LMFDB - Embedded newform 1001.2.i.b.144.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1001,2,Mod(144,1001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1001, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("1001.144");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1001 = 7 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1001.i (of order $3$, degree $2$, 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:	$7.99302524233$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			144.1
Character	$\chi$	$=$	1001.144
Dual form			1001.2.i.b.716.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.20504 - 2.08720i) q^{2} +(-0.407005 + 0.704953i) q^{3} +(-1.90426 + 3.29827i) q^{4} +(0.841551 + 1.45761i) q^{5} +1.96183 q^{6} +(2.42416 - 1.05992i) q^{7} +4.35868 q^{8} +(1.16869 + 2.02424i) q^{9} +O(q^{10})$	\(q+(-1.20504 - 2.08720i) q^{2} +(-0.407005 + 0.704953i) q^{3} +(-1.90426 + 3.29827i) q^{4} +(0.841551 + 1.45761i) q^{5} +1.96183 q^{6} +(2.42416 - 1.05992i) q^{7} +4.35868 q^{8} +(1.16869 + 2.02424i) q^{9} +(2.02821 - 3.51297i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-1.55008 - 2.68483i) q^{12} -1.00000 q^{13} +(-5.13349 - 3.78245i) q^{14} -1.37006 q^{15} +(-1.44388 - 2.50088i) q^{16} +(0.0790708 - 0.136955i) q^{17} +(2.81665 - 4.87859i) q^{18} +(-1.95948 - 3.39391i) q^{19} -6.41013 q^{20} +(-0.239451 + 2.14031i) q^{21} -2.41009 q^{22} +(3.82253 + 6.62081i) q^{23} +(-1.77400 + 3.07267i) q^{24} +(1.08358 - 1.87682i) q^{25} +(1.20504 + 2.08720i) q^{26} -4.34469 q^{27} +(-1.12032 + 10.0139i) q^{28} -1.97099 q^{29} +(1.65098 + 2.85959i) q^{30} +(-4.41926 + 7.65439i) q^{31} +(0.878797 - 1.52212i) q^{32} +(0.407005 + 0.704953i) q^{33} -0.381135 q^{34} +(3.58501 + 2.64151i) q^{35} -8.90198 q^{36} +(4.95725 + 8.58621i) q^{37} +(-4.72251 + 8.17963i) q^{38} +(0.407005 - 0.704953i) q^{39} +(3.66806 + 6.35326i) q^{40} +8.48331 q^{41} +(4.75580 - 2.07939i) q^{42} -10.0332 q^{43} +(1.90426 + 3.29827i) q^{44} +(-1.96703 + 3.40700i) q^{45} +(9.21263 - 15.9567i) q^{46} +(0.891918 + 1.54485i) q^{47} +2.35067 q^{48} +(4.75313 - 5.13884i) q^{49} -5.22306 q^{50} +(0.0643644 + 0.111482i) q^{51} +(1.90426 - 3.29827i) q^{52} +(-2.18926 + 3.79191i) q^{53} +(5.23553 + 9.06821i) q^{54} +1.68310 q^{55} +(10.5662 - 4.61986i) q^{56} +3.19007 q^{57} +(2.37513 + 4.11385i) q^{58} +(7.52228 - 13.0290i) q^{59} +(2.60895 - 4.51884i) q^{60} +(4.93081 + 8.54042i) q^{61} +21.3016 q^{62} +(4.97864 + 3.66836i) q^{63} -10.0115 q^{64} +(-0.841551 - 1.45761i) q^{65} +(0.980917 - 1.69900i) q^{66} +(-6.63582 + 11.4936i) q^{67} +(0.301143 + 0.521594i) q^{68} -6.22315 q^{69} +(1.19325 - 10.6657i) q^{70} +6.99786 q^{71} +(5.09397 + 8.82301i) q^{72} +(4.56961 - 7.91480i) q^{73} +(11.9474 - 20.6935i) q^{74} +(0.882047 + 1.52775i) q^{75} +14.9254 q^{76} +(0.294163 - 2.62935i) q^{77} -1.96183 q^{78} +(3.96825 + 6.87321i) q^{79} +(2.43021 - 4.20924i) q^{80} +(-1.73777 + 3.00991i) q^{81} +(-10.2228 - 17.7063i) q^{82} +1.10233 q^{83} +(-6.60336 - 4.86549i) q^{84} +0.266169 q^{85} +(12.0904 + 20.9412i) q^{86} +(0.802204 - 1.38946i) q^{87} +(2.17934 - 3.77473i) q^{88} +(-1.25784 - 2.17865i) q^{89} +9.48144 q^{90} +(-2.42416 + 1.05992i) q^{91} -29.1163 q^{92} +(-3.59732 - 6.23075i) q^{93} +(2.14960 - 3.72322i) q^{94} +(3.29800 - 5.71230i) q^{95} +(0.715349 + 1.23902i) q^{96} +3.21045 q^{97} +(-16.4535 - 3.72819i) q^{98} +2.33739 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{2} - q^{3} - 6 q^{4} - 12 q^{6} + 15 q^{7} - 4 q^{9}+O(q^{10}) $ 22 * q + 2 * q^2 - q^3 - 6 * q^4 - 12 * q^6 + 15 * q^7 - 4 * q^9	\( 22 q + 2 q^{2} - q^{3} - 6 q^{4} - 12 q^{6} + 15 q^{7} - 4 q^{9} - 12 q^{10} + 11 q^{11} - 13 q^{12} - 22 q^{13} + 8 q^{14} + 30 q^{15} + 4 q^{16} + 2 q^{17} + 21 q^{18} - 9 q^{19} - 24 q^{20} - 9 q^{21} + 4 q^{22} + 27 q^{23} + 7 q^{24} + 7 q^{25} - 2 q^{26} - 4 q^{27} - 4 q^{28} + 42 q^{29} + 12 q^{30} + 2 q^{31} + 7 q^{32} + q^{33} - 20 q^{34} + 13 q^{35} + 48 q^{36} + 38 q^{37} - 9 q^{38} + q^{39} + 22 q^{40} + 6 q^{41} + 17 q^{42} - 46 q^{43} + 6 q^{44} + 6 q^{46} - 2 q^{47} + 24 q^{48} + 7 q^{49} + 14 q^{50} + 11 q^{51} + 6 q^{52} - 5 q^{53} + 37 q^{54} + 9 q^{56} - 44 q^{57} + 5 q^{58} + 16 q^{59} + 22 q^{60} - 11 q^{61} + 44 q^{62} - 16 q^{63} - 12 q^{64} - 6 q^{66} + 15 q^{67} - 12 q^{68} - 12 q^{69} + 7 q^{70} - 20 q^{71} + 32 q^{72} - 5 q^{73} + 20 q^{74} - 10 q^{75} + 14 q^{76} - 3 q^{77} + 12 q^{78} - 3 q^{79} + 21 q^{80} + 21 q^{81} - 4 q^{82} - 32 q^{83} + 32 q^{84} - 76 q^{85} + 15 q^{86} - 29 q^{87} - 8 q^{89} + 10 q^{90} - 15 q^{91} - 40 q^{92} + 40 q^{93} - 31 q^{94} + 23 q^{95} + 4 q^{96} - 14 q^{97} - 31 q^{98} - 8 q^{99}+O(q^{100}) \) 22 * q + 2 * q^2 - q^3 - 6 * q^4 - 12 * q^6 + 15 * q^7 - 4 * q^9 - 12 * q^10 + 11 * q^11 - 13 * q^12 - 22 * q^13 + 8 * q^14 + 30 * q^15 + 4 * q^16 + 2 * q^17 + 21 * q^18 - 9 * q^19 - 24 * q^20 - 9 * q^21 + 4 * q^22 + 27 * q^23 + 7 * q^24 + 7 * q^25 - 2 * q^26 - 4 * q^27 - 4 * q^28 + 42 * q^29 + 12 * q^30 + 2 * q^31 + 7 * q^32 + q^33 - 20 * q^34 + 13 * q^35 + 48 * q^36 + 38 * q^37 - 9 * q^38 + q^39 + 22 * q^40 + 6 * q^41 + 17 * q^42 - 46 * q^43 + 6 * q^44 + 6 * q^46 - 2 * q^47 + 24 * q^48 + 7 * q^49 + 14 * q^50 + 11 * q^51 + 6 * q^52 - 5 * q^53 + 37 * q^54 + 9 * q^56 - 44 * q^57 + 5 * q^58 + 16 * q^59 + 22 * q^60 - 11 * q^61 + 44 * q^62 - 16 * q^63 - 12 * q^64 - 6 * q^66 + 15 * q^67 - 12 * q^68 - 12 * q^69 + 7 * q^70 - 20 * q^71 + 32 * q^72 - 5 * q^73 + 20 * q^74 - 10 * q^75 + 14 * q^76 - 3 * q^77 + 12 * q^78 - 3 * q^79 + 21 * q^80 + 21 * q^81 - 4 * q^82 - 32 * q^83 + 32 * q^84 - 76 * q^85 + 15 * q^86 - 29 * q^87 - 8 * q^89 + 10 * q^90 - 15 * q^91 - 40 * q^92 + 40 * q^93 - 31 * q^94 + 23 * q^95 + 4 * q^96 - 14 * q^97 - 31 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1001\mathbb{Z}\right)^\times$.

$n$	$365$	$430$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−1.20504	−	2.08720i	−0.852094	−	1.47587i	−0.879315	−	0.476241i	$-0.841999\pi$
$2$	−1.20504	−	2.08720i	−0.852094	−	1.47587i	0.0272205	−	0.999629i	$-0.491334\pi$
$3$	−0.407005	+	0.704953i	−0.234984	+	0.407005i	−0.959268	−	0.282497i	$-0.908837\pi$
$3$	−0.407005	+	0.704953i	−0.234984	+	0.407005i	0.724284	+	0.689502i	$0.242171\pi$
$4$	−1.90426	+	3.29827i	−0.952129	+	1.64914i
$5$	0.841551	+	1.45761i	0.376353	+	0.651863i	0.990529	−	0.137307i	$-0.0438446\pi$
$5$	0.841551	+	1.45761i	0.376353	+	0.651863i	−0.614175	+	0.789170i	$0.710511\pi$
$6$	1.96183			0.800915
$7$	2.42416	−	1.05992i	0.916248	−	0.400613i
$7$	2.42416	−	1.05992i	0.916248	−	0.400613i
$8$	4.35868			1.54103
$9$	1.16869	+	2.02424i	0.389565	+	0.674746i
$10$	2.02821	−	3.51297i	0.641377	−	1.11090i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$11$	0.500000	−	0.866025i	0.150756	−	0.261116i
$12$	−1.55008	−	2.68483i	−0.447471	−	0.775042i
$13$	−1.00000			−0.277350
$13$	−1.00000			−0.277350
$14$	−5.13349	−	3.78245i	−1.37198	−	1.01090i
$15$	−1.37006			−0.353748
$16$	−1.44388	−	2.50088i	−0.360971	−	0.625220i
$17$	0.0790708	−	0.136955i	0.0191775	−	0.0332164i	−0.856277	−	0.516516i	$-0.827229\pi$
$17$	0.0790708	−	0.136955i	0.0191775	−	0.0332164i	0.875455	+	0.483300i	$0.160562\pi$
$18$	2.81665	−	4.87859i	0.663892	−	1.14989i
$19$	−1.95948	−	3.39391i	−0.449535	−	0.778617i	0.548821	−	0.835940i	$-0.315077\pi$
$19$	−1.95948	−	3.39391i	−0.449535	−	0.778617i	−0.998356	+	0.0573228i	$0.981744\pi$
$20$	−6.41013			−1.43335
$21$	−0.239451	+	2.14031i	−0.0522525	+	0.467055i
$22$	−2.41009			−0.513832
$23$	3.82253	+	6.62081i	0.797052	+	1.38054i	0.921528	+	0.388313i	$0.126942\pi$
$23$	3.82253	+	6.62081i	0.797052	+	1.38054i	−0.124475	+	0.992223i	$0.539725\pi$
$24$	−1.77400	+	3.07267i	−0.362117	+	0.627205i
$25$	1.08358	−	1.87682i	0.216717	−	0.375364i
$26$	1.20504	+	2.08720i	0.236328	+	0.409333i
$27$	−4.34469			−0.836135
$28$	−1.12032	+	10.0139i	−0.211721	+	1.89245i
$29$	−1.97099			−0.366005			−0.183002	−	0.983112i	$-0.558582\pi$
$29$	−1.97099			−0.366005			−0.183002	+	0.983112i	$0.558582\pi$
$30$	1.65098	+	2.85959i	0.301427	+	0.522087i
$31$	−4.41926	+	7.65439i	−0.793723	+	1.37477i	0.129923	+	0.991524i	$0.458527\pi$
$31$	−4.41926	+	7.65439i	−0.793723	+	1.37477i	−0.923647	+	0.383245i	$0.874806\pi$
$32$	0.878797	−	1.52212i	0.155351	−	0.269076i
$33$	0.407005	+	0.704953i	0.0708504	+	0.122717i
$34$	−0.381135			−0.0653641
$35$	3.58501	+	2.64151i	0.605977	+	0.446496i
$36$	−8.90198			−1.48366
$37$	4.95725	+	8.58621i	0.814967	+	1.41156i	0.909352	+	0.416028i	$0.136578\pi$
$37$	4.95725	+	8.58621i	0.814967	+	1.41156i	−0.0943853	+	0.995536i	$0.530089\pi$
$38$	−4.72251	+	8.17963i	−0.766092	+	1.32691i
$39$	0.407005	−	0.704953i	0.0651729	−	0.112883i
$40$	3.66806	+	6.35326i	0.579970	+	1.00454i
$41$	8.48331			1.32487			0.662435	−	0.749119i	$-0.269523\pi$
$41$	8.48331			1.32487			0.662435	+	0.749119i	$0.269523\pi$
$42$	4.75580	−	2.07939i	0.733837	−	0.320857i
$43$	−10.0332			−1.53004			−0.765021	−	0.644005i	$-0.777271\pi$
$43$	−10.0332			−1.53004			−0.765021	+	0.644005i	$0.777271\pi$
$44$	1.90426	+	3.29827i	0.287078	+	0.497233i
$45$	−1.96703	+	3.40700i	−0.293228	+	0.507886i
$46$	9.21263	−	15.9567i	1.35833	−	2.35269i
$47$	0.891918	+	1.54485i	0.130100	+	0.225339i	0.923715	−	0.383081i	$-0.125137\pi$
$47$	0.891918	+	1.54485i	0.130100	+	0.225339i	−0.793615	+	0.608420i	$0.791804\pi$
$48$	2.35067			0.339290
$49$	4.75313	−	5.13884i	0.679019	−	0.734121i
$50$	−5.22306			−0.738652
$51$	0.0643644	+	0.111482i	0.00901282	+	0.0156107i
$52$	1.90426	−	3.29827i	0.264073	−	0.457388i
$53$	−2.18926	+	3.79191i	−0.300718	+	0.520859i	−0.976299	−	0.216427i	$-0.930560\pi$
$53$	−2.18926	+	3.79191i	−0.300718	+	0.520859i	0.675581	+	0.737286i	$0.263893\pi$
$54$	5.23553	+	9.06821i	0.712466	+	1.23403i
$55$	1.68310			0.226950
$56$	10.5662	−	4.61986i	1.41196	−	0.617355i
$57$	3.19007			0.422535
$58$	2.37513	+	4.11385i	0.311870	+	0.540175i
$59$	7.52228	−	13.0290i	0.979317	−	1.69623i	0.314435	−	0.949279i	$-0.398185\pi$
$59$	7.52228	−	13.0290i	0.979317	−	1.69623i	0.664882	−	0.746948i	$-0.268482\pi$
$60$	2.60895	−	4.51884i	0.336814	−	0.583379i
$61$	4.93081	+	8.54042i	0.631326	+	1.09349i	0.987281	+	0.158985i	$0.0508223\pi$
$61$	4.93081	+	8.54042i	0.631326	+	1.09349i	−0.355955	+	0.934503i	$0.615844\pi$
$62$	21.3016			2.70531
$63$	4.97864	+	3.66836i	0.627249	+	0.462170i
$64$	−10.0115			−1.25144
$65$	−0.841551	−	1.45761i	−0.104382	−	0.180794i
$66$	0.980917	−	1.69900i	0.120743	−	0.209132i
$67$	−6.63582	+	11.4936i	−0.810694	+	1.40416i	0.101685	+	0.994817i	$0.467577\pi$
$67$	−6.63582	+	11.4936i	−0.810694	+	1.40416i	−0.912379	+	0.409347i	$0.865757\pi$
$68$	0.301143	+	0.521594i	0.0365189	+	0.0632526i
$69$	−6.22315			−0.749179
$70$	1.19325	−	10.6657i	0.142620	−	1.27480i
$71$	6.99786			0.830493			0.415247	−	0.909709i	$-0.363695\pi$
$71$	6.99786			0.830493			0.415247	+	0.909709i	$0.363695\pi$
$72$	5.09397	+	8.82301i	0.600330	+	1.03980i
$73$	4.56961	−	7.91480i	0.534832	−	0.926357i	−0.464339	−	0.885657i	$-0.653708\pi$
$73$	4.56961	−	7.91480i	0.534832	−	0.926357i	0.999171	−	0.0406993i	$-0.0129586\pi$
$74$	11.9474	−	20.6935i	1.38886	−	2.40557i
$75$	0.882047	+	1.52775i	0.101850	+	0.176409i
$76$	14.9254			1.71206
$77$	0.294163	−	2.62935i	0.0335229	−	0.299642i
$78$	−1.96183			−0.222134
$79$	3.96825	+	6.87321i	0.446463	+	0.773296i	0.998153	−	0.0607530i	$-0.0193502\pi$
$79$	3.96825	+	6.87321i	0.446463	+	0.773296i	−0.551690	+	0.834049i	$0.686017\pi$
$80$	2.43021	−	4.20924i	0.271705	−	0.470607i
$81$	−1.73777	+	3.00991i	−0.193086	+	0.334435i
$82$	−10.2228	−	17.7063i	−1.12891	−	1.95534i
$83$	1.10233			0.120997			0.0604983	−	0.998168i	$-0.480731\pi$
$83$	1.10233			0.120997			0.0604983	+	0.998168i	$0.480731\pi$
$84$	−6.60336	−	4.86549i	−0.720486	−	0.530868i
$85$	0.266169			0.0288700
$86$	12.0904	+	20.9412i	1.30374	+	2.25814i
$87$	0.802204	−	1.38946i	0.0860053	−	0.148966i
$88$	2.17934	−	3.77473i	0.232319	−	0.402388i
$89$	−1.25784	−	2.17865i	−0.133331	−	0.230936i	0.791628	−	0.611004i	$-0.209234\pi$
$89$	−1.25784	−	2.17865i	−0.133331	−	0.230936i	−0.924959	+	0.380068i	$0.875901\pi$
$90$	9.48144			0.999431
$91$	−2.42416	+	1.05992i	−0.254121	+	0.111110i
$92$	−29.1163			−3.03559
$93$	−3.59732	−	6.23075i	−0.373025	−	0.646098i
$94$	2.14960	−	3.72322i	0.221714	−	0.384020i
$95$	3.29800	−	5.71230i	0.338368	−	0.586070i
$96$	0.715349	+	1.23902i	0.0730100	+	0.126457i
$97$	3.21045			0.325972			0.162986	−	0.986628i	$-0.447887\pi$
$97$	3.21045			0.325972			0.162986	+	0.986628i	$0.447887\pi$
$98$	−16.4535	−	3.72819i	−1.66206	−	0.376604i
$99$	2.33739			0.234916
$100$	4.12684	+	7.14790i	0.412684	+	0.714790i
$101$	2.35176	−	4.07336i	0.234009	−	0.405315i	−0.724976	−	0.688775i	$-0.758149\pi$
$101$	2.35176	−	4.07336i	0.234009	−	0.405315i	0.958984	+	0.283460i	$0.0914823\pi$
$102$	0.155124	−	0.268682i	0.0153595	−	0.0266035i
$103$	8.09853	+	14.0271i	0.797972	+	1.38213i	0.920935	+	0.389716i	$0.127427\pi$
$103$	8.09853	+	14.0271i	0.797972	+	1.38213i	−0.122963	+	0.992411i	$0.539240\pi$
$104$	−4.35868			−0.427404
$105$	−3.32125	+	1.45216i	−0.324121	+	0.141716i
$106$	10.5526			1.02496
$107$	−9.10080	−	15.7630i	−0.879807	−	1.52387i	−0.851552	−	0.524270i	$-0.824338\pi$
$107$	−9.10080	−	15.7630i	−0.879807	−	1.52387i	−0.0282556	−	0.999601i	$-0.508995\pi$
$108$	8.27340	−	14.3300i	0.796109	−	1.37890i
$109$	−3.94463	+	6.83231i	−0.377827	+	0.654416i	−0.990746	−	0.135730i	$-0.956662\pi$
$109$	−3.94463	+	6.83231i	−0.377827	+	0.654416i	0.612919	+	0.790146i	$0.289995\pi$
$110$	−2.02821	−	3.51297i	−0.193382	−	0.334948i
$111$	−8.07050			−0.766018
$112$	−6.15095	−	4.53214i	−0.581210	−	0.428247i
$113$	−7.28418			−0.685238			−0.342619	−	0.939474i	$-0.611314\pi$
$113$	−7.28418			−0.685238			−0.342619	+	0.939474i	$0.611314\pi$
$114$	−3.84417	−	6.65829i	−0.360039	−	0.623606i
$115$	−6.43371	+	11.1435i	−0.599946	+	1.03914i
$116$	3.75328	−	6.50088i	0.348484	−	0.603591i
$117$	−1.16869	−	2.02424i	−0.108046	−	0.187141i
$118$	−36.2587			−3.33788
$119$	0.0465194	−	0.415809i	0.00426442	−	0.0381172i
$120$	−5.97166			−0.545136
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	11.8837	−	20.5831i	1.07590	−	1.86351i
$123$	−3.45275	+	5.98033i	−0.311324	+	0.539229i
$124$	−16.8308	−	29.1519i	−1.51145	−	2.61792i
$125$	12.0631			1.07895
$126$	1.65711	−	14.8119i	0.147627	−	1.31955i
$127$	−8.76759			−0.777998			−0.388999	−	0.921238i	$-0.627179\pi$
$127$	−8.76759			−0.777998			−0.388999	+	0.921238i	$0.627179\pi$
$128$	10.3067	+	17.8517i	0.910991	+	1.57788i
$129$	4.08354	−	7.07290i	0.359536	−	0.622734i
$130$	−2.02821	+	3.51297i	−0.177886	+	0.308107i
$131$	2.41678	+	4.18599i	0.211155	+	0.365731i	0.952076	−	0.305861i	$-0.0989442\pi$
$131$	2.41678	+	4.18599i	0.211155	+	0.365731i	−0.740921	+	0.671592i	$0.765611\pi$
$132$	−3.10017			−0.269835
$133$	−8.34737	−	6.15051i	−0.723809	−	0.533317i
$134$	31.9858			2.76315
$135$	−3.65628	−	6.33286i	−0.314682	−	0.545045i
$136$	0.344645	−	0.596942i	0.0295530	−	0.0511874i
$137$	8.89537	−	15.4072i	0.759982	−	1.31633i	−0.182877	−	0.983136i	$-0.558541\pi$
$137$	8.89537	−	15.4072i	0.759982	−	1.31633i	0.942859	−	0.333192i	$-0.108126\pi$
$138$	7.49917	+	12.9889i	0.638371	+	1.10569i
$139$	2.43852			0.206832			0.103416	−	0.994638i	$-0.467023\pi$
$139$	2.43852			0.206832			0.103416	+	0.994638i	$0.467023\pi$
$140$	−15.5392	+	6.79423i	−1.31330	+	0.574217i
$141$	−1.45206			−0.122286
$142$	−8.43273	−	14.6059i	−0.707659	−	1.22570i
$143$	−0.500000	+	0.866025i	−0.0418121	+	0.0724207i
$144$	3.37492	−	5.84553i	0.281243	−	0.487127i
$145$	−1.65869	−	2.87294i	−0.137747	−	0.238585i
$146$	−22.0263			−1.82291
$147$	1.68810	+	5.44227i	0.139232	+	0.448871i
$148$	−37.7595			−3.10381
$149$	11.7203	+	20.3002i	0.960166	+	1.66306i	0.722076	+	0.691814i	$0.243188\pi$
$149$	11.7203	+	20.3002i	0.960166	+	1.66306i	0.238090	+	0.971243i	$0.423479\pi$
$150$	2.12581	−	3.68201i	0.173572	−	0.300635i
$151$	−10.1365	+	17.5570i	−0.824900	+	1.42877i	0.0770958	+	0.997024i	$0.475435\pi$
$151$	−10.1365	+	17.5570i	−0.824900	+	1.42877i	−0.901996	+	0.431745i	$0.857898\pi$
$152$	−8.54074	−	14.7930i	−0.692745	−	1.19987i
$153$	0.369638			0.0298835
$154$	−5.84244	+	2.55450i	−0.470797	+	0.205848i
$155$	−14.8762			−1.19488
$156$	1.55008	+	2.68483i	0.124106	+	0.214958i
$157$	−1.13499	+	1.96586i	−0.0905818	+	0.156892i	−0.907756	−	0.419498i	$-0.862206\pi$
$157$	−1.13499	+	1.96586i	−0.0905818	+	0.156892i	0.817174	+	0.576391i	$0.195539\pi$
$158$	9.56382	−	16.5650i	0.760857	−	1.31784i
$159$	−1.78208	−	3.08665i	−0.141328	−	0.244787i
$160$	2.95821			0.233867
$161$	16.2840	+	11.9984i	1.28336	+	0.945603i
$162$	8.37637			0.658110
$163$	2.56168	+	4.43696i	0.200646	+	0.347530i	0.948737	−	0.316067i	$-0.102362\pi$
$163$	2.56168	+	4.43696i	0.200646	+	0.347530i	−0.748090	+	0.663597i	$0.769029\pi$
$164$	−16.1544	+	27.9803i	−1.26145	+	2.18489i
$165$	−0.685031	+	1.18651i	−0.0533296	+	0.0923696i
$166$	−1.32836	−	2.30078i	−0.103101	−	0.178575i
$167$	16.7949			1.29963			0.649814	−	0.760093i	$-0.274847\pi$
$167$	16.7949			1.29963			0.649814	+	0.760093i	$0.274847\pi$
$168$	−1.04369	+	9.32895i	−0.0805226	+	0.719744i
$169$	1.00000			0.0769231
$170$	−0.320745	−	0.555546i	−0.0246000	−	0.0426084i
$171$	4.58006	−	7.93289i	0.350246	−	0.606644i
$172$	19.1057	−	33.0921i	1.45680	−	2.52325i
$173$	−2.64502	−	4.58131i	−0.201097	−	0.348310i	0.747785	−	0.663941i	$-0.231117\pi$
$173$	−2.64502	−	4.58131i	−0.201097	−	0.348310i	−0.948882	+	0.315630i	$0.897784\pi$
$174$	−3.86676			−0.293139
$175$	0.637499	−	5.69823i	0.0481904	−	0.430746i
$176$	−2.88777			−0.217674
$177$	6.12321	+	10.6057i	0.460248	+	0.797174i
$178$	−3.03151	+	5.25072i	−0.227221	+	0.393558i
$179$	6.69629	−	11.5983i	0.500504	−	0.866899i	−0.499495	−	0.866317i	$-0.666481\pi$
$179$	6.69629	−	11.5983i	0.500504	−	0.866899i	1.00000		0.000582634i	$-0.000185458\pi$
$180$	−7.49148	−	12.9756i	−0.558382	−	0.967145i
$181$	25.6516			1.90667			0.953333	−	0.301921i	$-0.0976279\pi$
$181$	25.6516			1.90667			0.953333	+	0.301921i	$0.0976279\pi$
$182$	5.13349	+	3.78245i	0.380519	+	0.280374i
$183$	−8.02746			−0.593407
$184$	16.6612	+	28.8580i	1.22828	+	2.12744i
$185$	−8.34356	+	14.4515i	−0.613431	+	1.06249i
$186$	−8.66986	+	15.0166i	−0.635705	+	1.10107i
$187$	−0.0790708	−	0.136955i	−0.00578223	−	0.0100151i
$188$	−6.79377			−0.495487
$189$	−10.5322	+	4.60503i	−0.766107	+	0.334966i
$190$	−15.8969			−1.15328
$191$	−7.27417	−	12.5992i	−0.526340	−	0.911648i	−0.999529	−	0.0306869i	$-0.990231\pi$
$191$	−7.27417	−	12.5992i	−0.526340	−	0.911648i	0.473189	−	0.880961i	$-0.343103\pi$
$192$	4.07473	−	7.05763i	0.294068	−	0.509341i
$193$	−7.63500	+	13.2242i	−0.549579	+	0.951899i	0.448724	+	0.893670i	$0.351879\pi$
$193$	−7.63500	+	13.2242i	−0.549579	+	0.951899i	−0.998303	+	0.0582287i	$0.981455\pi$
$194$	−3.86873	−	6.70084i	−0.277759	−	0.481092i
$195$	1.37006			0.0981122
$196$	7.89812	+	25.4628i	0.564151	+	1.81877i
$197$	0.582587			0.0415076			0.0207538	−	0.999785i	$-0.493393\pi$
$197$	0.582587			0.0415076			0.0207538	+	0.999785i	$0.493393\pi$
$198$	−2.81665	−	4.87859i	−0.200171	−	0.346706i
$199$	10.8033	−	18.7118i	0.765823	−	1.32644i	−0.173988	−	0.984748i	$-0.555665\pi$
$199$	10.8033	−	18.7118i	0.765823	−	1.32644i	0.939811	−	0.341696i	$-0.111001\pi$
$200$	4.72299	−	8.18046i	0.333966	−	0.578446i
$201$	−5.40162	−	9.35588i	−0.381001	−	0.659913i
$202$	−11.3359			−0.797589
$203$	−4.77801	+	2.08910i	−0.335351	+	0.146626i
$204$	−0.490266			−0.0343255
$205$	7.13914	+	12.3654i	0.498619	+	0.863634i
$206$	19.5182	−	33.8064i	1.35989	−	2.35541i
$207$	−8.93473	+	15.4754i	−0.621007	+	1.07562i
$208$	1.44388	+	2.50088i	0.100115	+	0.173405i
$209$	−3.91895			−0.271080
$210$	7.03319	+	5.18219i	0.485336	+	0.357605i
$211$	−13.8722			−0.955002			−0.477501	−	0.878631i	$-0.658457\pi$
$211$	−13.8722			−0.955002			−0.477501	+	0.878631i	$0.658457\pi$
$212$	−8.33783	−	14.4415i	−0.572645	−	0.991849i
$213$	−2.84816	+	4.93316i	−0.195153	+	0.338015i
$214$	−21.9337	+	37.9903i	−1.49936	+	2.59696i
$215$	−8.44341	−	14.6244i	−0.575836	−	0.997377i
$216$	−18.9371			−1.28851
$217$	−2.59997	+	23.2396i	−0.176497	+	1.57760i
$218$	19.0138			1.28778
$219$	3.71971	+	6.44272i	0.251354	+	0.435359i
$220$	−3.20506	+	5.55133i	−0.216085	+	0.374271i
$221$	−0.0790708	+	0.136955i	−0.00531888	+	0.00921257i
$222$	9.72530	+	16.8447i	0.652719	+	1.13054i
$223$	−7.23294			−0.484353			−0.242177	−	0.970232i	$-0.577861\pi$
$223$	−7.23294			−0.484353			−0.242177	+	0.970232i	$0.577861\pi$
$224$	0.517019	−	4.62133i	0.0345448	−	0.308775i
$225$	5.06551			0.337700
$226$	8.77775	+	15.2035i	0.583887	+	1.01132i
$227$	−8.74618	+	15.1488i	−0.580504	+	1.00546i	0.414915	+	0.909860i	$0.363811\pi$
$227$	−8.74618	+	15.1488i	−0.580504	+	1.00546i	−0.995420	+	0.0956028i	$0.969522\pi$
$228$	−6.07471	+	10.5217i	−0.402308	+	0.696817i
$229$	−6.21258	−	10.7605i	−0.410539	−	0.711074i	0.584410	−	0.811459i	$-0.301326\pi$
$229$	−6.21258	−	10.7605i	−0.410539	−	0.711074i	−0.994949	+	0.100384i	$0.967993\pi$
$230$	31.0116			2.04484
$231$	1.73384	+	1.27753i	0.114078	+	0.0840552i
$232$	−8.59094			−0.564023
$233$	−1.12172	−	1.94287i	−0.0734860	−	0.127282i	0.826941	−	0.562289i	$-0.190079\pi$
$233$	−1.12172	−	1.94287i	−0.0734860	−	0.127282i	−0.900427	+	0.435007i	$0.856746\pi$
$234$	−2.81665	+	4.87859i	−0.184130	+	0.318923i
$235$	−1.50119	+	2.60014i	−0.0979268	+	0.169614i
$236$	28.6487	+	49.6210i	1.86487	+	3.23005i
$237$	−6.46038			−0.419647
$238$	−0.923934	+	0.403973i	−0.0598897	+	0.0261857i
$239$	−7.15162			−0.462600			−0.231300	−	0.972883i	$-0.574298\pi$
$239$	−7.15162			−0.462600			−0.231300	+	0.972883i	$0.574298\pi$
$240$	1.97821	+	3.42636i	0.127693	+	0.221171i
$241$	7.84978	−	13.5962i	0.505649	−	0.875810i	−0.494330	−	0.869275i	$-0.664586\pi$
$241$	7.84978	−	13.5962i	0.505649	−	0.875810i	0.999979	−	0.00653521i	$-0.00208024\pi$
$242$	−1.20504	+	2.08720i	−0.0774631	+	0.134170i
$243$	−7.93159	−	13.7379i	−0.508812	−	0.881288i
$244$	−37.5582			−2.40442
$245$	11.4904	+	2.60361i	0.734097	+	0.166339i
$246$	16.6428			1.06111
$247$	1.95948	+	3.39391i	0.124679	+	0.215950i
$248$	−19.2622	+	33.3631i	−1.22315	+	2.11856i
$249$	−0.448654	+	0.777092i	−0.0284323	+	0.0492462i
$250$	−14.5365	−	25.1780i	−0.919371	−	1.59240i
$251$	13.5971			0.858241			0.429120	−	0.903247i	$-0.358824\pi$
$251$	13.5971			0.858241			0.429120	+	0.903247i	$0.358824\pi$
$252$	−21.5799	+	9.43540i	−1.35940	+	0.594374i
$253$	7.64506			0.480641
$254$	10.5653	+	18.2997i	0.662928	+	1.14822i
$255$	−0.108332	+	0.187636i	−0.00678401	+	0.0117502i
$256$	14.8285	−	25.6837i	0.926782	−	1.60523i
$257$	10.1856	+	17.6419i	0.635358	+	1.10047i	0.986439	+	0.164127i	$0.0524806\pi$
$257$	10.1856	+	17.6419i	0.635358	+	1.10047i	−0.351082	+	0.936345i	$0.614186\pi$
$258$	−19.6834			−1.22543
$259$	21.1179	+	15.5601i	1.31220	+	0.966856i
$260$	6.41013			0.397539
$261$	−2.30349	−	3.98976i	−0.142582	−	0.246960i
$262$	5.82465	−	10.0886i	0.359848	−	0.623275i
$263$	−6.52275	+	11.2977i	−0.402210	+	0.696648i	−0.993992	−	0.109450i	$-0.965091\pi$
$263$	−6.52275	+	11.2977i	−0.402210	+	0.696648i	0.591783	+	0.806098i	$0.298424\pi$
$264$	1.77400	+	3.07267i	0.109182	+	0.189110i
$265$	−7.36950			−0.452704
$266$	−2.77837	+	24.8342i	−0.170353	+	1.52268i
$267$	2.04779			0.125323
$268$	−25.2726	−	43.7735i	−1.54377	−	2.67389i
$269$	−13.7569	+	23.8277i	−0.838774	+	1.45280i	0.0521457	+	0.998639i	$0.483394\pi$
$269$	−13.7569	+	23.8277i	−0.838774	+	1.45280i	−0.890920	+	0.454160i	$0.849939\pi$
$270$	−8.81194	+	15.2627i	−0.536278	+	0.928860i
$271$	−3.57708	−	6.19568i	−0.217292	−	0.376361i	0.736687	−	0.676234i	$-0.236389\pi$
$271$	−3.57708	−	6.19568i	−0.217292	−	0.376361i	−0.953979	+	0.299873i	$0.903056\pi$
$272$	−0.456676			−0.0276901
$273$	0.239451	−	2.14031i	0.0144922	−	0.129538i
$274$	−42.8772			−2.59031
$275$	−1.08358	−	1.87682i	−0.0653425	−	0.113177i
$276$	11.8505	−	20.5256i	0.713316	−	1.23550i
$277$	2.02719	−	3.51119i	0.121802	−	0.210967i	−0.798676	−	0.601761i	$-0.794466\pi$
$277$	2.02719	−	3.51119i	0.121802	−	0.210967i	0.920478	+	0.390794i	$0.127799\pi$
$278$	−2.93852	−	5.08966i	−0.176241	−	0.305258i
$279$	−20.6591			−1.23683
$280$	15.6259	+	11.5135i	0.933827	+	0.688062i
$281$	1.76950			0.105559			0.0527796	−	0.998606i	$-0.483192\pi$
$281$	1.76950			0.105559			0.0527796	+	0.998606i	$0.483192\pi$
$282$	1.74980	+	3.03073i	0.104199	+	0.180478i
$283$	6.59157	−	11.4169i	0.391828	−	0.678666i	−0.600863	−	0.799352i	$-0.705176\pi$
$283$	6.59157	−	11.4169i	0.391828	−	0.678666i	0.992691	+	0.120686i	$0.0385095\pi$
$284$	−13.3257	+	23.0809i	−0.790737	+	1.36960i
$285$	2.68460	+	4.64987i	0.159022	+	0.275435i
$286$	2.41009			0.142511
$287$	20.5649	−	8.99164i	1.21391	−	0.530760i
$288$	4.10818			0.242077
$289$	8.48750	+	14.7008i	0.499264	+	0.864751i
$290$	−3.99759	+	6.92404i	−0.234747	+	0.406593i
$291$	−1.30667	+	2.26322i	−0.0765983	+	0.132672i
$292$	17.4034	+	30.1436i	1.01846	+	1.76402i
$293$	−10.8157			−0.631860			−0.315930	−	0.948782i	$-0.602316\pi$
$293$	−10.8157			−0.631860			−0.315930	+	0.948782i	$0.602316\pi$
$294$	9.32486	−	10.0816i	0.543837	−	0.587968i
$295$	25.3215			1.47428
$296$	21.6071	+	37.4245i	1.25589	+	2.17526i
$297$	−2.17234	+	3.76261i	−0.126052	+	0.218329i
$298$	28.2470	−	48.9252i	1.63630	−	2.83416i
$299$	−3.82253	−	6.62081i	−0.221063	−	0.382892i
$300$	−6.71858			−0.387897
$301$	−24.3220	+	10.6344i	−1.40190	+	0.612954i
$302$	48.8599			2.81157
$303$	1.91435	+	3.31576i	0.109977	+	0.190485i
$304$	−5.65851	+	9.80083i	−0.324538	+	0.562116i
$305$	−8.29906	+	14.3744i	−0.475203	+	0.823076i
$306$	−0.445430	−	0.771508i	−0.0254636	−	0.0441042i
$307$	−23.6341			−1.34887			−0.674434	−	0.738335i	$-0.735612\pi$
$307$	−23.6341			−1.34887			−0.674434	+	0.738335i	$0.735612\pi$
$308$	8.11214	+	5.97719i	0.462232	+	0.340582i
$309$	−13.1846			−0.750043
$310$	17.9264	+	31.0494i	1.01815	+	1.76349i
$311$	8.25552	−	14.2990i	0.468128	−	0.810821i	−0.531209	−	0.847241i	$-0.678262\pi$
$311$	8.25552	−	14.2990i	0.468128	−	0.810821i	0.999337	+	0.0364201i	$0.0115954\pi$
$312$	1.77400	−	3.07267i	0.100433	−	0.173955i
$313$	−10.4828	−	18.1568i	−0.592523	−	1.02628i	−0.993891	−	0.110364i	$-0.964798\pi$
$313$	−10.4828	−	18.1568i	−0.592523	−	1.02628i	0.401368	−	0.915917i	$-0.368535\pi$
$314$	5.47083			0.308737
$315$	−1.15725	+	10.3440i	−0.0652039	+	0.582820i
$316$	−30.2263			−1.70036
$317$	−7.41586	−	12.8447i	−0.416516	−	0.721428i	0.579070	−	0.815278i	$-0.303416\pi$
$317$	−7.41586	−	12.8447i	−0.416516	−	0.721428i	−0.995586	+	0.0938502i	$0.970083\pi$
$318$	−4.29496	+	7.43909i	−0.240850	+	0.417164i
$319$	−0.985497	+	1.70693i	−0.0551773	+	0.0955698i
$320$	−8.42518	−	14.5928i	−0.470982	−	0.815765i
$321$	14.8163			0.826964
$322$	5.42002	−	48.4464i	0.302046	−	2.69981i
$323$	−0.619750			−0.0344838
$324$	−6.61834	−	11.4633i	−0.367686	−	0.636850i
$325$	−1.08358	+	1.87682i	−0.0601064	+	0.104107i
$326$	6.17388	−	10.6935i	0.341939	−	0.592256i
$327$	−3.21097	−	5.56156i	−0.177567	−	0.307555i
$328$	36.9760			2.04166
$329$	3.79957	+	2.79960i	0.209477	+	0.154347i
$330$	3.30197			0.181767
$331$	−9.75395	−	16.8943i	−0.536126	−	0.928597i	−0.999108	−	0.0422292i	$-0.986554\pi$
$331$	−9.75395	−	16.8943i	−0.536126	−	0.928597i	0.462982	−	0.886367i	$-0.346779\pi$
$332$	−2.09912	+	3.63579i	−0.115204	+	0.199540i
$333$	−11.5870	+	20.0693i	−0.634964	+	1.09979i
$334$	−20.2386	−	35.0542i	−1.10741	−	1.91808i
$335$	−22.3375			−1.22043
$336$	5.69841	−	2.49153i	0.310874	−	0.135924i
$337$	−27.3278			−1.48864			−0.744320	−	0.667823i	$-0.767226\pi$
$337$	−27.3278			−1.48864			−0.744320	+	0.667823i	$0.767226\pi$
$338$	−1.20504	−	2.08720i	−0.0655457	−	0.113529i
$339$	2.96470	−	5.13500i	0.161020	−	0.278895i
$340$	−0.506854	+	0.877897i	−0.0274880	+	0.0476106i
$341$	4.41926	+	7.65439i	0.239317	+	0.414508i
$342$	−22.0767			−1.19377
$343$	6.07560	−	17.4953i	0.328051	−	0.944660i
$344$	−43.7313			−2.35784
$345$	−5.23710	−	9.07093i	−0.281956	−	0.488362i
$346$	−6.37473	+	11.0413i	−0.342707	+	0.593587i
$347$	17.1984	−	29.7886i	0.923261	−	1.59913i	0.128926	−	0.991654i	$-0.458847\pi$
$347$	17.1984	−	29.7886i	0.923261	−	1.59913i	0.794335	−	0.607480i	$-0.207820\pi$
$348$	3.05521	+	5.29178i	0.163776	+	0.283669i
$349$	−6.08961			−0.325969			−0.162985	−	0.986629i	$-0.552112\pi$
$349$	−6.08961			−0.325969			−0.162985	+	0.986629i	$0.552112\pi$
$350$	−12.6615	+	5.53603i	−0.676788	+	0.295913i
$351$	4.34469			0.231902
$352$	−0.878797	−	1.52212i	−0.0468400	−	0.0811293i
$353$	−10.0302	+	17.3728i	−0.533852	+	0.924659i	0.465366	+	0.885119i	$0.345923\pi$
$353$	−10.0302	+	17.3728i	−0.533852	+	0.924659i	−0.999218	+	0.0395408i	$0.987410\pi$
$354$	14.7575	−	25.5607i	0.784350	−	1.35853i
$355$	5.88906	+	10.2001i	0.312559	+	0.541368i
$356$	9.58102			0.507793
$357$	0.274192	+	0.202030i	0.0145118	+	0.0106926i
$358$	−32.2773			−1.70591
$359$	−8.31175	−	14.3964i	−0.438677	−	0.759811i	0.558910	−	0.829228i	$-0.311220\pi$
$359$	−8.31175	−	14.3964i	−0.438677	−	0.759811i	−0.997588	+	0.0694166i	$0.977886\pi$
$360$	−8.57367	+	14.8500i	−0.451872	+	0.782665i
$361$	1.82090	−	3.15389i	0.0958369	−	0.165994i
$362$	−30.9112	−	53.5399i	−1.62466	−	2.81399i
$363$	0.814010			0.0427244
$364$	1.12032	−	10.0139i	0.0587209	−	0.524872i
$365$	15.3822			0.805143
$366$	9.67344	+	16.7549i	0.505639	+	0.875792i
$367$	10.5436	−	18.2621i	0.550373	−	0.953274i	−0.447874	−	0.894097i	$-0.647819\pi$
$367$	10.5436	−	18.2621i	0.550373	−	0.953274i	0.998247	−	0.0591777i	$-0.0188479\pi$
$368$	11.0386	−	19.1194i	0.575426	−	0.996666i
$369$	9.91439	+	17.1722i	0.516123	+	0.893951i
$370$	40.2174			2.09080
$371$	−1.28800	+	11.5126i	−0.0668694	+	0.597707i
$372$	27.4009			1.42067
$373$	−11.7262	−	20.3104i	−0.607160	−	1.05163i	−0.991706	−	0.128526i	$-0.958975\pi$
$373$	−11.7262	−	20.3104i	−0.607160	−	1.05163i	0.384546	−	0.923106i	$-0.374358\pi$
$374$	−0.190568	+	0.330073i	−0.00985401	+	0.0170676i
$375$	−4.90973	+	8.50390i	−0.253537	+	0.439140i
$376$	3.88759	+	6.73350i	0.200487	+	0.347254i
$377$	1.97099			0.101511
$378$	22.3034	+	16.4336i	1.14716	+	0.845252i
$379$	−13.1404			−0.674978			−0.337489	−	0.941329i	$-0.609578\pi$
$379$	−13.1404			−0.674978			−0.337489	+	0.941329i	$0.609578\pi$
$380$	12.5605	+	21.7554i	0.644340	+	1.11603i
$381$	3.56845	−	6.18074i	0.182817	−	0.316649i
$382$	−17.5314	+	30.3652i	−0.896983	+	1.55362i
$383$	−9.68591	−	16.7765i	−0.494927	−	0.857238i	0.505056	−	0.863086i	$-0.331472\pi$
$383$	−9.68591	−	16.7765i	−0.494927	−	0.857238i	−0.999983	+	0.00584832i	$0.998138\pi$
$384$	−16.7795			−0.856274
$385$	4.08012	−	1.78396i	0.207942	−	0.0909188i
$386$	36.8020			1.87317
$387$	−11.7257	−	20.3095i	−0.596050	−	1.03239i
$388$	−6.11353	+	10.5889i	−0.310367	+	0.537572i
$389$	−4.93911	+	8.55479i	−0.250423	+	0.433745i	−0.963642	−	0.267196i	$-0.913903\pi$
$389$	−4.93911	+	8.55479i	−0.250423	+	0.433745i	0.713219	+	0.700941i	$0.247236\pi$
$390$	−1.65098	−	2.85959i	−0.0836008	−	0.144801i
$391$	1.20900			0.0611419
$392$	20.7174	−	22.3986i	1.04639	−	1.13130i
$393$	−3.93457			−0.198473
$394$	−0.702043	−	1.21597i	−0.0353684	−	0.0612599i
$395$	−6.67897	+	11.5683i	−0.336055	+	0.582065i
$396$	−4.45099	+	7.70934i	−0.223671	+	0.387409i
$397$	−7.64086	−	13.2344i	−0.383484	−	0.664214i	0.608074	−	0.793881i	$-0.291943\pi$
$397$	−7.64086	−	13.2344i	−0.383484	−	0.664214i	−0.991558	+	0.129667i	$0.958609\pi$
$398$	−52.0736			−2.61021
$399$	7.73324	−	3.38122i	0.387146	−	0.169273i
$400$	−6.25827			−0.312914
$401$	−5.94476	−	10.2966i	−0.296867	−	0.514189i	0.678550	−	0.734554i	$-0.262608\pi$
$401$	−5.94476	−	10.2966i	−0.296867	−	0.514189i	−0.975417	+	0.220365i	$0.929275\pi$
$402$	−13.0184	+	22.5485i	−0.649297	+	1.12462i
$403$	4.41926	−	7.65439i	0.220139	−	0.381292i
$404$	8.95670	+	15.5135i	0.445613	+	0.771824i
$405$	−5.84970			−0.290674
$406$	10.1181	+	7.45519i	0.502152	+	0.369995i
$407$	9.91450			0.491443
$408$	0.280544	+	0.485917i	0.0138890	+	0.0240565i
$409$	1.83264	−	3.17422i	0.0906180	−	0.156955i	−0.817153	−	0.576420i	$-0.804449\pi$
$409$	1.83264	−	3.17422i	0.0906180	−	0.156955i	0.907771	+	0.419465i	$0.137782\pi$
$410$	17.2059	−	29.8016i	0.849741	−	1.47179i
$411$	7.24091	+	12.5416i	0.357168	+	0.618633i
$412$	−61.6868			−3.03909
$413$	4.42555	−	39.5574i	0.217767	−	1.94649i
$414$	43.0670			2.11663
$415$	0.927669	+	1.60677i	0.0455375	+	0.0788732i
$416$	−0.878797	+	1.52212i	−0.0430866	+	0.0746281i
$417$	−0.992488	+	1.71904i	−0.0486023	+	0.0841817i
$418$	4.72251	+	8.17963i	0.230985	+	0.400079i
$419$	−6.89636			−0.336909			−0.168455	−	0.985709i	$-0.553878\pi$
$419$	−6.89636			−0.336909			−0.168455	+	0.985709i	$0.553878\pi$
$420$	1.53491	−	13.7197i	0.0748961	−	0.669452i
$421$	1.84635			0.0899857			0.0449928	−	0.998987i	$-0.485673\pi$
$421$	1.84635			0.0899857			0.0449928	+	0.998987i	$0.485673\pi$
$422$	16.7166	+	28.9540i	0.813751	+	1.40946i
$423$	−2.08476	+	3.61091i	−0.101364	+	0.175568i
$424$	−9.54229	+	16.5277i	−0.463414	+	0.802657i
$425$	−0.171360	−	0.296803i	−0.00831216	−	0.0143971i
$426$	13.7286			0.665155
$427$	21.0053	+	15.4771i	1.01652	+	0.748989i
$428$	69.3211			3.35076
$429$	−0.407005	−	0.704953i	−0.0196504	−	0.0340355i
$430$	−20.3494	+	35.2461i	−0.981333	+	1.69972i
$431$	3.96025	−	6.85936i	0.190759	−	0.330404i	−0.754743	−	0.656020i	$-0.772239\pi$
$431$	3.96025	−	6.85936i	0.190759	−	0.330404i	0.945502	+	0.325617i	$0.105572\pi$
$432$	6.27322	+	10.8655i	0.301821	+	0.522769i
$433$	2.58517			0.124235			0.0621177	−	0.998069i	$-0.480215\pi$
$433$	2.58517			0.124235			0.0621177	+	0.998069i	$0.480215\pi$
$434$	51.6386	−	22.5780i	2.47873	−	1.08378i
$435$	2.70038			0.129474
$436$	−15.0232	−	26.0210i	−0.719481	−	1.24618i
$437$	14.9803	−	25.9467i	0.716606	−	1.24120i
$438$	8.96481	−	15.5275i	0.428355	−	0.741933i
$439$	−12.3872	−	21.4553i	−0.591210	−	1.02401i	−0.994070	−	0.108745i	$-0.965317\pi$
$439$	−12.3872	−	21.4553i	−0.591210	−	1.02401i	0.402859	−	0.915262i	$-0.368016\pi$
$440$	7.33611			0.349735
$441$	15.9572	+	3.61573i	0.759867	+	0.172178i
$442$	0.381135			0.0181287
$443$	0.164523	+	0.284963i	0.00781674	+	0.0135390i	0.869907	−	0.493215i	$-0.164178\pi$
$443$	0.164523	+	0.284963i	0.00781674	+	0.0135390i	−0.862091	+	0.506754i	$0.830845\pi$
$444$	15.3683	−	26.6187i	0.729348	−	1.26327i
$445$	2.11708	−	3.66688i	0.100359	−	0.173827i
$446$	8.71600	+	15.0966i	0.412715	+	0.714843i
$447$	−19.0809			−0.902496
$448$	−24.2695	+	10.6114i	−1.14663	+	0.501341i
$449$	25.5787			1.20714			0.603568	−	0.797312i	$-0.293745\pi$
$449$	25.5787			1.20714			0.603568	+	0.797312i	$0.293745\pi$
$450$	−6.10416	−	10.5727i	−0.287753	−	0.498402i
$451$	4.24165	−	7.34676i	0.199732	−	0.345945i
$452$	13.8710	−	24.0252i	0.652435	−	1.13005i
$453$	−8.25124	−	14.2916i	−0.387677	−	0.671477i
$454$	42.1581			1.97858
$455$	−3.58501	−	2.64151i	−0.168068	−	0.123836i
$456$	13.9045			0.651137
$457$	10.0550	+	17.4158i	0.470354	+	0.814677i	0.999425	−	0.0339004i	$-0.0107929\pi$
$457$	10.0550	+	17.4158i	0.470354	+	0.814677i	−0.529071	+	0.848577i	$0.677460\pi$
$458$	−14.9729	+	25.9337i	−0.699636	+	1.21180i
$459$	−0.343538	+	0.595025i	−0.0160350	+	0.0277734i
$460$	−24.5029	−	42.4403i	−1.14245	−	1.97879i
$461$	23.5037			1.09468			0.547339	−	0.836911i	$-0.315641\pi$
$461$	23.5037			1.09468			0.547339	+	0.836911i	$0.315641\pi$
$462$	0.577098	−	5.15834i	0.0268490	−	0.239988i
$463$	−0.473228			−0.0219928			−0.0109964	−	0.999940i	$-0.503500\pi$
$463$	−0.473228			−0.0219928			−0.0109964	+	0.999940i	$0.503500\pi$
$464$	2.84589	+	4.92922i	0.132117	+	0.228833i
$465$	6.05467	−	10.4870i	0.280778	−	0.486322i
$466$	−2.70343	+	4.68248i	−0.125234	+	0.216912i
$467$	−15.5502	−	26.9338i	−0.719578	−	1.24635i	−0.961167	−	0.275968i	$-0.911002\pi$
$467$	−15.5502	−	26.9338i	−0.719578	−	1.24635i	0.241589	−	0.970379i	$-0.422332\pi$
$468$	8.90198			0.411494
$469$	−3.90402	+	34.8957i	−0.180271	+	1.61134i
$470$	7.23599			0.333772
$471$	−0.923891	−	1.60023i	−0.0425706	−	0.0737345i
$472$	32.7872	−	56.7891i	1.50915	−	2.61393i
$473$	−5.01658	+	8.68897i	−0.230662	+	0.399519i
$474$	7.78504	+	13.4841i	0.357579	+	0.619345i
$475$	−8.49302			−0.389687
$476$	1.28287	+	0.945242i	0.0588001	+	0.0433251i
$477$	−10.2343			−0.468596
$478$	8.61801	+	14.9268i	0.394179	+	0.682737i
$479$	−15.6576	+	27.1197i	−0.715414	+	1.23913i	0.247386	+	0.968917i	$0.420428\pi$
$479$	−15.6576	+	27.1197i	−0.715414	+	1.23913i	−0.962800	+	0.270216i	$0.912905\pi$
$480$	−1.20401	+	2.08540i	−0.0549551	+	0.0951851i
$481$	−4.95725	−	8.58621i	−0.226031	−	0.391497i
$482$	−37.8373			−1.72344
$483$	−15.0859	+	6.59605i	−0.686434	+	0.300131i
$484$	3.80852			0.173114
$485$	2.70176	+	4.67958i	0.122681	+	0.212489i
$486$	−19.1158	+	33.1096i	−0.867112	+	1.50188i
$487$	12.5868	−	21.8010i	0.570363	−	0.987898i	−0.426165	−	0.904645i	$-0.640136\pi$
$487$	12.5868	−	21.8010i	0.570363	−	0.987898i	0.996528	−	0.0832530i	$-0.0265310\pi$
$488$	21.4918	+	37.2250i	0.972890	+	1.68510i
$489$	−4.17047			−0.188595
$490$	−8.41222	−	27.1203i	−0.380026	−	1.22517i
$491$	−4.36264			−0.196883			−0.0984416	−	0.995143i	$-0.531386\pi$
$491$	−4.36264			−0.196883			−0.0984416	+	0.995143i	$0.531386\pi$
$492$	−13.1498	−	22.7762i	−0.592841	−	1.02683i
$493$	−0.155848	+	0.269937i	−0.00701905	+	0.0121574i
$494$	4.72251	−	8.17963i	0.212476	−	0.368019i
$495$	1.96703	+	3.40700i	0.0884115	+	0.153133i
$496$	25.5236			1.14604
$497$	16.9640	−	7.41718i	0.760937	−	0.332706i
$498$	2.16259			0.0969080
$499$	−3.20322	−	5.54814i	−0.143396	−	0.248369i	0.785377	−	0.619017i	$-0.212469\pi$
$499$	−3.20322	−	5.54814i	−0.143396	−	0.248369i	−0.928773	+	0.370648i	$0.879136\pi$
$500$	−22.9712	+	39.7873i	−1.02730	+	1.77934i
$501$	−6.83560	+	11.8396i	−0.305392	+	0.528955i
$502$	−16.3851	−	28.3798i	−0.731302	−	1.26665i
$503$	−26.1344			−1.16527			−0.582637	−	0.812733i	$-0.697979\pi$
$503$	−26.1344			−1.16527			−0.582637	+	0.812733i	$0.697979\pi$
$504$	21.7003	+	15.9892i	0.966608	+	0.712216i
$505$	7.91649			0.352279
$506$	−9.21263	−	15.9567i	−0.409551	−	0.709363i
$507$	−0.407005	+	0.704953i	−0.0180757	+	0.0313081i
$508$	16.6958	−	28.9179i	0.740755	−	1.28303i
$509$	−18.0317	−	31.2318i	−0.799240	−	1.38432i	−0.920112	−	0.391655i	$-0.871903\pi$
$509$	−18.0317	−	31.2318i	−0.799240	−	1.38432i	0.120872	−	0.992668i	$-0.461431\pi$
$510$	0.522179			0.0231225
$511$	2.68842	−	24.0302i	0.118929	−	1.06303i
$512$	−30.2493			−1.33684
$513$	8.51331	+	14.7455i	0.375872	+	0.651029i
$514$	24.5481	−	42.5185i	1.08277	−	1.87541i
$515$	−13.6307	+	23.6090i	−0.600638	+	1.04034i
$516$	15.5522	+	26.9373i	0.684649	+	1.18585i
$517$	1.78384			0.0784530
$518$	7.02896	−	62.8277i	0.308835	−	2.76049i
$519$	4.30614			0.189019
$520$	−3.66806	−	6.35326i	−0.160855	−	0.278609i
$521$	−2.90117	+	5.02498i	−0.127103	+	0.220148i	−0.922553	−	0.385871i	$-0.873901\pi$
$521$	−2.90117	+	5.02498i	−0.127103	+	0.220148i	0.795450	+	0.606019i	$0.207234\pi$
$522$	−5.55161	+	9.61567i	−0.242987	+	0.420867i
$523$	−2.12639	−	3.68302i	−0.0929806	−	0.161047i	0.815783	−	0.578357i	$-0.196306\pi$
$523$	−2.12639	−	3.68302i	−0.0929806	−	0.161047i	−0.908764	+	0.417310i	$0.862973\pi$
$524$	−18.4087			−0.804188
$525$	3.75752	+	2.76861i	0.163992	+	0.120832i
$526$	31.4408			1.37088
$527$	0.698870	+	1.21048i	0.0304432	+	0.0527292i
$528$	1.17534	−	2.03574i	0.0511499	−	0.0885943i
$529$	−17.7235	+	30.6979i	−0.770585	+	1.33469i
$530$	8.88056	+	15.3816i	0.385747	+	0.668133i
$531$	35.1650			1.52603
$532$	36.1816	−	15.8198i	1.56867	−	0.685873i
$533$	−8.48331			−0.367453
$534$	−2.46768	−	4.27414i	−0.106787	−	0.184960i
$535$	15.3176	−	26.5308i	0.662237	−	1.14703i
$536$	−28.9234	+	50.0968i	−1.24930	+	2.16385i
$537$	5.45085	+	9.44115i	0.235221	+	0.407416i
$538$	66.3107			2.85886
$539$	−2.07380	−	6.68576i	−0.0893250	−	0.287976i
$540$	27.8500			1.19847
$541$	8.05702	+	13.9552i	0.346398	+	0.599979i	0.985607	−	0.169054i	$-0.0540712\pi$
$541$	8.05702	+	13.9552i	0.346398	+	0.599979i	−0.639208	+	0.769034i	$0.720738\pi$
$542$	−8.62107	+	14.9321i	−0.370307	+	0.641390i
$543$	−10.4403	+	18.0832i	−0.448037	+	0.776022i
$544$	−0.138974	−	0.240711i	−0.00595848	−	0.0103204i
$545$	−13.2784			−0.568786
$546$	−4.75580	+	2.07939i	−0.203530	+	0.0889897i
$547$	−17.2386			−0.737068			−0.368534	−	0.929614i	$-0.620140\pi$
$547$	−17.2386			−0.737068			−0.368534	+	0.929614i	$0.620140\pi$
$548$	33.8782	+	58.6787i	1.44720	+	2.50663i
$549$	−11.5252	+	19.9623i	−0.491885	+	0.851969i
$550$	−2.61153	+	4.52330i	−0.111356	+	0.192874i
$551$	3.86212	+	6.68939i	0.164532	+	0.284977i
$552$	−27.1247			−1.15451
$553$	16.9047	+	12.4557i	0.718863	+	0.529672i
$554$	−9.77139			−0.415147
$555$	−6.79174	−	11.7636i	−0.288293	−	0.499338i
$556$	−4.64357	+	8.04289i	−0.196931	+	0.341095i
$557$	3.96015	−	6.85918i	0.167797	−	0.290633i	−0.769848	−	0.638227i	$-0.779668\pi$
$557$	3.96015	−	6.85918i	0.167797	−	0.290633i	0.937645	+	0.347594i	$0.113001\pi$
$558$	24.8951	+	43.1195i	1.05389	+	1.82540i
$559$	10.0332			0.424357
$560$	1.42975	−	12.7797i	0.0604180	−	0.540041i
$561$	0.128729			0.00543494
$562$	−2.13232	−	3.69329i	−0.0899465	−	0.155792i
$563$	4.83595	−	8.37610i	0.203811	−	0.353011i	−0.745942	−	0.666010i	$-0.768001\pi$
$563$	4.83595	−	8.37610i	0.203811	−	0.353011i	0.949753	+	0.313000i	$0.101334\pi$
$564$	2.76510	−	4.78929i	0.116432	−	0.201665i
$565$	−6.13001	−	10.6175i	−0.257891	−	0.446681i
$566$	−31.7725			−1.33550
$567$	−1.02238	+	9.13842i	−0.0429358	+	0.383778i
$568$	30.5015			1.27981
$569$	3.36663	+	5.83117i	0.141136	+	0.244455i	0.927925	−	0.372767i	$-0.121591\pi$
$569$	3.36663	+	5.83117i	0.141136	+	0.244455i	−0.786788	+	0.617223i	$0.788258\pi$
$570$	6.47013	−	11.2066i	0.271004	−	0.469392i
$571$	12.2891	−	21.2854i	0.514285	−	0.890767i	−0.485578	−	0.874193i	$-0.661391\pi$
$571$	12.2891	−	21.2854i	0.514285	−	0.890767i	0.999863	−	0.0165739i	$-0.00527587\pi$
$572$	−1.90426	−	3.29827i	−0.0796210	−	0.137908i
$573$	11.8425			0.494727
$574$	−43.5489	−	32.0877i	−1.81770	−	1.33932i
$575$	16.5681			0.690938
$576$	−11.7004	−	20.2656i	−0.487515	−	0.844401i
$577$	5.89294	−	10.2069i	0.245326	−	0.424918i	−0.716897	−	0.697179i	$-0.754438\pi$
$577$	5.89294	−	10.2069i	0.245326	−	0.424918i	0.962223	+	0.272261i	$0.0877715\pi$
$578$	20.4556	−	35.4301i	0.850841	−	1.47370i
$579$	−6.21496	−	10.7646i	−0.258285	−	0.447363i
$580$	12.6343			0.524612
$581$	2.67223	−	1.16838i	0.110863	−	0.0484728i
$582$	6.29837			0.261076
$583$	2.18926	+	3.79191i	0.0906698	+	0.157045i
$584$	19.9175	−	34.4981i	0.824191	−	1.42754i
$585$	1.96703	−	3.40700i	0.0813268	−	0.140862i
$586$	13.0334	+	22.5745i	0.538404	+	0.932544i
$587$	19.5040			0.805018			0.402509	−	0.915416i	$-0.368138\pi$
$587$	19.5040			0.805018			0.402509	+	0.915416i	$0.368138\pi$
$588$	−21.1647	−	4.79569i	−0.872816	−	0.197771i
$589$	34.6378			1.42723
$590$	−30.5135	−	52.8510i	−1.25622	−	2.17584i
$591$	−0.237116	+	0.410697i	−0.00975364	+	0.0168938i
$592$	14.3154	−	24.7950i	0.588359	−	1.01907i
$593$	21.3060	+	36.9031i	0.874933	+	1.51543i	0.856834	+	0.515593i	$0.172428\pi$
$593$	21.3060	+	36.9031i	0.874933	+	1.51543i	0.0180999	+	0.999836i	$0.494238\pi$
$594$	10.4711			0.429633
$595$	0.645236	−	0.282118i	0.0264521	−	0.0115657i
$596$	−89.2741			−3.65681
$597$	8.79396	+	15.2316i	0.359913	+	0.623387i
$598$	−9.21263	+	15.9567i	−0.376732	+	0.652519i
$599$	−2.42096	+	4.19322i	−0.0989176	+	0.171330i	−0.911237	−	0.411883i	$-0.864871\pi$
$599$	−2.42096	+	4.19322i	−0.0989176	+	0.171330i	0.812319	+	0.583213i	$0.198205\pi$
$600$	3.84456	+	6.65898i	0.156954	+	0.271852i
$601$	23.0812			0.941500			0.470750	−	0.882267i	$-0.343983\pi$
$601$	23.0812			0.941500			0.470750	+	0.882267i	$0.343983\pi$
$602$	51.5051	+	37.9499i	2.09919	+	1.54672i
$603$	−31.0210			−1.26327
$604$	−38.6052	−	66.8661i	−1.57082	−	2.72074i
$605$	0.841551	−	1.45761i	0.0342139	−	0.0592603i
$606$	4.61376	−	7.99126i	0.187421	−	0.324623i
$607$	1.63997	+	2.84050i	0.0665642	+	0.115293i	0.897387	−	0.441245i	$-0.145463\pi$
$607$	1.63997	+	2.84050i	0.0665642	+	0.115293i	−0.830823	+	0.556537i	$0.812130\pi$
$608$	−6.88793			−0.279342
$609$	0.471957	−	4.21855i	0.0191247	−	0.170944i
$610$	40.0029			1.61967
$611$	−0.891918	−	1.54485i	−0.0360831	−	0.0624978i
$612$	−0.703887	+	1.21917i	−0.0284530	+	0.0492820i
$613$	7.69967	−	13.3362i	0.310987	−	0.538645i	−0.667589	−	0.744530i	$-0.732674\pi$
$613$	7.69967	−	13.3362i	0.310987	−	0.538645i	0.978576	+	0.205885i	$0.0660072\pi$
$614$	28.4801	+	49.3290i	1.14936	+	1.99075i
$615$	−11.6227			−0.468671
$616$	1.28216	−	11.4605i	0.0516598	−	0.461756i
$617$	5.78864			0.233042			0.116521	−	0.993188i	$-0.462826\pi$
$617$	5.78864			0.233042			0.116521	+	0.993188i	$0.462826\pi$
$618$	15.8880	+	27.5188i	0.639108	+	1.10697i
$619$	15.3974	−	26.6691i	0.618875	−	1.07192i	−0.370816	−	0.928706i	$-0.620922\pi$
$619$	15.3974	−	26.6691i	0.618875	−	1.07192i	0.989691	−	0.143217i	$-0.0457446\pi$
$620$	28.3280	−	49.0656i	1.13768	−	1.97052i
$621$	−16.6077	−	28.7654i	−0.666444	−	1.15431i
$622$	−39.7930			−1.59556
$623$	−5.35841	−	3.94818i	−0.214680	−	0.158180i
$624$	−2.35067			−0.0941022
$625$	4.73378	+	8.19915i	0.189351	+	0.327966i
$626$	−25.2645	+	43.7594i	−1.00977	+	1.74898i
$627$	1.59503	−	2.76268i	0.0636995	−	0.110331i
$628$	−4.32262	−	7.48699i	−0.172491	−	0.298764i
$629$	1.56789			0.0625161
$630$	22.9845	−	10.0496i	0.915726	−	0.400385i
$631$	47.8955			1.90669			0.953346	−	0.301881i	$-0.0976144\pi$
$631$	47.8955			1.90669			0.953346	+	0.301881i	$0.0976144\pi$
$632$	17.2963	+	29.9581i	0.688011	+	1.19167i
$633$	5.64605	−	9.77925i	0.224410	−	0.388690i
$634$	−17.8729	+	30.9567i	−0.709823	+	1.22945i
$635$	−7.37838	−	12.7797i	−0.292802	−	0.507148i
$636$	13.5741			0.538250
$637$	−4.75313	+	5.13884i	−0.188326	+	0.203608i
$638$	4.75027			0.188065
$639$	8.17836	+	14.1653i	0.323531	+	0.560372i
$640$	−17.3472	+	30.0462i	−0.685709	+	1.18768i
$641$	−4.44881	+	7.70557i	−0.175718	+	0.304352i	−0.940409	−	0.340044i	$-0.889558\pi$
$641$	−4.44881	+	7.70557i	−0.175718	+	0.304352i	0.764692	+	0.644396i	$0.222891\pi$
$642$	−17.8543	−	30.9245i	−0.704651	−	1.22049i
$643$	−36.2224			−1.42847			−0.714236	−	0.699905i	$-0.753226\pi$
$643$	−36.2224			−1.42847			−0.714236	+	0.699905i	$0.753226\pi$
$644$	−70.5827	+	30.8610i	−2.78135	+	1.21609i
$645$	13.7460			0.541250
$646$	0.746825	+	1.29354i	0.0293834	+	0.0508936i
$647$	19.3161	−	33.4565i	0.759396	−	1.31531i	−0.183763	−	0.982970i	$-0.558828\pi$
$647$	19.3161	−	33.4565i	0.759396	−	1.31531i	0.943159	−	0.332341i	$-0.107839\pi$
$648$	−7.57441	+	13.1193i	−0.297551	+	0.515373i
$649$	−7.52228	−	13.0290i	−0.295275	−	0.511432i
$650$	5.22306			0.204865
$651$	−15.3246	−	11.2915i	−0.600619	−	0.442548i
$652$	−19.5124			−0.764165
$653$	−11.5591	−	20.0209i	−0.452343	−	0.783480i	0.546189	−	0.837662i	$-0.316078\pi$
$653$	−11.5591	−	20.0209i	−0.452343	−	0.783480i	−0.998531	+	0.0541821i	$0.982745\pi$
$654$	−7.73871	+	13.4038i	−0.302608	+	0.524132i
$655$	−4.06769	+	7.04544i	−0.158938	+	0.275288i
$656$	−12.2489	−	21.2157i	−0.478240	−	0.828335i
$657$	21.3619			0.833407
$658$	1.26466	−	11.3041i	0.0493017	−	0.440679i
$659$	−9.07707			−0.353592			−0.176796	−	0.984247i	$-0.556573\pi$
$659$	−9.07707			−0.353592			−0.176796	+	0.984247i	$0.556573\pi$
$660$	−2.60895	−	4.51884i	−0.101553	−	0.175896i
$661$	−5.68099	+	9.83977i	−0.220965	+	0.382723i	−0.955101	−	0.296280i	$-0.904254\pi$
$661$	−5.68099	+	9.83977i	−0.220965	+	0.382723i	0.734136	+	0.679002i	$0.237587\pi$
$662$	−23.5079	+	40.7168i	−0.913659	+	1.58250i
$663$	−0.0643644	−	0.111482i	−0.00249971	−	0.00432962i
$664$	4.80471			0.186459
$665$	1.94030	−	17.3432i	0.0752415	−	0.672540i
$666$	55.8514			2.16420
$667$	−7.53419	−	13.0496i	−0.291725	−	0.505282i
$668$	−31.9818	+	55.3941i	−1.23741	+	2.14326i
$669$	2.94384	−	5.09888i	0.113815	−	0.197134i
$670$	26.9177	+	46.6228i	1.03992	+	1.80120i
$671$	9.86163			0.380704
$672$	3.04739	+	2.24538i	0.117556	+	0.0866173i
$673$	−26.1148			−1.00665			−0.503325	−	0.864097i	$-0.667890\pi$
$673$	−26.1148			−1.00665			−0.503325	+	0.864097i	$0.667890\pi$
$674$	32.9312	+	57.0385i	1.26846	+	2.19704i
$675$	−4.70783	+	8.15419i	−0.181204	+	0.313855i
$676$	−1.90426	+	3.29827i	−0.0732407	+	0.126857i
$677$	−2.84621	−	4.92978i	−0.109389	−	0.189467i	0.806134	−	0.591733i	$-0.201556\pi$
$677$	−2.84621	−	4.92978i	−0.109389	−	0.189467i	−0.915523	+	0.402266i	$0.868223\pi$
$678$	−14.2903			−0.548818
$679$	7.78265	−	3.40283i	0.298671	−	0.130588i
$680$	1.16014			0.0444895
$681$	−7.11947	−	12.3313i	−0.272819	−	0.472536i
$682$	10.6508	−	18.4477i	0.407841	−	0.706401i
$683$	14.4931	−	25.1027i	0.554562	−	0.960530i	−0.443375	−	0.896336i	$-0.646219\pi$
$683$	14.4931	−	25.1027i	0.554562	−	0.960530i	0.997937	−	0.0641938i	$-0.0204476\pi$
$684$	17.4432	+	30.2126i	0.666959	+	1.15521i
$685$	29.9436			1.14409
$686$	−43.8376	+	8.40168i	−1.67373	+	0.320778i
$687$	10.1142			0.385881
$688$	14.4867	+	25.0917i	0.552301	+	0.956613i
$689$	2.18926	−	3.79191i	0.0834041	−	0.144460i
$690$	−12.6219	+	21.8617i	−0.480506	+	0.832261i
$691$	−13.5711	−	23.5058i	−0.516268	−	0.894202i	−0.999822	−	0.0188875i	$-0.993988\pi$
$691$	−13.5711	−	23.5058i	−0.516268	−	0.894202i	0.483554	−	0.875315i	$-0.339346\pi$
$692$	20.1472			0.765882
$693$	5.66621	−	2.47745i	0.215242	−	0.0941105i
$694$	−82.8995			−3.14682
$695$	2.05214	+	3.55440i	0.0778420	+	0.134826i
$696$	3.49655	−	6.05621i	0.132537	−	0.229560i
$697$	0.670782	−	1.16183i	0.0254077	−	0.0440074i
$698$	7.33824	+	12.7102i	0.277756	+	0.481088i
$699$	1.82617			0.0690723
$700$	17.5804	+	12.9536i	0.664475	+	0.489598i
$701$	−20.7023			−0.781916			−0.390958	−	0.920409i	$-0.627856\pi$
$701$	−20.7023			−0.781916			−0.390958	+	0.920409i	$0.627856\pi$
$702$	−5.23553	−	9.06821i	−0.197603	−	0.342258i
$703$	19.4272	−	33.6489i	0.732712	−	1.26909i
$704$	−5.00575	+	8.67021i	−0.188661	+	0.326771i
$705$	−1.22198	−	2.11654i	−0.0460225	−	0.0797134i
$706$	48.3472			1.81957
$707$	1.38360	−	12.3672i	0.0520356	−	0.465115i
$708$	−46.6407			−1.75286
$709$	14.4685	+	25.0602i	0.543377	+	0.941157i	0.998707	+	0.0508339i	$0.0161879\pi$
$709$	14.4685	+	25.0602i	0.543377	+	0.941157i	−0.455330	+	0.890323i	$0.650479\pi$
$710$	14.1931	−	24.5832i	0.532659	−	0.922593i
$711$	−9.27534	+	16.0654i	−0.347852	+	0.602498i
$712$	−5.48253	−	9.49603i	−0.205467	−	0.355879i
$713$	−67.5711			−2.53056
$714$	0.0912633	−	0.815749i	0.00341544	−	0.0305286i
$715$	−1.68310			−0.0629445
$716$	25.5029	+	44.1724i	0.953090	+	1.65080i
$717$	2.91074	−	5.04155i	0.108704	−	0.188280i
$718$	−20.0320	+	34.6965i	−0.747589	+	1.29486i
$719$	21.3908	+	37.0500i	0.797742	+	1.38173i	0.921083	+	0.389366i	$0.127306\pi$
$719$	21.3908	+	37.0500i	0.797742	+	1.38173i	−0.123341	+	0.992364i	$0.539361\pi$
$720$	11.3607			0.423387
$721$	34.4997	+	25.4201i	1.28484	+	0.946693i
$722$	−8.77706			−0.326648
$723$	6.38980	+	11.0675i	0.237639	+	0.411603i
$724$	−48.8472	+	84.6059i	−1.81539	+	3.14435i
$725$	−2.13574	+	3.69920i	−0.0793192	+	0.137385i
$726$	−0.980917	−	1.69900i	−0.0364052	−	0.0630557i
$727$	−29.2512			−1.08487			−0.542434	−	0.840098i	$-0.682497\pi$
$727$	−29.2512			−1.08487			−0.542434	+	0.840098i	$0.682497\pi$
$728$	−10.5662	+	4.61986i	−0.391608	+	0.171223i
$729$	2.48614			0.0920794
$730$	−18.5363	−	32.1058i	−0.686058	−	1.18829i
$731$	−0.793330	+	1.37409i	−0.0293424	+	0.0508225i
$732$	15.2864	−	26.4767i	0.565000	−	0.978609i
$733$	5.51846	+	9.55825i	0.203829	+	0.353042i	0.949759	−	0.312982i	$-0.101328\pi$
$733$	5.51846	+	9.55825i	0.203829	+	0.353042i	−0.745930	+	0.666024i	$0.767995\pi$
$734$	−50.8221			−1.87588
$735$	−6.51209	+	7.04054i	−0.240202	+	0.259694i
$736$	13.4369			0.495291
$737$	6.63582	+	11.4936i	0.244433	+	0.423371i
$738$	23.8945	−	41.3866i	0.879570	−	1.52346i
$739$	0.869510	−	1.50604i	0.0319854	−	0.0554004i	−0.849590	−	0.527444i	$-0.823150\pi$
$739$	0.869510	−	1.50604i	0.0319854	−	0.0554004i	0.881575	+	0.472044i	$0.156484\pi$
$740$	−31.7766	−	55.0387i	−1.16813	−	2.02326i
$741$	−3.19007			−0.117190
$742$	25.5812	−	11.1849i	0.939117	−	0.410612i
$743$	−32.8741			−1.20604			−0.603018	−	0.797728i	$-0.706035\pi$
$743$	−32.8741			−1.20604			−0.603018	+	0.797728i	$0.706035\pi$
$744$	−15.6796	−	27.1579i	−0.574842	−	0.995655i
$745$	−19.7265	+	34.1673i	−0.722723	+	1.25179i
$746$	−28.2612	+	48.9498i	−1.03472	+	1.79218i
$747$	1.28829	+	2.23138i	0.0471360	+	0.0816420i
$748$	0.602285			0.0220217
$749$	−38.7694	−	28.5661i	−1.41660	−	1.04378i
$750$	23.6657			0.864151
$751$	0.466244	+	0.807558i	0.0170135	+	0.0294682i	0.874407	−	0.485194i	$-0.161251\pi$
$751$	0.466244	+	0.807558i	0.0170135	+	0.0294682i	−0.857393	+	0.514662i	$0.827918\pi$
$752$	2.57565	−	4.46116i	0.0939244	−	0.162682i
$753$	−5.53408	+	9.58531i	−0.201673	+	0.349308i
$754$	−2.37513	−	4.11385i	−0.0864973	−	0.149818i
$755$	−34.1217			−1.24181
$756$	4.86745	−	43.5073i	0.177028	−	1.58235i
$757$	−14.2014			−0.516158			−0.258079	−	0.966124i	$-0.583090\pi$
$757$	−14.2014			−0.516158			−0.258079	+	0.966124i	$0.583090\pi$
$758$	15.8348	+	27.4266i	0.575145	+	0.996180i
$759$	−3.11158	+	5.38941i	−0.112943	+	0.195623i
$760$	14.3749	−	24.8981i	0.521434	−	0.903150i
$761$	−1.23801	−	2.14430i	−0.0448779	−	0.0777308i	0.842714	−	0.538362i	$-0.180957\pi$
$761$	−1.23801	−	2.14430i	−0.0448779	−	0.0777308i	−0.887592	+	0.460631i	$0.847623\pi$
$762$	−17.2006			−0.623111
$763$	−2.32073	+	20.7436i	−0.0840160	+	0.750970i
$764$	55.4076			2.00458
$765$	0.311070	+	0.538789i	0.0112467	+	0.0194799i
$766$	−23.3439	+	40.4328i	−0.843448	+	1.46090i
$767$	−7.52228	+	13.0290i	−0.271614	+	0.470449i
$768$	12.0706	+	20.9068i	0.435559	+	0.754410i
$769$	32.4091			1.16870			0.584352	−	0.811500i	$-0.301349\pi$
$769$	32.4091			1.16870			0.584352	+	0.811500i	$0.301349\pi$
$770$	−8.64018	−	6.36626i	−0.311371	−	0.229424i
$771$	−16.5823			−0.597196
$772$	−29.0780	−	50.3646i	−1.04654	−	1.81266i
$773$	12.8817	−	22.3117i	0.463321	−	0.802496i	−0.535803	−	0.844343i	$-0.679991\pi$
$773$	12.8817	−	22.3117i	0.463321	−	0.802496i	0.999124	+	0.0418473i	$0.0133243\pi$
$774$	−28.2599	+	48.9476i	−1.01578	+	1.75939i
$775$	9.57728	+	16.5883i	0.344026	+	0.595870i
$776$	13.9933			0.502331
$777$	−19.5642	+	8.55409i	−0.701862	+	0.306876i
$778$	23.8074			0.853536
$779$	−16.6228	−	28.7916i	−0.595575	−	1.03157i
$780$	−2.60895	+	4.51884i	−0.0934155	+	0.161800i
$781$	3.49893	−	6.06033i	0.125202	−	0.216855i
$782$	−1.45690	−	2.52342i	−0.0520986	−	0.0902375i
$783$	8.56335			0.306029
$784$	−19.7146	−	4.46712i	−0.704093	−	0.159540i
$785$	−3.82060			−0.136363
$786$	4.74132	+	8.21221i	0.169117	+	0.292920i
$787$	−3.38999	+	5.87164i	−0.120840	+	0.209301i	−0.920099	−	0.391685i	$-0.871892\pi$
$787$	−3.38999	+	5.87164i	−0.120840	+	0.209301i	0.799259	+	0.600987i	$0.205226\pi$
$788$	−1.10940	+	1.92153i	−0.0395206	+	0.0684517i
$789$	−5.30958	−	9.19646i	−0.189026	−	0.327403i
$790$	32.1938			1.14540
$791$	−17.6580	+	7.72066i	−0.627848	+	0.274515i
$792$	10.1879			0.362012
$793$	−4.93081	−	8.54042i	−0.175098	−	0.303279i
$794$	−18.4151	+	31.8960i	−0.653529	+	1.13195i
$795$	2.99942	−	5.19515i	0.106378	−	0.184253i
$796$	41.1444	+	71.2642i	1.45832	+	2.52589i
$797$	3.68345			0.130474			0.0652372	−	0.997870i	$-0.479220\pi$
$797$	3.68345			0.130474			0.0652372	+	0.997870i	$0.479220\pi$
$798$	−16.3762	−	12.0663i	−0.579710	−	0.427141i
$799$	0.282099			0.00997994
$800$	−1.90450	−	3.29869i	−0.0673342	−	0.116626i
$801$	2.94006	−	5.09234i	0.103882	−	0.179929i
$802$	−14.3274	+	24.8158i	−0.505917	+	0.876275i
$803$	−4.56961	−	7.91480i	−0.161258	−	0.279307i
$804$	41.1443			1.45105
$805$	−3.78511	+	33.8329i	−0.133408	+	1.19245i
$806$	−21.3016			−0.750318
$807$	−11.1983	−	19.3960i	−0.394198	−	0.682770i
$808$	10.2506	−	17.7545i	0.360613	−	0.624601i
$809$	21.9573	−	38.0312i	0.771979	−	1.33711i	−0.164498	−	0.986377i	$-0.552600\pi$
$809$	21.9573	−	38.0312i	0.771979	−	1.33711i	0.936477	−	0.350730i	$-0.114066\pi$
$810$	7.04915	+	12.2095i	0.247682	+	0.428997i
$811$	16.9292			0.594466			0.297233	−	0.954805i	$-0.403936\pi$
$811$	16.9292			0.594466			0.297233	+	0.954805i	$0.403936\pi$
$812$	2.20815	−	19.7374i	0.0774909	−	0.692646i
$813$	5.82356			0.204241
$814$	−11.9474	−	20.6935i	−0.418756	−	0.725307i
$815$	−4.31157	+	7.46786i	−0.151028	+	0.261588i
$816$	0.185870	−	0.321935i	0.00650673	−	0.0112700i
$817$	19.6597	+	34.0517i	0.687807	+	1.19132i
$818$	−8.83362			−0.308860
$819$	−4.97864	−	3.66836i	−0.173968	−	0.128183i
$820$	−54.3791			−1.89900
$821$	−18.8837	−	32.7075i	−0.659045	−	1.14150i	−0.980863	−	0.194698i	$-0.937627\pi$
$821$	−18.8837	−	32.7075i	−0.659045	−	1.14150i	0.321818	−	0.946801i	$-0.395706\pi$
$822$	17.4512	−	30.2264i	0.608682	−	1.05427i
$823$	−1.69533	+	2.93640i	−0.0590956	+	0.102357i	−0.894060	−	0.447948i	$-0.852155\pi$
$823$	−1.69533	+	2.93640i	−0.0590956	+	0.102357i	0.834964	+	0.550304i	$0.185488\pi$
$824$	35.2989	+	61.1395i	1.22970	+	2.12990i
$825$	1.76409			0.0614179
$826$	−87.8970	+	38.4314i	−3.05833	+	1.33720i
$827$	27.9675			0.972524			0.486262	−	0.873813i	$-0.338360\pi$
$827$	27.9675			0.972524			0.486262	+	0.873813i	$0.338360\pi$
$828$	−34.0281	−	58.9384i	−1.18256	−	2.04825i
$829$	0.00391814	−	0.00678642i	0.000136083	−	0.000235702i	−0.865957	−	0.500118i	$-0.833290\pi$
$829$	0.00391814	−	0.00678642i	0.000136083	−	0.000235702i	0.866093	+	0.499882i	$0.166623\pi$
$830$	2.23576	−	3.87245i	0.0776044	−	0.134415i
$831$	1.65015	+	2.85814i	0.0572430	+	0.0991479i
$832$	10.0115			0.347086
$833$	−0.327955	−	1.05730i	−0.0113630	−	0.0366332i
$834$	4.78396			0.165655
$835$	14.1338	+	24.4804i	0.489119	+	0.847179i
$836$	7.46270	−	12.9258i	0.258103	−	0.447047i
$837$	19.2003	−	33.2559i	0.663660	−	1.14949i
$838$	8.31042	+	14.3941i	0.287079	+	0.497235i
$839$	10.4001			0.359052			0.179526	−	0.983753i	$-0.442544\pi$
$839$	10.4001			0.359052			0.179526	+	0.983753i	$0.442544\pi$
$840$	−14.4763	+	6.32950i	−0.499479	+	0.218388i
$841$	−25.1152			−0.866041
$842$	−2.22493	−	3.85370i	−0.0766763	−	0.132807i
$843$	−0.720193	+	1.24741i	−0.0248048	+	0.0429631i
$844$	26.4163	−	45.7543i	0.909285	−	1.57493i
$845$	0.841551	+	1.45761i	0.0289502	+	0.0501433i
$846$	10.0489			0.345488
$847$	−2.13000	−	1.56943i	−0.0731877	−	0.0539261i
$848$	12.6441			0.434202
$849$	5.36560	+	9.29349i	0.184147	+	0.318952i
$850$	−0.412991	+	0.715322i	−0.0141655	+	0.0245353i
$851$	−37.8985	+	65.6420i	−1.29914	+	2.25018i
$852$	−10.8473	−	18.7880i	−0.371622	−	0.643668i
$853$	3.48524			0.119332			0.0596661	−	0.998218i	$-0.480996\pi$
$853$	3.48524			0.119332			0.0596661	+	0.998218i	$0.480996\pi$
$854$	6.99147	−	62.4927i	0.239243	−	2.13846i
$855$	15.4174			0.527264
$856$	−39.6675	−	68.7061i	−1.35581	−	2.34833i
$857$	−13.7915	+	23.8875i	−0.471107	+	0.815982i	−0.999454	−	0.0330469i	$-0.989479\pi$
$857$	−13.7915	+	23.8875i	−0.471107	+	0.815982i	0.528346	+	0.849029i	$0.322812\pi$
$858$	−0.980917	+	1.69900i	−0.0334880	+	0.0580028i
$859$	15.9887	+	27.6933i	0.545528	+	0.944883i	0.998573	+	0.0533953i	$0.0170043\pi$
$859$	15.9887	+	27.6933i	0.545528	+	0.944883i	−0.453045	+	0.891488i	$0.649662\pi$
$860$	64.3138			2.19308
$861$	−2.03134	+	18.1569i	−0.0692278	+	0.618787i
$862$	−19.0891			−0.650178
$863$	13.7107	+	23.7477i	0.466719	+	0.808381i	0.999277	−	0.0380121i	$-0.0121025\pi$
$863$	13.7107	+	23.7477i	0.466719	+	0.808381i	−0.532558	+	0.846393i	$0.678769\pi$
$864$	−3.81810	+	6.61314i	−0.129894	+	0.224984i
$865$	4.45184	−	7.71081i	0.151367	−	0.262175i
$866$	−3.11524	−	5.39576i	−0.105860	−	0.183355i
$867$	−13.8178			−0.469277
$868$	−71.6994	−	52.8295i	−2.43364	−	1.79315i
$869$	7.93650			0.269227
$870$	−3.25408	−	5.63623i	−0.110324	−	0.191086i
$871$	6.63582	−	11.4936i	0.224846	−	0.389445i
$872$	−17.1934	+	29.7799i	−0.582242	+	1.00847i
$873$	3.75203	+	6.49871i	0.126987	+	0.219948i
$874$	−72.2077			−2.44246
$875$	29.2429	−	12.7859i	0.988589	−	0.432243i
$876$	−28.3331			−0.957288
$877$	10.2528	+	17.7583i	0.346211	+	0.599655i	0.985573	−	0.169251i	$-0.0541349\pi$
$877$	10.2528	+	17.7583i	0.346211	+	0.599655i	−0.639362	+	0.768906i	$0.720802\pi$
$878$	−29.8543	+	51.7092i	−1.00753	+	1.74510i
$879$	4.40204	−	7.62456i	0.148477	−	0.257170i
$880$	−2.43021	−	4.20924i	−0.0819222	−	0.141893i
$881$	−30.9178			−1.04165			−0.520824	−	0.853664i	$-0.674375\pi$
$881$	−30.9178			−1.04165			−0.520824	+	0.853664i	$0.674375\pi$
$882$	−11.6824	−	37.6629i	−0.393366	−	1.26818i
$883$	51.5332			1.73423			0.867115	−	0.498109i	$-0.165972\pi$
$883$	51.5332			1.73423			0.867115	+	0.498109i	$0.165972\pi$
$884$	−0.301143	−	0.521594i	−0.0101285	−	0.0175431i
$885$	−10.3060	+	17.8505i	−0.346432	+	0.600038i
$886$	0.396516	−	0.686785i	0.0133212	−	0.0230730i
$887$	−12.6731	−	21.9505i	−0.425521	−	0.737024i	0.570948	−	0.820986i	$-0.306576\pi$
$887$	−12.6731	−	21.9505i	−0.425521	−	0.737024i	−0.996469	+	0.0839621i	$0.973243\pi$
$888$	−35.1767			−1.18045
$889$	−21.2541	+	9.29296i	−0.712839	+	0.311676i
$890$	−10.2047			−0.342062
$891$	1.73777	+	3.00991i	0.0582176	+	0.100836i
$892$	13.7734	−	23.8562i	0.461167	−	0.798764i
$893$	3.49539	−	6.05419i	0.116969	−	0.202596i
$894$	22.9933	+	39.8256i	0.769012	+	1.33197i
$895$	22.5411			0.753466
$896$	43.9065	+	32.3512i	1.46681	+	1.08078i
$897$	6.22315			0.207785
$898$	−30.8235	−	53.3878i	−1.02859	−	1.78158i
$899$	8.71035	−	15.0868i	0.290506	−	0.503172i
$900$	−9.64604	+	16.7074i	−0.321535	+	0.556914i
$901$	0.346213	+	0.599659i	0.0115340	+	0.0199775i
$902$	−20.4455			−0.680761
$903$	2.40245	−	21.4741i	0.0799486	−	0.714614i
$904$	−31.7494			−1.05597
$905$	21.5871	+	37.3900i	0.717580	+	1.24288i
$906$	−19.8862	+	34.4439i	−0.660675	+	1.14432i
$907$	−9.57881	+	16.5910i	−0.318059	+	0.550894i	−0.980083	−	0.198588i	$-0.936364\pi$
$907$	−9.57881	+	16.5910i	−0.318059	+	0.550894i	0.662024	+	0.749483i	$0.269698\pi$
$908$	−33.3100	−	57.6946i	−1.10543	−	1.91466i
$909$	10.9939			0.364646
$910$	−1.19325	+	10.6657i	−0.0395558	+	0.353566i
$911$	−17.6400			−0.584440			−0.292220	−	0.956351i	$-0.594394\pi$
$911$	−17.6400			−0.584440			−0.292220	+	0.956351i	$0.594394\pi$
$912$	−4.60609	−	7.97797i	−0.152523	−	0.264177i
$913$	0.551166	−	0.954647i	0.0182409	−	0.0315942i
$914$	24.2335	−	41.9736i	0.801572	−	1.38836i
$915$	−6.75552	−	11.7009i	−0.223331	−	0.386820i
$916$	47.3214			1.56354
$917$	10.2955	+	7.58592i	0.339987	+	0.250509i
$918$	1.65591			0.0546532
$919$	15.4030	+	26.6788i	0.508099	+	0.880053i	0.999956	+	0.00937696i	$0.00298482\pi$
$919$	15.4030	+	26.6788i	0.508099	+	0.880053i	−0.491857	+	0.870676i	$0.663682\pi$
$920$	−28.0425	+	48.5710i	−0.924534	+	1.60134i
$921$	9.61919	−	16.6609i	0.316963	−	0.548996i
$922$	−28.3230	−	49.0569i	−0.932769	−	1.61560i
$923$	−6.99786			−0.230337
$924$	−7.51532	+	3.28594i	−0.247236	+	0.108099i
$925$	21.4864			0.706467
$926$	0.570260	+	0.987719i	0.0187399	+	0.0324585i
$927$	−18.9294	+	32.7867i	−0.621723	+	1.07686i
$928$	−1.73210	+	3.00009i	−0.0568591	+	0.0984829i
$929$	15.3666	+	26.6157i	0.504160	+	0.873231i	0.999988	+	0.00481065i	$0.00153128\pi$
$929$	15.3666	+	26.6157i	0.504160	+	0.873231i	−0.495828	+	0.868421i	$0.665135\pi$
$930$	−29.1845			−0.956999
$931$	−26.7544	−	6.06228i	−0.876842	−	0.198683i
$932$	8.54415			0.279873
$933$	6.72007	+	11.6395i	0.220005	+	0.381060i
$934$	−37.4774	+	64.9127i	−1.22630	+	2.12401i
$935$	0.133084	−	0.230509i	0.00435232	−	0.00753844i
$936$	−5.09397	−	8.82301i	−0.166502	−	0.288389i
$937$	5.36515			0.175272			0.0876359	−	0.996153i	$-0.472069\pi$
$937$	5.36515			0.175272			0.0876359	+	0.996153i	$0.472069\pi$
$938$	77.5388	−	33.9024i	2.53173	−	1.10695i
$939$	17.0662			0.556935
$940$	−5.71731	−	9.90267i	−0.186478	−	0.322989i
$941$	−1.50135	+	2.60042i	−0.0489427	+	0.0847713i	−0.889459	−	0.457015i	$-0.848919\pi$
$941$	−1.50135	+	2.60042i	−0.0489427	+	0.0847713i	0.840516	+	0.541786i	$0.182252\pi$
$942$	−2.22666	+	3.85668i	−0.0725484	+	0.125657i
$943$	32.4277	+	56.1664i	1.05599	+	1.82903i
$944$	−43.4452			−1.41402
$945$	−15.5757	−	11.4765i	−0.506679	−	0.373331i
$946$	24.1808			0.786185
$947$	12.1217	+	20.9954i	0.393902	+	0.682259i	0.992960	−	0.118447i	$-0.0377915\pi$
$947$	12.1217	+	20.9954i	0.393902	+	0.682259i	−0.599058	+	0.800706i	$0.704458\pi$
$948$	12.3022	−	21.3081i	0.399558	−	0.692055i
$949$	−4.56961	+	7.91480i	−0.148336	+	0.256925i
$950$	10.2345	+	17.7266i	0.332050	+	0.575127i
$951$	12.0732			0.391499
$952$	0.202763	−	1.81238i	0.00657159	−	0.0587396i
$953$	57.3257			1.85696			0.928481	−	0.371381i	$-0.121115\pi$
$953$	57.3257			1.85696			0.928481	+	0.371381i	$0.121115\pi$
$954$	12.3328	+	21.3610i	0.399288	+	0.691587i
$955$	12.2432	−	21.2058i	0.396180	−	0.686203i
$956$	13.6185	−	23.5880i	0.440455	−	0.762890i
$957$	−0.802204	−	1.38946i	−0.0259316	−	0.0449148i
$958$	75.4723			2.43840
$959$	5.23337	−	46.7780i	0.168994	−	1.51054i
$960$	13.7164			0.442694
$961$	−23.5598	−	40.8068i	−0.759993	−	1.31635i
$962$	−11.9474	+	20.6935i	−0.385200	+	0.667185i
$963$	21.2721	−	36.8444i	0.685484	−	1.18729i
$964$	29.8960	+	51.7814i	0.962886	+	1.66777i
$965$	−25.7010			−0.827344
$966$	31.9465	+	23.5388i	1.02786	+	0.757348i
$967$	−26.9022			−0.865115			−0.432557	−	0.901606i	$-0.642389\pi$
$967$	−26.9022			−0.865115			−0.432557	+	0.901606i	$0.642389\pi$
$968$	−2.17934	−	3.77473i	−0.0700467	−	0.121324i
$969$	0.252241	−	0.436895i	0.00810315	−	0.0140351i
$970$	6.51147	−	11.2782i	0.209071	−	0.362121i
$971$	−22.1913	−	38.4365i	−0.712153	−	1.23349i	−0.964047	−	0.265731i	$-0.914387\pi$
$971$	−22.1913	−	38.4365i	−0.712153	−	1.23349i	0.251894	−	0.967755i	$-0.418947\pi$
$972$	60.4152			1.93782
$973$	5.91136	−	2.58464i	0.189510	−	0.0828596i
$974$	−60.6707			−1.94401
$975$	−0.882047	−	1.52775i	−0.0282481	−	0.0489272i
$976$	14.2390	−	24.6627i	0.455781	−	0.789435i
$977$	15.9574	−	27.6390i	0.510523	−	0.884251i	−0.489403	−	0.872058i	$-0.662785\pi$
$977$	15.9574	−	27.6390i	0.510523	−	0.884251i	0.999926	−	0.0121935i	$-0.00388141\pi$
$978$	5.02559	+	8.70458i	0.160701	+	0.278342i
$979$	−2.51568			−0.0804016
$980$	−30.4682	+	32.9406i	−0.973270	+	1.05225i
$981$	−18.4403			−0.588753
$982$	5.25717	+	9.10569i	0.167763	+	0.290574i
$983$	6.91836	−	11.9829i	0.220661	−	0.382197i	−0.734348	−	0.678774i	$-0.762512\pi$
$983$	6.91836	−	11.9829i	0.220661	−	0.382197i	0.955009	+	0.296577i	$0.0958451\pi$
$984$	−15.0494	+	26.0664i	−0.479758	+	0.830966i
$985$	0.490277	+	0.849185i	0.0156215	+	0.0270573i
$986$	0.751215			0.0239236
$987$	−3.52003	+	1.53907i	−0.112044	+	0.0489891i
$988$	−14.9254			−0.474840
$989$	−38.3520	−	66.4277i	−1.21952	−	2.11228i
$990$	4.74072	−	8.21116i	0.150670	−	0.260968i
$991$	19.0863	−	33.0584i	0.606296	−	1.05014i	−0.385549	−	0.922687i	$-0.625988\pi$
$991$	19.0863	−	33.0584i	0.606296	−	1.05014i	0.991845	−	0.127448i	$-0.0406786\pi$
$992$	7.76727	+	13.4533i	0.246611	+	0.427143i
$993$	15.8796			0.503924
$994$	−35.9234	−	26.4691i	−1.13942	−	0.839548i
$995$	36.3660			1.15288
$996$	−1.70871	−	2.95957i	−0.0541425	−	0.0937775i
$997$	6.50813	−	11.2724i	0.206114	−	0.357001i	−0.744373	−	0.667764i	$-0.767251\pi$
$997$	6.50813	−	11.2724i	0.206114	−	0.357001i	0.950487	+	0.310764i	$0.100585\pi$
$998$	−7.72004	+	13.3715i	−0.244374	+	0.423267i
$999$	−21.5377	−	37.3044i	−0.681422	−	1.18026i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1001.2.i.b.144.1	✓	22
7.2	even	3	inner	1001.2.i.b.716.1	yes	22
7.3	odd	6		7007.2.a.u.1.11		11
7.4	even	3		7007.2.a.v.1.11		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1001.2.i.b.144.1	✓	22	1.1	even	1	trivial
1001.2.i.b.716.1	yes	22	7.2	even	3	inner
7007.2.a.u.1.11		11	7.3	odd	6
7007.2.a.v.1.11		11	7.4	even	3

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:	\( N \)	\(=\)	\( 1001 = 7 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1001.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.20504 - 2.08720i) q^{2} +(-0.407005 + 0.704953i) q^{3} +(-1.90426 + 3.29827i) q^{4} +(0.841551 + 1.45761i) q^{5} +1.96183 q^{6} +(2.42416 - 1.05992i) q^{7} +4.35868 q^{8} +(1.16869 + 2.02424i) q^{9} +O(q^{10})\)	\(q+(-1.20504 - 2.08720i) q^{2} +(-0.407005 + 0.704953i) q^{3} +(-1.90426 + 3.29827i) q^{4} +(0.841551 + 1.45761i) q^{5} +1.96183 q^{6} +(2.42416 - 1.05992i) q^{7} +4.35868 q^{8} +(1.16869 + 2.02424i) q^{9} +(2.02821 - 3.51297i) q^{10} +(0.500000 - 0.866025i) q^{11} +(-1.55008 - 2.68483i) q^{12} -1.00000 q^{13} +(-5.13349 - 3.78245i) q^{14} -1.37006 q^{15} +(-1.44388 - 2.50088i) q^{16} +(0.0790708 - 0.136955i) q^{17} +(2.81665 - 4.87859i) q^{18} +(-1.95948 - 3.39391i) q^{19} -6.41013 q^{20} +(-0.239451 + 2.14031i) q^{21} -2.41009 q^{22} +(3.82253 + 6.62081i) q^{23} +(-1.77400 + 3.07267i) q^{24} +(1.08358 - 1.87682i) q^{25} +(1.20504 + 2.08720i) q^{26} -4.34469 q^{27} +(-1.12032 + 10.0139i) q^{28} -1.97099 q^{29} +(1.65098 + 2.85959i) q^{30} +(-4.41926 + 7.65439i) q^{31} +(0.878797 - 1.52212i) q^{32} +(0.407005 + 0.704953i) q^{33} -0.381135 q^{34} +(3.58501 + 2.64151i) q^{35} -8.90198 q^{36} +(4.95725 + 8.58621i) q^{37} +(-4.72251 + 8.17963i) q^{38} +(0.407005 - 0.704953i) q^{39} +(3.66806 + 6.35326i) q^{40} +8.48331 q^{41} +(4.75580 - 2.07939i) q^{42} -10.0332 q^{43} +(1.90426 + 3.29827i) q^{44} +(-1.96703 + 3.40700i) q^{45} +(9.21263 - 15.9567i) q^{46} +(0.891918 + 1.54485i) q^{47} +2.35067 q^{48} +(4.75313 - 5.13884i) q^{49} -5.22306 q^{50} +(0.0643644 + 0.111482i) q^{51} +(1.90426 - 3.29827i) q^{52} +(-2.18926 + 3.79191i) q^{53} +(5.23553 + 9.06821i) q^{54} +1.68310 q^{55} +(10.5662 - 4.61986i) q^{56} +3.19007 q^{57} +(2.37513 + 4.11385i) q^{58} +(7.52228 - 13.0290i) q^{59} +(2.60895 - 4.51884i) q^{60} +(4.93081 + 8.54042i) q^{61} +21.3016 q^{62} +(4.97864 + 3.66836i) q^{63} -10.0115 q^{64} +(-0.841551 - 1.45761i) q^{65} +(0.980917 - 1.69900i) q^{66} +(-6.63582 + 11.4936i) q^{67} +(0.301143 + 0.521594i) q^{68} -6.22315 q^{69} +(1.19325 - 10.6657i) q^{70} +6.99786 q^{71} +(5.09397 + 8.82301i) q^{72} +(4.56961 - 7.91480i) q^{73} +(11.9474 - 20.6935i) q^{74} +(0.882047 + 1.52775i) q^{75} +14.9254 q^{76} +(0.294163 - 2.62935i) q^{77} -1.96183 q^{78} +(3.96825 + 6.87321i) q^{79} +(2.43021 - 4.20924i) q^{80} +(-1.73777 + 3.00991i) q^{81} +(-10.2228 - 17.7063i) q^{82} +1.10233 q^{83} +(-6.60336 - 4.86549i) q^{84} +0.266169 q^{85} +(12.0904 + 20.9412i) q^{86} +(0.802204 - 1.38946i) q^{87} +(2.17934 - 3.77473i) q^{88} +(-1.25784 - 2.17865i) q^{89} +9.48144 q^{90} +(-2.42416 + 1.05992i) q^{91} -29.1163 q^{92} +(-3.59732 - 6.23075i) q^{93} +(2.14960 - 3.72322i) q^{94} +(3.29800 - 5.71230i) q^{95} +(0.715349 + 1.23902i) q^{96} +3.21045 q^{97} +(-16.4535 - 3.72819i) q^{98} +2.33739 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{2} - q^{3} - 6 q^{4} - 12 q^{6} + 15 q^{7} - 4 q^{9}+O(q^{10}) \) 22 * q + 2 * q^2 - q^3 - 6 * q^4 - 12 * q^6 + 15 * q^7 - 4 * q^9	\( 22 q + 2 q^{2} - q^{3} - 6 q^{4} - 12 q^{6} + 15 q^{7} - 4 q^{9} - 12 q^{10} + 11 q^{11} - 13 q^{12} - 22 q^{13} + 8 q^{14} + 30 q^{15} + 4 q^{16} + 2 q^{17} + 21 q^{18} - 9 q^{19} - 24 q^{20} - 9 q^{21} + 4 q^{22} + 27 q^{23} + 7 q^{24} + 7 q^{25} - 2 q^{26} - 4 q^{27} - 4 q^{28} + 42 q^{29} + 12 q^{30} + 2 q^{31} + 7 q^{32} + q^{33} - 20 q^{34} + 13 q^{35} + 48 q^{36} + 38 q^{37} - 9 q^{38} + q^{39} + 22 q^{40} + 6 q^{41} + 17 q^{42} - 46 q^{43} + 6 q^{44} + 6 q^{46} - 2 q^{47} + 24 q^{48} + 7 q^{49} + 14 q^{50} + 11 q^{51} + 6 q^{52} - 5 q^{53} + 37 q^{54} + 9 q^{56} - 44 q^{57} + 5 q^{58} + 16 q^{59} + 22 q^{60} - 11 q^{61} + 44 q^{62} - 16 q^{63} - 12 q^{64} - 6 q^{66} + 15 q^{67} - 12 q^{68} - 12 q^{69} + 7 q^{70} - 20 q^{71} + 32 q^{72} - 5 q^{73} + 20 q^{74} - 10 q^{75} + 14 q^{76} - 3 q^{77} + 12 q^{78} - 3 q^{79} + 21 q^{80} + 21 q^{81} - 4 q^{82} - 32 q^{83} + 32 q^{84} - 76 q^{85} + 15 q^{86} - 29 q^{87} - 8 q^{89} + 10 q^{90} - 15 q^{91} - 40 q^{92} + 40 q^{93} - 31 q^{94} + 23 q^{95} + 4 q^{96} - 14 q^{97} - 31 q^{98} - 8 q^{99}+O(q^{100}) \) 22 * q + 2 * q^2 - q^3 - 6 * q^4 - 12 * q^6 + 15 * q^7 - 4 * q^9 - 12 * q^10 + 11 * q^11 - 13 * q^12 - 22 * q^13 + 8 * q^14 + 30 * q^15 + 4 * q^16 + 2 * q^17 + 21 * q^18 - 9 * q^19 - 24 * q^20 - 9 * q^21 + 4 * q^22 + 27 * q^23 + 7 * q^24 + 7 * q^25 - 2 * q^26 - 4 * q^27 - 4 * q^28 + 42 * q^29 + 12 * q^30 + 2 * q^31 + 7 * q^32 + q^33 - 20 * q^34 + 13 * q^35 + 48 * q^36 + 38 * q^37 - 9 * q^38 + q^39 + 22 * q^40 + 6 * q^41 + 17 * q^42 - 46 * q^43 + 6 * q^44 + 6 * q^46 - 2 * q^47 + 24 * q^48 + 7 * q^49 + 14 * q^50 + 11 * q^51 + 6 * q^52 - 5 * q^53 + 37 * q^54 + 9 * q^56 - 44 * q^57 + 5 * q^58 + 16 * q^59 + 22 * q^60 - 11 * q^61 + 44 * q^62 - 16 * q^63 - 12 * q^64 - 6 * q^66 + 15 * q^67 - 12 * q^68 - 12 * q^69 + 7 * q^70 - 20 * q^71 + 32 * q^72 - 5 * q^73 + 20 * q^74 - 10 * q^75 + 14 * q^76 - 3 * q^77 + 12 * q^78 - 3 * q^79 + 21 * q^80 + 21 * q^81 - 4 * q^82 - 32 * q^83 + 32 * q^84 - 76 * q^85 + 15 * q^86 - 29 * q^87 - 8 * q^89 + 10 * q^90 - 15 * q^91 - 40 * q^92 + 40 * q^93 - 31 * q^94 + 23 * q^95 + 4 * q^96 - 14 * q^97 - 31 * q^98 - 8 * q^99

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