.395331i	0.322639	−	0.0147331i
$721$	14.3828	+	3.85387i	0.535645	+	0.143526i
$722$	−16.3722	−	4.38691i	−0.609309	−	0.163264i
$723$	14.2269	+	5.51616i	0.529103	+	0.205148i
$724$	7.11616	+	12.3256i	0.264470	+	0.458076i
$725$	5.11747	−	8.86371i	0.190058	−	0.329190i
$726$	−8.71079	−	10.8312i	−0.323288	−	0.401984i
$727$		−	7.28473i		−	0.270176i	−0.990834	−	0.135088i	$-0.956868\pi$
$727$		−	7.28473i		−	0.270176i	0.990834	−	0.135088i	$-0.0431316\pi$
$728$	0.192141	−	3.60043i	0.00712122	−	0.133441i
$729$	−21.5187	−	16.3078i	−0.796991	−	0.603992i
$730$	−7.03079	−	26.2393i	−0.260221	−	0.971159i
$731$	−69.1006	−	39.8953i	−2.55578	−	1.47558i
$732$	5.26533	−	7.19608i	0.194612	−	0.265975i
$733$	−24.5636	+	24.5636i	−0.907278	+	0.907278i	−0.996052	−	0.0887735i	$-0.971705\pi$
$733$	−24.5636	+	24.5636i	−0.907278	+	0.907278i	0.0887735	+	0.996052i	$0.471705\pi$
$734$	5.08130	−	18.9637i	0.187554	−	0.699962i
$735$	−4.94452	+	0.766095i	−0.182381	+	0.0282578i
$736$	5.57307	+	5.57307i	0.205426	+	0.205426i
$737$	−2.00177	+	1.15572i	−0.0737362	+	0.0425716i
$738$	9.02879	−	2.86663i	0.332354	−	0.105522i
$739$	7.84445	−	2.10191i	0.288563	−	0.0773201i	−0.111634	−	0.993749i	$-0.535608\pi$
$739$	7.84445	−	2.10191i	0.288563	−	0.0773201i	0.400197	+	0.916429i	$0.368942\pi$
$740$	17.2126			0.632747
$741$	30.3875	−	21.8779i	1.11631	−	0.803704i
$742$	1.27079			0.0466522
$743$	−34.2598	+	9.17990i	−1.25687	+	0.336778i	−0.824987	−	0.565151i	$-0.808818\pi$
$743$	−34.2598	+	9.17990i	−1.25687	+	0.336778i	−0.431884	+	0.901929i	$0.642151\pi$
$744$	−13.7889	−	1.49618i	−0.505524	−	0.0548525i
$745$	48.6642	−	28.0963i	1.78292	−	1.02937i
$746$	−10.8395	−	10.8395i	−0.396863	−	0.396863i
$747$	23.2182	+	36.2850i	0.849511	+	1.32760i
$748$	3.10327	−	11.5816i	0.113467	−	0.423464i
$749$	−10.9284	+	10.9284i	−0.399317	+	0.399317i
$750$	6.68270	+	4.88969i	0.244018	+	0.178546i
$751$	−12.5690	−	7.25670i	−0.458648	−	0.264801i	0.252827	−	0.967511i	$-0.418640\pi$
$751$	−12.5690	−	7.25670i	−0.458648	−	0.264801i	−0.711476	+	0.702711i	$0.751973\pi$
$752$	0.777035	+	2.89993i	0.0283355	+	0.105750i
$753$	3.66552	−	1.61724i	0.133579	−	0.0589356i
$754$	7.37400	+	8.20541i	0.268545	+	0.298824i
$755$		−	20.5081i		−	0.746366i
$756$	5.18602	+	0.324292i	0.188614	+	0.0117944i
$757$	−22.5379	+	39.0368i	−0.819155	+	1.41882i	0.0871511	+	0.996195i	$0.472224\pi$
$757$	−22.5379	+	39.0368i	−0.819155	+	1.41882i	−0.906306	+	0.422623i	$0.861110\pi$
$758$	4.07903	+	7.06509i	0.148157	+	0.256616i
$759$	−8.51222	+	21.9541i	−0.308974	+	0.796883i
$760$	−16.7304	−	4.48289i	−0.606875	−	0.162612i
$761$	46.9700	+	12.5856i	1.70266	+	0.456227i	0.973608	−	0.228229i	$-0.0732933\pi$
$761$	46.9700	+	12.5856i	1.70266	+	0.456227i	0.729055	+	0.684455i	$0.239960\pi$
$762$	−13.1028	+	33.7939i	−0.474666	+	1.22422i
$763$	4.24371	+	7.35032i	0.153633	+	0.266099i
$764$	−0.430073	+	0.744908i	−0.0155595	+	0.0269498i
$765$	27.7099	−	53.4911i	1.00185	−	1.93398i
$766$			26.4593i			0.956015i
$767$	−6.35877	−	7.07571i	−0.229602	−	0.255489i
$768$	1.58467	−	0.699162i	0.0571818	−	0.0252288i
$769$	1.71215	+	6.38984i	0.0617418	+	0.230423i	0.989901	−	0.141760i	$-0.0452760\pi$
$769$	1.71215	+	6.38984i	0.0617418	+	0.230423i	−0.928159	+	0.372183i	$0.878609\pi$
$770$	−4.31521	−	2.49139i	−0.155509	−	0.0897834i
$771$	−11.7209	−	8.57614i	−0.422119	−	0.308862i
$772$	1.30749	−	1.30749i	0.0470575	−	0.0470575i
$773$	−11.4518	+	42.7389i	−0.411894	+	1.53721i	0.379082	+	0.925363i	$0.376240\pi$
$773$	−11.4518	+	42.7389i	−0.411894	+	1.53721i	−0.790976	+	0.611847i	$0.790427\pi$
$774$	29.0055	−	18.5602i	1.04258	−	0.667133i
$775$	18.9408	+	18.9408i	0.680372	+	0.680372i
$776$	7.20506	−	4.15984i	0.258646	−	0.149330i
$777$	10.2601	+	1.11328i	0.368078	+	0.0399388i
$778$	14.9356	−	4.00199i	0.535469	−	0.143478i
$779$	−18.9327			−0.678333
$780$	14.6407	−	10.5408i	0.524220	−	0.377420i
$781$	−19.1261			−0.684384
$782$	52.9200	−	14.1799i	1.89242	−	0.507071i
$783$	−11.9218	+	10.5186i	−0.426052	+	0.375904i
$784$	−0.866025	+	0.500000i	−0.0309295	+	0.0178571i
$785$	−15.3840	−	15.3840i	−0.549080	−	0.549080i
$786$	−12.3199	+	1.90883i	−0.439438	+	0.0680858i
$787$	12.1111	−	45.1994i	0.431716	−	1.61119i	−0.317090	−	0.948396i	$-0.602706\pi$
$787$	12.1111	−	45.1994i	0.431716	−	1.61119i	0.748806	−	0.662790i	$-0.230628\pi$
$788$	−9.49241	+	9.49241i	−0.338153	+	0.338153i
$789$	1.70587	−	2.33140i	0.0607306	−	0.0830000i
$790$	−21.0289	−	12.1410i	−0.748175	−	0.431959i
$791$	−2.72719	−	10.1780i	−0.0969677	−	0.361888i
$792$	3.82211	+	3.48828i	0.135813	+	0.123951i
$793$	0.989152	−	18.5352i	0.0351258	−	0.658204i
$794$		−	23.5727i		−	0.836563i
$795$	3.98484	+	4.95485i	0.141328	+	0.175731i
$796$	−11.9711	+	20.7346i	−0.424305	+	0.734918i
$797$	6.21149	+	10.7586i	0.220022	+	0.381090i	0.954815	−	0.297202i	$-0.0960536\pi$
$797$	6.21149	+	10.7586i	0.220022	+	0.381090i	−0.734792	+	0.678292i	$0.762720\pi$
$798$	−9.68270	−	3.75426i	−0.342764	−	0.132899i
$799$	20.1583	+	5.40140i	0.713150	+	0.191088i
$800$	−3.23107	−	0.865763i	−0.114236	−	0.0306093i
$801$	−0.453538	−	9.93199i	−0.0160250	−	0.350930i
$802$	5.56585	+	9.64034i	0.196537	+	0.340412i
$803$	8.10999	−	14.0469i	0.286195	−	0.495705i
$804$	−1.80871	+	1.45462i	−0.0637883	+	0.0513005i
$805$		−	22.7680i		−	0.802465i
$806$	−25.7379	+	13.0831i	−0.906579	+	0.460834i
$807$	13.9950	+	31.7199i	0.492646	+	1.11659i
$808$	−1.61254	−	6.01810i	−0.0567291	−	0.211716i
$809$	−45.1620	−	26.0743i	−1.58781	−	0.916723i	−0.993667	−	0.112364i	$-0.964158\pi$
$809$	−45.1620	−	26.0743i	−1.58781	−	0.916723i	−0.594144	−	0.804359i	$-0.702509\pi$
$810$	14.9975	+	21.2373i	0.526957	+	0.746204i
$811$	23.1215	−	23.1215i	0.811905	−	0.811905i	−0.173014	−	0.984919i	$-0.555351\pi$
$811$	23.1215	−	23.1215i	0.811905	−	0.811905i	0.984919	+	0.173014i	$0.0553507\pi$
$812$	0.791914	−	2.95546i	0.0277907	−	0.103716i
$813$	5.47329	+	35.3256i	0.191957	+	1.23892i
$814$	7.26731	+	7.26731i	0.254719	+	0.254719i
$815$	3.84453	−	2.21964i	0.134668	−	0.0777507i
$816$	1.29879	−	11.9698i	0.0454668	−	0.419025i
$817$	−66.4778	+	17.8127i	−2.32576	+	0.623186i
$818$	19.2262			0.672230
$819$	9.40877	−	5.33620i	0.328769	−	0.186462i
$820$	−9.12175			−0.318545
$821$	−49.9173	+	13.3753i	−1.74213	+	0.466802i	−0.982918	−	0.184045i	$-0.941081\pi$
$821$	−49.9173	+	13.3753i	−1.74213	+	0.466802i	−0.759209	+	0.650846i	$0.774414\pi$
$822$	0.338217	−	3.11703i	0.0117967	−	0.108719i
$823$	−3.26283	+	1.88380i	−0.113735	+	0.0656650i	−0.555788	−	0.831324i	$-0.687584\pi$
$823$	−3.26283	+	1.88380i	−0.113735	+	0.0656650i	0.442053	+	0.896989i	$0.354250\pi$
$824$	10.5290	+	10.5290i	0.366794	+	0.366794i
$825$	−1.53013	−	9.87573i	−0.0532722	−	0.343829i
$826$	−0.682885	+	2.54856i	−0.0237606	+	0.0886759i
$827$	−4.95114	+	4.95114i	−0.172168	+	0.172168i	−0.787931	−	0.615763i	$-0.788848\pi$
$827$	−4.95114	+	4.95114i	−0.172168	+	0.172168i	0.615763	+	0.787931i	$0.288848\pi$
$828$	−5.07145	+	23.0943i	−0.176245	+	0.802581i
$829$	8.77230	+	5.06469i	0.304675	+	0.175904i	0.644541	−	0.764570i	$-0.277048\pi$
$829$	8.77230	+	5.06469i	0.304675	+	0.175904i	−0.339866	+	0.940474i	$0.610382\pi$
$830$	−10.7360	−	40.0673i	−0.372652	−	1.39075i
$831$	5.58086	+	12.6491i	0.193598	+	0.438794i
$832$	1.96661	−	3.02199i	0.0681800	−	0.104769i
$833$			6.95130i			0.240848i
$834$	21.3045	−	17.1337i	0.737714	−	0.593292i
$835$	−10.4994	+	18.1855i	−0.363346	+	0.629334i
$836$	−5.17100	−	8.95643i	−0.178843	−	0.309765i
$837$	−18.5152	−	37.2630i	−0.639979	−	1.28800i
$838$	−17.8412	−	4.78055i	−0.616316	−	0.165141i
$839$	33.0855	+	8.86523i	1.14224	+	0.306062i	0.779850	−	0.625966i	$-0.215295\pi$
$839$	33.0855	+	8.86523i	1.14224	+	0.306062i	0.362387	+	0.932028i	$0.381962\pi$
$840$	−4.66513	−	1.80880i	−0.160962	−	0.0624096i
$841$	−9.81905	−	17.0071i	−0.338588	−	0.586451i
$842$	−14.8280	+	25.6828i	−0.511005	+	0.885087i
$843$	17.5319	+	21.7996i	0.603830	+	0.750817i
$844$			2.92564i			0.100705i
$845$	13.5252	−	35.0340i	0.465281	−	1.20521i
$846$	−6.07155	+	6.65259i	−0.208744	+	0.228721i
$847$	2.07698	+	7.75138i	0.0713657	+	0.266340i
$848$	1.10054	+	0.635396i	0.0377926	+	0.0218196i
$849$	−8.43294	+	11.5252i	−0.289418	+	0.395545i
$850$	−16.4420	+	16.4420i	−0.563955	+	0.563955i
$851$	−12.1545	+	45.3613i	−0.416651	+	1.55496i
$852$	−18.9792	+	2.94061i	−0.650217	+	0.100743i
$853$	23.2961	+	23.2961i	0.797644	+	0.797644i	0.982723	−	0.185080i	$-0.0592544\pi$
$853$	23.2961	+	23.2961i	0.797644	+	0.797644i	−0.185080	+	0.982723i	$0.559254\pi$
$854$	−4.45834	+	2.57403i	−0.152561	+	0.0880814i
$855$	−15.7242	−	49.5254i	−0.537758	−	1.69373i
$856$	−14.9285	+	4.00009i	−0.510247	+	0.136720i
$857$	3.90760			0.133481			0.0667405	−	0.997770i	$-0.478740\pi$
$857$	3.90760			0.133481			0.0667405	+	0.997770i	$0.478740\pi$
$858$	10.6318	+	1.73102i	0.362965	+	0.0590961i
$859$	46.2425			1.57777			0.788887	−	0.614539i	$-0.210658\pi$
$859$	46.2425			1.57777			0.788887	+	0.614539i	$0.210658\pi$
$860$	−32.0290	+	8.58214i	−1.09218	+	0.292649i
$861$	−5.43729	−	0.589980i	−0.185302	−	0.0201065i
$862$	−8.63877	+	4.98760i	−0.294238	+	0.169878i
$863$	8.38383	+	8.38383i	0.285389	+	0.285389i	0.835254	−	0.549865i	$-0.185321\pi$
$863$	8.38383	+	8.38383i	0.285389	+	0.285389i	−0.549865	+	0.835254i	$0.685321\pi$
$864$	4.32908	+	2.87386i	0.147278	+	0.0977706i
$865$	−10.6098	+	39.5963i	−0.360744	+	1.34632i
$866$	−18.4434	+	18.4434i	−0.626731	+	0.626731i
$867$	−43.7808	−	32.0341i	−1.48687	−	1.08794i
$868$	6.93490	+	4.00386i	0.235386	+	0.135900i
$869$	−3.75253	−	14.0046i	−0.127296	−	0.475075i
$870$	14.0067	−	6.17980i	0.474870	−	0.209515i
$871$	−1.49746	+	4.59378i	−0.0507396	+	0.155654i
$872$			8.48742i			0.287420i
$873$	22.1619	+	11.4805i	0.750068	+	0.388557i
$874$	23.6280	−	40.9249i	0.799230	−	1.38431i
$875$	−2.39039	−	4.14028i	−0.0808100	−	0.139967i
$876$	5.88803	−	15.1860i	0.198938	−	0.513086i
$877$	3.63895	+	0.975054i	0.122879	+	0.0329252i	0.319734	−	0.947507i	$-0.396406\pi$
$877$	3.63895	+	0.975054i	0.122879	+	0.0329252i	−0.196856	+	0.980432i	$0.563073\pi$
$878$	−15.3565	−	4.11477i	−0.518258	−	0.138867i
$879$	−9.22924	+	23.8034i	−0.311295	+	0.802868i
$880$	−2.49139	−	4.31521i	−0.0839847	−	0.145466i
$881$	−11.6281	+	20.1405i	−0.391762	+	0.678552i	−0.992682	−	0.120757i	$-0.961468\pi$
$881$	−11.6281	+	20.1405i	−0.391762	+	0.678552i	0.600920	+	0.799309i	$0.294801\pi$
$882$	−2.66380	−	1.37992i	−0.0896947	−	0.0464644i
$883$			52.4326i			1.76450i	0.470784	+	0.882248i	$0.343971\pi$
$883$			52.4326i			1.76450i	−0.470784	+	0.882248i	$0.656029\pi$
$884$	−11.3571	−	22.3424i	−0.381982	−	0.751457i
$885$	−12.0783	+	5.32898i	−0.406006	+	0.179132i
$886$	1.39882	+	5.22047i	0.0469943	+	0.175385i
$887$	−15.8997	−	9.17967i	−0.533858	−	0.308223i	0.208728	−	0.977974i	$-0.433068\pi$
$887$	−15.8997	−	9.17967i	−0.533858	−	0.308223i	−0.742586	+	0.669750i	$0.766401\pi$
$888$	8.32885	+	6.09417i	0.279498	+	0.204507i
$889$	14.7970	−	14.7970i	0.496276	−	0.496276i
$890$	−2.47787	+	9.24753i	−0.0830583	+	0.309978i
$891$	−2.63453	+	15.2987i	−0.0882601	+	0.512524i
$892$	−11.2465	−	11.2465i	−0.376561	−	0.376561i
$893$	15.5892	−	9.00040i	0.521671	−	0.301187i
$894$	33.4952	+	3.63444i	1.12025	+	0.121554i
$895$	−15.0350	+	4.02862i	−0.502565	+	0.134662i
$896$	−1.00000			−0.0334077
$897$	17.4402	+	46.0266i	0.582313	+	1.53678i
$898$	16.9663			0.566173
$899$	−23.6666	+	6.34144i	−0.789324	+	0.211499i
$900$	−3.03676	−	9.56465i	−0.101225	−	0.318822i
$901$	7.65017	−	4.41683i	0.254864	−	0.147146i
$902$	−3.85128	−	3.85128i	−0.128234	−	0.128234i
$903$	−19.6469	+	3.04406i	−0.653809	+	0.101300i
$904$	2.72719	−	10.1780i	0.0907050	−	0.338516i
$905$	29.0720	−	29.0720i	0.966387	−	0.966387i
$906$	7.26096	−	9.92348i	0.241229	−	0.329686i
$907$	29.7986	+	17.2042i	0.989445	+	0.571256i	0.905108	−	0.425181i	$-0.139789\pi$
$907$	29.7986	+	17.2042i	0.989445	+	0.571256i	0.0843368	+	0.996437i	$0.473123\pi$
$908$	−3.35272	−	12.5125i	−0.111264	−	0.415242i
$909$	12.6000	−	13.8058i	0.417916	−	0.457910i
$910$	−10.1901	+	2.15580i	−0.337799	+	0.0714640i
$911$			4.55472i			0.150905i	0.997149	+	0.0754523i	$0.0240401\pi$
$911$			4.55472i			0.150905i	−0.997149	+	0.0754523i	$0.975960\pi$
$912$	−6.50834	−	8.09263i	−0.215513	−	0.267974i
$913$	12.3839	−	21.4496i	0.409848	−	0.709877i
$914$	−0.136294	−	0.236068i	−0.00450820	−	0.00780844i
$915$	−24.0163	−	9.31180i	−0.793955	−	0.307839i
$916$	−13.3165	−	3.56814i	−0.439989	−	0.117895i
$917$	6.95253	+	1.86293i	0.229593	+	0.0615192i
$918$	32.3470	−	16.0726i	1.06761	−	0.530474i
$919$	−12.8663	−	22.2851i	−0.424420	−	0.735117i	0.571946	−	0.820291i	$-0.306189\pi$
$919$	−12.8663	−	22.2851i	−0.424420	−	0.735117i	−0.996366	+	0.0851740i	$0.972855\pi$
$920$	11.3840	−	19.7176i	0.375319	−	0.650071i
$921$	−14.3896	+	11.5725i	−0.474152	+	0.381327i
$922$		−	22.8604i		−	0.752866i
$923$	−29.7363	+	26.7233i	−0.978782	+	0.879607i
$924$	−1.20597	−	2.73335i	−0.0396734	−	0.0899206i
$925$	−5.15859	−	19.2521i	−0.169613	−	0.633005i
$926$	5.18245	+	2.99209i	0.170306	+	0.0983261i
$927$	−9.58128	+	43.6310i	−0.314690	+	1.43303i
$928$	2.16355	−	2.16355i	0.0710220	−	0.0710220i
$929$	12.4325	−	46.3989i	0.407899	−	1.52230i	−0.390748	−	0.920498i	$-0.627784\pi$
$929$	12.4325	−	46.3989i	0.407899	−	1.52230i	0.798647	−	0.601800i	$-0.205550\pi$
$930$	6.13468	+	39.5944i	0.201164	+	1.29835i
$931$	4.23968	+	4.23968i	0.138950	+	0.138950i
$932$	15.3458	−	8.85988i	0.502667	−	0.290215i
$933$	2.46607	−	22.7275i	0.0807356	−	0.744065i
$934$	−10.8906	+	2.91813i	−0.356352	+	0.0954842i
$935$	−34.6368			−1.13274
$936$	10.8163	+	0.0831022i	0.353543	+	0.00271628i
$937$	34.8238			1.13764			0.568822	−	0.822461i	$-0.307399\pi$
$937$	34.8238			1.13764			0.568822	+	0.822461i	$0.307399\pi$
$938$	1.29441	−	0.346835i	0.0422639	−	0.0113246i
$939$	3.59433	−	33.1256i	0.117297	−	1.08101i
$940$	7.51085	−	4.33639i	0.244977	−	0.141438i
$941$	32.2919	+	32.2919i	1.05269	+	1.05269i	0.998533	+	0.0541537i	$0.0172461\pi$
$941$	32.2919	+	32.2919i	1.05269	+	1.05269i	0.0541537	+	0.998533i	$0.482754\pi$
$942$	−1.99728	−	12.8908i	−0.0650749	−	0.420005i
$943$	6.44124	−	24.0390i	0.209756	−	0.782819i
$944$	−1.86568	+	1.86568i	−0.0607226	+	0.0607226i
$945$	−2.97255	−	14.7133i	−0.0966972	−	0.478623i
$946$	−17.1464	−	9.89947i	−0.557477	−	0.321860i
$947$	−5.80669	−	21.6709i	−0.188692	−	0.704209i	−0.993810	−	0.111094i	$-0.964565\pi$
$947$	−5.80669	−	21.6709i	−0.188692	−	0.704209i	0.805118	−	0.593115i	$-0.202102\pi$
$948$	−5.87692	−	13.3202i	−0.190873	−	0.432619i
$949$	−7.01757	−	33.1709i	−0.227800	−	1.07677i
$950$			20.0563i			0.650712i
$951$	−8.72930	+	7.02036i	−0.283067	+	0.227651i
$952$	−3.47565	+	6.02001i	−0.112647	+	0.195109i
$953$	3.04642	+	5.27655i	0.0986832	+	0.170924i	0.911140	−	0.412097i	$-0.135204\pi$
$953$	3.04642	+	5.27655i	0.0986832	+	0.170924i	−0.812457	+	0.583022i	$0.801870\pi$
$954$	0.173908	+	3.80840i	0.00563050	+	0.123302i
$955$	2.40010	+	0.643106i	0.0776656	+	0.0208104i
$956$	5.37303	+	1.43970i	0.173776	+	0.0465632i
$957$	8.52291	+	3.30457i	0.275506	+	0.106822i
$958$	−0.456037	−	0.789880i	−0.0147339	−	0.0255199i
$959$	−0.905090	+	1.56766i	−0.0292269	+	0.0506225i
$960$	−3.13572	−	3.89903i	−0.101205	−	0.125841i
$961$		−	33.1237i		−	1.06851i
$962$	21.4529	+	1.14486i	0.691669	+	0.0369117i
$963$	−34.2468	−	31.2557i	−1.10359	−	1.00720i
$964$	−2.28012	−	8.50951i	−0.0734376	−	0.274073i
$965$	−4.62592	−	2.67078i	−0.148914	−	0.0859753i
$966$	8.06107	−	11.0170i	0.259361	−	0.354466i
$967$	29.9904	−	29.9904i	0.964426	−	0.964426i	−0.0349622	−	0.999389i	$-0.511131\pi$
$967$	29.9904	−	29.9904i	0.964426	−	0.964426i	0.999389	+	0.0349622i	$0.0111311\pi$
$968$	−2.07698	+	7.75138i	−0.0667565	+	0.249139i
$969$	−71.3384	+	11.0530i	−2.29172	+	0.355075i
$970$	−16.9944	−	16.9944i	−0.545658	−	0.545658i
$971$	−25.8769	+	14.9401i	−0.830431	+	0.479449i	−0.854000	−	0.520273i	$-0.825830\pi$
$971$	−25.8769	+	14.9401i	−0.830431	+	0.479449i	0.0235694	+	0.999722i	$0.492497\pi$
$972$	−0.262154	+	15.5863i	−0.00840858	+	0.499929i
$973$	−15.2466	+	4.08531i	−0.488783	+	0.130969i
$974$	7.29423			0.233722
$975$	−16.1775	−	13.2164i	−0.518095	−	0.423264i
$976$	−5.14805			−0.164785
$977$	2.46578	−	0.660703i	0.0788871	−	0.0211377i	−0.219160	−	0.975689i	$-0.570332\pi$
$977$	2.46578	−	0.660703i	0.0788871	−	0.0211377i	0.298047	+	0.954551i	$0.403665\pi$
$978$	2.64617	+	0.287126i	0.0846151	+	0.00918126i
$979$	−4.95056	+	2.85821i	−0.158221	+	0.0913488i
$980$	2.04268	+	2.04268i	0.0652509	+	0.0652509i
$981$	−21.4472	+	13.7238i	−0.684758	+	0.438166i
$982$	8.68412	−	32.4096i	0.277121	−	1.03423i
$983$	−3.28424	+	3.28424i	−0.104751	+	0.104751i	−0.757540	−	0.652789i	$-0.773599\pi$
$983$	−3.28424	+	3.28424i	−0.104751	+	0.104751i	0.652789	+	0.757540i	$0.273599\pi$
$984$	−4.41384	−	3.22958i	−0.140708	−	0.102955i
$985$	33.5843	+	19.3899i	1.07009	+	0.617814i
$986$	−5.50484	−	20.5443i	−0.175310	−	0.654265i
$987$	4.75754	−	2.09905i	0.151434	−	0.0668134i
$988$	−20.5537	−	6.70003i	−0.653901	−	0.213157i
$989$		−	90.4680i		−	2.87671i
$990$	6.87584	−	13.2731i	0.218529	−	0.421847i
$991$	4.50317	−	7.79972i	0.143048	−	0.247766i	−0.785595	−	0.618741i	$-0.787643\pi$
$991$	4.50317	−	7.79972i	0.143048	−	0.247766i	0.928643	+	0.370975i	$0.120976\pi$
$992$	4.00386	+	6.93490i	0.127123	+	0.220183i
$993$	−14.8200	+	38.2226i	−0.470298	+	1.21296i
$994$	10.7106	+	2.86989i	0.339718	+	0.0910273i
$995$	66.8071	+	17.9009i	2.11793	+	0.567497i
$996$	8.99099	−	23.1889i	0.284890	−	0.734768i
$997$	−8.44727	−	14.6311i	−0.267528	−	0.463372i	0.700695	−	0.713461i	$-0.252873\pi$
$997$	−8.44727	−	14.6311i	−0.267528	−	0.463372i	−0.968223	+	0.250089i	$0.919540\pi$
$998$	−2.95559	+	5.11923i	−0.0935575	+	0.162046i
$999$	−1.93227	+	30.9005i	−0.0611344	+	0.977650i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bu.b.71.4	yes	56
3.2	odd	2		546.2.bu.a.71.9	✓	56
13.11	odd	12		546.2.bu.a.323.9	yes	56
39.11	even	12	inner	546.2.bu.b.323.4	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bu.a.71.9	✓	56	3.2	odd	2
546.2.bu.a.323.9	yes	56	13.11	odd	12
546.2.bu.b.71.4	yes	56	1.1	even	1	trivial
546.2.bu.b.323.4	yes	56	39.11	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bu (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.186842 + 1.72194i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.04268 - 2.04268i) q^{5} +(-0.265197 - 1.71163i) q^{6} +(-0.258819 + 0.965926i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.93018 - 0.643461i) q^{9} +O(q^{10})\)	\(q+(-0.965926 + 0.258819i) q^{2} +(-0.186842 + 1.72194i) q^{3} +(0.866025 - 0.500000i) q^{4} +(-2.04268 - 2.04268i) q^{5} +(-0.265197 - 1.71163i) q^{6} +(-0.258819 + 0.965926i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(-2.93018 - 0.643461i) q^{9} +(2.50176 + 1.44439i) q^{10} +(0.446430 + 1.66610i) q^{11} +(0.699162 + 1.58467i) q^{12} +(3.02199 + 1.96661i) q^{13} -1.00000i q^{14} +(3.89903 - 3.13572i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-3.47565 - 6.02001i) q^{17} +(2.99688 - 0.136851i) q^{18} +(-5.79151 - 1.55183i) q^{19} +(-2.79035 - 0.747671i) q^{20} +(-1.61491 - 0.626147i) q^{21} +(-0.862436 - 1.49378i) q^{22} +(3.94076 - 6.82559i) q^{23} +(-1.08548 - 1.34972i) q^{24} +3.34505i q^{25} +(-3.42802 - 1.11745i) q^{26} +(1.65548 - 4.92538i) q^{27} +(0.258819 + 0.965926i) q^{28} +(-2.64980 - 1.52986i) q^{29} +(-2.95459 + 4.03801i) q^{30} +(5.66232 - 5.66232i) q^{31} +(-0.258819 + 0.965926i) q^{32} +(-2.95234 + 0.457430i) q^{33} +(4.91531 + 4.91531i) q^{34} +(2.50176 - 1.44439i) q^{35} +(-2.85934 + 0.907836i) q^{36} +(-5.75540 + 1.54215i) q^{37} +5.99581 q^{38} +(-3.95103 + 4.83625i) q^{39} +2.88878 q^{40} +(3.05005 - 0.817259i) q^{41} +(1.72194 + 0.186842i) q^{42} +(9.94067 - 5.73925i) q^{43} +(1.21967 + 1.21967i) q^{44} +(4.67103 + 7.29979i) q^{45} +(-2.03989 + 7.61296i) q^{46} +(-2.12290 + 2.12290i) q^{47} +(1.39783 + 1.02278i) q^{48} +(-0.866025 - 0.500000i) q^{49} +(-0.865763 - 3.23107i) q^{50} +(11.0155 - 4.86009i) q^{51} +(3.60043 + 0.192141i) q^{52} +1.27079i q^{53} +(-0.324292 + 5.18602i) q^{54} +(2.49139 - 4.31521i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(3.75426 - 9.68270i) q^{57} +(2.95546 + 0.791914i) q^{58} +(-2.54856 - 0.682885i) q^{59} +(1.80880 - 4.66513i) q^{60} +(-2.57403 - 4.45834i) q^{61} +(-4.00386 + 6.93490i) q^{62} +(1.37992 - 2.66380i) q^{63} -1.00000i q^{64} +(-2.15580 - 10.1901i) q^{65} +(2.73335 - 1.20597i) q^{66} +(0.346835 + 1.29441i) q^{67} +(-6.02001 - 3.47565i) q^{68} +(11.0170 + 8.06107i) q^{69} +(-2.04268 + 2.04268i) q^{70} +(-2.86989 + 10.7106i) q^{71} +(2.52695 - 1.61695i) q^{72} +(-6.64934 - 6.64934i) q^{73} +(5.16015 - 2.97921i) q^{74} +(-5.75999 - 0.624995i) q^{75} +(-5.79151 + 1.55183i) q^{76} -1.72487 q^{77} +(2.56469 - 5.69407i) q^{78} -8.40565 q^{79} +(-2.79035 + 0.747671i) q^{80} +(8.17191 + 3.77092i) q^{81} +(-2.73460 + 1.57882i) q^{82} +(-10.1535 - 10.1535i) q^{83} +(-1.71163 + 0.265197i) q^{84} +(-5.19729 + 19.3966i) q^{85} +(-8.11652 + 8.11652i) q^{86} +(3.12943 - 4.27696i) q^{87} +(-1.49378 - 0.862436i) q^{88} +(0.857755 + 3.20119i) q^{89} +(-6.40119 - 5.84211i) q^{90} +(-2.68175 + 2.41002i) q^{91} -7.88152i q^{92} +(8.69224 + 10.8082i) q^{93} +(1.50112 - 2.60001i) q^{94} +(8.66029 + 15.0001i) q^{95} +(-1.61491 - 0.626147i) q^{96} +(-8.03620 - 2.15329i) q^{97} +(0.965926 + 0.258819i) q^{98} +(-0.236050 - 5.16923i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{6} - 24 q^{9}+O(q^{10}) \) 56 * q + 8 * q^6 - 24 * q^9	\( 56 q + 8 q^{6} - 24 q^{9} + 24 q^{10} + 8 q^{11} + 24 q^{13} + 4 q^{15} + 28 q^{16} - 4 q^{17} - 8 q^{18} + 8 q^{19} + 4 q^{21} - 8 q^{23} - 8 q^{24} - 4 q^{26} - 24 q^{27} - 8 q^{30} - 8 q^{31} + 8 q^{33} - 24 q^{34} + 24 q^{35} - 12 q^{36} - 8 q^{37} - 20 q^{39} - 28 q^{41} + 8 q^{44} + 72 q^{45} - 20 q^{46} + 64 q^{50} + 16 q^{54} + 8 q^{55} - 28 q^{56} + 4 q^{58} - 8 q^{59} + 20 q^{60} + 8 q^{61} - 32 q^{62} - 16 q^{63} - 24 q^{65} + 32 q^{66} - 16 q^{69} - 112 q^{71} + 8 q^{73} + 48 q^{74} + 40 q^{75} + 8 q^{76} + 16 q^{79} + 12 q^{81} - 4 q^{83} - 4 q^{84} + 32 q^{85} - 16 q^{86} - 144 q^{87} + 88 q^{89} - 8 q^{90} - 8 q^{91} + 52 q^{93} - 8 q^{94} - 48 q^{95} + 4 q^{96} - 64 q^{97} + 56 q^{99}+O(q^{100}) \) 56 * q + 8 * q^6 - 24 * q^9 + 24 * q^10 + 8 * q^11 + 24 * q^13 + 4 * q^15 + 28 * q^16 - 4 * q^17 - 8 * q^18 + 8 * q^19 + 4 * q^21 - 8 * q^23 - 8 * q^24 - 4 * q^26 - 24 * q^27 - 8 * q^30 - 8 * q^31 + 8 * q^33 - 24 * q^34 + 24 * q^35 - 12 * q^36 - 8 * q^37 - 20 * q^39 - 28 * q^41 + 8 * q^44 + 72 * q^45 - 20 * q^46 + 64 * q^50 + 16 * q^54 + 8 * q^55 - 28 * q^56 + 4 * q^58 - 8 * q^59 + 20 * q^60 + 8 * q^61 - 32 * q^62 - 16 * q^63 - 24 * q^65 + 32 * q^66 - 16 * q^69 - 112 * q^71 + 8 * q^73 + 48 * q^74 + 40 * q^75 + 8 * q^76 + 16 * q^79 + 12 * q^81 - 4 * q^83 - 4 * q^84 + 32 * q^85 - 16 * q^86 - 144 * q^87 + 88 * q^89 - 8 * q^90 - 8 * q^91 + 52 * q^93 - 8 * q^94 - 48 * q^95 + 4 * q^96 - 64 * q^97 + 56 * q^99

Introduction

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