LMFDB - Embedded newform 847.2.f.y.372.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [847,2,Mod(148,847)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(847, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("847.148");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 847 = 7 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	847.f (of order $5$, degree $4$, not 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:	$6.76332905120$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			372.4
Character	$\chi$	$=$	847.372
Dual form			847.2.f.y.148.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.394480 - 1.21408i) q^{2} +(2.08406 - 1.51415i) q^{3} +(0.299647 + 0.217706i) q^{4} +(-1.26432 - 3.89119i) q^{5} +(-1.01619 - 3.12752i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(2.44804 - 1.77861i) q^{8} +(1.12357 - 3.45799i) q^{9} +O(q^{10})$	\(q+(0.394480 - 1.21408i) q^{2} +(2.08406 - 1.51415i) q^{3} +(0.299647 + 0.217706i) q^{4} +(-1.26432 - 3.89119i) q^{5} +(-1.01619 - 3.12752i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(2.44804 - 1.77861i) q^{8} +(1.12357 - 3.45799i) q^{9} -5.22298 q^{10} +0.954122 q^{12} +(-1.35686 + 4.17600i) q^{13} +(-1.03276 + 0.750346i) q^{14} +(-8.52678 - 6.19507i) q^{15} +(-0.964766 - 2.96924i) q^{16} +(1.29523 + 3.98632i) q^{17} +(-3.75507 - 2.72822i) q^{18} +(1.01030 - 0.734025i) q^{19} +(0.468285 - 1.44123i) q^{20} -2.57603 q^{21} +4.97180 q^{23} +(2.40877 - 7.41343i) q^{24} +(-9.49775 + 6.90052i) q^{25} +(4.53476 + 3.29470i) q^{26} +(-0.506241 - 1.55805i) q^{27} +(-0.114455 - 0.352256i) q^{28} +(1.56579 + 1.13761i) q^{29} +(-10.8850 + 7.90840i) q^{30} +(-0.482926 + 1.48629i) q^{31} +2.06640 q^{32} +5.35067 q^{34} +(-1.26432 + 3.89119i) q^{35} +(1.08950 - 0.791570i) q^{36} +(0.579496 + 0.421028i) q^{37} +(-0.492626 - 1.51615i) q^{38} +(3.49533 + 10.7575i) q^{39} +(-10.0160 - 7.27706i) q^{40} +(-3.88834 + 2.82505i) q^{41} +(-1.01619 + 3.12752i) q^{42} +1.35362 q^{43} -14.8763 q^{45} +(1.96128 - 6.03619i) q^{46} +(8.46734 - 6.15188i) q^{47} +(-6.50652 - 4.72726i) q^{48} +(0.309017 + 0.951057i) q^{49} +(4.63114 + 14.2532i) q^{50} +(8.73524 + 6.34652i) q^{51} +(-1.31572 + 0.955928i) q^{52} +(-1.22735 + 3.77741i) q^{53} -2.09131 q^{54} -3.02595 q^{56} +(0.994091 - 3.05950i) q^{57} +(1.99883 - 1.45223i) q^{58} +(-11.1311 - 8.08724i) q^{59} +(-1.20632 - 3.71267i) q^{60} +(-3.62388 - 11.1532i) q^{61} +(1.61398 + 1.17263i) q^{62} +(-2.94155 + 2.13716i) q^{63} +(2.74469 - 8.44727i) q^{64} +17.9651 q^{65} +7.59274 q^{67} +(-0.479734 + 1.47647i) q^{68} +(10.3615 - 7.52808i) q^{69} +(4.22548 + 3.06999i) q^{70} +(0.0674634 + 0.207631i) q^{71} +(-3.39987 - 10.4637i) q^{72} +(-8.87607 - 6.44884i) q^{73} +(0.739763 - 0.537470i) q^{74} +(-9.34538 + 28.7621i) q^{75} +0.462535 q^{76} +14.4394 q^{78} +(-1.40988 + 4.33917i) q^{79} +(-10.3341 + 7.50817i) q^{80} +(5.41047 + 3.93094i) q^{81} +(1.89597 + 5.83520i) q^{82} +(0.758506 + 2.33444i) q^{83} +(-0.771901 - 0.560819i) q^{84} +(13.8739 - 10.0800i) q^{85} +(0.533974 - 1.64340i) q^{86} +4.98571 q^{87} +4.20456 q^{89} +(-5.86839 + 18.0610i) q^{90} +(3.55232 - 2.58091i) q^{91} +(1.48979 + 1.08239i) q^{92} +(1.24403 + 3.82874i) q^{93} +(-4.12871 - 12.7069i) q^{94} +(-4.13358 - 3.00322i) q^{95} +(4.30649 - 3.12885i) q^{96} +(-3.37598 + 10.3902i) q^{97} +1.27656 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 6 q^{6} - 6 q^{7} - 12 q^{8} - 8 q^{9}+O(q^{10}) $ 24 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 6 * q^6 - 6 * q^7 - 12 * q^8 - 8 * q^9	\( 24 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 6 q^{6} - 6 q^{7} - 12 q^{8} - 8 q^{9} - 32 q^{10} - 56 q^{12} - 4 q^{13} - 4 q^{14} - 2 q^{15} - 8 q^{16} - 22 q^{17} - 24 q^{18} - 6 q^{19} - 2 q^{20} - 8 q^{21} + 8 q^{23} + 20 q^{24} - 4 q^{25} - 6 q^{26} + 2 q^{27} - 4 q^{28} - 12 q^{29} - 20 q^{30} + 2 q^{31} + 32 q^{32} + 96 q^{34} + 4 q^{35} - 18 q^{36} - 14 q^{37} + 22 q^{38} - 20 q^{39} - 18 q^{40} - 26 q^{41} + 6 q^{42} - 16 q^{43} - 144 q^{45} - 12 q^{46} + 16 q^{47} + 24 q^{48} - 6 q^{49} + 4 q^{50} + 4 q^{51} - 12 q^{52} - 4 q^{53} - 128 q^{54} + 48 q^{56} - 20 q^{57} + 2 q^{58} + 4 q^{59} - 24 q^{60} + 8 q^{61} - 20 q^{62} - 8 q^{63} - 26 q^{64} + 96 q^{65} + 24 q^{67} - 12 q^{68} + 14 q^{69} + 8 q^{70} - 22 q^{71} - 16 q^{72} - 14 q^{73} - 44 q^{74} + 20 q^{75} - 120 q^{76} + 128 q^{78} + 28 q^{79} + 4 q^{80} + 6 q^{81} + 4 q^{82} - 22 q^{83} + 14 q^{84} + 24 q^{85} + 30 q^{86} + 88 q^{87} + 22 q^{90} - 4 q^{91} - 10 q^{92} + 50 q^{93} + 38 q^{94} + 24 q^{95} + 62 q^{96} + 4 q^{97} + 16 q^{98}+O(q^{100}) \) 24 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 6 * q^6 - 6 * q^7 - 12 * q^8 - 8 * q^9 - 32 * q^10 - 56 * q^12 - 4 * q^13 - 4 * q^14 - 2 * q^15 - 8 * q^16 - 22 * q^17 - 24 * q^18 - 6 * q^19 - 2 * q^20 - 8 * q^21 + 8 * q^23 + 20 * q^24 - 4 * q^25 - 6 * q^26 + 2 * q^27 - 4 * q^28 - 12 * q^29 - 20 * q^30 + 2 * q^31 + 32 * q^32 + 96 * q^34 + 4 * q^35 - 18 * q^36 - 14 * q^37 + 22 * q^38 - 20 * q^39 - 18 * q^40 - 26 * q^41 + 6 * q^42 - 16 * q^43 - 144 * q^45 - 12 * q^46 + 16 * q^47 + 24 * q^48 - 6 * q^49 + 4 * q^50 + 4 * q^51 - 12 * q^52 - 4 * q^53 - 128 * q^54 + 48 * q^56 - 20 * q^57 + 2 * q^58 + 4 * q^59 - 24 * q^60 + 8 * q^61 - 20 * q^62 - 8 * q^63 - 26 * q^64 + 96 * q^65 + 24 * q^67 - 12 * q^68 + 14 * q^69 + 8 * q^70 - 22 * q^71 - 16 * q^72 - 14 * q^73 - 44 * q^74 + 20 * q^75 - 120 * q^76 + 128 * q^78 + 28 * q^79 + 4 * q^80 + 6 * q^81 + 4 * q^82 - 22 * q^83 + 14 * q^84 + 24 * q^85 + 30 * q^86 + 88 * q^87 + 22 * q^90 - 4 * q^91 - 10 * q^92 + 50 * q^93 + 38 * q^94 + 24 * q^95 + 62 * q^96 + 4 * q^97 + 16 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/847\mathbb{Z}\right)^\times$.

$n$	$122$	$365$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	0.394480	−	1.21408i	0.278939	−	0.858487i	−0.709211	−	0.704997i	$-0.750948\pi$
$2$	0.394480	−	1.21408i	0.278939	−	0.858487i	0.988150	−	0.153491i	$-0.0490515\pi$
$3$	2.08406	−	1.51415i	1.20323	−	0.874198i	0.208631	−	0.977994i	$-0.433099\pi$
$3$	2.08406	−	1.51415i	1.20323	−	0.874198i	0.994599	+	0.103797i	$0.0330991\pi$
$4$	0.299647	+	0.217706i	0.149824	+	0.108853i
$5$	−1.26432	−	3.89119i	−0.565423	−	1.74019i	−0.666692	−	0.745333i	$-0.732290\pi$
$5$	−1.26432	−	3.89119i	−0.565423	−	1.74019i	0.101269	−	0.994859i	$-0.467710\pi$
$6$	−1.01619	−	3.12752i	−0.414859	−	1.27681i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$7$	−0.809017	−	0.587785i	−0.305780	−	0.222162i
$8$	2.44804	−	1.77861i	0.865514	−	0.628833i
$9$	1.12357	−	3.45799i	0.374524	−	1.15266i
$10$	−5.22298			−1.65165
$11$		0			0
$11$		0			0
$12$	0.954122			0.275431
$13$	−1.35686	+	4.17600i	−0.376327	+	1.15821i	0.566253	+	0.824232i	$0.308393\pi$
$13$	−1.35686	+	4.17600i	−0.376327	+	1.15821i	−0.942579	+	0.333983i	$0.891607\pi$
$14$	−1.03276	+	0.750346i	−0.276017	+	0.200538i
$15$	−8.52678	−	6.19507i	−2.20161	−	1.59956i
$16$	−0.964766	−	2.96924i	−0.241191	−	0.742311i
$17$	1.29523	+	3.98632i	0.314140	+	0.966824i	0.976107	+	0.217291i	$0.0697220\pi$
$17$	1.29523	+	3.98632i	0.314140	+	0.966824i	−0.661967	+	0.749533i	$0.730278\pi$
$18$	−3.75507	−	2.72822i	−0.885079	−	0.643047i
$19$	1.01030	−	0.734025i	0.231779	−	0.168397i	−0.465834	−	0.884872i	$-0.654246\pi$
$19$	1.01030	−	0.734025i	0.231779	−	0.168397i	0.697613	+	0.716475i	$0.254246\pi$
$20$	0.468285	−	1.44123i	0.104712	−	0.322270i
$21$	−2.57603			−0.562137
$22$		0			0
$23$	4.97180			1.03669			0.518346	−	0.855171i	$-0.326548\pi$
$23$	4.97180			1.03669			0.518346	+	0.855171i	$0.326548\pi$
$24$	2.40877	−	7.41343i	0.491688	−	1.51326i
$25$	−9.49775	+	6.90052i	−1.89955	+	1.38010i
$26$	4.53476	+	3.29470i	0.889340	+	0.646143i
$27$	−0.506241	−	1.55805i	−0.0974262	−	0.299847i
$28$	−0.114455	−	0.352256i	−0.0216300	−	0.0665702i
$29$	1.56579	+	1.13761i	0.290760	+	0.211249i	0.723597	−	0.690223i	$-0.242488\pi$
$29$	1.56579	+	1.13761i	0.290760	+	0.211249i	−0.432837	+	0.901472i	$0.642488\pi$
$30$	−10.8850	+	7.90840i	−1.98732	+	1.44387i
$31$	−0.482926	+	1.48629i	−0.0867361	+	0.266946i	−0.985012	−	0.172486i	$-0.944820\pi$
$31$	−0.482926	+	1.48629i	−0.0867361	+	0.266946i	0.898276	+	0.439432i	$0.144820\pi$
$32$	2.06640			0.365292
$33$		0			0
$34$	5.35067			0.917632
$35$	−1.26432	+	3.89119i	−0.213710	+	0.657731i
$36$	1.08950	−	0.791570i	0.181584	−	0.131928i
$37$	0.579496	+	0.421028i	0.0952685	+	0.0692166i	0.634400	−	0.773005i	$-0.281247\pi$
$37$	0.579496	+	0.421028i	0.0952685	+	0.0692166i	−0.539131	+	0.842222i	$0.681247\pi$
$38$	−0.492626	−	1.51615i	−0.0799145	−	0.245952i
$39$	3.49533	+	10.7575i	0.559701	+	1.72258i
$40$	−10.0160	−	7.27706i	−1.58367	−	1.15060i
$41$	−3.88834	+	2.82505i	−0.607257	+	0.441198i	−0.848448	−	0.529280i	$-0.822462\pi$
$41$	−3.88834	+	2.82505i	−0.607257	+	0.441198i	0.241190	+	0.970478i	$0.422462\pi$
$42$	−1.01619	+	3.12752i	−0.156802	+	0.482587i
$43$	1.35362			0.206424			0.103212	−	0.994659i	$-0.467088\pi$
$43$	1.35362			0.206424			0.103212	+	0.994659i	$0.467088\pi$
$44$		0			0
$45$	−14.8763			−2.21762
$46$	1.96128	−	6.03619i	0.289174	−	0.889987i
$47$	8.46734	−	6.15188i	1.23509	−	0.897344i	0.237827	−	0.971307i	$-0.423565\pi$
$47$	8.46734	−	6.15188i	1.23509	−	0.897344i	0.997261	+	0.0739632i	$0.0235647\pi$
$48$	−6.50652	−	4.72726i	−0.939135	−	0.682322i
$49$	0.309017	+	0.951057i	0.0441453	+	0.135865i
$50$	4.63114	+	14.2532i	0.654942	+	2.01570i
$51$	8.73524	+	6.34652i	1.22318	+	0.888691i
$52$	−1.31572	+	0.955928i	−0.182458	+	0.132563i
$53$	−1.22735	+	3.77741i	−0.168590	+	0.518867i	−0.999283	−	0.0378642i	$-0.987945\pi$
$53$	−1.22735	+	3.77741i	−0.168590	+	0.518867i	0.830693	+	0.556731i	$0.187945\pi$
$54$	−2.09131			−0.284591
$55$		0			0
$56$	−3.02595			−0.404359
$57$	0.994091	−	3.05950i	0.131671	−	0.405240i
$58$	1.99883	−	1.45223i	0.262459	−	0.190688i
$59$	−11.1311	−	8.08724i	−1.44915	−	1.05287i	−0.986029	−	0.166575i	$-0.946729\pi$
$59$	−11.1311	−	8.08724i	−1.44915	−	1.05287i	−0.463122	−	0.886295i	$-0.653271\pi$
$60$	−1.20632	−	3.71267i	−0.155735	−	0.479303i
$61$	−3.62388	−	11.1532i	−0.463991	−	1.42802i	−0.860247	−	0.509877i	$-0.829691\pi$
$61$	−3.62388	−	11.1532i	−0.463991	−	1.42802i	0.396256	−	0.918140i	$-0.370309\pi$
$62$	1.61398	+	1.17263i	0.204976	+	0.148924i
$63$	−2.94155	+	2.13716i	−0.370600	+	0.269257i
$64$	2.74469	−	8.44727i	0.343086	−	1.05591i
$65$	17.9651			2.22830
$66$		0			0
$67$	7.59274			0.927600			0.463800	−	0.885940i	$-0.346486\pi$
$67$	7.59274			0.927600			0.463800	+	0.885940i	$0.346486\pi$
$68$	−0.479734	+	1.47647i	−0.0581763	+	0.179048i
$69$	10.3615	−	7.52808i	1.24738	−	0.906274i
$70$	4.22548	+	3.06999i	0.505042	+	0.366934i
$71$	0.0674634	+	0.207631i	0.00800644	+	0.0246413i	0.954980	−	0.296670i	$-0.0958763\pi$
$71$	0.0674634	+	0.207631i	0.00800644	+	0.0246413i	−0.946973	+	0.321312i	$0.895876\pi$
$72$	−3.39987	−	10.4637i	−0.400678	−	1.23316i
$73$	−8.87607	−	6.44884i	−1.03887	−	0.754780i	−0.0688019	−	0.997630i	$-0.521918\pi$
$73$	−8.87607	−	6.44884i	−1.03887	−	0.754780i	−0.970064	+	0.242850i	$0.921918\pi$
$74$	0.739763	−	0.537470i	0.0859957	−	0.0624796i
$75$	−9.34538	+	28.7621i	−1.07911	+	3.32116i
$76$	0.462535			0.0530564
$77$		0			0
$78$	14.4394			1.63494
$79$	−1.40988	+	4.33917i	−0.158624	+	0.488195i	−0.998510	−	0.0545680i	$-0.982622\pi$
$79$	−1.40988	+	4.33917i	−0.158624	+	0.488195i	0.839886	+	0.542763i	$0.182622\pi$
$80$	−10.3341	+	7.50817i	−1.15539	+	0.839439i
$81$	5.41047	+	3.93094i	0.601164	+	0.436771i
$82$	1.89597	+	5.83520i	0.209375	+	0.644391i
$83$	0.758506	+	2.33444i	0.0832568	+	0.256238i	0.984016	−	0.178081i	$-0.0569890\pi$
$83$	0.758506	+	2.33444i	0.0832568	+	0.256238i	−0.900759	+	0.434319i	$0.856989\pi$
$84$	−0.771901	−	0.560819i	−0.0842213	−	0.0611904i
$85$	13.8739	−	10.0800i	1.50484	−	1.09333i
$86$	0.533974	−	1.64340i	0.0575799	−	0.177213i
$87$	4.98571			0.534524
$88$		0			0
$89$	4.20456			0.445683			0.222841	−	0.974855i	$-0.428467\pi$
$89$	4.20456			0.445683			0.222841	+	0.974855i	$0.428467\pi$
$90$	−5.86839	+	18.0610i	−0.618583	+	1.90380i
$91$	3.55232	−	2.58091i	0.372384	−	0.270553i
$92$	1.48979	+	1.08239i	0.155321	+	0.112847i
$93$	1.24403	+	3.82874i	0.129000	+	0.397022i
$94$	−4.12871	−	12.7069i	−0.425844	−	1.31061i
$95$	−4.13358	−	3.00322i	−0.424096	−	0.308124i
$96$	4.30649	−	3.12885i	0.439530	−	0.319337i
$97$	−3.37598	+	10.3902i	−0.342778	+	1.05496i	0.619984	+	0.784614i	$0.287139\pi$
$97$	−3.37598	+	10.3902i	−0.342778	+	1.05496i	−0.962762	+	0.270349i	$0.912861\pi$
$98$	1.27656			0.128952
$99$		0			0
$100$	−4.34826			−0.434826
$101$	2.27616	−	7.00529i	0.226486	−	0.697052i	−0.771651	−	0.636046i	$-0.780569\pi$
$101$	2.27616	−	7.00529i	0.226486	−	0.697052i	0.998137	−	0.0610064i	$-0.0194310\pi$
$102$	11.1511	−	8.10174i	1.10412	−	0.802192i
$103$	0.124497	+	0.0904521i	0.0122670	+	0.00891251i	0.593902	−	0.804537i	$-0.297587\pi$
$103$	0.124497	+	0.0904521i	0.0122670	+	0.00891251i	−0.581635	+	0.813450i	$0.697587\pi$
$104$	4.10580	+	12.6364i	0.402607	+	1.23910i
$105$	3.25694	+	10.0238i	0.317845	+	0.978226i
$106$	4.10193	+	2.98022i	0.398414	+	0.289465i
$107$	−6.42858	+	4.67064i	−0.621475	+	0.451528i	−0.853436	−	0.521197i	$-0.825486\pi$
$107$	−6.42858	+	4.67064i	−0.621475	+	0.451528i	0.231962	+	0.972725i	$0.425486\pi$
$108$	0.187504	−	0.577077i	0.0180426	−	0.0555293i
$109$	−4.91440			−0.470714			−0.235357	−	0.971909i	$-0.575626\pi$
$109$	−4.91440			−0.470714			−0.235357	+	0.971909i	$0.575626\pi$
$110$		0			0
$111$	1.84520			0.175139
$112$	−0.964766	+	2.96924i	−0.0911618	+	0.280567i
$113$	−2.46110	+	1.78809i	−0.231521	+	0.168210i	−0.697497	−	0.716587i	$-0.745703\pi$
$113$	−2.46110	+	1.78809i	−0.231521	+	0.168210i	0.465977	+	0.884797i	$0.345703\pi$
$114$	−3.32234	−	2.41382i	−0.311166	−	0.226075i
$115$	−6.28597	−	19.3462i	−0.586169	−	1.80404i
$116$	0.221519	+	0.681764i	0.0205675	+	0.0633002i
$117$	12.9161	+	9.38406i	1.19409	+	0.867557i
$118$	−14.2096	+	10.3239i	−1.30810	+	0.950391i
$119$	1.29523	−	3.98632i	0.118734	−	0.365425i
$120$	−31.8925			−2.91138
$121$		0			0
$122$	−14.9704			−1.35536
$123$	−3.82597	+	11.7751i	−0.344976	+	1.06173i
$124$	−0.468283	+	0.340227i	−0.0420530	+	0.0305533i
$125$	22.3092	+	16.2086i	1.99540	+	1.44974i
$126$	1.43431	+	4.41435i	0.127778	+	0.393262i
$127$	−3.33595	−	10.2670i	−0.296017	−	0.911048i	−0.982878	−	0.184259i	$-0.941012\pi$
$127$	−3.33595	−	10.2670i	−0.296017	−	0.911048i	0.686860	−	0.726789i	$-0.258988\pi$
$128$	−5.82947	−	4.23536i	−0.515257	−	0.374356i
$129$	2.82101	−	2.04958i	0.248376	−	0.180456i
$130$	7.08688	−	21.8112i	0.621561	−	1.91297i
$131$	−8.70429			−0.760497			−0.380249	−	0.924884i	$-0.624162\pi$
$131$	−8.70429			−0.760497			−0.380249	+	0.924884i	$0.624162\pi$
$132$		0			0
$133$	−1.24880			−0.108285
$134$	2.99518	−	9.21822i	0.258744	−	0.796333i
$135$	−5.42261	+	3.93976i	−0.466704	+	0.339080i
$136$	10.2609	+	7.45496i	0.879863	+	0.639258i
$137$	3.70749	+	11.4105i	0.316753	+	0.974864i	0.975027	+	0.222086i	$0.0712866\pi$
$137$	3.70749	+	11.4105i	0.316753	+	0.974864i	−0.658275	+	0.752778i	$0.728713\pi$
$138$	−5.05231	−	15.5494i	−0.430082	−	1.32365i
$139$	−6.62558	−	4.81377i	−0.561975	−	0.408298i	0.270206	−	0.962802i	$-0.412908\pi$
$139$	−6.62558	−	4.81377i	−0.561975	−	0.408298i	−0.832181	+	0.554504i	$0.812908\pi$
$140$	−1.22599	+	0.890732i	−0.103615	+	0.0752806i
$141$	8.33150	−	25.6417i	0.701639	−	2.15942i
$142$	0.278695			0.0233875
$143$		0			0
$144$	−11.3516			−0.945968
$145$	2.44700	−	7.53109i	0.203212	−	0.625423i
$146$	−11.3309	+	8.23236i	−0.937750	+	0.681315i
$147$	2.08406	+	1.51415i	0.171890	+	0.124885i
$148$	0.0819837	+	0.252320i	0.00673902	+	0.0207406i
$149$	3.73343	+	11.4903i	0.305855	+	0.941323i	0.979357	+	0.202138i	$0.0647891\pi$
$149$	3.73343	+	11.4903i	0.305855	+	0.941323i	−0.673502	+	0.739185i	$0.735211\pi$
$150$	31.2331	+	22.6922i	2.55017	+	1.85281i
$151$	5.62146	−	4.08423i	0.457468	−	0.332370i	−0.335069	−	0.942193i	$-0.608760\pi$
$151$	5.62146	−	4.08423i	0.457468	−	0.332370i	0.792537	+	0.609824i	$0.208760\pi$
$152$	1.16771	−	3.59385i	0.0947140	−	0.291500i
$153$	15.2399			1.23208
$154$		0			0
$155$	6.39402			0.513580
$156$	−1.29461	+	3.98441i	−0.103652	+	0.319009i
$157$	−8.48905	+	6.16765i	−0.677500	+	0.492232i	−0.872527	−	0.488565i	$-0.837520\pi$
$157$	−8.48905	+	6.16765i	−0.677500	+	0.492232i	0.195028	+	0.980798i	$0.437520\pi$
$158$	4.71195	+	3.42343i	0.374863	+	0.272354i
$159$	3.16171	+	9.73073i	0.250740	+	0.771697i
$160$	−2.61260	−	8.04076i	−0.206544	−	0.635678i
$161$	−4.02227	−	2.92235i	−0.316999	−	0.230314i
$162$	6.90682	−	5.01810i	0.542651	−	0.394259i
$163$	−2.41572	+	7.43482i	−0.189214	+	0.582340i	−0.999995	−	0.00300851i	$-0.999042\pi$
$163$	−2.41572	+	7.43482i	−0.189214	+	0.582340i	0.810782	+	0.585349i	$0.199042\pi$
$164$	−1.78016			−0.139007
$165$		0			0
$166$	3.13342			0.243201
$167$	6.59761	−	20.3053i	0.510538	−	1.57127i	−0.280718	−	0.959790i	$-0.590573\pi$
$167$	6.59761	−	20.3053i	0.510538	−	1.57127i	0.791256	−	0.611484i	$-0.209427\pi$
$168$	−6.30624	+	4.58175i	−0.486537	+	0.353490i
$169$	−5.08068	−	3.69133i	−0.390822	−	0.283949i
$170$	−6.76498	−	20.8205i	−0.518850	−	1.59686i
$171$	−1.40311	−	4.31834i	−0.107299	−	0.330232i
$172$	0.405607	+	0.294691i	0.0309272	+	0.0224700i
$173$	−15.7260	+	11.4256i	−1.19562	+	0.868671i	−0.993847	−	0.110760i	$-0.964671\pi$
$173$	−15.7260	+	11.4256i	−1.19562	+	0.868671i	−0.201776	+	0.979432i	$0.564671\pi$
$174$	1.96676	−	6.05307i	0.149100	−	0.458882i
$175$	11.7399			0.887450
$176$		0			0
$177$	−35.4432			−2.66408
$178$	1.65862	−	5.10470i	0.124319	−	0.382613i
$179$	−14.5594	+	10.5780i	−1.08822	+	0.790639i	−0.979098	−	0.203390i	$-0.934804\pi$
$179$	−14.5594	+	10.5780i	−1.08822	+	0.790639i	−0.109123	+	0.994028i	$0.534804\pi$
$180$	−4.45763	−	3.23866i	−0.332252	−	0.241395i
$181$	4.68394	+	14.4157i	0.348154	+	1.07151i	0.959873	+	0.280434i	$0.0904784\pi$
$181$	4.68394	+	14.4157i	0.348154	+	1.07151i	−0.611719	+	0.791075i	$0.709522\pi$
$182$	−1.73213	−	5.33093i	−0.128394	−	0.395155i
$183$	−24.4400	−	17.7567i	−1.80666	−	1.31261i
$184$	12.1712	−	8.84288i	0.897271	−	0.651906i
$185$	0.905630	−	2.78724i	0.0665832	−	0.204922i
$186$	5.13916			0.376822
$187$		0			0
$188$	3.87652			0.282724
$189$	−0.506241	+	1.55805i	−0.0368236	+	0.113331i
$190$	−5.27677	+	3.83380i	−0.382817	+	0.278133i
$191$	19.2201	+	13.9642i	1.39072	+	1.01042i	0.995786	+	0.0917083i	$0.0292327\pi$
$191$	19.2201	+	13.9642i	1.39072	+	1.01042i	0.394935	+	0.918709i	$0.370767\pi$
$192$	−7.07040	−	21.7605i	−0.510262	−	1.57043i
$193$	4.34421	+	13.3701i	0.312703	+	0.962402i	0.976689	+	0.214657i	$0.0688634\pi$
$193$	4.34421	+	13.3701i	0.312703	+	0.962402i	−0.663986	+	0.747745i	$0.731137\pi$
$194$	11.2828	+	8.19744i	0.810058	+	0.588542i
$195$	37.4403	−	27.2020i	2.68116	−	1.94797i
$196$	−0.114455	+	0.352256i	−0.00817536	+	0.0251612i
$197$	18.0665			1.28718			0.643591	−	0.765369i	$-0.277444\pi$
$197$	18.0665			1.28718			0.643591	+	0.765369i	$0.277444\pi$
$198$		0			0
$199$	1.54374			0.109433			0.0547163	−	0.998502i	$-0.482575\pi$
$199$	1.54374			0.109433			0.0547163	+	0.998502i	$0.482575\pi$
$200$	−10.9776	+	33.7855i	−0.776232	+	2.38900i
$201$	15.8237	−	11.4966i	1.11612	−	0.810906i
$202$	−7.60711	−	5.52689i	−0.535235	−	0.388871i
$203$	−0.598078	−	1.84069i	−0.0419768	−	0.129191i
$204$	1.23581	+	3.80343i	0.0865240	+	0.266294i
$205$	15.9089	+	11.5585i	1.11113	+	0.807281i
$206$	0.158928	−	0.115468i	0.0110730	−	0.00804503i
$207$	5.58617	−	17.1925i	0.388266	−	1.19496i
$208$	13.7086			0.950522
$209$		0			0
$210$	13.4546			0.928454
$211$	−6.82421	+	21.0027i	−0.469798	+	1.44589i	0.383049	+	0.923728i	$0.374874\pi$
$211$	−6.82421	+	21.0027i	−0.469798	+	1.44589i	−0.852847	+	0.522161i	$0.825126\pi$
$212$	−1.19014	+	0.864686i	−0.0817391	+	0.0593869i
$213$	0.454983	+	0.330565i	0.0311749	+	0.0226499i
$214$	3.13460	+	9.64732i	0.214277	+	0.659477i
$215$	−1.71141	−	5.26717i	−0.116717	−	0.359218i
$216$	−4.01046	−	2.91377i	−0.272877	−	0.198257i
$217$	1.26432	−	0.918580i	0.0858274	−	0.0623573i
$218$	−1.93863	+	5.96649i	−0.131301	+	0.404102i
$219$	−28.2628			−1.90982
$220$		0			0
$221$	−18.4043			−1.23801
$222$	0.727896	−	2.24023i	0.0488532	−	0.150355i
$223$	6.93662	−	5.03975i	0.464511	−	0.337487i	−0.330787	−	0.943705i	$-0.607314\pi$
$223$	6.93662	−	5.03975i	0.464511	−	0.337487i	0.795298	+	0.606219i	$0.207314\pi$
$224$	−1.67175	−	1.21460i	−0.111699	−	0.0811539i
$225$	13.1906	+	40.5964i	0.879371	+	2.70643i
$226$	1.20004	+	3.69335i	0.0798256	+	0.245678i
$227$	21.4963	+	15.6180i	1.42676	+	1.03660i	0.990609	+	0.136728i	$0.0436585\pi$
$227$	21.4963	+	15.6180i	1.42676	+	1.03660i	0.436151	+	0.899874i	$0.356341\pi$
$228$	0.963949	−	0.700350i	0.0638391	−	0.0463818i
$229$	3.52629	−	10.8528i	0.233024	−	0.717173i	−0.764354	−	0.644797i	$-0.776942\pi$
$229$	3.52629	−	10.8528i	0.233024	−	0.717173i	0.997377	−	0.0723760i	$-0.0230582\pi$
$230$	−25.9676			−1.71225
$231$		0			0
$232$	5.85648			0.384497
$233$	8.22387	−	25.3105i	0.538764	−	1.65814i	−0.196609	−	0.980482i	$-0.562993\pi$
$233$	8.22387	−	25.3105i	0.538764	−	1.65814i	0.735373	−	0.677662i	$-0.237007\pi$
$234$	16.4882	−	11.9794i	1.07787	−	0.783115i
$235$	−34.6436	−	25.1700i	−2.25990	−	1.64191i
$236$	−1.57477	−	4.84664i	−0.102509	−	0.315489i
$237$	3.63191	+	11.1779i	0.235918	+	0.726080i
$238$	−4.32878	−	3.14504i	−0.280593	−	0.203863i
$239$	6.07798	−	4.41591i	0.393152	−	0.285642i	−0.373594	−	0.927592i	$-0.621875\pi$
$239$	6.07798	−	4.41591i	0.393152	−	0.285642i	0.766746	+	0.641951i	$0.221875\pi$
$240$	−10.1683	+	31.2949i	−0.656362	+	2.02008i
$241$	27.4388			1.76749			0.883744	−	0.467971i	$-0.155015\pi$
$241$	27.4388			1.76749			0.883744	+	0.467971i	$0.155015\pi$
$242$		0			0
$243$	22.1425			1.42044
$244$	1.34223	−	4.13096i	0.0859274	−	0.264457i
$245$	3.31004	−	2.40489i	0.211471	−	0.153643i
$246$	12.7867	+	9.29009i	0.815251	+	0.592315i
$247$	1.69445	+	5.21498i	0.107815	+	0.331821i
$248$	1.46131	+	4.49745i	0.0927932	+	0.285588i
$249$	5.11547	+	3.71661i	0.324180	+	0.235530i
$250$	28.4792	−	20.6913i	1.80118	−	1.30863i
$251$	0.594900	−	1.83091i	0.0375498	−	0.115566i	−0.930525	−	0.366229i	$-0.880649\pi$
$251$	0.594900	−	1.83091i	0.0375498	−	0.115566i	0.968074	+	0.250663i	$0.0806486\pi$
$252$	−1.34670			−0.0848340
$253$		0			0
$254$	−13.7810			−0.864694
$255$	13.6513	−	42.0145i	0.854880	−	2.63105i
$256$	6.92966	−	5.03469i	0.433104	−	0.314668i
$257$	−8.21997	−	5.97216i	−0.512748	−	0.372533i	0.301117	−	0.953587i	$-0.402640\pi$
$257$	−8.21997	−	5.97216i	−0.512748	−	0.372533i	−0.813865	+	0.581054i	$0.802640\pi$
$258$	−1.37554	−	4.23347i	−0.0856371	−	0.263564i
$259$	−0.221348	−	0.681238i	−0.0137539	−	0.0423301i
$260$	5.38320	+	3.91112i	0.333852	+	0.242557i
$261$	5.69313	−	4.13630i	0.352396	−	0.256031i
$262$	−3.43367	+	10.5677i	−0.212133	+	0.652877i
$263$	−4.38774			−0.270560			−0.135280	−	0.990807i	$-0.543193\pi$
$263$	−4.38774			−0.270560			−0.135280	+	0.990807i	$0.543193\pi$
$264$		0			0
$265$	16.2504			0.998253
$266$	−0.492626	+	1.51615i	−0.0302048	+	0.0929609i
$267$	8.76254	−	6.36636i	0.536259	−	0.389615i
$268$	2.27514	+	1.65299i	0.138976	+	0.100972i
$269$	0.193253	+	0.594770i	0.0117828	+	0.0362638i	0.956775	−	0.290829i	$-0.0939311\pi$
$269$	0.193253	+	0.594770i	0.0117828	+	0.0362638i	−0.944992	+	0.327093i	$0.893931\pi$
$270$	2.64409	+	8.13767i	0.160914	+	0.495243i
$271$	9.65763	+	7.01668i	0.586659	+	0.426233i	0.841119	−	0.540851i	$-0.181898\pi$
$271$	9.65763	+	7.01668i	0.586659	+	0.426233i	−0.254460	+	0.967083i	$0.581898\pi$
$272$	10.5867	−	7.69172i	0.641916	−	0.466379i
$273$	3.49533	−	10.7575i	0.211547	−	0.651075i
$274$	15.3158			0.925263
$275$		0			0
$276$	4.74371			0.285538
$277$	8.82463	−	27.1594i	0.530221	−	1.63185i	−0.223534	−	0.974696i	$-0.571760\pi$
$277$	8.82463	−	27.1594i	0.530221	−	1.63185i	0.753755	−	0.657155i	$-0.228240\pi$
$278$	−8.45798	+	6.14508i	−0.507276	+	0.368558i
$279$	4.59699	+	3.33991i	0.275215	+	0.199955i
$280$	3.82578	+	11.7745i	0.228634	+	0.703663i
$281$	4.54196	+	13.9787i	0.270950	+	0.833900i	0.990263	+	0.139213i	$0.0444571\pi$
$281$	4.54196	+	13.9787i	0.270950	+	0.833900i	−0.719312	+	0.694687i	$0.755543\pi$
$282$	−27.8446	−	20.2303i	−1.65812	−	1.20470i
$283$	−18.2349	+	13.2485i	−1.08395	+	0.787539i	−0.978368	−	0.206871i	$-0.933672\pi$
$283$	−18.2349	+	13.2485i	−1.08395	+	0.787539i	−0.105586	+	0.994410i	$0.533672\pi$
$284$	−0.0249874	+	0.0769033i	−0.00148273	+	0.00456337i
$285$	−13.1619			−0.779646
$286$		0			0
$287$	4.80626			0.283704
$288$	2.32175	−	7.14560i	0.136810	−	0.421059i
$289$	−0.459804	+	0.334067i	−0.0270473	+	0.0196510i
$290$	−8.17808	−	5.94173i	−0.480234	−	0.348910i
$291$	8.69663	+	26.7655i	0.509805	+	1.56902i
$292$	−1.25573	−	3.86475i	−0.0734863	−	0.226168i
$293$	−13.6142	−	9.89128i	−0.795349	−	0.577855i	0.114197	−	0.993458i	$-0.463570\pi$
$293$	−13.6142	−	9.89128i	−0.795349	−	0.577855i	−0.909546	+	0.415603i	$0.863570\pi$
$294$	2.66043	−	1.93292i	0.155159	−	0.112730i
$295$	−17.3956	+	53.5382i	−1.01281	+	3.11712i
$296$	2.16747			0.125982
$297$		0			0
$298$	15.4230			0.893429
$299$	−6.74606	+	20.7622i	−0.390135	+	1.20071i
$300$	−9.06201	+	6.58394i	−0.523195	+	0.380124i
$301$	−1.09510	−	0.795636i	−0.0631204	−	0.0458597i
$302$	−2.74104	−	8.43607i	−0.157729	−	0.485441i
$303$	−5.86345	−	18.0459i	−0.336847	−	1.03671i
$304$	−3.15420	−	2.29166i	−0.180906	−	0.131436i
$305$	−38.8173	+	28.2024i	−2.22267	+	1.61487i
$306$	6.01185	−	18.5026i	0.343675	−	1.05772i
$307$	0.238354			0.0136036			0.00680179	−	0.999977i	$-0.497835\pi$
$307$	0.238354			0.0136036			0.00680179	+	0.999977i	$0.497835\pi$
$308$		0			0
$309$	0.396416			0.0225513
$310$	2.52231	−	7.76288i	0.143258	−	0.440902i
$311$	0.531138	−	0.385895i	0.0301181	−	0.0218821i	−0.572624	−	0.819818i	$-0.694075\pi$
$311$	0.531138	−	0.385895i	0.0301181	−	0.0218821i	0.602742	+	0.797936i	$0.294075\pi$
$312$	27.6901	+	20.1181i	1.56764	+	1.13896i
$313$	−2.30299	−	7.08787i	−0.130173	−	0.400630i	0.864635	−	0.502400i	$-0.167549\pi$
$313$	−2.30299	−	7.08787i	−0.130173	−	0.400630i	−0.994808	+	0.101770i	$0.967549\pi$
$314$	4.13929	+	12.7394i	0.233594	+	0.718928i
$315$	12.0352	+	8.74405i	0.678104	+	0.492671i
$316$	−1.36713	+	0.993280i	−0.0769072	+	0.0558764i
$317$	5.38962	−	16.5876i	0.302711	−	0.931650i	−0.677810	−	0.735237i	$-0.737071\pi$
$317$	5.38962	−	16.5876i	0.302711	−	0.931650i	0.980521	−	0.196413i	$-0.0629292\pi$
$318$	13.0612			0.732433
$319$		0			0
$320$	−36.3401			−2.03147
$321$	−6.32545	+	19.4677i	−0.353052	+	1.08658i
$322$	−5.13469	+	3.73057i	−0.286145	+	0.207896i
$323$	4.23463	+	3.07664i	0.235621	+	0.171189i
$324$	0.765442	+	2.35579i	0.0425246	+	0.130877i
$325$	−15.9294	−	49.0257i	−0.883604	−	2.71945i
$326$	8.07355	+	5.86578i	0.447153	+	0.324875i
$327$	−10.2419	+	7.44116i	−0.566377	+	0.411497i
$328$	−4.49418	+	13.8317i	−0.248150	+	0.763727i
$329$	−10.4662			−0.577021
$330$		0			0
$331$	−28.6146			−1.57280			−0.786399	−	0.617719i	$-0.788057\pi$
$331$	−28.6146			−1.57280			−0.786399	+	0.617719i	$0.788057\pi$
$332$	−0.280938	+	0.864640i	−0.0154185	+	0.0474533i
$333$	2.10702	−	1.53084i	0.115464	−	0.0838894i
$334$	−22.0498	−	16.0201i	−1.20651	−	0.876581i
$335$	−9.59968	−	29.5448i	−0.524486	−	1.61420i
$336$	2.48527	+	7.64887i	0.135583	+	0.417280i
$337$	−1.40003	−	1.01718i	−0.0762643	−	0.0554093i	0.549000	−	0.835822i	$-0.315009\pi$
$337$	−1.40003	−	1.01718i	−0.0762643	−	0.0554093i	−0.625264	+	0.780413i	$0.715009\pi$
$338$	−6.48581	+	4.71222i	−0.352782	+	0.256311i
$339$	−2.42162	+	7.45297i	−0.131524	+	0.404790i
$340$	6.35176			0.344472
$341$		0			0
$342$	−5.79633			−0.313430
$343$	0.309017	−	0.951057i	0.0166853	−	0.0513522i
$344$	3.31371	−	2.40755i	0.178663	−	0.129806i
$345$	−42.3935	−	30.8007i	−2.28239	−	1.65825i
$346$	7.66805	+	23.5998i	0.412237	+	1.26873i
$347$	0.843646	+	2.59647i	0.0452893	+	0.139386i	0.971144	−	0.238493i	$-0.0766535\pi$
$347$	0.843646	+	2.59647i	0.0452893	+	0.139386i	−0.925855	+	0.377879i	$0.876653\pi$
$348$	1.49395	+	1.08542i	0.0800843	+	0.0581846i
$349$	−25.0037	+	18.1662i	−1.33842	+	0.972417i	−0.338916	+	0.940817i	$0.610060\pi$
$349$	−25.0037	+	18.1662i	−1.33842	+	0.972417i	−0.999501	+	0.0316002i	$0.989940\pi$
$350$	4.63114	−	14.2532i	0.247545	−	0.761865i
$351$	7.19332			0.383951
$352$		0			0
$353$	−23.9543			−1.27496			−0.637480	−	0.770467i	$-0.720023\pi$
$353$	−23.9543			−1.27496			−0.637480	+	0.770467i	$0.720023\pi$
$354$	−13.9817	+	43.0311i	−0.743116	+	2.28708i
$355$	0.722636	−	0.525026i	0.0383535	−	0.0278655i
$356$	1.25989	+	0.915360i	0.0667738	+	0.0485140i
$357$	−3.33656	−	10.2689i	−0.176590	−	0.543487i
$358$	7.09922	+	21.8492i	0.375206	+	1.15476i
$359$	1.22656	+	0.891145i	0.0647351	+	0.0470328i	0.619682	−	0.784853i	$-0.287261\pi$
$359$	1.22656	+	0.891145i	0.0647351	+	0.0470328i	−0.554947	+	0.831886i	$0.687261\pi$
$360$	−36.4177	+	26.4590i	−1.91938	+	1.39451i
$361$	−5.38941	+	16.5869i	−0.283653	+	0.872995i
$362$	19.3496			1.01699
$363$		0			0
$364$	1.62632			0.0852425
$365$	−13.8714	+	42.6919i	−0.726064	+	2.23460i
$366$	−31.1992	+	22.6676i	−1.63081	+	1.18485i
$367$	−7.05630	−	5.12671i	−0.368336	−	0.267612i	0.388185	−	0.921582i	$-0.373102\pi$
$367$	−7.05630	−	5.12671i	−0.368336	−	0.267612i	−0.756521	+	0.653970i	$0.773102\pi$
$368$	−4.79662	−	14.7625i	−0.250041	−	0.769548i
$369$	5.40017	+	16.6200i	0.281122	+	0.865203i
$370$	−3.02670	−	2.19902i	−0.157350	−	0.114322i
$371$	3.21325	−	2.33457i	0.166824	−	0.121205i
$372$	−0.460770	+	1.41811i	−0.0238898	+	0.0735253i
$373$	−36.8111			−1.90601			−0.953004	−	0.302957i	$-0.902026\pi$
$373$	−36.8111			−1.90601			−0.953004	+	0.302957i	$0.902026\pi$
$374$		0			0
$375$	71.0360			3.66828
$376$	9.78663	−	30.1201i	0.504707	−	1.55333i
$377$	−6.87523	+	4.99515i	−0.354092	+	0.257263i
$378$	1.69190	+	1.22924i	0.0870221	+	0.0632252i
$379$	0.802943	+	2.47121i	0.0412444	+	0.126937i	0.969559	−	0.244859i	$-0.0787418\pi$
$379$	0.802943	+	2.47121i	0.0412444	+	0.126937i	−0.928314	+	0.371797i	$0.878742\pi$
$380$	−0.584794	−	1.79981i	−0.0299993	−	0.0923284i
$381$	−22.4981	−	16.3458i	−1.15261	−	0.837422i
$382$	24.5357	−	17.8263i	1.25536	−	0.912071i
$383$	5.94524	−	18.2976i	0.303788	−	0.934963i	−0.676339	−	0.736590i	$-0.736435\pi$
$383$	5.94524	−	18.2976i	0.303788	−	0.934963i	0.980127	−	0.198372i	$-0.0635655\pi$
$384$	−18.5619			−0.947235
$385$		0			0
$386$	17.9462			0.913435
$387$	1.52088	−	4.68080i	0.0773108	−	0.237938i
$388$	−3.27361	+	2.37842i	−0.166192	+	0.120746i
$389$	22.9219	+	16.6538i	1.16219	+	0.844380i	0.990053	−	0.140694i	$-0.0449333\pi$
$389$	22.9219	+	16.6538i	1.16219	+	0.844380i	0.172136	+	0.985073i	$0.444933\pi$
$390$	−18.2560	−	56.1863i	−0.924431	−	2.84511i
$391$	6.43964	+	19.8192i	0.325667	+	1.00230i
$392$	2.44804	+	1.77861i	0.123645	+	0.0898332i
$393$	−18.1402	+	13.1796i	−0.915053	+	0.664825i
$394$	7.12686	−	21.9342i	0.359046	−	1.10503i
$395$	18.6671			0.939243
$396$		0			0
$397$	−10.3666			−0.520287			−0.260143	−	0.965570i	$-0.583770\pi$
$397$	−10.3666			−0.520287			−0.260143	+	0.965570i	$0.583770\pi$
$398$	0.608973	−	1.87423i	0.0305251	−	0.0939465i
$399$	−2.60256	+	1.89087i	−0.130291	+	0.0946621i
$400$	29.6524	+	21.5437i	1.48262	+	1.07719i
$401$	−3.95165	−	12.1619i	−0.197336	−	0.607337i	−0.999941	−	0.0108271i	$-0.996554\pi$
$401$	−3.95165	−	12.1619i	−0.197336	−	0.607337i	0.802606	−	0.596510i	$-0.203446\pi$
$402$	−7.71569	−	23.7465i	−0.384824	−	1.18437i
$403$	−5.55150	−	4.03340i	−0.276540	−	0.200918i
$404$	2.20714	−	1.60358i	0.109809	−	0.0797811i
$405$	8.45544	−	26.0232i	0.420154	−	1.29310i
$406$	−2.47069			−0.122618
$407$		0			0
$408$	32.6722			1.61752
$409$	−9.89526	+	30.4545i	−0.489289	+	1.50588i	0.336382	+	0.941726i	$0.390797\pi$
$409$	−9.89526	+	30.4545i	−0.489289	+	1.50588i	−0.825671	+	0.564151i	$0.809203\pi$
$410$	20.3088	−	14.7552i	1.00298	−	0.728706i
$411$	25.0039	+	18.1664i	1.23335	+	0.896081i
$412$	0.0176130	+	0.0542074i	0.000867733	+	0.00267061i
$413$	4.25172	+	13.0854i	0.209213	+	0.643892i
$414$	−18.6695	−	13.5642i	−0.917554	−	0.666642i
$415$	8.12475	−	5.90298i	0.398828	−	0.289766i
$416$	−2.80383	+	8.62929i	−0.137469	+	0.423086i
$417$	−21.0969			−1.03312
$418$		0			0
$419$	−20.0934			−0.981629			−0.490815	−	0.871264i	$-0.663301\pi$
$419$	−20.0934			−0.981629			−0.490815	+	0.871264i	$0.663301\pi$
$420$	−1.20632	+	3.71267i	−0.0588624	+	0.181160i
$421$	18.1416	−	13.1807i	0.884169	−	0.642386i	−0.0501822	−	0.998740i	$-0.515980\pi$
$421$	18.1416	−	13.1807i	0.884169	−	0.642386i	0.934351	+	0.356354i	$0.115980\pi$
$422$	22.8071	+	16.5703i	1.11023	+	0.806631i
$423$	−11.7595	−	36.1921i	−0.571768	−	1.75972i
$424$	3.71391	+	11.4302i	0.180363	+	0.555101i
$425$	−39.8094	−	28.9233i	−1.93104	−	1.40298i
$426$	0.580815	−	0.421987i	0.0281406	−	0.0204453i
$427$	−3.62388	+	11.1532i	−0.175372	+	0.539740i
$428$	−2.94313			−0.142262
$429$		0			0
$430$	−7.06991			−0.340941
$431$	3.73466	−	11.4941i	0.179892	−	0.553652i	−0.819931	−	0.572463i	$-0.805988\pi$
$431$	3.73466	−	11.4941i	0.179892	−	0.553652i	0.999823	+	0.0188109i	$0.00598804\pi$
$432$	−4.13783	+	3.00631i	−0.199081	+	0.144641i
$433$	0.244690	+	0.177778i	0.0117591	+	0.00854345i	0.593649	−	0.804724i	$-0.297687\pi$
$433$	0.244690	+	0.177778i	0.0117591	+	0.00854345i	−0.581890	+	0.813267i	$0.697687\pi$
$434$	−0.616486	−	1.89735i	−0.0295923	−	0.0910757i
$435$	−6.30355	−	19.4003i	−0.302232	−	0.930175i
$436$	−1.47258	−	1.06990i	−0.0705240	−	0.0512387i
$437$	5.02301	−	3.64943i	0.240283	−	0.174576i
$438$	−11.1491	+	34.3134i	−0.532725	+	1.63956i
$439$	−3.52592			−0.168283			−0.0841416	−	0.996454i	$-0.526815\pi$
$439$	−3.52592			−0.168283			−0.0841416	+	0.996454i	$0.526815\pi$
$440$		0			0
$441$	3.63595			0.173141
$442$	−7.26014	+	22.3444i	−0.345329	+	1.06281i
$443$	17.6724	−	12.8398i	0.839643	−	0.610036i	−0.0826282	−	0.996580i	$-0.526331\pi$
$443$	17.6724	−	12.8398i	0.839643	−	0.610036i	0.922271	+	0.386544i	$0.126331\pi$
$444$	0.552910	+	0.401712i	0.0262399	+	0.0190644i
$445$	−5.31593	−	16.3608i	−0.251999	−	0.775574i
$446$	−3.38233	−	10.4097i	−0.160158	−	0.492915i
$447$	25.1788	+	18.2935i	1.19092	+	0.865251i
$448$	−7.18568	+	5.22070i	−0.339491	+	0.246655i
$449$	2.87439	−	8.84646i	0.135651	−	0.417490i	−0.860040	−	0.510227i	$-0.829561\pi$
$449$	2.87439	−	8.84646i	0.135651	−	0.417490i	0.995691	+	0.0927365i	$0.0295614\pi$
$450$	54.4908			2.56872
$451$		0			0
$452$	−1.12674			−0.0529974
$453$	5.53127	−	17.0235i	0.259882	−	0.799834i
$454$	27.4414	−	19.9373i	1.28789	−	0.935706i
$455$	−14.5341	−	10.5596i	−0.681369	−	0.495043i
$456$	−3.00807	−	9.25788i	−0.140866	−	0.433540i
$457$	−3.49700	−	10.7627i	−0.163583	−	0.503456i	0.835346	−	0.549724i	$-0.185267\pi$
$457$	−3.49700	−	10.7627i	−0.163583	−	0.503456i	−0.998929	+	0.0462679i	$0.985267\pi$
$458$	−11.7852	−	8.56243i	−0.550685	−	0.400096i
$459$	5.55518	−	4.03608i	0.259294	−	0.188388i
$460$	2.32822	−	7.16553i	0.108554	−	0.334095i
$461$	−0.678821			−0.0316158			−0.0158079	−	0.999875i	$-0.505032\pi$
$461$	−0.678821			−0.0316158			−0.0158079	+	0.999875i	$0.505032\pi$
$462$		0			0
$463$	−13.4936			−0.627103			−0.313551	−	0.949571i	$-0.601519\pi$
$463$	−13.4936			−0.627103			−0.313551	+	0.949571i	$0.601519\pi$
$464$	1.86723	−	5.74673i	0.0866839	−	0.266785i
$465$	13.3255	−	9.68154i	0.617955	−	0.448971i
$466$	−27.4849	−	19.9690i	−1.27321	−	0.925044i
$467$	9.16445	+	28.2053i	0.424080	+	1.30518i	0.903872	+	0.427803i	$0.140712\pi$
$467$	9.16445	+	28.2053i	0.424080	+	1.30518i	−0.479792	+	0.877382i	$0.659288\pi$
$468$	1.82729	+	5.62381i	0.0844664	+	0.259961i
$469$	−6.14265	−	4.46290i	−0.283641	−	0.206077i
$470$	−44.2248	+	32.1312i	−2.03994	+	1.48210i
$471$	−8.35286	+	25.7075i	−0.384879	+	1.18454i
$472$	−41.6335			−1.91634
$473$		0			0
$474$	15.0036			0.689137
$475$	−4.53041	+	13.9432i	−0.207870	+	0.639757i
$476$	1.25596	−	0.912508i	0.0575668	−	0.0418247i
$477$	11.6832	+	8.48837i	0.534939	+	0.388656i
$478$	−2.96365	−	9.12117i	−0.135554	−	0.417193i
$479$	1.45280	+	4.47126i	0.0663801	+	0.204297i	0.978745	−	0.205081i	$-0.0657458\pi$
$479$	1.45280	+	4.47126i	0.0663801	+	0.204297i	−0.912365	+	0.409378i	$0.865746\pi$
$480$	−17.6198	−	12.8015i	−0.804228	−	0.584306i
$481$	−2.54451	+	1.84870i	−0.116020	+	0.0842933i
$482$	10.8241	−	33.3130i	0.493022	−	1.51737i
$483$	−12.8075			−0.582763
$484$		0			0
$485$	44.6985			2.02965
$486$	8.73476	−	26.8828i	0.396217	−	1.21943i
$487$	−26.1909	+	19.0288i	−1.18682	+	0.862278i	−0.992925	−	0.118743i	$-0.962114\pi$
$487$	−26.1909	+	19.0288i	−1.18682	+	0.862278i	−0.193899	+	0.981021i	$0.562114\pi$
$488$	−28.7085	−	20.8580i	−1.29957	−	0.944196i
$489$	6.22298	+	19.1524i	0.281413	+	0.866099i
$490$	−1.61399	−	4.96735i	−0.0729126	−	0.224402i
$491$	5.54657	+	4.02982i	0.250313	+	0.181863i	0.705866	−	0.708346i	$-0.250558\pi$
$491$	5.54657	+	4.02982i	0.250313	+	0.181863i	−0.455552	+	0.890209i	$0.650558\pi$
$492$	−3.70996	+	2.69544i	−0.167258	+	0.121520i
$493$	−2.50682	+	7.71520i	−0.112902	+	0.347475i
$494$	6.99986			0.314939
$495$		0			0
$496$	4.87908			0.219077
$497$	0.0674634	−	0.207631i	0.00302615	−	0.00931353i
$498$	6.53023	−	4.74449i	0.292626	−	0.212606i
$499$	−8.87252	−	6.44626i	−0.397189	−	0.288574i	0.371206	−	0.928550i	$-0.378944\pi$
$499$	−8.87252	−	6.44626i	−0.397189	−	0.288574i	−0.768395	+	0.639976i	$0.778944\pi$
$500$	3.15618	+	9.71372i	0.141149	+	0.434411i
$501$	−16.9957	−	52.3073i	−0.759310	−	2.33692i
$502$	−1.98821	−	1.44452i	−0.0887381	−	0.0644720i
$503$	21.7896	−	15.8311i	0.971550	−	0.705872i	0.0157457	−	0.999876i	$-0.494988\pi$
$503$	21.7896	−	15.8311i	0.971550	−	0.705872i	0.955804	+	0.294004i	$0.0949878\pi$
$504$	−3.39987	+	10.4637i	−0.151442	+	0.466091i
$505$	−30.1367			−1.34106
$506$		0			0
$507$	−16.1777			−0.718475
$508$	1.23558	−	3.80273i	0.0548201	−	0.168719i
$509$	−24.5907	+	17.8662i	−1.08997	+	0.791906i	−0.979393	−	0.201962i	$-0.935268\pi$
$509$	−24.5907	+	17.8662i	−1.08997	+	0.791906i	−0.110572	+	0.993868i	$0.535268\pi$
$510$	−45.6240	−	33.1478i	−2.02026	−	1.46781i
$511$	3.39036	+	10.4344i	0.149981	+	0.461593i
$512$	−7.83225	−	24.1052i	−0.346140	−	1.06531i
$513$	−1.65510	−	1.20250i	−0.0730746	−	0.0530918i
$514$	−10.4933	+	7.62384i	−0.462840	+	0.336273i
$515$	0.194562	−	0.598800i	0.00857343	−	0.0263863i
$516$	1.29151			0.0568558
$517$		0			0
$518$	−0.914398			−0.0401763
$519$	−15.4737	+	47.6231i	−0.679219	+	2.09042i
$520$	43.9794	−	31.9529i	1.92862	−	1.40123i
$521$	0.756776	+	0.549830i	0.0331549	+	0.0240885i	0.604239	−	0.796803i	$-0.293477\pi$
$521$	0.756776	+	0.549830i	0.0331549	+	0.0240885i	−0.571084	+	0.820891i	$0.693477\pi$
$522$	−2.77599	−	8.54363i	−0.121502	−	0.373944i
$523$	8.09171	+	24.9037i	0.353826	+	1.08896i	0.956687	+	0.291118i	$0.0940272\pi$
$523$	8.09171	+	24.9037i	0.353826	+	1.08896i	−0.602861	+	0.797846i	$0.705973\pi$
$524$	−2.60821	−	1.89498i	−0.113940	−	0.0827825i
$525$	24.4665	−	17.7760i	1.06781	−	0.775807i
$526$	−1.73088	+	5.32709i	−0.0754698	+	0.232272i
$527$	−6.55034			−0.285337
$528$		0			0
$529$	1.71881			0.0747307
$530$	6.41045	−	19.7293i	0.278452	−	0.856987i
$531$	−40.4723	+	29.4048i	−1.75635	+	1.27606i
$532$	−0.374199	−	0.271871i	−0.0162236	−	0.0117871i
$533$	−6.52144	−	20.0709i	−0.282475	−	0.869369i
$534$	−4.27265	−	13.1499i	−0.184896	−	0.569051i
$535$	26.3021	+	19.1096i	1.13714	+	0.826181i
$536$	18.5873	−	13.5045i	0.802851	−	0.583305i
$537$	−14.3258	+	44.0904i	−0.618205	+	1.90264i
$538$	0.798336			0.0344187
$539$		0			0
$540$	−2.48258			−0.106833
$541$	8.26823	−	25.4470i	0.355479	−	1.09405i	−0.600252	−	0.799811i	$-0.704933\pi$
$541$	8.26823	−	25.4470i	0.355479	−	1.09405i	0.955731	−	0.294241i	$-0.0950669\pi$
$542$	12.3286	−	8.95724i	0.529558	−	0.384746i
$543$	31.5892	+	22.9509i	1.35562	+	0.984916i
$544$	2.67647	+	8.23733i	0.114753	+	0.353173i
$545$	6.21339	+	19.1228i	0.266152	+	0.819133i
$546$	−11.6817	−	8.48725i	−0.499931	−	0.363221i
$547$	−37.5854	+	27.3074i	−1.60704	+	1.16758i	−0.735101	+	0.677957i	$0.762865\pi$
$547$	−37.5854	+	27.3074i	−1.60704	+	1.16758i	−0.871934	+	0.489623i	$0.837135\pi$
$548$	−1.37320	+	4.22626i	−0.0586601	+	0.180537i
$549$	−42.6393			−1.81980
$550$		0			0
$551$	2.41695			0.102966
$552$	11.9759	−	36.8581i	0.509729	−	1.56879i
$553$	3.69112	−	2.68176i	0.156962	−	0.114040i
$554$	−29.4927	−	21.4277i	−1.25302	−	0.910376i
$555$	−2.33293	−	7.18003i	−0.0990275	−	0.304775i
$556$	−0.937349	−	2.88486i	−0.0397524	−	0.122345i
$557$	−28.3944	−	20.6297i	−1.20311	−	0.874109i	−0.208521	−	0.978018i	$-0.566865\pi$
$557$	−28.3944	−	20.6297i	−1.20311	−	0.874109i	−0.994587	+	0.103909i	$0.966865\pi$
$558$	5.86836	−	4.26361i	0.248427	−	0.180493i
$559$	−1.83667	+	5.65270i	−0.0776830	+	0.239084i
$560$	12.7737			0.539786
$561$		0			0
$562$	18.7630			0.791471
$563$	−2.76506	+	8.50997i	−0.116533	+	0.358652i	−0.992264	−	0.124148i	$-0.960380\pi$
$563$	−2.76506	+	8.50997i	−0.116533	+	0.358652i	0.875731	+	0.482800i	$0.160380\pi$
$564$	8.07888	−	5.86965i	0.340182	−	0.247157i
$565$	10.0694	+	7.31587i	0.423624	+	0.307781i
$566$	8.89143	+	27.3650i	0.373735	+	1.15024i
$567$	−2.06662	−	6.36039i	−0.0867898	−	0.267111i
$568$	0.534448	+	0.388299i	0.0224249	+	0.0162927i
$569$	−15.7157	+	11.4181i	−0.658835	+	0.478672i	−0.866269	−	0.499577i	$-0.833489\pi$
$569$	−15.7157	+	11.4181i	−0.658835	+	0.478672i	0.207434	+	0.978249i	$0.433489\pi$
$570$	−5.19212	+	15.9797i	−0.217474	+	0.669316i
$571$	16.0171			0.670295			0.335148	−	0.942166i	$-0.391214\pi$
$571$	16.0171			0.670295			0.335148	+	0.942166i	$0.391214\pi$
$572$		0			0
$573$	61.1999			2.55666
$574$	1.89597	−	5.83520i	0.0791364	−	0.243557i
$575$	−47.2209	+	34.3080i	−1.96925	+	1.43074i
$576$	−26.1268	−	18.9822i	−1.08862	−	0.790926i
$577$	−10.1726	−	31.3080i	−0.423490	−	1.30337i	−0.904433	−	0.426617i	$-0.859705\pi$
$577$	−10.1726	−	31.3080i	−0.423490	−	1.30337i	0.480942	−	0.876752i	$-0.340295\pi$
$578$	0.224203	+	0.690024i	0.00932560	+	0.0287012i
$579$	29.2980	+	21.2863i	1.21758	+	0.884626i
$580$	2.37280	−	1.72394i	0.0985252	−	0.0715827i
$581$	0.758506	−	2.33444i	0.0314681	−	0.0968489i
$582$	35.9262			1.48919
$583$		0			0
$584$	−33.1990			−1.37378
$585$	20.1851	−	62.1233i	0.834550	−	2.56848i
$586$	−17.3794	+	12.6269i	−0.717935	+	0.521610i
$587$	−22.1972	−	16.1272i	−0.916176	−	0.665641i	0.0263933	−	0.999652i	$-0.491598\pi$
$587$	−22.1972	−	16.1272i	−0.916176	−	0.665641i	−0.942569	+	0.334011i	$0.891598\pi$
$588$	0.294840	+	0.907424i	0.0121590	+	0.0374215i
$589$	0.603077	+	1.85608i	0.0248494	+	0.0764785i
$590$	58.1377	+	42.2395i	2.39349	+	1.73897i
$591$	37.6515	−	27.3554i	1.54878	−	1.12525i
$592$	0.691058	−	2.12686i	0.0284023	−	0.0874133i
$593$	14.6132			0.600092			0.300046	−	0.953925i	$-0.402998\pi$
$593$	14.6132			0.600092			0.300046	+	0.953925i	$0.402998\pi$
$594$		0			0
$595$	−17.1491			−0.703045
$596$	−1.38280	+	4.25583i	−0.0566418	+	0.174326i
$597$	3.21723	−	2.33746i	0.131673	−	0.0956657i
$598$	22.5459	+	16.3806i	0.921972	+	0.669852i
$599$	7.81086	+	24.0393i	0.319143	+	0.982221i	0.974015	+	0.226482i	$0.0727224\pi$
$599$	7.81086	+	24.0393i	0.319143	+	0.982221i	−0.654872	+	0.755739i	$0.727278\pi$
$600$	28.2786	+	87.0326i	1.15447	+	3.55309i
$601$	7.52465	+	5.46698i	0.306937	+	0.223003i	0.730581	−	0.682826i	$-0.239249\pi$
$601$	7.52465	+	5.46698i	0.306937	+	0.223003i	−0.423644	+	0.905829i	$0.639249\pi$
$602$	−1.39796	+	1.01568i	−0.0569767	+	0.0413960i
$603$	8.53097	−	26.2556i	0.347408	−	1.06921i
$604$	2.57361			0.104719
$605$		0			0
$606$	−24.2222			−0.983960
$607$	−0.657191	+	2.02263i	−0.0266746	+	0.0820959i	−0.963508	−	0.267681i	$-0.913743\pi$
$607$	−0.657191	+	2.02263i	−0.0266746	+	0.0820959i	0.936833	+	0.349777i	$0.113743\pi$
$608$	2.08768	−	1.51679i	0.0846667	−	0.0615140i
$609$	−4.03352	−	2.93053i	−0.163447	−	0.118751i
$610$	18.9275	+	58.2528i	0.766351	+	2.35859i
$611$	14.2012	+	43.7069i	0.574520	+	1.76819i
$612$	4.56661	+	3.31783i	0.184594	+	0.134115i
$613$	33.1250	−	24.0667i	1.33791	−	0.972046i	0.338389	−	0.941006i	$-0.390118\pi$
$613$	33.1250	−	24.0667i	1.33791	−	0.972046i	0.999518	−	0.0310402i	$-0.00988199\pi$
$614$	0.0940259	−	0.289382i	0.00379458	−	0.0116785i
$615$	50.6564			2.04266
$616$		0			0
$617$	−7.53813			−0.303474			−0.151737	−	0.988421i	$-0.548487\pi$
$617$	−7.53813			−0.303474			−0.151737	+	0.988421i	$0.548487\pi$
$618$	0.156378	−	0.481283i	0.00629046	−	0.0193600i
$619$	15.7803	−	11.4651i	0.634264	−	0.460820i	−0.223611	−	0.974679i	$-0.571784\pi$
$619$	15.7803	−	11.4651i	0.634264	−	0.460820i	0.857875	+	0.513858i	$0.171784\pi$
$620$	1.91595	+	1.39202i	0.0769464	+	0.0559048i
$621$	−2.51693	−	7.74631i	−0.101001	−	0.310849i
$622$	−0.258985	−	0.797075i	−0.0103844	−	0.0319598i
$623$	−3.40156	−	2.47138i	−0.136281	−	0.0990138i
$624$	28.5695	−	20.7570i	1.14370	−	0.830944i
$625$	16.7256	−	51.4760i	0.669022	−	2.05904i
$626$	−9.51375			−0.380246
$627$		0			0
$628$	−3.88645			−0.155086
$629$	−0.927770	+	2.85538i	−0.0369926	+	0.113852i
$630$	15.3636	−	11.1623i	0.612102	−	0.444718i
$631$	8.62846	+	6.26894i	0.343494	+	0.249563i	0.746134	−	0.665795i	$-0.231908\pi$
$631$	8.62846	+	6.26894i	0.343494	+	0.249563i	−0.402641	+	0.915358i	$0.631908\pi$
$632$	4.26623	+	13.1301i	0.169702	+	0.522288i
$633$	17.5794	+	54.1038i	0.698718	+	2.15043i
$634$	−18.0126	−	13.0869i	−0.715372	−	0.519748i
$635$	−35.7331	+	25.9616i	−1.41802	+	1.03025i
$636$	−1.17105	+	3.60411i	−0.0464350	+	0.142912i
$637$	−4.39091			−0.173974
$638$		0			0
$639$	0.793787			0.0314017
$640$	−9.11024	+	28.0384i	−0.360114	+	1.10832i
$641$	−0.362722	+	0.263533i	−0.0143267	+	0.0104089i	−0.594926	−	0.803781i	$-0.702818\pi$
$641$	−0.362722	+	0.263533i	−0.0143267	+	0.0104089i	0.580599	+	0.814190i	$0.302818\pi$
$642$	21.1402	+	15.3593i	0.834338	+	0.606182i
$643$	−9.77853	−	30.0952i	−0.385627	−	1.18684i	−0.936024	−	0.351936i	$-0.885524\pi$
$643$	−9.77853	−	30.0952i	−0.385627	−	1.18684i	0.550397	−	0.834903i	$-0.314476\pi$
$644$	−0.569047	−	1.75135i	−0.0224236	−	0.0690128i
$645$	−11.5420	−	8.38574i	−0.454465	−	0.330188i
$646$	5.40578	−	3.92753i	0.212687	−	0.154526i
$647$	−9.30888	+	28.6498i	−0.365970	+	1.12634i	0.583402	+	0.812184i	$0.301721\pi$
$647$	−9.30888	+	28.6498i	−0.365970	+	1.12634i	−0.949371	+	0.314156i	$0.898279\pi$
$648$	20.2367			0.794972
$649$		0			0
$650$	−65.8051			−2.58109
$651$	1.24403	−	3.82874i	0.0487575	−	0.150060i
$652$	−2.34247	+	1.70190i	−0.0917382	+	0.0666517i
$653$	−28.0009	−	20.3438i	−1.09576	−	0.796116i	−0.115397	−	0.993319i	$-0.536814\pi$
$653$	−28.0009	−	20.3438i	−1.09576	−	0.796116i	−0.980363	+	0.197203i	$0.936814\pi$
$654$	4.99398	+	15.3699i	0.195280	+	0.601010i
$655$	11.0050	+	33.8700i	0.430002	+	1.32341i
$656$	12.1396	+	8.81993i	0.473972	+	0.344361i
$657$	−32.2730	+	23.4477i	−1.25909	+	0.914781i
$658$	−4.12871	+	12.7069i	−0.160954	+	0.495365i
$659$	−20.2587			−0.789167			−0.394584	−	0.918860i	$-0.629111\pi$
$659$	−20.2587			−0.789167			−0.394584	+	0.918860i	$0.629111\pi$
$660$		0			0
$661$	40.6737			1.58202			0.791012	−	0.611801i	$-0.209555\pi$
$661$	40.6737			1.58202			0.791012	+	0.611801i	$0.209555\pi$
$662$	−11.2879	+	34.7405i	−0.438716	+	1.35023i
$663$	−38.3556	+	27.8670i	−1.48961	+	1.08226i
$664$	6.00891	+	4.36573i	0.233191	+	0.169423i
$665$	1.57889	+	4.85931i	0.0612266	+	0.188436i
$666$	−1.02739	−	3.16198i	−0.0398106	−	0.122524i
$667$	7.78479	+	5.65598i	0.301428	+	0.219000i
$668$	6.39755	−	4.64810i	0.247529	−	0.179840i
$669$	6.82534	−	21.0062i	0.263883	−	0.812148i
$670$	−39.6567			−1.53207
$671$		0			0
$672$	−5.32312			−0.205344
$673$	7.64767	−	23.5371i	0.294796	−	0.907289i	−0.688494	−	0.725242i	$-0.741728\pi$
$673$	7.64767	−	23.5371i	0.294796	−	0.907289i	0.983290	−	0.182047i	$-0.0582722\pi$
$674$	−1.78722	+	1.29849i	−0.0688413	+	0.0500161i
$675$	15.5595	+	11.3046i	0.598885	+	0.435116i
$676$	−0.718785	−	2.21219i	−0.0276456	−	0.0850843i
$677$	−3.51728	−	10.8251i	−0.135180	−	0.416041i	0.860438	−	0.509555i	$-0.170190\pi$
$677$	−3.51728	−	10.8251i	−0.135180	−	0.416041i	−0.995618	+	0.0935140i	$0.970190\pi$
$678$	8.09325	+	5.88009i	0.310820	+	0.225824i
$679$	8.83842	−	6.42149i	0.339187	−	0.246434i
$680$	16.0356	−	49.3525i	0.614937	−	1.89258i
$681$	68.4475			2.62291
$682$		0			0
$683$	−0.212700			−0.00813875			−0.00406938	−	0.999992i	$-0.501295\pi$
$683$	−0.212700			−0.00813875			−0.00406938	+	0.999992i	$0.501295\pi$
$684$	0.519691	−	1.59944i	0.0198709	−	0.0611563i
$685$	39.7129	−	28.8531i	1.51735	−	1.10242i
$686$	−1.03276	−	0.750346i	−0.0394310	−	0.0286483i
$687$	−9.08384	−	27.9572i	−0.346570	−	1.06663i
$688$	−1.30592	−	4.01922i	−0.0497878	−	0.153231i
$689$	−14.1091	−	10.2509i	−0.537514	−	0.390527i
$690$	−54.1180	+	39.3190i	−2.06024	+	1.49685i
$691$	11.2422	−	34.5998i	0.427672	−	1.31624i	−0.472740	−	0.881202i	$-0.656735\pi$
$691$	11.2422	−	34.5998i	0.427672	−	1.31624i	0.900412	−	0.435038i	$-0.143265\pi$
$692$	−7.19966			−0.273690
$693$		0			0
$694$	3.48514			0.132294
$695$	−10.3544	+	31.8676i	−0.392765	+	1.20881i
$696$	12.2052	−	8.86762i	0.462638	−	0.336126i
$697$	−16.2978	−	11.8411i	−0.617325	−	0.448513i
$698$	12.1919	+	37.5228i	0.461470	+	1.42026i
$699$	−21.1850	−	65.2006i	−0.801289	−	2.46611i
$700$	3.51781	+	2.55584i	0.132961	+	0.0966018i
$701$	15.1605	−	11.0148i	0.572605	−	0.416022i	−0.263446	−	0.964674i	$-0.584859\pi$
$701$	15.1605	−	11.0148i	0.572605	−	0.416022i	0.836051	+	0.548652i	$0.184859\pi$
$702$	2.83762	−	8.73330i	0.107099	−	0.329617i
$703$	0.894509			0.0337371
$704$		0			0
$705$	−110.310			−4.15453
$706$	−9.44950	+	29.0826i	−0.355636	+	1.09454i
$707$	−5.95905	+	4.32950i	−0.224113	+	0.162828i
$708$	−10.6205	−	7.71622i	−0.399141	−	0.289993i
$709$	−3.94292	−	12.1351i	−0.148079	−	0.455742i	0.849315	−	0.527887i	$-0.177015\pi$
$709$	−3.94292	−	12.1351i	−0.148079	−	0.455742i	−0.997394	+	0.0721452i	$0.977015\pi$
$710$	−0.352360	−	1.08445i	−0.0132238	−	0.0406988i
$711$	13.4207	+	9.75073i	0.503317	+	0.365681i
$712$	10.2930	−	7.47827i	0.385745	−	0.280260i
$713$	−2.40101	+	7.38956i	−0.0899186	+	0.276741i
$714$	−13.7835			−0.515835
$715$		0			0
$716$	−6.66558			−0.249105
$717$	5.98048	−	18.4060i	0.223345	−	0.687385i
$718$	1.56578	−	1.13760i	0.0584343	−	0.0424550i
$719$	13.8526	+	10.0645i	0.516615	+	0.375343i	0.815327	−	0.579000i	$-0.196557\pi$
$719$	13.8526	+	10.0645i	0.516615	+	0.375343i	−0.298712	+	0.954343i	$0.596557\pi$
$720$	14.3521	+	44.1713i	0.534872	+	1.64617i
$721$	−0.0475535	−	0.146354i	−0.00177098	−	0.00545053i
$722$	18.0119	+	13.0864i	0.670333	+	0.487025i
$723$	57.1839	−	41.5466i	2.12669	−	1.54513i
$724$	−1.73486	+	5.33934i	−0.0644754	+	0.198435i
$725$	−22.7216			−0.843858
$726$		0			0
$727$	−8.65786			−0.321102			−0.160551	−	0.987028i	$-0.551327\pi$
$727$	−8.65786			−0.321102			−0.160551	+	0.987028i	$0.551327\pi$
$728$	4.10580	−	12.6364i	0.152171	−	0.468335i
$729$	29.9147	−	21.7343i	1.10795	−	0.804974i
$730$	46.3596	+	33.6822i	1.71584	+	1.24663i
$731$	1.75325	+	5.39594i	0.0648462	+	0.199576i
$732$	−3.45763	−	10.6415i	−0.127798	−	0.393321i
$733$	−22.7226	−	16.5089i	−0.839277	−	0.609770i	0.0828918	−	0.996559i	$-0.473584\pi$
$733$	−22.7226	−	16.5089i	−0.839277	−	0.609770i	−0.922169	+	0.386788i	$0.873584\pi$
$734$	−9.00783	+	6.54457i	−0.332485	+	0.241564i
$735$	3.25694	−	10.0238i	0.120134	−	0.369735i
$736$	10.2737			0.378695
$737$		0			0
$738$	22.3084			0.821182
$739$	−10.4746	+	32.2375i	−0.385314	+	1.18587i	0.550938	+	0.834546i	$0.314270\pi$
$739$	−10.4746	+	32.2375i	−0.385314	+	1.18587i	−0.936252	+	0.351329i	$0.885730\pi$
$740$	0.878170	−	0.638028i	0.0322822	−	0.0234544i
$741$	11.4276	+	8.30265i	0.419804	+	0.305006i
$742$	−1.56680	−	4.82210i	−0.0575189	−	0.177025i
$743$	−1.74694	−	5.37652i	−0.0640890	−	0.197246i	0.913885	−	0.405974i	$-0.133068\pi$
$743$	−1.74694	−	5.37652i	−0.0640890	−	0.197246i	−0.977974	+	0.208728i	$0.933068\pi$
$744$	9.85528	+	7.16028i	0.361312	+	0.262509i
$745$	39.9907	−	29.0550i	1.46515	−	1.06449i
$746$	−14.5213	+	44.6918i	−0.531661	+	1.63628i
$747$	8.92472			0.326538
$748$		0			0
$749$	7.94617			0.290347
$750$	28.0223	−	86.2437i	1.02323	−	3.14917i
$751$	−35.8726	+	26.0629i	−1.30901	+	0.951050i	−1.00000		8.77932e-6i	$-0.999997\pi$
$751$	−35.8726	+	26.0629i	−1.30901	+	0.951050i	−0.309009	+	0.951059i	$0.599997\pi$
$752$	−26.4354	−	19.2065i	−0.964001	−	0.700388i
$753$	−1.53248	−	4.71650i	−0.0558468	−	0.171879i
$754$	3.35239	+	10.3176i	0.122087	+	0.375745i
$755$	−22.9998	−	16.7104i	−0.837050	−	0.608152i
$756$	−0.490891	+	0.356653i	−0.0178535	+	0.0129714i
$757$	−6.60620	+	20.3318i	−0.240106	+	0.738972i	0.756296	+	0.654229i	$0.227007\pi$
$757$	−6.60620	+	20.3318i	−0.240106	+	0.738972i	−0.996403	+	0.0847425i	$0.972993\pi$
$758$	3.31700			0.120479
$759$		0			0
$760$	−15.4607			−0.560819
$761$	−1.41707	+	4.36129i	−0.0513688	+	0.158097i	−0.973450	−	0.228899i	$-0.926487\pi$
$761$	−1.41707	+	4.36129i	−0.0513688	+	0.158097i	0.922081	+	0.386996i	$0.126487\pi$
$762$	−28.7203	+	20.8665i	−1.04043	+	0.755914i
$763$	3.97583	+	2.88861i	0.143935	+	0.104575i
$764$	2.71915	+	8.36869i	0.0983755	+	0.302769i
$765$	−19.2682	−	59.3015i	−0.696644	−	2.14405i
$766$	−19.8695	−	14.4361i	−0.717915	−	0.521596i
$767$	48.8758	−	35.5103i	1.76480	−	1.28220i
$768$	6.81849	−	20.9852i	0.246041	−	0.757237i
$769$	12.8223			0.462385			0.231193	−	0.972908i	$-0.425737\pi$
$769$	12.8223			0.462385			0.231193	+	0.972908i	$0.425737\pi$
$770$		0			0
$771$	−26.1736			−0.942621
$772$	−1.60903	+	4.95208i	−0.0579102	+	0.178229i
$773$	−43.7386	+	31.7780i	−1.57317	+	1.14297i	−0.649128	+	0.760679i	$0.724866\pi$
$773$	−43.7386	+	31.7780i	−1.57317	+	1.14297i	−0.924041	+	0.382295i	$0.875134\pi$
$774$	−5.08293	−	3.69296i	−0.182702	−	0.132741i
$775$	−5.66948	−	17.4489i	−0.203654	−	0.626782i
$776$	10.2155	+	31.4401i	0.366716	+	1.12864i
$777$	−1.49280	−	1.08458i	−0.0535539	−	0.0389092i
$778$	29.2613	−	21.2596i	1.04907	−	0.762194i
$779$	−1.85473	+	5.70829i	−0.0664528	+	0.204521i
$780$	17.1409			0.613743
$781$		0			0
$782$	26.6025			0.951302
$783$	0.979790	−	3.01548i	0.0350148	−	0.107765i
$784$	2.52579	−	1.83509i	0.0902068	−	0.0655390i
$785$	34.7324	+	25.2346i	1.23965	+	0.900660i
$786$	8.84524	+	27.2229i	0.315499	+	0.971007i
$787$	−13.5508	−	41.7052i	−0.483035	−	1.48663i	−0.834806	−	0.550544i	$-0.814420\pi$
$787$	−13.5508	−	41.7052i	−0.483035	−	1.48663i	0.351771	−	0.936086i	$-0.385580\pi$
$788$	5.41356	+	3.93318i	0.192850	+	0.140114i
$789$	−9.14430	+	6.64372i	−0.325546	+	0.236523i
$790$	7.36379	−	22.6634i	0.261992	−	0.806328i
$791$	3.04208			0.108164
$792$		0			0
$793$	51.4928			1.82856
$794$	−4.08943	+	12.5860i	−0.145128	+	0.446659i
$795$	33.8667	−	24.6056i	1.20113	−	0.872670i
$796$	0.462576	+	0.336081i	0.0163956	+	0.0119121i
$797$	−11.0534	−	34.0190i	−0.391533	−	1.20502i	−0.931629	−	0.363412i	$-0.881612\pi$
$797$	−11.0534	−	34.0190i	−0.391533	−	1.20502i	0.540095	−	0.841604i	$-0.318388\pi$
$798$	1.26902	+	3.90565i	0.0449229	+	0.138258i
$799$	35.4905	+	25.7854i	1.25556	+	0.912221i
$800$	−19.6262	+	14.2592i	−0.693889	+	0.504140i
$801$	4.72413	−	14.5394i	0.166919	−	0.513723i
$802$	−16.3244			−0.576436
$803$		0			0
$804$	7.24440			0.255490
$805$	−6.28597	+	19.3462i	−0.221551	+	0.681864i
$806$	−7.08684	+	5.14889i	−0.249623	+	0.181362i
$807$	1.30332	+	0.946920i	0.0458792	+	0.0333332i
$808$	−6.88753	−	21.1976i	−0.242302	−	0.745730i
$809$	−9.48893	−	29.2039i	−0.333613	−	1.02676i	−0.967401	−	0.253249i	$-0.918501\pi$
$809$	−9.48893	−	29.2039i	−0.333613	−	1.02676i	0.633788	−	0.773507i	$-0.281499\pi$
$810$	−28.2588	−	20.5312i	−0.992913	−	0.721394i
$811$	−13.8329	+	10.0502i	−0.485737	+	0.352909i	−0.803543	−	0.595247i	$-0.797054\pi$
$811$	−13.8329	+	10.0502i	−0.485737	+	0.352909i	0.317805	+	0.948156i	$0.397054\pi$
$812$	0.221519	−	0.681764i	0.00777378	−	0.0239252i
$813$	30.7514			1.07850
$814$		0			0
$815$	31.9845			1.12037
$816$	10.4169	−	32.0600i	0.364665	−	1.12232i
$817$	1.36756	−	0.993588i	0.0478448	−	0.0347613i
$818$	33.0708	+	24.0274i	1.15629	+	0.840097i
$819$	−4.93349	−	15.1837i	−0.172390	−	0.530563i
$820$	2.25070	+	6.92695i	0.0785979	+	0.241899i
$821$	10.0174	+	7.27807i	0.349610	+	0.254006i	0.748705	−	0.662903i	$-0.230676\pi$
$821$	10.0174	+	7.27807i	0.349610	+	0.254006i	−0.399095	+	0.916909i	$0.630676\pi$
$822$	31.9190	−	23.1905i	1.11330	−	0.808863i
$823$	14.2576	−	43.8803i	0.496987	−	1.52957i	−0.316849	−	0.948476i	$-0.602625\pi$
$823$	14.2576	−	43.8803i	0.496987	−	1.52957i	0.813836	−	0.581094i	$-0.197375\pi$
$824$	0.465652			0.0162217
$825$		0			0
$826$	17.5640			0.611131
$827$	14.4343	−	44.4241i	0.501929	−	1.54478i	−0.303945	−	0.952690i	$-0.598304\pi$
$827$	14.4343	−	44.4241i	0.501929	−	1.54478i	0.805873	−	0.592088i	$-0.201696\pi$
$828$	5.41679	−	3.93553i	0.188246	−	0.136769i
$829$	−3.25674	−	2.36616i	−0.113111	−	0.0821801i	0.529792	−	0.848128i	$-0.322270\pi$
$829$	−3.25674	−	2.36616i	−0.113111	−	0.0821801i	−0.642903	+	0.765948i	$0.722270\pi$
$830$	−3.96166	−	12.1927i	−0.137511	−	0.423216i
$831$	−22.7325	−	69.9636i	−0.788583	−	2.42701i
$832$	31.5517	+	22.9236i	1.09386	+	0.794733i
$833$	−3.39096	+	2.46368i	−0.117490	+	0.0853614i
$834$	−8.32229	+	25.6134i	−0.288177	+	0.886919i
$835$	−87.3534			−3.02299
$836$		0			0
$837$	2.56020			0.0884933
$838$	−7.92646	+	24.3951i	−0.273815	+	0.842716i
$839$	11.5707	−	8.40658i	0.399464	−	0.290227i	−0.369859	−	0.929088i	$-0.620594\pi$
$839$	11.5707	−	8.40658i	0.399464	−	0.290227i	0.769323	+	0.638861i	$0.220594\pi$
$840$	25.8016	+	18.7460i	0.890239	+	0.646797i
$841$	−7.80396	−	24.0181i	−0.269102	−	0.828211i
$842$	−8.84593	−	27.2250i	−0.304851	−	0.938235i
$843$	30.6316	+	22.2552i	1.05501	+	0.766509i
$844$	−6.61728	+	4.80774i	−0.227776	+	0.165489i
$845$	−7.94004	+	24.4369i	−0.273146	+	0.840656i
$846$	−48.5792			−1.67019
$847$		0			0
$848$	12.4002			0.425823
$849$	−17.9424	+	55.2210i	−0.615782	+	1.89518i
$850$	−50.8193	+	36.9224i	−1.74309	+	1.26643i
$851$	2.88114	+	2.09327i	0.0987641	+	0.0717563i
$852$	0.0643684	+	0.198105i	0.00220522	+	0.00678698i
$853$	−9.98146	−	30.7198i	−0.341759	−	1.05182i	−0.963296	−	0.268440i	$-0.913492\pi$
$853$	−9.98146	−	30.7198i	−0.341759	−	1.05182i	0.621538	−	0.783384i	$-0.286508\pi$
$854$	12.1113	+	8.79940i	0.414442	+	0.301109i
$855$	−15.0295	+	10.9196i	−0.513997	+	0.373441i
$856$	−7.43021	+	22.8678i	−0.253960	+	0.781607i
$857$	16.2318			0.554468			0.277234	−	0.960802i	$-0.410582\pi$
$857$	16.2318			0.554468			0.277234	+	0.960802i	$0.410582\pi$
$858$		0			0
$859$	−28.2893			−0.965220			−0.482610	−	0.875835i	$-0.660311\pi$
$859$	−28.2893			−0.965220			−0.482610	+	0.875835i	$0.660311\pi$
$860$	0.633879	−	1.95088i	0.0216151	−	0.0665244i
$861$	10.0165	−	7.27742i	0.341362	−	0.248014i
$862$	−12.4816	−	9.06840i	−0.425124	−	0.308871i
$863$	9.88438	+	30.4210i	0.336468	+	1.03554i	0.965994	+	0.258563i	$0.0832491\pi$
$863$	9.88438	+	30.4210i	0.336468	+	1.03554i	−0.629526	+	0.776979i	$0.716751\pi$
$864$	−1.04610	−	3.21956i	−0.0355890	−	0.109532i
$865$	64.3418	+	46.7471i	2.18769	+	1.58945i
$866$	0.312362	−	0.226945i	0.0106145	−	0.00771189i
$867$	−0.452428	+	1.39243i	−0.0153653	+	0.0472894i
$868$	0.578830			0.0196468
$869$		0			0
$870$	−26.0403			−0.882848
$871$	−10.3023	+	31.7073i	−0.349081	+	1.07436i
$872$	−12.0307	+	8.74078i	−0.407409	+	0.296000i
$873$	32.1361	+	23.3482i	1.08764	+	0.790217i
$874$	−2.44924	−	7.53798i	−0.0828467	−	0.254976i
$875$	−8.52137	−	26.2261i	−0.288075	−	0.886603i
$876$	−8.46886	−	6.15299i	−0.286136	−	0.207890i
$877$	−37.0504	+	26.9187i	−1.25110	+	0.908979i	−0.998285	−	0.0585353i	$-0.981357\pi$
$877$	−37.0504	+	26.9187i	−1.25110	+	0.908979i	−0.252817	+	0.967514i	$0.581357\pi$
$878$	−1.39091	+	4.28077i	−0.0469408	+	0.144469i
$879$	−43.3496			−1.46215
$880$		0			0
$881$	26.7142			0.900025			0.450012	−	0.893022i	$-0.351420\pi$
$881$	26.7142			0.900025			0.450012	+	0.893022i	$0.351420\pi$
$882$	1.43431	−	4.41435i	0.0482957	−	0.148639i
$883$	23.0464	−	16.7442i	0.775574	−	0.563487i	−0.128074	−	0.991765i	$-0.540879\pi$
$883$	23.0464	−	16.7442i	0.775574	−	0.563487i	0.903647	+	0.428277i	$0.140879\pi$
$884$	−5.51480	−	4.00674i	−0.185483	−	0.134761i
$885$	44.8117	+	137.916i	1.50633	+	4.63601i
$886$	−8.61715	−	26.5209i	−0.289499	−	0.890986i
$887$	19.1041	+	13.8799i	0.641452	+	0.466042i	0.860349	−	0.509706i	$-0.170246\pi$
$887$	19.1041	+	13.8799i	0.641452	+	0.466042i	−0.218896	+	0.975748i	$0.570246\pi$
$888$	4.51714	−	3.28189i	0.151585	−	0.110133i
$889$	−3.33595	+	10.2670i	−0.111884	+	0.344344i
$890$	−21.9604			−0.736113
$891$		0			0
$892$	3.17572			0.106331
$893$	4.03891	−	12.4305i	0.135157	−	0.415970i
$894$	32.1423	−	23.3528i	1.07500	−	0.781034i
$895$	59.5689	+	43.2793i	1.99117	+	1.44667i
$896$	2.22666	+	6.85296i	0.0743875	+	0.228941i
$897$	17.3781	+	53.4843i	0.580237	+	1.78579i
$898$	−9.60646	−	6.97950i	−0.320572	−	0.232909i
$899$	−2.44698	+	1.77784i	−0.0816115	+	0.0592942i
$900$	−4.88558	+	15.0363i	−0.162853	+	0.501208i
$901$	−16.6477			−0.554614
$902$		0			0
$903$	−3.48696			−0.116039
$904$	−2.84456	+	8.75465i	−0.0946086	+	0.291175i
$905$	50.1721	−	36.4522i	1.66778	−	1.21171i
$906$	−18.4860	−	13.4309i	−0.614156	−	0.446211i
$907$	7.39893	+	22.7716i	0.245677	+	0.756117i	0.995524	+	0.0945058i	$0.0301271\pi$
$907$	7.39893	+	22.7716i	0.245677	+	0.756117i	−0.749847	+	0.661611i	$0.769873\pi$
$908$	3.04117	+	9.35976i	0.100925	+	0.310615i
$909$	−21.6668	−	15.7419i	−0.718643	−	0.522125i
$910$	−18.5537	+	13.4800i	−0.615049	+	0.446859i
$911$	5.63611	−	17.3462i	0.186733	−	0.574704i	−0.813241	−	0.581927i	$-0.802299\pi$
$911$	5.63611	−	17.3462i	0.186733	−	0.574704i	0.999974	+	0.00722260i	$0.00229905\pi$
$912$	−10.0435			−0.332572
$913$		0			0
$914$	−14.4463			−0.477841
$915$	−38.1946	+	117.551i	−1.26267	+	3.88611i
$916$	3.41937	−	2.48431i	0.112979	−	0.0820841i
$917$	7.04192	+	5.11625i	0.232545	+	0.168954i
$918$	−2.70873	−	8.33661i	−0.0894014	−	0.275149i
$919$	8.77683	+	27.0123i	0.289521	+	0.891053i	0.985007	+	0.172514i	$0.0551890\pi$
$919$	8.77683	+	27.0123i	0.289521	+	0.891053i	−0.695486	+	0.718539i	$0.744811\pi$
$920$	−49.7976	−	36.1801i	−1.64178	−	1.19282i
$921$	0.496743	−	0.360905i	0.0163682	−	0.0118922i
$922$	−0.267781	+	0.824146i	−0.00881891	+	0.0271418i
$923$	−0.958607			−0.0315529
$924$		0			0
$925$	−8.40922			−0.276493
$926$	−5.32297	+	16.3824i	−0.174924	+	0.538360i
$927$	0.452663	−	0.328879i	0.0148674	−	0.0108018i
$928$	3.23555	+	2.35076i	0.106212	+	0.0771675i
$929$	1.04745	+	3.22373i	0.0343658	+	0.105767i	0.966768	−	0.255655i	$-0.0822912\pi$
$929$	1.04745	+	3.22373i	0.0343658	+	0.105767i	−0.932402	+	0.361422i	$0.882291\pi$
$930$	−6.49757	−	19.9975i	−0.213064	−	0.655742i
$931$	1.01030	+	0.734025i	0.0331112	+	0.0240567i
$932$	7.97451	−	5.79382i	0.261214	−	0.189783i
$933$	0.522618	−	1.60845i	0.0171097	−	0.0526583i
$934$	37.8588			1.23878
$935$		0			0
$936$	48.3096			1.57905
$937$	14.0254	−	43.1657i	0.458190	−	1.41016i	−0.409160	−	0.912463i	$-0.634178\pi$
$937$	14.0254	−	43.1657i	0.458190	−	1.41016i	0.867349	−	0.497700i	$-0.165822\pi$
$938$	−7.84149	+	5.69718i	−0.256034	+	0.186019i
$939$	−15.5317	−	11.2844i	−0.506857	−	0.368253i
$940$	−4.90117	−	15.0843i	−0.159859	−	0.491994i
$941$	6.65248	+	20.4742i	0.216865	+	0.667441i	0.999016	+	0.0443523i	$0.0141224\pi$
$941$	6.65248	+	20.4742i	0.216865	+	0.667441i	−0.782151	+	0.623089i	$0.785878\pi$
$942$	27.9160	+	20.2822i	0.909552	+	0.660828i
$943$	−19.3321	+	14.0456i	−0.629539	+	0.457387i
$944$	−13.2741	+	40.8534i	−0.432034	+	1.32966i
$945$	6.70272			0.218039
$946$		0			0
$947$	−11.2673			−0.366140			−0.183070	−	0.983100i	$-0.558603\pi$
$947$	−11.2673			−0.366140			−0.183070	+	0.983100i	$0.558603\pi$
$948$	−1.34520	+	4.14010i	−0.0436901	+	0.134464i
$949$	38.9740	−	28.3163i	1.26515	−	0.919185i
$950$	15.1410	+	11.0006i	0.491240	+	0.356907i
$951$	−13.8839	−	42.7301i	−0.450215	−	1.38562i
$952$	−3.91931	−	12.0624i	−0.127025	−	0.390944i
$953$	19.3109	+	14.0302i	0.625543	+	0.454483i	0.854853	−	0.518870i	$-0.173647\pi$
$953$	19.3109	+	14.0302i	0.625543	+	0.454483i	−0.229310	+	0.973353i	$0.573647\pi$
$954$	14.9144	−	10.8359i	0.482871	−	0.350827i
$955$	30.0370	−	92.4445i	0.971976	−	2.99143i
$956$	2.78262			0.0899964
$957$		0			0
$958$	6.00159			0.193902
$959$	3.70749	−	11.4105i	0.119721	−	0.368464i
$960$	−75.7348	+	55.0245i	−2.44433	+	1.77591i
$961$	23.1037	+	16.7858i	0.745280	+	0.541478i
$962$	1.24071	+	3.81853i	0.0400022	+	0.123114i
$963$	8.92808	+	27.4778i	0.287703	+	0.885460i
$964$	8.22195	+	5.97360i	0.264811	+	0.192397i
$965$	46.5332	−	33.8083i	1.49796	−	1.08833i
$966$	−5.05231	+	15.5494i	−0.162556	+	0.500294i
$967$	20.5165			0.659765			0.329882	−	0.944022i	$-0.392991\pi$
$967$	20.5165			0.659765			0.329882	+	0.944022i	$0.392991\pi$
$968$		0			0
$969$	13.4837			0.433159
$970$	17.6327	−	54.2677i	0.566151	−	1.74243i
$971$	28.1251	−	20.4341i	0.902577	−	0.655761i	−0.0365493	−	0.999332i	$-0.511637\pi$
$971$	28.1251	−	20.4341i	0.902577	−	0.655761i	0.939127	+	0.343571i	$0.111637\pi$
$972$	6.63493	+	4.82056i	0.212815	+	0.154619i
$973$	2.53075	+	7.78884i	0.0811320	+	0.249699i
$974$	12.7708	+	39.3045i	0.409203	+	1.25940i
$975$	−107.430	−	78.0526i	−3.44052	−	2.49968i
$976$	−29.6203	+	21.5204i	−0.948122	+	0.688851i
$977$	1.78703	−	5.49991i	0.0571721	−	0.175958i	−0.918392	−	0.395671i	$-0.870512\pi$
$977$	1.78703	−	5.49991i	0.0571721	−	0.175958i	0.975565	+	0.219713i	$0.0705121\pi$
$978$	25.7074			0.822032
$979$		0			0
$980$	1.51540			0.0484078
$981$	−5.52167	+	16.9940i	−0.176293	+	0.542575i
$982$	7.08055	−	5.14432i	0.225950	−	0.164162i
$983$	13.9410	+	10.1288i	0.444650	+	0.323057i	0.787480	−	0.616340i	$-0.211385\pi$
$983$	13.9410	+	10.1288i	0.444650	+	0.323057i	−0.342830	+	0.939398i	$0.611385\pi$
$984$	11.5772	+	35.6309i	0.369067	+	1.13587i
$985$	−22.8419	−	70.3000i	−0.727802	−	2.23994i
$986$	8.37801	+	6.08698i	0.266810	+	0.193849i
$987$	−21.8122	+	15.8475i	−0.694289	+	0.504430i
$988$	−0.627598	+	1.93155i	−0.0199665	+	0.0614507i
$989$	6.72991			0.213999
$990$		0			0
$991$	−24.0077			−0.762630			−0.381315	−	0.924445i	$-0.624529\pi$
$991$	−24.0077			−0.762630			−0.381315	+	0.924445i	$0.624529\pi$
$992$	−0.997919	+	3.07128i	−0.0316840	+	0.0975132i
$993$	−59.6343	+	43.3269i	−1.89244	+	1.37494i
$994$	−0.225469	−	0.163813i	−0.00715144	−	0.00519582i
$995$	−1.95178	−	6.00697i	−0.0618757	−	0.190434i
$996$	0.723707	+	2.22734i	0.0229315	+	0.0705760i
$997$	−29.1517	−	21.1800i	−0.923244	−	0.670776i	0.0210855	−	0.999778i	$-0.493288\pi$
$997$	−29.1517	−	21.1800i	−0.923244	−	0.670776i	−0.944329	+	0.329002i	$0.893288\pi$
$998$	−11.3263	+	8.22907i	−0.358529	+	0.260487i
$999$	0.362619	−	1.11603i	0.0114727	−	0.0353095i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	847.2.f.y.372.4		24
11.2	odd	10		847.2.f.z.729.4		24
11.3	even	5	inner	847.2.f.y.323.3		24
11.4	even	5		847.2.a.n.1.4	yes	6
11.5	even	5	inner	847.2.f.y.148.4		24
11.6	odd	10		847.2.f.z.148.3		24
11.7	odd	10		847.2.a.m.1.3	✓	6
11.8	odd	10		847.2.f.z.323.4		24
11.9	even	5	inner	847.2.f.y.729.3		24
11.10	odd	2		847.2.f.z.372.3		24
33.26	odd	10		7623.2.a.cp.1.3		6
33.29	even	10		7623.2.a.cs.1.4		6
77.48	odd	10		5929.2.a.bm.1.4		6
77.62	even	10		5929.2.a.bj.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
847.2.a.m.1.3	✓	6	11.7	odd	10
847.2.a.n.1.4	yes	6	11.4	even	5
847.2.f.y.148.4		24	11.5	even	5	inner
847.2.f.y.323.3		24	11.3	even	5	inner
847.2.f.y.372.4		24	1.1	even	1	trivial
847.2.f.y.729.3		24	11.9	even	5	inner
847.2.f.z.148.3		24	11.6	odd	10
847.2.f.z.323.4		24	11.8	odd	10
847.2.f.z.372.3		24	11.10	odd	2
847.2.f.z.729.4		24	11.2	odd	10
5929.2.a.bj.1.3		6	77.62	even	10
5929.2.a.bm.1.4		6	77.48	odd	10
7623.2.a.cp.1.3		6	33.26	odd	10
7623.2.a.cs.1.4		6	33.29	even	10

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:	\( N \)	\(=\)	\( 847 = 7 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	847.f (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.394480 - 1.21408i) q^{2} +(2.08406 - 1.51415i) q^{3} +(0.299647 + 0.217706i) q^{4} +(-1.26432 - 3.89119i) q^{5} +(-1.01619 - 3.12752i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(2.44804 - 1.77861i) q^{8} +(1.12357 - 3.45799i) q^{9} +O(q^{10})\)	\(q+(0.394480 - 1.21408i) q^{2} +(2.08406 - 1.51415i) q^{3} +(0.299647 + 0.217706i) q^{4} +(-1.26432 - 3.89119i) q^{5} +(-1.01619 - 3.12752i) q^{6} +(-0.809017 - 0.587785i) q^{7} +(2.44804 - 1.77861i) q^{8} +(1.12357 - 3.45799i) q^{9} -5.22298 q^{10} +0.954122 q^{12} +(-1.35686 + 4.17600i) q^{13} +(-1.03276 + 0.750346i) q^{14} +(-8.52678 - 6.19507i) q^{15} +(-0.964766 - 2.96924i) q^{16} +(1.29523 + 3.98632i) q^{17} +(-3.75507 - 2.72822i) q^{18} +(1.01030 - 0.734025i) q^{19} +(0.468285 - 1.44123i) q^{20} -2.57603 q^{21} +4.97180 q^{23} +(2.40877 - 7.41343i) q^{24} +(-9.49775 + 6.90052i) q^{25} +(4.53476 + 3.29470i) q^{26} +(-0.506241 - 1.55805i) q^{27} +(-0.114455 - 0.352256i) q^{28} +(1.56579 + 1.13761i) q^{29} +(-10.8850 + 7.90840i) q^{30} +(-0.482926 + 1.48629i) q^{31} +2.06640 q^{32} +5.35067 q^{34} +(-1.26432 + 3.89119i) q^{35} +(1.08950 - 0.791570i) q^{36} +(0.579496 + 0.421028i) q^{37} +(-0.492626 - 1.51615i) q^{38} +(3.49533 + 10.7575i) q^{39} +(-10.0160 - 7.27706i) q^{40} +(-3.88834 + 2.82505i) q^{41} +(-1.01619 + 3.12752i) q^{42} +1.35362 q^{43} -14.8763 q^{45} +(1.96128 - 6.03619i) q^{46} +(8.46734 - 6.15188i) q^{47} +(-6.50652 - 4.72726i) q^{48} +(0.309017 + 0.951057i) q^{49} +(4.63114 + 14.2532i) q^{50} +(8.73524 + 6.34652i) q^{51} +(-1.31572 + 0.955928i) q^{52} +(-1.22735 + 3.77741i) q^{53} -2.09131 q^{54} -3.02595 q^{56} +(0.994091 - 3.05950i) q^{57} +(1.99883 - 1.45223i) q^{58} +(-11.1311 - 8.08724i) q^{59} +(-1.20632 - 3.71267i) q^{60} +(-3.62388 - 11.1532i) q^{61} +(1.61398 + 1.17263i) q^{62} +(-2.94155 + 2.13716i) q^{63} +(2.74469 - 8.44727i) q^{64} +17.9651 q^{65} +7.59274 q^{67} +(-0.479734 + 1.47647i) q^{68} +(10.3615 - 7.52808i) q^{69} +(4.22548 + 3.06999i) q^{70} +(0.0674634 + 0.207631i) q^{71} +(-3.39987 - 10.4637i) q^{72} +(-8.87607 - 6.44884i) q^{73} +(0.739763 - 0.537470i) q^{74} +(-9.34538 + 28.7621i) q^{75} +0.462535 q^{76} +14.4394 q^{78} +(-1.40988 + 4.33917i) q^{79} +(-10.3341 + 7.50817i) q^{80} +(5.41047 + 3.93094i) q^{81} +(1.89597 + 5.83520i) q^{82} +(0.758506 + 2.33444i) q^{83} +(-0.771901 - 0.560819i) q^{84} +(13.8739 - 10.0800i) q^{85} +(0.533974 - 1.64340i) q^{86} +4.98571 q^{87} +4.20456 q^{89} +(-5.86839 + 18.0610i) q^{90} +(3.55232 - 2.58091i) q^{91} +(1.48979 + 1.08239i) q^{92} +(1.24403 + 3.82874i) q^{93} +(-4.12871 - 12.7069i) q^{94} +(-4.13358 - 3.00322i) q^{95} +(4.30649 - 3.12885i) q^{96} +(-3.37598 + 10.3902i) q^{97} +1.27656 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 6 q^{6} - 6 q^{7} - 12 q^{8} - 8 q^{9}+O(q^{10}) \) 24 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 6 * q^6 - 6 * q^7 - 12 * q^8 - 8 * q^9	\( 24 q - 4 q^{2} + 2 q^{3} - 4 q^{4} + 4 q^{5} + 6 q^{6} - 6 q^{7} - 12 q^{8} - 8 q^{9} - 32 q^{10} - 56 q^{12} - 4 q^{13} - 4 q^{14} - 2 q^{15} - 8 q^{16} - 22 q^{17} - 24 q^{18} - 6 q^{19} - 2 q^{20} - 8 q^{21} + 8 q^{23} + 20 q^{24} - 4 q^{25} - 6 q^{26} + 2 q^{27} - 4 q^{28} - 12 q^{29} - 20 q^{30} + 2 q^{31} + 32 q^{32} + 96 q^{34} + 4 q^{35} - 18 q^{36} - 14 q^{37} + 22 q^{38} - 20 q^{39} - 18 q^{40} - 26 q^{41} + 6 q^{42} - 16 q^{43} - 144 q^{45} - 12 q^{46} + 16 q^{47} + 24 q^{48} - 6 q^{49} + 4 q^{50} + 4 q^{51} - 12 q^{52} - 4 q^{53} - 128 q^{54} + 48 q^{56} - 20 q^{57} + 2 q^{58} + 4 q^{59} - 24 q^{60} + 8 q^{61} - 20 q^{62} - 8 q^{63} - 26 q^{64} + 96 q^{65} + 24 q^{67} - 12 q^{68} + 14 q^{69} + 8 q^{70} - 22 q^{71} - 16 q^{72} - 14 q^{73} - 44 q^{74} + 20 q^{75} - 120 q^{76} + 128 q^{78} + 28 q^{79} + 4 q^{80} + 6 q^{81} + 4 q^{82} - 22 q^{83} + 14 q^{84} + 24 q^{85} + 30 q^{86} + 88 q^{87} + 22 q^{90} - 4 q^{91} - 10 q^{92} + 50 q^{93} + 38 q^{94} + 24 q^{95} + 62 q^{96} + 4 q^{97} + 16 q^{98}+O(q^{100}) \) 24 * q - 4 * q^2 + 2 * q^3 - 4 * q^4 + 4 * q^5 + 6 * q^6 - 6 * q^7 - 12 * q^8 - 8 * q^9 - 32 * q^10 - 56 * q^12 - 4 * q^13 - 4 * q^14 - 2 * q^15 - 8 * q^16 - 22 * q^17 - 24 * q^18 - 6 * q^19 - 2 * q^20 - 8 * q^21 + 8 * q^23 + 20 * q^24 - 4 * q^25 - 6 * q^26 + 2 * q^27 - 4 * q^28 - 12 * q^29 - 20 * q^30 + 2 * q^31 + 32 * q^32 + 96 * q^34 + 4 * q^35 - 18 * q^36 - 14 * q^37 + 22 * q^38 - 20 * q^39 - 18 * q^40 - 26 * q^41 + 6 * q^42 - 16 * q^43 - 144 * q^45 - 12 * q^46 + 16 * q^47 + 24 * q^48 - 6 * q^49 + 4 * q^50 + 4 * q^51 - 12 * q^52 - 4 * q^53 - 128 * q^54 + 48 * q^56 - 20 * q^57 + 2 * q^58 + 4 * q^59 - 24 * q^60 + 8 * q^61 - 20 * q^62 - 8 * q^63 - 26 * q^64 + 96 * q^65 + 24 * q^67 - 12 * q^68 + 14 * q^69 + 8 * q^70 - 22 * q^71 - 16 * q^72 - 14 * q^73 - 44 * q^74 + 20 * q^75 - 120 * q^76 + 128 * q^78 + 28 * q^79 + 4 * q^80 + 6 * q^81 + 4 * q^82 - 22 * q^83 + 14 * q^84 + 24 * q^85 + 30 * q^86 + 88 * q^87 + 22 * q^90 - 4 * q^91 - 10 * q^92 + 50 * q^93 + 38 * q^94 + 24 * q^95 + 62 * q^96 + 4 * q^97 + 16 * q^98

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