LMFDB - Embedded newform 847.2.f.z.372.3

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			372.3
Character	$\chi$	$=$	847.372
Dual form			847.2.f.z.148.3

$q$-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	$0.249052\pi$
$2$	−0.394480	+	1.21408i	−0.278939	+	0.858487i	−0.988150	+	0.153491i	$0.950948\pi$
$3$	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	$-0.691607\pi$
$13$	1.35686	−	4.17600i	0.376327	−	1.15821i	0.942579	−	0.333983i	$-0.108393\pi$
$14$	−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	$-0.930278\pi$
$17$	−1.29523	−	3.98632i	−0.314140	−	0.966824i	0.661967	−	0.749533i	$-0.269722\pi$
$18$	3.75507	+	2.72822i	0.885079	+	0.643047i
$19$	−1.01030	+	0.734025i	−0.231779	+	0.168397i	−0.697613	−	0.716475i	$-0.745754\pi$
$19$	−1.01030	+	0.734025i	−0.231779	+	0.168397i	0.465834	+	0.884872i	$0.345754\pi$
$20$	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	0.432837	−	0.901472i	$-0.357512\pi$
$29$	−1.56579	−	1.13761i	−0.290760	−	0.211249i	−0.723597	+	0.690223i	$0.757512\pi$
$30$	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	−0.241190	−	0.970478i	$-0.577538\pi$
$41$	3.88834	−	2.82505i	0.607257	−	0.441198i	0.848448	+	0.529280i	$0.177538\pi$
$42$	−1.01619	+	3.12752i	−0.156802	+	0.482587i
$43$	−1.35362			−0.206424			−0.103212	−	0.994659i	$-0.532912\pi$
$43$	−1.35362			−0.206424			−0.103212	+	0.994659i	$0.532912\pi$
$44$		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	$0.170309\pi$
$61$	3.62388	+	11.1532i	0.463991	+	1.42802i	−0.396256	+	0.918140i	$0.629691\pi$
$62$	−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	0.970064	−	0.242850i	$-0.0780823\pi$
$73$	8.87607	+	6.44884i	1.03887	+	0.754780i	0.0688019	+	0.997630i	$0.478082\pi$
$74$	−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	−0.839886	−	0.542763i	$-0.817378\pi$
$79$	1.40988	−	4.33917i	0.158624	−	0.488195i	0.998510	+	0.0545680i	$0.0173782\pi$
$80$	−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	0.900759	−	0.434319i	$-0.143011\pi$
$83$	−0.758506	−	2.33444i	−0.0832568	−	0.256238i	−0.984016	+	0.178081i	$0.943011\pi$
$84$	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	$0.219431\pi$
$101$	−2.27616	+	7.00529i	−0.226486	+	0.697052i	−0.998137	+	0.0610064i	$0.980569\pi$
$102$	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	−0.231962	−	0.972725i	$-0.574514\pi$
$107$	6.42858	−	4.67064i	0.621475	−	0.451528i	0.853436	+	0.521197i	$0.174514\pi$
$108$	0.187504	−	0.577077i	0.0180426	−	0.0555293i
$109$	4.91440			0.470714			0.235357	−	0.971909i	$-0.424374\pi$
$109$	4.91440			0.470714			0.235357	+	0.971909i	$0.424374\pi$
$110$		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	$0.0589884\pi$
$127$	3.33595	+	10.2670i	0.296017	+	0.911048i	−0.686860	+	0.726789i	$0.741012\pi$
$128$	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	$-0.375838\pi$
$131$	8.70429			0.760497			0.380249	+	0.924884i	$0.375838\pi$
$132$		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	0.832181	−	0.554504i	$-0.187092\pi$
$139$	6.62558	+	4.81377i	0.561975	+	0.408298i	−0.270206	+	0.962802i	$0.587092\pi$
$140$	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	$-0.935211\pi$
$149$	−3.73343	−	11.4903i	−0.305855	−	0.941323i	0.673502	−	0.739185i	$-0.264789\pi$
$150$	−31.2331	−	22.6922i	−2.55017	−	1.85281i
$151$	−5.62146	+	4.08423i	−0.457468	+	0.332370i	−0.792537	−	0.609824i	$-0.791240\pi$
$151$	−5.62146	+	4.08423i	−0.457468	+	0.332370i	0.335069	+	0.942193i	$0.391240\pi$
$152$	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	$0.409427\pi$
$167$	−6.59761	+	20.3053i	−0.510538	+	1.57127i	−0.791256	+	0.611484i	$0.790573\pi$
$168$	−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	0.201776	−	0.979432i	$-0.435329\pi$
$173$	15.7260	−	11.4256i	1.19562	−	0.868671i	0.993847	+	0.110760i	$0.0353286\pi$
$174$	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	$-0.931137\pi$
$193$	−4.34421	−	13.3701i	−0.312703	−	0.962402i	0.663986	−	0.747745i	$-0.268863\pi$
$194$	−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	$-0.722556\pi$
$197$	−18.0665			−1.28718			−0.643591	+	0.765369i	$0.722556\pi$
$198$		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	$-0.625126\pi$
$211$	6.82421	−	21.0027i	0.469798	−	1.44589i	0.852847	−	0.522161i	$-0.174874\pi$
$212$	−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	$-0.956341\pi$
$227$	−21.4963	−	15.6180i	−1.42676	−	1.03660i	−0.436151	−	0.899874i	$-0.643659\pi$
$228$	−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	$0.437007\pi$
$233$	−8.22387	+	25.3105i	−0.538764	+	1.65814i	−0.735373	+	0.677662i	$0.762993\pi$
$234$	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	−0.766746	−	0.641951i	$-0.778125\pi$
$239$	−6.07798	+	4.41591i	−0.393152	+	0.285642i	0.373594	+	0.927592i	$0.378125\pi$
$240$	−10.1683	+	31.2949i	−0.656362	+	2.02008i
$241$	−27.4388			−1.76749			−0.883744	−	0.467971i	$-0.844985\pi$
$241$	−27.4388			−1.76749			−0.883744	+	0.467971i	$0.844985\pi$
$242$		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	$-0.456807\pi$
$263$	4.38774			0.270560			0.135280	+	0.990807i	$0.456807\pi$
$264$		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	0.254460	−	0.967083i	$-0.418102\pi$
$271$	−9.65763	−	7.01668i	−0.586659	−	0.426233i	−0.841119	+	0.540851i	$0.818102\pi$
$272$	−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	$0.428240\pi$
$277$	−8.82463	+	27.1594i	−0.530221	+	1.63185i	−0.753755	+	0.657155i	$0.771760\pi$
$278$	−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	$-0.955543\pi$
$281$	−4.54196	−	13.9787i	−0.270950	−	0.833900i	0.719312	−	0.694687i	$-0.244457\pi$
$282$	27.8446	+	20.2303i	1.65812	+	1.20470i
$283$	18.2349	−	13.2485i	1.08395	−	0.787539i	0.105586	−	0.994410i	$-0.466328\pi$
$283$	18.2349	−	13.2485i	1.08395	−	0.787539i	0.978368	+	0.206871i	$0.0663281\pi$
$284$	−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	0.909546	−	0.415603i	$-0.136430\pi$
$293$	13.6142	+	9.89128i	0.795349	+	0.577855i	−0.114197	+	0.993458i	$0.536430\pi$
$294$	−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	$-0.502165\pi$
$307$	−0.238354			−0.0136036			−0.00680179	+	0.999977i	$0.502165\pi$
$308$		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	0.625264	−	0.780413i	$-0.284991\pi$
$337$	1.40003	+	1.01718i	0.0762643	+	0.0554093i	−0.549000	+	0.835822i	$0.684991\pi$
$338$	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	0.925855	−	0.377879i	$-0.123347\pi$
$347$	−0.843646	−	2.59647i	−0.0452893	−	0.139386i	−0.971144	+	0.238493i	$0.923347\pi$
$348$	−1.49395	−	1.08542i	−0.0800843	−	0.0581846i
$349$	25.0037	−	18.1662i	1.33842	−	0.972417i	0.338916	−	0.940817i	$-0.389940\pi$
$349$	25.0037	−	18.1662i	1.33842	−	0.972417i	0.999501	−	0.0316002i	$-0.0100603\pi$
$350$	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	0.554947	−	0.831886i	$-0.312739\pi$
$359$	−1.22656	−	0.891145i	−0.0647351	−	0.0470328i	−0.619682	+	0.784853i	$0.712739\pi$
$360$	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	$-0.0979739\pi$
$373$	36.8111			1.90601			0.953004	+	0.302957i	$0.0979739\pi$
$374$		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	$-0.609203\pi$
$409$	9.89526	−	30.4545i	0.489289	−	1.50588i	0.825671	−	0.564151i	$-0.190797\pi$
$410$	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	−0.999823	−	0.0188109i	$-0.994012\pi$
$431$	−3.73466	+	11.4941i	−0.179892	+	0.553652i	0.819931	+	0.572463i	$0.194012\pi$
$432$	−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	$-0.473185\pi$
$439$	3.52592			0.168283			0.0841416	+	0.996454i	$0.473185\pi$
$440$		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	0.998929	−	0.0462679i	$-0.0147328\pi$
$457$	3.49700	+	10.7627i	0.163583	+	0.503456i	−0.835346	+	0.549724i	$0.814733\pi$
$458$	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	$-0.494968\pi$
$461$	0.678821			0.0316158			0.0158079	+	0.999875i	$0.494968\pi$
$462$		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	0.912365	−	0.409378i	$-0.134254\pi$
$479$	−1.45280	−	4.47126i	−0.0663801	−	0.204297i	−0.978745	+	0.205081i	$0.934254\pi$
$480$	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	0.455552	−	0.890209i	$-0.349442\pi$
$491$	−5.54657	−	4.02982i	−0.250313	−	0.181863i	−0.705866	+	0.708346i	$0.749442\pi$
$492$	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	−0.955804	−	0.294004i	$-0.905012\pi$
$503$	−21.7896	+	15.8311i	−0.971550	+	0.705872i	−0.0157457	+	0.999876i	$0.505012\pi$
$504$	−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	$-0.905973\pi$
$523$	−8.09171	−	24.9037i	−0.353826	−	1.08896i	0.602861	−	0.797846i	$-0.294027\pi$
$524$	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	$0.295067\pi$
$541$	−8.26823	+	25.4470i	−0.355479	+	1.09405i	−0.955731	+	0.294241i	$0.904933\pi$
$542$	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	$-0.237135\pi$
$547$	37.5854	−	27.3074i	1.60704	−	1.16758i	0.871934	−	0.489623i	$-0.162865\pi$
$548$	−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	0.994587	−	0.103909i	$-0.0331350\pi$
$557$	28.3944	+	20.6297i	1.20311	+	0.874109i	0.208521	+	0.978018i	$0.433135\pi$
$558$	−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	−0.875731	−	0.482800i	$-0.839620\pi$
$563$	2.76506	−	8.50997i	0.116533	−	0.358652i	0.992264	+	0.124148i	$0.0396197\pi$
$564$	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	−0.207434	−	0.978249i	$-0.566511\pi$
$569$	15.7157	−	11.4181i	0.658835	−	0.478672i	0.866269	+	0.499577i	$0.166511\pi$
$570$	−5.19212	+	15.9797i	−0.217474	+	0.669316i
$571$	−16.0171			−0.670295			−0.335148	−	0.942166i	$-0.608786\pi$
$571$	−16.0171			−0.670295			−0.335148	+	0.942166i	$0.608786\pi$
$572$		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	$-0.597002\pi$
$593$	−14.6132			−0.600092			−0.300046	+	0.953925i	$0.597002\pi$
$594$		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	0.423644	−	0.905829i	$-0.360751\pi$
$601$	−7.52465	−	5.46698i	−0.306937	−	0.223003i	−0.730581	+	0.682826i	$0.760751\pi$
$602$	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	−0.936833	−	0.349777i	$-0.886257\pi$
$607$	0.657191	−	2.02263i	0.0266746	−	0.0820959i	0.963508	+	0.267681i	$0.0862574\pi$
$608$	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	$0.609882\pi$
$613$	−33.1250	+	24.0667i	−1.33791	+	0.972046i	−0.999518	+	0.0310402i	$0.990118\pi$
$614$	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	$-0.370889\pi$
$659$	20.2587			0.789167			0.394584	+	0.918860i	$0.370889\pi$
$660$		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	$0.258272\pi$
$673$	−7.64767	+	23.5371i	−0.294796	+	0.907289i	−0.983290	+	0.182047i	$0.941728\pi$
$674$	−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	0.995618	−	0.0935140i	$-0.0298100\pi$
$677$	3.51728	+	10.8251i	0.135180	+	0.416041i	−0.860438	+	0.509555i	$0.829810\pi$
$678$	−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	−0.836051	−	0.548652i	$-0.815141\pi$
$701$	−15.1605	+	11.0148i	−0.572605	+	0.416022i	0.263446	+	0.964674i	$0.415141\pi$
$702$	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	0.922169	−	0.386788i	$-0.126416\pi$
$733$	22.7226	+	16.5089i	0.839277	+	0.609770i	−0.0828918	+	0.996559i	$0.526416\pi$
$734$	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	$-0.685730\pi$
$739$	10.4746	−	32.2375i	0.385314	−	1.18587i	0.936252	−	0.351329i	$-0.114270\pi$
$740$	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	0.977974	−	0.208728i	$-0.0669324\pi$
$743$	1.74694	+	5.37652i	0.0640890	+	0.197246i	−0.913885	+	0.405974i	$0.866932\pi$
$744$	−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	−0.922081	−	0.386996i	$-0.873513\pi$
$761$	1.41707	−	4.36129i	0.0513688	−	0.158097i	0.973450	+	0.228899i	$0.0735127\pi$
$762$	−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	$-0.574263\pi$
$769$	−12.8223			−0.462385			−0.231193	+	0.972908i	$0.574263\pi$
$770$		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	$0.185580\pi$
$787$	13.5508	+	41.7052i	0.483035	+	1.48663i	−0.351771	+	0.936086i	$0.614420\pi$
$788$	−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	$0.0814992\pi$
$809$	9.48893	+	29.2039i	0.333613	+	1.02676i	−0.633788	+	0.773507i	$0.718501\pi$
$810$	28.2588	+	20.5312i	0.992913	+	0.721394i
$811$	13.8329	−	10.0502i	0.485737	−	0.352909i	−0.317805	−	0.948156i	$-0.602946\pi$
$811$	13.8329	−	10.0502i	0.485737	−	0.352909i	0.803543	+	0.595247i	$0.202946\pi$
$812$	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	0.399095	−	0.916909i	$-0.369324\pi$
$821$	−10.0174	−	7.27807i	−0.349610	−	0.254006i	−0.748705	+	0.662903i	$0.769324\pi$
$822$	−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	$0.401696\pi$
$827$	−14.4343	+	44.4241i	−0.501929	+	1.54478i	−0.805873	+	0.592088i	$0.798304\pi$
$828$	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	$0.0865082\pi$
$853$	9.98146	+	30.7198i	0.341759	+	1.05182i	−0.621538	+	0.783384i	$0.713492\pi$
$854$	−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	$-0.589418\pi$
$857$	−16.2318			−0.554468			−0.277234	+	0.960802i	$0.589418\pi$
$858$		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	0.252817	−	0.967514i	$-0.418643\pi$
$877$	37.0504	−	26.9187i	1.25110	−	0.908979i	0.998285	+	0.0585353i	$0.0186430\pi$
$878$	−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	0.218896	−	0.975748i	$-0.429754\pi$
$887$	−19.1041	−	13.8799i	−0.641452	−	0.466042i	−0.860349	+	0.509706i	$0.829754\pi$
$888$	−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	$-0.944811\pi$
$919$	−8.77683	−	27.0123i	−0.289521	−	0.891053i	0.695486	−	0.718539i	$-0.255189\pi$
$920$	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	$0.365822\pi$
$937$	−14.0254	+	43.1657i	−0.458190	+	1.41016i	−0.867349	+	0.497700i	$0.834178\pi$
$938$	−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	$-0.985878\pi$
$941$	−6.65248	−	20.4742i	−0.216865	−	0.667441i	0.782151	−	0.623089i	$-0.214122\pi$
$942$	−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	0.229310	−	0.973353i	$-0.426353\pi$
$953$	−19.3109	−	14.0302i	−0.625543	−	0.454483i	−0.854853	+	0.518870i	$0.826353\pi$
$954$	−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	$-0.607009\pi$
$967$	−20.5165			−0.659765			−0.329882	+	0.944022i	$0.607009\pi$
$968$		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	0.944329	−	0.329002i	$-0.106712\pi$
$997$	29.1517	+	21.1800i	0.923244	+	0.670776i	−0.0210855	+	0.999778i	$0.506712\pi$
$998$	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.z.372.3		24
11.2	odd	10		847.2.f.y.729.3		24
11.3	even	5	inner	847.2.f.z.323.4		24
11.4	even	5		847.2.a.m.1.3	✓	6
11.5	even	5	inner	847.2.f.z.148.3		24
11.6	odd	10		847.2.f.y.148.4		24
11.7	odd	10		847.2.a.n.1.4	yes	6
11.8	odd	10		847.2.f.y.323.3		24
11.9	even	5	inner	847.2.f.z.729.4		24
11.10	odd	2		847.2.f.y.372.4		24
33.26	odd	10		7623.2.a.cs.1.4		6
33.29	even	10		7623.2.a.cp.1.3		6
77.48	odd	10		5929.2.a.bj.1.3		6
77.62	even	10		5929.2.a.bm.1.4		6

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