LMFDB - Embedded newform 287.2.e.d.247.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [287,2,Mod(165,287)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(287, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("287.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 287 = 7 \cdot 41 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	287.e (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:	$2.29170653801$
Analytic rank:	$0$
Dimension:	$34$
Relative dimension:	$17$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			247.4
Character	$\chi$	$=$	287.247
Dual form			287.2.e.d.165.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.18475 + 2.05204i) q^{2} +(0.823159 + 1.42575i) q^{3} +(-1.80725 - 3.13025i) q^{4} +(2.01488 - 3.48988i) q^{5} -3.90094 q^{6} +(0.327045 - 2.62546i) q^{7} +3.82554 q^{8} +(0.144819 - 0.250833i) q^{9} +O(q^{10})$	\(q+(-1.18475 + 2.05204i) q^{2} +(0.823159 + 1.42575i) q^{3} +(-1.80725 - 3.13025i) q^{4} +(2.01488 - 3.48988i) q^{5} -3.90094 q^{6} +(0.327045 - 2.62546i) q^{7} +3.82554 q^{8} +(0.144819 - 0.250833i) q^{9} +(4.77425 + 8.26924i) q^{10} +(1.09966 + 1.90466i) q^{11} +(2.97531 - 5.15338i) q^{12} +2.49374 q^{13} +(5.00009 + 3.78162i) q^{14} +6.63427 q^{15} +(-0.917802 + 1.58968i) q^{16} +(-2.36884 - 4.10295i) q^{17} +(0.343147 + 0.594347i) q^{18} +(-0.280091 + 0.485132i) q^{19} -14.5656 q^{20} +(4.01247 - 1.69489i) q^{21} -5.21126 q^{22} +(-3.93444 + 6.81465i) q^{23} +(3.14903 + 5.45428i) q^{24} +(-5.61949 - 9.73324i) q^{25} +(-2.95445 + 5.11726i) q^{26} +5.41579 q^{27} +(-8.80939 + 3.72113i) q^{28} +1.33395 q^{29} +(-7.85993 + 13.6138i) q^{30} +(-2.09368 - 3.62635i) q^{31} +(1.65082 + 2.85930i) q^{32} +(-1.81038 + 3.13568i) q^{33} +11.2259 q^{34} +(-8.50357 - 6.43134i) q^{35} -1.04689 q^{36} +(-4.32436 + 7.49002i) q^{37} +(-0.663674 - 1.14952i) q^{38} +(2.05274 + 3.55546i) q^{39} +(7.70801 - 13.3507i) q^{40} +1.00000 q^{41} +(-1.27578 + 10.2418i) q^{42} +2.23622 q^{43} +(3.97471 - 6.88439i) q^{44} +(-0.583584 - 1.01080i) q^{45} +(-9.32263 - 16.1473i) q^{46} +(-1.59813 + 2.76804i) q^{47} -3.02199 q^{48} +(-6.78608 - 1.71729i) q^{49} +26.6307 q^{50} +(3.89986 - 6.75475i) q^{51} +(-4.50681 - 7.80602i) q^{52} +(6.86587 + 11.8920i) q^{53} +(-6.41634 + 11.1134i) q^{54} +8.86270 q^{55} +(1.25113 - 10.0438i) q^{56} -0.922238 q^{57} +(-1.58039 + 2.73732i) q^{58} +(7.08274 + 12.2677i) q^{59} +(-11.9898 - 20.7669i) q^{60} +(3.20490 - 5.55105i) q^{61} +9.92190 q^{62} +(-0.611190 - 0.462249i) q^{63} -11.4944 q^{64} +(5.02459 - 8.70284i) q^{65} +(-4.28969 - 7.42996i) q^{66} +(-0.349745 - 0.605775i) q^{67} +(-8.56216 + 14.8301i) q^{68} -12.9547 q^{69} +(23.2719 - 9.83018i) q^{70} -5.49009 q^{71} +(0.554010 - 0.959573i) q^{72} +(-3.03493 - 5.25666i) q^{73} +(-10.2466 - 17.7475i) q^{74} +(9.25146 - 16.0240i) q^{75} +2.02478 q^{76} +(5.36025 - 2.26419i) q^{77} -9.72793 q^{78} +(-0.125178 + 0.216815i) q^{79} +(3.69852 + 6.40603i) q^{80} +(4.02360 + 6.96908i) q^{81} +(-1.18475 + 2.05204i) q^{82} +7.93567 q^{83} +(-12.5569 - 9.49694i) q^{84} -19.0917 q^{85} +(-2.64936 + 4.58882i) q^{86} +(1.09805 + 1.90188i) q^{87} +(4.20678 + 7.28636i) q^{88} +(-2.78839 + 4.82963i) q^{89} +2.76560 q^{90} +(0.815565 - 6.54721i) q^{91} +28.4421 q^{92} +(3.44686 - 5.97013i) q^{93} +(-3.78675 - 6.55884i) q^{94} +(1.12870 + 1.95497i) q^{95} +(-2.71777 + 4.70732i) q^{96} +9.96956 q^{97} +(11.5637 - 11.8908i) q^{98} +0.637002 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 34 q - 3 q^{2} - q^{3} - 25 q^{4} + q^{5} + 4 q^{6} - 2 q^{7} + 18 q^{8} - 26 q^{9}+O(q^{10}) $ 34 * q - 3 * q^2 - q^3 - 25 * q^4 + q^5 + 4 * q^6 - 2 * q^7 + 18 * q^8 - 26 * q^9	\( 34 q - 3 q^{2} - q^{3} - 25 q^{4} + q^{5} + 4 q^{6} - 2 q^{7} + 18 q^{8} - 26 q^{9} + 2 q^{10} - 15 q^{11} - 4 q^{12} - 10 q^{13} + 21 q^{14} + 48 q^{15} - 33 q^{16} - 4 q^{17} - 10 q^{18} - 5 q^{19} - 52 q^{20} + 12 q^{21} + 32 q^{22} - 12 q^{23} - 16 q^{24} - 24 q^{25} - 31 q^{26} - 22 q^{27} + 60 q^{28} + 28 q^{29} + 33 q^{30} + 3 q^{31} - 16 q^{32} - 4 q^{33} - 48 q^{34} + 45 q^{35} + 114 q^{36} - 24 q^{37} - 45 q^{39} - 36 q^{40} + 34 q^{41} + 65 q^{42} + 28 q^{43} + 9 q^{44} + 21 q^{45} - 44 q^{46} - 19 q^{47} - 120 q^{48} - 10 q^{49} - 8 q^{50} - 2 q^{51} + 25 q^{52} - 4 q^{53} - 68 q^{54} + 18 q^{55} + 25 q^{56} - 24 q^{57} + q^{58} + 27 q^{59} - 66 q^{60} + q^{61} - 46 q^{62} + 37 q^{63} + 150 q^{64} - 22 q^{65} + 16 q^{66} - 49 q^{67} - 45 q^{68} + 24 q^{69} + 73 q^{70} + 80 q^{71} + 23 q^{72} + 14 q^{73} - 33 q^{74} - 27 q^{75} - 18 q^{76} - 20 q^{77} - 24 q^{78} - 61 q^{79} + 82 q^{80} - 53 q^{81} - 3 q^{82} - 36 q^{83} + 188 q^{84} - 26 q^{85} + 4 q^{86} + 17 q^{87} - 74 q^{88} - 18 q^{89} - 40 q^{90} + 7 q^{91} + 56 q^{92} + 36 q^{93} + 5 q^{94} - 20 q^{95} - 148 q^{96} + 52 q^{97} + 142 q^{98} + 76 q^{99}+O(q^{100}) \) 34 * q - 3 * q^2 - q^3 - 25 * q^4 + q^5 + 4 * q^6 - 2 * q^7 + 18 * q^8 - 26 * q^9 + 2 * q^10 - 15 * q^11 - 4 * q^12 - 10 * q^13 + 21 * q^14 + 48 * q^15 - 33 * q^16 - 4 * q^17 - 10 * q^18 - 5 * q^19 - 52 * q^20 + 12 * q^21 + 32 * q^22 - 12 * q^23 - 16 * q^24 - 24 * q^25 - 31 * q^26 - 22 * q^27 + 60 * q^28 + 28 * q^29 + 33 * q^30 + 3 * q^31 - 16 * q^32 - 4 * q^33 - 48 * q^34 + 45 * q^35 + 114 * q^36 - 24 * q^37 - 45 * q^39 - 36 * q^40 + 34 * q^41 + 65 * q^42 + 28 * q^43 + 9 * q^44 + 21 * q^45 - 44 * q^46 - 19 * q^47 - 120 * q^48 - 10 * q^49 - 8 * q^50 - 2 * q^51 + 25 * q^52 - 4 * q^53 - 68 * q^54 + 18 * q^55 + 25 * q^56 - 24 * q^57 + q^58 + 27 * q^59 - 66 * q^60 + q^61 - 46 * q^62 + 37 * q^63 + 150 * q^64 - 22 * q^65 + 16 * q^66 - 49 * q^67 - 45 * q^68 + 24 * q^69 + 73 * q^70 + 80 * q^71 + 23 * q^72 + 14 * q^73 - 33 * q^74 - 27 * q^75 - 18 * q^76 - 20 * q^77 - 24 * q^78 - 61 * q^79 + 82 * q^80 - 53 * q^81 - 3 * q^82 - 36 * q^83 + 188 * q^84 - 26 * q^85 + 4 * q^86 + 17 * q^87 - 74 * q^88 - 18 * q^89 - 40 * q^90 + 7 * q^91 + 56 * q^92 + 36 * q^93 + 5 * q^94 - 20 * q^95 - 148 * q^96 + 52 * q^97 + 142 * q^98 + 76 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/287\mathbb{Z}\right)^\times$.

$n$	$206$	$211$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

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 $

$2$	−1.18475	+	2.05204i	−0.837742	+	1.45101i	0.0540355	+	0.998539i	$0.482792\pi$
$2$	−1.18475	+	2.05204i	−0.837742	+	1.45101i	−0.891778	+	0.452473i	$0.850542\pi$
$3$	0.823159	+	1.42575i	0.475251	+	0.823159i	0.999598	−	0.0283456i	$-0.00902390\pi$
$3$	0.823159	+	1.42575i	0.475251	+	0.823159i	−0.524347	+	0.851505i	$0.675691\pi$
$4$	−1.80725	−	3.13025i	−0.903625	−	1.56512i
$5$	2.01488	−	3.48988i	0.901082	−	1.56072i	0.0749903	−	0.997184i	$-0.476107\pi$
$5$	2.01488	−	3.48988i	0.901082	−	1.56072i	0.826092	−	0.563536i	$-0.190559\pi$
$6$	−3.90094			−1.59255
$7$	0.327045	−	2.62546i	0.123611	−	0.992331i
$7$	0.327045	−	2.62546i	0.123611	−	0.992331i
$8$	3.82554			1.35253
$9$	0.144819	−	0.250833i	0.0482729	−	0.0836110i
$10$	4.77425	+	8.26924i	1.50975	+	2.61496i
$11$	1.09966	+	1.90466i	0.331559	+	0.574277i	0.982818	−	0.184579i	$-0.0590921\pi$
$11$	1.09966	+	1.90466i	0.331559	+	0.574277i	−0.651259	+	0.758856i	$0.725759\pi$
$12$	2.97531	−	5.15338i	0.858897	−	1.48765i
$13$	2.49374			0.691639			0.345819	−	0.938301i	$-0.387601\pi$
$13$	2.49374			0.691639			0.345819	+	0.938301i	$0.387601\pi$
$14$	5.00009	+	3.78162i	1.33633	+	1.01068i
$15$	6.63427			1.71296
$16$	−0.917802	+	1.58968i	−0.229450	+	0.397420i
$17$	−2.36884	−	4.10295i	−0.574527	−	0.995111i	−0.996093	−	0.0883127i	$-0.971853\pi$
$17$	−2.36884	−	4.10295i	−0.574527	−	0.995111i	0.421565	−	0.906798i	$-0.361481\pi$
$18$	0.343147	+	0.594347i	0.0808804	+	0.140089i
$19$	−0.280091	+	0.485132i	−0.0642573	+	0.111297i	−0.896364	−	0.443318i	$-0.853801\pi$
$19$	−0.280091	+	0.485132i	−0.0642573	+	0.111297i	0.832107	+	0.554615i	$0.187134\pi$
$20$	−14.5656			−3.25696
$21$	4.01247	−	1.69489i	0.875592	−	0.369854i
$22$	−5.21126			−1.11104
$23$	−3.93444	+	6.81465i	−0.820387	+	1.42095i	0.0850068	+	0.996380i	$0.472909\pi$
$23$	−3.93444	+	6.81465i	−0.820387	+	1.42095i	−0.905394	+	0.424572i	$0.860425\pi$
$24$	3.14903	+	5.45428i	0.642793	+	1.11335i
$25$	−5.61949	−	9.73324i	−1.12390	−	1.94665i
$26$	−2.95445	+	5.11726i	−0.579415	+	1.00358i
$27$	5.41579			1.04227
$28$	−8.80939	+	3.72113i	−1.66482	+	0.703227i
$29$	1.33395			0.247708			0.123854	−	0.992300i	$-0.460474\pi$
$29$	1.33395			0.247708			0.123854	+	0.992300i	$0.460474\pi$
$30$	−7.85993	+	13.6138i	−1.43502	+	2.48553i
$31$	−2.09368	−	3.62635i	−0.376035	−	0.651312i	0.614446	−	0.788959i	$-0.289380\pi$
$31$	−2.09368	−	3.62635i	−0.376035	−	0.651312i	−0.990481	+	0.137647i	$0.956046\pi$
$32$	1.65082	+	2.85930i	0.291826	+	0.505458i
$33$	−1.81038	+	3.13568i	−0.315147	+	0.545851i
$34$	11.2259			1.92522
$35$	−8.50357	−	6.43134i	−1.43737	−	1.08709i
$36$	−1.04689			−0.174482
$37$	−4.32436	+	7.49002i	−0.710921	+	1.23135i	0.253591	+	0.967312i	$0.418388\pi$
$37$	−4.32436	+	7.49002i	−0.710921	+	1.23135i	−0.964512	+	0.264040i	$0.914945\pi$
$38$	−0.663674	−	1.14952i	−0.107662	−	0.186476i
$39$	2.05274	+	3.55546i	0.328702	+	0.569329i
$40$	7.70801	−	13.3507i	1.21874	−	2.11093i
$41$	1.00000			0.156174
$41$	1.00000			0.156174
$42$	−1.27578	+	10.2418i	−0.196858	+	1.58034i
$43$	2.23622			0.341020			0.170510	−	0.985356i	$-0.445458\pi$
$43$	2.23622			0.341020			0.170510	+	0.985356i	$0.445458\pi$
$44$	3.97471	−	6.88439i	0.599209	−	1.03786i
$45$	−0.583584	−	1.01080i	−0.0869956	−	0.150681i
$46$	−9.32263	−	16.1473i	−1.37455	−	2.38078i
$47$	−1.59813	+	2.76804i	−0.233111	+	0.403760i	−0.958722	−	0.284345i	$-0.908224\pi$
$47$	−1.59813	+	2.76804i	−0.233111	+	0.403760i	0.725611	+	0.688105i	$0.241557\pi$
$48$	−3.02199			−0.436186
$49$	−6.78608	−	1.71729i	−0.969440	−	0.245327i
$50$	26.6307			3.76615
$51$	3.89986	−	6.75475i	0.546090	−	0.945855i
$52$	−4.50681	−	7.80602i	−0.624982	−	1.08250i
$53$	6.86587	+	11.8920i	0.943100	+	1.63350i	0.759512	+	0.650493i	$0.225438\pi$
$53$	6.86587	+	11.8920i	0.943100	+	1.63350i	0.183587	+	0.983003i	$0.441229\pi$
$54$	−6.41634	+	11.1134i	−0.873153	+	1.51235i
$55$	8.86270			1.19505
$56$	1.25113	−	10.0438i	0.167189	−	1.34216i
$57$	−0.922238			−0.122153
$58$	−1.58039	+	2.73732i	−0.207516	+	0.359428i
$59$	7.08274	+	12.2677i	0.922094	+	1.59711i	0.796170	+	0.605073i	$0.206856\pi$
$59$	7.08274	+	12.2677i	0.922094	+	1.59711i	0.125924	+	0.992040i	$0.459811\pi$
$60$	−11.9898	−	20.7669i	−1.54787	−	2.68100i
$61$	3.20490	−	5.55105i	0.410345	−	0.710739i	−0.584582	−	0.811334i	$-0.698742\pi$
$61$	3.20490	−	5.55105i	0.410345	−	0.710739i	0.994927	+	0.100596i	$0.0320749\pi$
$62$	9.92190			1.26008
$63$	−0.611190	−	0.462249i	−0.0770027	−	0.0582379i
$64$	−11.4944			−1.43680
$65$	5.02459	−	8.70284i	0.623223	−	1.07945i
$66$	−4.28969	−	7.42996i	−0.528025	−	0.914565i
$67$	−0.349745	−	0.605775i	−0.0427281	−	0.0740072i	0.843870	−	0.536547i	$-0.180272\pi$
$67$	−0.349745	−	0.605775i	−0.0427281	−	0.0740072i	−0.886599	+	0.462540i	$0.846938\pi$
$68$	−8.56216	+	14.8301i	−1.03831	+	1.79841i
$69$	−12.9547			−1.55956
$70$	23.2719	−	9.83018i	2.78153	−	1.17493i
$71$	−5.49009			−0.651553			−0.325777	−	0.945447i	$-0.605626\pi$
$71$	−5.49009			−0.651553			−0.325777	+	0.945447i	$0.605626\pi$
$72$	0.554010	−	0.959573i	0.0652907	−	0.113087i
$73$	−3.03493	−	5.25666i	−0.355212	−	0.615245i	0.631942	−	0.775016i	$-0.282258\pi$
$73$	−3.03493	−	5.25666i	−0.355212	−	0.615245i	−0.987154	+	0.159770i	$0.948925\pi$
$74$	−10.2466	−	17.7475i	−1.19114	−	2.06311i
$75$	9.25146	−	16.0240i	1.06827	−	1.85029i
$76$	2.02478			0.232258
$77$	5.36025	−	2.26419i	0.610857	−	0.258029i
$78$	−9.72793			−1.10147
$79$	−0.125178	+	0.216815i	−0.0140836	+	0.0243936i	−0.872981	−	0.487754i	$-0.837816\pi$
$79$	−0.125178	+	0.216815i	−0.0140836	+	0.0243936i	0.858898	+	0.512147i	$0.171150\pi$
$80$	3.69852	+	6.40603i	0.413507	+	0.716216i
$81$	4.02360	+	6.96908i	0.447067	+	0.774342i
$82$	−1.18475	+	2.05204i	−0.130833	+	0.226610i
$83$	7.93567			0.871053			0.435527	−	0.900176i	$-0.356562\pi$
$83$	7.93567			0.871053			0.435527	+	0.900176i	$0.356562\pi$
$84$	−12.5569	−	9.49694i	−1.37007	−	1.03620i
$85$	−19.0917			−2.07079
$86$	−2.64936	+	4.58882i	−0.285687	+	0.494825i
$87$	1.09805	+	1.90188i	0.117724	+	0.203903i
$88$	4.20678	+	7.28636i	0.448445	+	0.776729i
$89$	−2.78839	+	4.82963i	−0.295568	+	0.511939i	−0.975117	−	0.221691i	$-0.928842\pi$
$89$	−2.78839	+	4.82963i	−0.295568	+	0.511939i	0.679549	+	0.733630i	$0.262176\pi$
$90$	2.76560			0.291520
$91$	0.815565	−	6.54721i	0.0854944	−	0.686334i
$92$	28.4421			2.96529
$93$	3.44686	−	5.97013i	0.357422	−	0.619074i
$94$	−3.78675	−	6.55884i	−0.390573	−	0.676493i
$95$	1.12870	+	1.95497i	0.115802	+	0.200575i
$96$	−2.71777	+	4.70732i	−0.277381	+	0.480439i
$97$	9.96956			1.01226			0.506128	−	0.862458i	$-0.331076\pi$
$97$	9.96956			1.01226			0.506128	+	0.862458i	$0.331076\pi$
$98$	11.5637	−	11.8908i	1.16811	−	1.20115i
$99$	0.637002			0.0640212
$100$	−20.3116	+	35.1808i	−2.03116	+	3.51808i
$101$	−0.986285	−	1.70830i	−0.0981390	−	0.169982i	0.812775	−	0.582577i	$-0.197956\pi$
$101$	−0.986285	−	1.70830i	−0.0981390	−	0.169982i	−0.910914	+	0.412595i	$0.864622\pi$
$102$	9.24069	+	16.0053i	0.914965	+	1.58477i
$103$	−9.80809	+	16.9881i	−0.966420	+	1.67389i	−0.260669	+	0.965428i	$0.583943\pi$
$103$	−9.80809	+	16.9881i	−0.966420	+	1.67389i	−0.705751	+	0.708460i	$0.749390\pi$
$104$	9.53991			0.935465
$105$	2.16970	−	17.4180i	0.211741	−	1.69982i
$106$	−32.5373			−3.16030
$107$	−1.78730	+	3.09569i	−0.172785	+	0.299272i	−0.939392	−	0.342844i	$-0.888610\pi$
$107$	−1.78730	+	3.09569i	−0.172785	+	0.299272i	0.766608	+	0.642116i	$0.221943\pi$
$108$	−9.78768	−	16.9528i	−0.941820	−	1.63128i
$109$	−4.71885	−	8.17330i	−0.451984	−	0.782860i	0.546525	−	0.837443i	$-0.315950\pi$
$109$	−4.71885	−	8.17330i	−0.451984	−	0.782860i	−0.998509	+	0.0545831i	$0.982617\pi$
$110$	−10.5001	+	18.1866i	−1.00114	+	1.73403i
$111$	−14.2386			−1.35146
$112$	3.87348	+	2.92955i	0.366009	+	0.276816i
$113$	6.51816			0.613177			0.306588	−	0.951842i	$-0.400813\pi$
$113$	6.51816			0.613177			0.306588	+	0.951842i	$0.400813\pi$
$114$	1.09262	−	1.89247i	0.102333	−	0.177246i
$115$	15.8549	+	27.4614i	1.47847	+	2.56079i
$116$	−2.41078	−	4.17559i	−0.223835	−	0.387694i
$117$	0.361140	−	0.625512i	0.0333874	−	0.0578286i
$118$	−33.5650			−3.08991
$119$	−11.5468	+	4.87744i	−1.05850	+	0.447114i
$120$	25.3797			2.31684
$121$	3.08151	−	5.33734i	0.280138	−	0.485213i
$122$	7.59398	+	13.1532i	0.687527	+	1.19083i
$123$	0.823159	+	1.42575i	0.0742217	+	0.128556i
$124$	−7.56759	+	13.1075i	−0.679590	+	1.17708i
$125$	−25.1416			−2.24873
$126$	1.67266	−	0.706539i	0.149012	−	0.0629435i
$127$	11.4657			1.01742			0.508709	−	0.860939i	$-0.330123\pi$
$127$	11.4657			1.01742			0.508709	+	0.860939i	$0.330123\pi$
$128$	10.3163	−	17.8684i	0.911844	−	1.57936i
$129$	1.84077	+	3.18830i	0.162070	+	0.280714i
$130$	11.9057	+	20.6213i	1.04420	+	1.80861i
$131$	0.875990	−	1.51726i	0.0765356	−	0.132564i	−0.825217	−	0.564815i	$-0.808947\pi$
$131$	0.875990	−	1.51726i	0.0765356	−	0.132564i	0.901753	+	0.432252i	$0.142281\pi$
$132$	13.0873			1.13910
$133$	1.18209	+	0.894028i	0.102500	+	0.0775220i
$134$	1.65743			0.143181
$135$	10.9122	−	18.9004i	0.939170	−	1.62669i
$136$	−9.06209	−	15.6960i	−0.777068	−	1.34592i
$137$	−6.35114	−	11.0005i	−0.542615	−	0.939837i	−0.998753	−	0.0499275i	$-0.984101\pi$
$137$	−6.35114	−	11.0005i	−0.542615	−	0.939837i	0.456138	−	0.889909i	$-0.349232\pi$
$138$	15.3480	−	26.5835i	1.30651	−	2.26294i
$139$	3.13302			0.265739			0.132869	−	0.991134i	$-0.457581\pi$
$139$	3.13302			0.265739			0.132869	+	0.991134i	$0.457581\pi$
$140$	−4.76360	+	38.2413i	−0.402597	+	3.23198i
$141$	−5.26205			−0.443144
$142$	6.50436	−	11.2659i	0.545834	−	0.945412i
$143$	2.74226	+	4.74973i	0.229319	+	0.397192i
$144$	0.265829	+	0.460430i	0.0221525	+	0.0383692i
$145$	2.68775	−	4.65532i	0.223206	−	0.386603i
$146$	14.3825			1.19030
$147$	−3.13760	−	11.0889i	−0.258785	−	0.914595i
$148$	31.2608			2.56962
$149$	−5.01026	+	8.67802i	−0.410456	+	0.710931i	−0.994940	−	0.100474i	$-0.967964\pi$
$149$	−5.01026	+	8.67802i	−0.410456	+	0.710931i	0.584483	+	0.811406i	$0.301297\pi$
$150$	21.9213	+	37.9688i	1.78987	+	3.10014i
$151$	−6.00065	−	10.3934i	−0.488326	−	0.845805i	0.511584	−	0.859233i	$-0.329059\pi$
$151$	−6.00065	−	10.3934i	−0.488326	−	0.845805i	−0.999910	+	0.0134283i	$0.995725\pi$
$152$	−1.07150	+	1.85589i	−0.0869102	+	0.150533i
$153$	−1.37221			−0.110936
$154$	−1.70432	+	13.6819i	−0.137338	+	1.10252i
$155$	−16.8740			−1.35535
$156$	7.41964	−	12.8512i	0.594047	−	1.02892i
$157$	7.12737	+	12.3450i	0.568826	+	0.985236i	0.996682	+	0.0813891i	$0.0259357\pi$
$157$	7.12737	+	12.3450i	0.568826	+	0.985236i	−0.427856	+	0.903847i	$0.640731\pi$
$158$	−0.296609	−	0.513742i	−0.0235969	−	0.0408711i
$159$	−11.3034	+	19.5781i	−0.896418	+	1.55264i
$160$	13.3048			1.05184
$161$	16.6049	+	12.5584i	1.30865	+	0.989741i
$162$	−19.0678			−1.49811
$163$	3.63140	−	6.28977i	0.284433	−	0.492653i	−0.688038	−	0.725674i	$-0.741528\pi$
$163$	3.63140	−	6.28977i	0.284433	−	0.492653i	0.972472	+	0.233021i	$0.0748612\pi$
$164$	−1.80725	−	3.13025i	−0.141122	−	0.244431i
$165$	7.29541	+	12.6360i	0.567947	+	0.983713i
$166$	−9.40176	+	16.2843i	−0.729718	+	1.26391i
$167$	−2.96940			−0.229779			−0.114890	−	0.993378i	$-0.536651\pi$
$167$	−2.96940			−0.229779			−0.114890	+	0.993378i	$0.536651\pi$
$168$	15.3499	−	6.48386i	1.18427	−	0.500241i
$169$	−6.78127			−0.521636
$170$	22.6188	−	39.1770i	1.73478	−	3.00474i
$171$	0.0811248	+	0.140512i	0.00620376	+	0.0107452i
$172$	−4.04141	−	6.99993i	−0.308155	−	0.533739i
$173$	−10.1693	+	17.6138i	−0.773158	+	1.33915i	0.162665	+	0.986681i	$0.447991\pi$
$173$	−10.1693	+	17.6138i	−0.773158	+	1.33915i	−0.935824	+	0.352468i	$0.885342\pi$
$174$	−5.20366			−0.394488
$175$	−27.3921	+	11.5705i	−2.07065	+	0.874650i
$176$	−4.03707			−0.304305
$177$	−11.6604	+	20.1965i	−0.876452	+	1.51806i
$178$	−6.60706	−	11.4438i	−0.495220	−	0.857747i
$179$	−8.14043	−	14.0996i	−0.608444	−	1.05386i	−0.991497	−	0.130129i	$-0.958461\pi$
$179$	−8.14043	−	14.0996i	−0.608444	−	1.05386i	0.383053	−	0.923726i	$-0.374873\pi$
$180$	−2.10936	+	3.65353i	−0.157223	+	0.272318i
$181$	−10.2189			−0.759567			−0.379783	−	0.925075i	$-0.624001\pi$
$181$	−10.2189			−0.759567			−0.379783	+	0.925075i	$0.624001\pi$
$182$	12.4689	+	9.43036i	0.924257	+	0.699025i
$183$	10.5526			0.780068
$184$	−15.0514	+	26.0697i	−1.10960	+	1.92189i
$185$	17.4262	+	30.1830i	1.28120	+	2.21910i
$186$	8.16730	+	14.1462i	0.598856	+	1.03725i
$187$	5.20981	−	9.02366i	0.380979	−	0.659875i
$188$	11.5529			0.842578
$189$	1.77121	−	14.2189i	0.128836	−	1.03428i
$190$	−5.34889			−0.388050
$191$	5.51906	−	9.55929i	0.399345	−	0.691686i	−0.594300	−	0.804243i	$-0.702571\pi$
$191$	5.51906	−	9.55929i	0.399345	−	0.691686i	0.993645	+	0.112558i	$0.0359043\pi$
$192$	−9.46173	−	16.3882i	−0.682842	−	1.18272i
$193$	−10.2439	−	17.7429i	−0.737369	−	1.27716i	−0.953676	−	0.300835i	$-0.902735\pi$
$193$	−10.2439	−	17.7429i	−0.737369	−	1.27716i	0.216308	−	0.976325i	$-0.430599\pi$
$194$	−11.8114	+	20.4580i	−0.848009	+	1.46880i
$195$	16.5441			1.18475
$196$	6.88861	+	24.3457i	0.492044	+	1.73898i
$197$	−2.42929			−0.173079			−0.0865397	−	0.996248i	$-0.527581\pi$
$197$	−2.42929			−0.173079			−0.0865397	+	0.996248i	$0.527581\pi$
$198$	−0.754686	+	1.30716i	−0.0536332	+	0.0928955i
$199$	0.907709	+	1.57220i	0.0643458	+	0.111450i	0.896404	−	0.443239i	$-0.146171\pi$
$199$	0.907709	+	1.57220i	0.0643458	+	0.111450i	−0.832058	+	0.554689i	$0.812837\pi$
$200$	−21.4976	−	37.2349i	−1.52011	−	2.63291i
$201$	0.575791	−	0.997299i	0.0406131	−	0.0703440i
$202$	4.67399			0.328861
$203$	0.436262	−	3.50223i	0.0306196	−	0.245809i
$204$	−28.1921			−1.97384
$205$	2.01488	−	3.48988i	0.140725	−	0.243743i
$206$	−23.2402	−	40.2532i	−1.61922	−	2.80457i
$207$	1.13956	+	1.97378i	0.0792049	+	0.137187i
$208$	−2.28876	+	3.96425i	−0.158697	+	0.274871i
$209$	−1.23201			−0.0852203
$210$	33.1719	+	25.0883i	2.28908	+	1.73125i
$211$	17.1401			1.17997			0.589986	−	0.807414i	$-0.299133\pi$
$211$	17.1401			1.17997			0.589986	+	0.807414i	$0.299133\pi$
$212$	24.8167	−	42.9837i	1.70442	−	2.95214i
$213$	−4.51921	−	7.82751i	−0.309651	−	0.536332i
$214$	−4.23499	−	7.33522i	−0.289498	−	0.501425i
$215$	4.50572	−	7.80413i	0.307287	−	0.532237i
$216$	20.7183			1.40970
$217$	−10.2056	+	4.31088i	−0.692799	+	0.292642i
$218$	22.3626			1.51459
$219$	4.99647	−	8.65413i	0.337630	−	0.584792i
$220$	−16.0171	−	27.7425i	−1.07987	−	1.87040i
$221$	−5.90726	−	10.2317i	−0.397365	−	0.688257i
$222$	16.8691	−	29.2181i	1.13218	−	1.96099i
$223$	−13.3594			−0.894612			−0.447306	−	0.894381i	$-0.647616\pi$
$223$	−13.3594			−0.894612			−0.447306	+	0.894381i	$0.647616\pi$
$224$	8.04688	−	3.39904i	0.537654	−	0.227108i
$225$	−3.25522			−0.217015
$226$	−7.72237	+	13.3755i	−0.513684	+	0.889727i
$227$	−5.59509	−	9.69098i	−0.371359	−	0.643213i	0.618416	−	0.785851i	$-0.287775\pi$
$227$	−5.59509	−	9.69098i	−0.371359	−	0.643213i	−0.989775	+	0.142638i	$0.954441\pi$
$228$	1.66671	+	2.88683i	0.110381	+	0.191185i
$229$	−0.497226	+	0.861221i	−0.0328576	+	0.0569111i	−0.881987	−	0.471274i	$-0.843794\pi$
$229$	−0.497226	+	0.861221i	−0.0328576	+	0.0569111i	0.849129	+	0.528186i	$0.177127\pi$
$230$	−75.1359			−4.95432
$231$	7.64052	+	5.77860i	0.502709	+	0.380204i
$232$	5.10309			0.335034
$233$	−10.9827	+	19.0227i	−0.719503	+	1.24622i	0.241694	+	0.970353i	$0.422297\pi$
$233$	−10.9827	+	19.0227i	−0.719503	+	1.24622i	−0.961197	+	0.275863i	$0.911036\pi$
$234$	0.855718	+	1.48215i	0.0559400	+	0.0968910i
$235$	6.44007	+	11.1545i	0.420104	+	0.727641i
$236$	25.6005	−	44.3414i	1.66645	−	2.88638i
$237$	−0.412166			−0.0267731
$238$	3.67137	−	29.4731i	0.237980	−	1.91046i
$239$	−16.3177			−1.05550			−0.527752	−	0.849399i	$-0.676965\pi$
$239$	−16.3177			−1.05550			−0.527752	+	0.849399i	$0.676965\pi$
$240$	−6.08894	+	10.5464i	−0.393040	+	0.680765i
$241$	−0.832317	−	1.44162i	−0.0536143	−	0.0928626i	0.837973	−	0.545712i	$-0.183741\pi$
$241$	−0.832317	−	1.44162i	−0.0536143	−	0.0928626i	−0.891587	+	0.452850i	$0.850407\pi$
$242$	7.30163	+	12.6468i	0.469366	+	0.812966i
$243$	1.49956	−	2.59731i	0.0961968	−	0.166618i
$244$	−23.1682			−1.48319
$245$	−19.6663	+	20.2225i	−1.25643	+	1.29197i
$246$	−3.90094			−0.248715
$247$	−0.698474	+	1.20979i	−0.0444428	+	0.0769772i
$248$	−8.00945	−	13.8728i	−0.508601	−	0.880922i
$249$	6.53232	+	11.3143i	0.413969	+	0.717015i
$250$	29.7864	−	51.5916i	1.88386	−	3.26294i
$251$	−17.0667			−1.07724			−0.538620	−	0.842549i	$-0.681054\pi$
$251$	−17.0667			−1.07724			−0.538620	+	0.842549i	$0.681054\pi$
$252$	−0.342381	+	2.74858i	−0.0215680	+	0.173144i
$253$	−17.3061			−1.08803
$254$	−13.5840	+	23.5281i	−0.852333	+	1.47628i
$255$	−15.7155	−	27.2200i	−0.984143	−	1.70459i
$256$	12.9501	+	22.4302i	0.809379	+	1.40189i
$257$	12.0485	−	20.8687i	0.751566	−	1.30175i	−0.195497	−	0.980704i	$-0.562632\pi$
$257$	12.0485	−	20.8687i	0.751566	−	1.30175i	0.947063	−	0.321047i	$-0.104035\pi$
$258$	−8.72336			−0.543093
$259$	18.2505	+	13.8030i	1.13403	+	0.857678i
$260$	−36.3227			−2.25264
$261$	0.193181	−	0.334599i	0.0119576	−	0.0207112i
$262$	2.07565	+	3.59514i	0.128234	+	0.222108i
$263$	−1.65418	−	2.86513i	−0.102001	−	0.176672i	0.810508	−	0.585728i	$-0.199191\pi$
$263$	−1.65418	−	2.86513i	−0.102001	−	0.176672i	−0.912509	+	0.409056i	$0.865858\pi$
$264$	−6.92570	+	11.9957i	−0.426247	+	0.738282i
$265$	55.3356			3.39924
$266$	−3.23506	+	1.36651i	−0.198354	+	0.0837858i
$267$	−9.18114			−0.561877
$268$	−1.26415	+	2.18957i	−0.0772203	+	0.133750i
$269$	−5.81303	−	10.0685i	−0.354426	−	0.613885i	0.632593	−	0.774484i	$-0.281991\pi$
$269$	−5.81303	−	10.0685i	−0.354426	−	0.613885i	−0.987020	+	0.160600i	$0.948657\pi$
$270$	25.8563	+	44.7844i	1.57356	+	2.72549i
$271$	13.6597	−	23.6592i	0.829765	−	1.43719i	−0.0684577	−	0.997654i	$-0.521808\pi$
$271$	13.6597	−	23.6592i	0.829765	−	1.43719i	0.898223	−	0.439541i	$-0.144859\pi$
$272$	8.69649			0.527302
$273$	10.0060	−	4.22660i	0.605594	−	0.255806i
$274$	30.0980			1.81829
$275$	12.3590	−	21.4064i	0.745276	−	1.29086i
$276$	23.4123	+	40.5513i	1.40926	+	2.44090i
$277$	12.4221	+	21.5157i	0.746370	+	1.29275i	0.949552	+	0.313610i	$0.101538\pi$
$277$	12.4221	+	21.5157i	0.746370	+	1.29275i	−0.203182	+	0.979141i	$0.565128\pi$
$278$	−3.71183	+	6.42908i	−0.222621	+	0.385591i
$279$	−1.21281			−0.0726092
$280$	−32.5308	−	24.6034i	−1.94409	−	1.47033i
$281$	−9.03067			−0.538725			−0.269362	−	0.963039i	$-0.586813\pi$
$281$	−9.03067			−0.538725			−0.269362	+	0.963039i	$0.586813\pi$
$282$	6.23419	−	10.7979i	0.371241	−	0.643008i
$283$	8.19672	+	14.1971i	0.487244	+	0.843932i	0.999892	−	0.0146668i	$-0.00466874\pi$
$283$	8.19672	+	14.1971i	0.487244	+	0.843932i	−0.512648	+	0.858599i	$0.671335\pi$
$284$	9.92195	+	17.1853i	0.588760	+	1.01976i
$285$	−1.85820	+	3.21849i	−0.110070	+	0.190647i
$286$	−12.9955			−0.768441
$287$	0.327045	−	2.62546i	0.0193049	−	0.154976i
$288$	0.956277			0.0563491
$289$	−2.72278	+	4.71599i	−0.160163	+	0.277411i
$290$	6.36861	+	11.0308i	0.373977	+	0.647748i
$291$	8.20653	+	14.2141i	0.481076	+	0.833247i
$292$	−10.9698	+	19.0002i	−0.641957	+	1.11190i
$293$	17.5786			1.02695			0.513476	−	0.858104i	$-0.328358\pi$
$293$	17.5786			1.02695			0.513476	+	0.858104i	$0.328358\pi$
$294$	26.4721	+	6.69903i	1.54388	+	0.390696i
$295$	57.0835			3.32353
$296$	−16.5430	+	28.6534i	−0.961545	+	1.66544i
$297$	5.95550	+	10.3152i	0.345573	+	0.598551i
$298$	−11.8718	−	20.5625i	−0.687713	−	1.19115i
$299$	−9.81147	+	16.9940i	−0.567412	+	0.982786i
$300$	−66.8788			−3.86125
$301$	0.731345	−	5.87111i	0.0421540	−	0.338405i
$302$	28.4370			1.63636
$303$	1.62374	−	2.81240i	0.0932813	−	0.161568i
$304$	−0.514136	−	0.890510i	−0.0294877	−	0.0510742i
$305$	−12.9150	−	22.3694i	−0.739509	−	1.28087i
$306$	1.62572	−	2.81582i	0.0929361	−	0.160970i
$307$	16.4924			0.941273			0.470637	−	0.882327i	$-0.344024\pi$
$307$	16.4924			0.941273			0.470637	+	0.882327i	$0.344024\pi$
$308$	−16.7748	−	12.6869i	−0.955832	−	0.722905i
$309$	−32.2945			−1.83717
$310$	19.9915	−	34.6262i	1.13544	−	1.96664i
$311$	12.3106	+	21.3225i	0.698068	+	1.20909i	0.969136	+	0.246529i	$0.0792899\pi$
$311$	12.3106	+	21.3225i	0.698068	+	1.20909i	−0.271068	+	0.962560i	$0.587377\pi$
$312$	7.85286	+	13.6016i	0.444581	+	0.770036i
$313$	−1.49930	+	2.59687i	−0.0847455	+	0.146784i	−0.905283	−	0.424810i	$-0.860341\pi$
$313$	−1.49930	+	2.59687i	−0.0847455	+	0.146784i	0.820537	+	0.571593i	$0.193674\pi$
$314$	−33.7765			−1.90612
$315$	−2.84467	+	1.20160i	−0.160279	+	0.0677025i
$316$	0.904913			0.0509053
$317$	−4.59179	+	7.95322i	−0.257901	+	0.446697i	−0.965679	−	0.259737i	$-0.916364\pi$
$317$	−4.59179	+	7.95322i	−0.257901	+	0.446697i	0.707779	+	0.706434i	$0.249697\pi$
$318$	−26.7833	−	46.3901i	−1.50193	−	2.60143i
$319$	1.46689	+	2.54072i	0.0821299	+	0.142253i
$320$	−23.1599	+	40.1141i	−1.29468	+	2.24245i
$321$	−5.88492			−0.328464
$322$	−45.4429	+	19.1953i	−2.53244	+	1.06971i
$323$	2.65396			0.147670
$324$	14.5433	−	25.1897i	0.807961	−	1.39943i
$325$	−14.0135	−	24.2722i	−0.777331	−	1.34638i
$326$	8.60458	+	14.9036i	0.476564	+	0.825433i
$327$	7.76873	−	13.4558i	0.429612	−	0.744110i
$328$	3.82554			0.211230
$329$	6.74471	+	5.10109i	0.371848	+	0.281232i
$330$	−34.5729			−1.90317
$331$	−14.9497	+	25.8937i	−0.821710	+	1.42324i	0.0826975	+	0.996575i	$0.473646\pi$
$331$	−14.9497	+	25.8937i	−0.821710	+	1.42324i	−0.904408	+	0.426669i	$0.859687\pi$
$332$	−14.3417	−	24.8406i	−0.787105	−	1.36331i
$333$	1.25250	+	2.16939i	0.0686364	+	0.118882i
$334$	3.51799	−	6.09334i	0.192496	−	0.333413i
$335$	−2.81877			−0.154006
$336$	−0.988326	+	7.93411i	−0.0539176	+	0.432841i
$337$	−17.8607			−0.972937			−0.486468	−	0.873698i	$-0.661715\pi$
$337$	−17.8607			−0.972937			−0.486468	+	0.873698i	$0.661715\pi$
$338$	8.03408	−	13.9154i	0.436996	−	0.756900i
$339$	5.36548	+	9.29328i	0.291413	+	0.504742i
$340$	34.5035	+	59.7617i	1.87121	+	3.24104i
$341$	4.60465	−	7.97548i	0.249356	−	0.431897i
$342$	−0.384449			−0.0207886
$343$	−6.72802	+	17.2550i	−0.363279	+	0.931680i
$344$	8.55476			0.461242
$345$	−26.1021	+	45.2102i	−1.40529	+	2.43404i
$346$	−24.0961	−	41.7357i	−1.29542	−	2.24373i
$347$	−5.54640	−	9.60664i	−0.297746	−	0.515712i	0.677874	−	0.735178i	$-0.262902\pi$
$347$	−5.54640	−	9.60664i	−0.297746	−	0.515712i	−0.975620	+	0.219467i	$0.929568\pi$
$348$	3.96891	−	6.87436i	0.212756	−	0.368504i
$349$	34.6956			1.85721			0.928607	−	0.371064i	$-0.121007\pi$
$349$	34.6956			1.85721			0.928607	+	0.371064i	$0.121007\pi$
$350$	8.70943	−	69.9178i	0.465539	−	3.73726i
$351$	13.5056			0.720874
$352$	−3.63067	+	6.28850i	−0.193515	+	0.335178i
$353$	15.4953	+	26.8386i	0.824729	+	1.42847i	0.902126	+	0.431473i	$0.142006\pi$
$353$	15.4953	+	26.8386i	0.824729	+	1.42847i	−0.0773964	+	0.997000i	$0.524661\pi$
$354$	−27.6293	−	47.8554i	−1.46848	−	2.54349i
$355$	−11.0619	+	19.1597i	−0.587103	+	1.01689i
$356$	20.1572			1.06833
$357$	−16.4589	−	12.4480i	−0.871098	−	0.658820i
$358$	38.5774			2.03888
$359$	0.386842	−	0.670030i	0.0204167	−	0.0353628i	−0.855637	−	0.517577i	$-0.826834\pi$
$359$	0.386842	−	0.670030i	0.0204167	−	0.0353628i	0.876053	+	0.482214i	$0.160167\pi$
$360$	−2.23253	−	3.86685i	−0.117665	−	0.203801i
$361$	9.34310	+	16.1827i	0.491742	+	0.851722i
$362$	12.1068	−	20.9697i	0.636321	−	1.10214i
$363$	10.1463			0.532543
$364$	−21.9683	+	9.27953i	−1.15145	+	0.486379i
$365$	−24.4601			−1.28030
$366$	−12.5021	+	21.6543i	−0.653496	+	1.13189i
$367$	−11.0814	−	19.1936i	−0.578446	−	1.00190i	−0.995658	−	0.0930888i	$-0.970326\pi$
$367$	−11.0814	−	19.1936i	−0.578446	−	1.00190i	0.417212	−	0.908809i	$-0.363007\pi$
$368$	−7.22207	−	12.5090i	−0.376476	−	0.652076i
$369$	0.144819	−	0.250833i	0.00753895	−	0.0130579i
$370$	−82.5823			−4.29325
$371$	33.4675	−	14.1368i	1.73755	−	0.733948i
$372$	−24.9173			−1.29190
$373$	−4.89129	+	8.47197i	−0.253262	+	0.438662i	−0.964422	−	0.264368i	$-0.914837\pi$
$373$	−4.89129	+	8.47197i	−0.253262	+	0.438662i	0.711160	+	0.703030i	$0.248170\pi$
$374$	12.3446	+	21.3815i	0.638325	+	1.10561i
$375$	−20.6955	−	35.8457i	−1.06871	−	1.85106i
$376$	−6.11370	+	10.5892i	−0.315290	+	0.546099i
$377$	3.32652			0.171325
$378$	27.0794	+	20.4804i	1.39282	+	1.05340i
$379$	23.5584			1.21011			0.605056	−	0.796183i	$-0.293151\pi$
$379$	23.5584			1.21011			0.605056	+	0.796183i	$0.293151\pi$
$380$	4.07968	−	7.06622i	0.209283	−	0.362489i
$381$	9.43810	+	16.3473i	0.483529	+	0.837496i
$382$	13.0774	+	22.6507i	0.669096	+	1.15891i
$383$	−8.23501	+	14.2635i	−0.420789	+	0.728828i	−0.996017	−	0.0891650i	$-0.971580\pi$
$383$	−8.23501	+	14.2635i	−0.420789	+	0.728828i	0.575228	+	0.817993i	$0.304913\pi$
$384$	33.9679			1.73342
$385$	2.89850	−	23.2687i	0.147721	−	1.18588i
$386$	48.5455			2.47090
$387$	0.323846	−	0.560918i	0.0164620	−	0.0285131i
$388$	−18.0175	−	31.2072i	−0.914699	−	1.58431i
$389$	−0.398812	−	0.690763i	−0.0202206	−	0.0350231i	0.855738	−	0.517409i	$-0.173104\pi$
$389$	−0.398812	−	0.690763i	−0.0202206	−	0.0350231i	−0.875959	+	0.482386i	$0.839770\pi$
$390$	−19.6006	+	33.9493i	−0.992515	+	1.71909i
$391$	37.2802			1.88534
$392$	−25.9605	−	6.56956i	−1.31120	−	0.331813i
$393$	2.88432			0.145495
$394$	2.87809	−	4.98500i	0.144996	−	0.251140i
$395$	0.504438	+	0.873712i	0.0253810	+	0.0439612i
$396$	−1.15122	−	1.99398i	−0.0578511	−	0.100201i
$397$	−8.50745	+	14.7353i	−0.426977	+	0.739545i	−0.996603	−	0.0823587i	$-0.973755\pi$
$397$	−8.50745	+	14.7353i	−0.426977	+	0.739545i	0.569626	+	0.821904i	$0.307088\pi$
$398$	−4.30162			−0.215621
$399$	−0.301613	+	2.42130i	−0.0150995	+	0.121217i
$400$	20.6303			1.03152
$401$	12.3634	−	21.4141i	0.617399	−	1.06937i	−0.372559	−	0.928008i	$-0.621520\pi$
$401$	12.3634	−	21.4141i	0.617399	−	1.06937i	0.989958	−	0.141359i	$-0.0451470\pi$
$402$	1.36433	+	2.36309i	0.0680467	+	0.117860i
$403$	−5.22108	−	9.04318i	−0.260081	−	0.450473i
$404$	−3.56492	+	6.17463i	−0.177362	+	0.307199i
$405$	32.4283			1.61137
$406$	6.66987	+	5.04449i	0.331020	+	0.250354i
$407$	−19.0212			−0.942848
$408$	14.9191	−	25.8406i	0.738605	−	1.27930i
$409$	−3.83082	−	6.63517i	−0.189422	−	0.328088i	0.755636	−	0.654992i	$-0.227328\pi$
$409$	−3.83082	−	6.63517i	−0.189422	−	0.328088i	−0.945058	+	0.326904i	$0.893995\pi$
$410$	4.77425	+	8.26924i	0.235783	+	0.408389i
$411$	10.4560	−	18.1103i	0.515757	−	0.893317i
$412$	70.9027			3.49312
$413$	34.5246	−	14.5834i	1.69885	−	0.717600i
$414$	−5.40036			−0.265413
$415$	15.9894	−	27.6945i	0.784890	−	1.35947i
$416$	4.11671	+	7.13035i	0.201838	+	0.349594i
$417$	2.57897	+	4.46691i	0.126293	+	0.218745i
$418$	1.45963	−	2.52815i	0.0713926	−	0.123656i
$419$	−13.6434			−0.666524			−0.333262	−	0.942834i	$-0.608149\pi$
$419$	−13.6434			−0.666524			−0.333262	+	0.942834i	$0.608149\pi$
$420$	−58.4439	+	24.6870i	−2.85177	+	1.20460i
$421$	−36.1007			−1.75944			−0.879720	−	0.475492i	$-0.842270\pi$
$421$	−36.1007			−1.75944			−0.879720	+	0.475492i	$0.842270\pi$
$422$	−20.3066	+	35.1721i	−0.988512	+	1.71215i
$423$	0.462877	+	0.801726i	0.0225058	+	0.0389812i
$424$	26.2657	+	45.4935i	1.27557	+	2.20936i
$425$	−26.6233	+	46.1129i	−1.29142	+	2.23681i
$426$	21.4165			1.03763
$427$	−13.5259	−	10.2298i	−0.654564	−	0.495053i
$428$	12.9204			0.624530
$429$	−4.51462	+	7.81956i	−0.217968	+	0.377532i
$430$	10.6763	+	18.4918i	0.514855	+	0.891756i
$431$	−3.04020	−	5.26578i	−0.146441	−	0.253643i	0.783469	−	0.621431i	$-0.213449\pi$
$431$	−3.04020	−	5.26578i	−0.146441	−	0.253643i	−0.929910	+	0.367788i	$0.880115\pi$
$432$	−4.97062	+	8.60937i	−0.239149	+	0.414218i
$433$	−13.6259			−0.654817			−0.327409	−	0.944883i	$-0.606175\pi$
$433$	−13.6259			−0.654817			−0.327409	+	0.944883i	$0.606175\pi$
$434$	3.24491	−	26.0496i	0.155761	−	1.25042i
$435$	8.84978			0.424315
$436$	−17.0563	+	29.5424i	−0.816848	+	1.41482i
$437$	−2.20400	−	3.81744i	−0.105432	−	0.182613i
$438$	11.8391	+	20.5059i	0.565694	+	0.979810i
$439$	−12.4601	+	21.5815i	−0.594686	+	1.03003i	0.398905	+	0.916992i	$0.369390\pi$
$439$	−12.4601	+	21.5815i	−0.594686	+	1.03003i	−0.993591	+	0.113034i	$0.963943\pi$
$440$	33.9047			1.61634
$441$	−1.41350	+	1.45348i	−0.0673097	+	0.0692133i
$442$	27.9944			1.33156
$443$	−9.46957	+	16.4018i	−0.449913	+	0.779272i	−0.998380	−	0.0569002i	$-0.981878\pi$
$443$	−9.46957	+	16.4018i	−0.449913	+	0.779272i	0.548467	+	0.836172i	$0.315212\pi$
$444$	25.7326	+	44.5702i	1.22122	+	2.11521i
$445$	11.2365	+	19.4622i	0.532663	+	0.922599i
$446$	15.8275	−	27.4140i	0.749454	−	1.29809i
$447$	−16.4970			−0.780279
$448$	−3.75919	+	30.1781i	−0.177605	+	1.42578i
$449$	−11.0724			−0.522540			−0.261270	−	0.965266i	$-0.584141\pi$
$449$	−11.0724			−0.522540			−0.261270	+	0.965266i	$0.584141\pi$
$450$	3.85662	−	6.67986i	0.181803	−	0.314891i
$451$	1.09966	+	1.90466i	0.0517808	+	0.0896869i
$452$	−11.7799	−	20.4034i	−0.554082	−	0.959698i
$453$	9.87897	−	17.1109i	0.464155	−	0.803939i
$454$	26.5151			1.24441
$455$	−21.2057	−	16.0381i	−0.994138	−	0.751876i
$456$	−3.52806			−0.165217
$457$	10.2913	−	17.8250i	0.481405	−	0.833818i	−0.518367	−	0.855158i	$-0.673460\pi$
$457$	10.2913	−	17.8250i	0.481405	−	0.833818i	0.999772	+	0.0213402i	$0.00679331\pi$
$458$	−1.17817	−	2.04066i	−0.0550525	−	0.0953537i
$459$	−12.8291	−	22.2207i	−0.598812	−	1.03717i
$460$	57.3073	−	99.2592i	2.67197	−	4.62799i
$461$	−6.29857			−0.293354			−0.146677	−	0.989184i	$-0.546858\pi$
$461$	−6.29857			−0.293354			−0.146677	+	0.989184i	$0.546858\pi$
$462$	−20.9100	+	8.83248i	−0.972821	+	0.410924i
$463$	19.5859			0.910234			0.455117	−	0.890432i	$-0.349597\pi$
$463$	19.5859			0.910234			0.455117	+	0.890432i	$0.349597\pi$
$464$	−1.22430	+	2.12055i	−0.0568368	+	0.0984442i
$465$	−13.8900	−	24.0582i	−0.644134	−	1.11567i
$466$	−26.0235	−	45.0741i	−1.20552	−	2.08802i
$467$	16.9305	−	29.3244i	0.783448	−	1.35697i	−0.146473	−	0.989215i	$-0.546792\pi$
$467$	16.9305	−	29.3244i	0.783448	−	1.35697i	0.929922	−	0.367758i	$-0.119874\pi$
$468$	−2.61068			−0.120679
$469$	−1.70482	+	0.720125i	−0.0787213	+	0.0332523i
$470$	−30.5194			−1.40775
$471$	−11.7339	+	20.3237i	−0.540671	+	0.936469i
$472$	27.0953	+	46.9305i	1.24716	+	2.16015i
$473$	2.45907	+	4.25924i	0.113068	+	0.195840i
$474$	0.488312	−	0.845782i	0.0224289	−	0.0388480i
$475$	6.29587			0.288874
$476$	36.1356	+	27.3297i	1.65627	+	1.25266i
$477$	3.97722			0.182104
$478$	19.3323	−	33.4846i	0.884240	−	1.53155i
$479$	−1.85507	−	3.21307i	−0.0847602	−	0.146809i	0.820529	−	0.571605i	$-0.193679\pi$
$479$	−1.85507	−	3.21307i	−0.0847602	−	0.146809i	−0.905289	+	0.424796i	$0.860346\pi$
$480$	10.9520	+	18.9694i	0.499887	+	0.865830i
$481$	−10.7838	+	18.6781i	−0.491701	+	0.851650i
$482$	3.94434			0.179660
$483$	−4.23676	+	34.0120i	−0.192779	+	1.54760i
$484$	−22.2763			−1.01256
$485$	20.0875	−	34.7925i	0.912125	−	1.57985i
$486$	3.55319	+	6.15431i	0.161176	+	0.279165i
$487$	−1.39419	−	2.41481i	−0.0631769	−	0.109426i	0.832707	−	0.553714i	$-0.186790\pi$
$487$	−1.39419	−	2.41481i	−0.0631769	−	0.109426i	−0.895884	+	0.444288i	$0.853457\pi$
$488$	12.2605	−	21.2358i	0.555006	−	0.961298i
$489$	11.9569			0.540709
$490$	−18.1978	−	64.3145i	−0.822092	−	2.90543i
$491$	−16.3264			−0.736799			−0.368400	−	0.929668i	$-0.620094\pi$
$491$	−16.3264			−0.736799			−0.368400	+	0.929668i	$0.620094\pi$
$492$	2.97531	−	5.15338i	0.134137	−	0.232332i
$493$	−3.15991	−	5.47313i	−0.142315	−	0.246497i
$494$	−1.65503	−	2.86659i	−0.0744633	−	0.128974i
$495$	1.28348	−	2.22306i	0.0576883	−	0.0999191i
$496$	7.68632			0.345126
$497$	−1.79551	+	14.4140i	−0.0805394	+	0.646556i
$498$	−30.9566			−1.38720
$499$	−1.73097	+	2.99813i	−0.0774890	+	0.134215i	−0.902166	−	0.431389i	$-0.858024\pi$
$499$	−1.73097	+	2.99813i	−0.0774890	+	0.134215i	0.824677	+	0.565604i	$0.191357\pi$
$500$	45.4371	+	78.6994i	2.03201	+	3.51954i
$501$	−2.44429	−	4.23364i	−0.109203	−	0.189145i
$502$	20.2197	−	35.0215i	0.902449	−	1.56309i
$503$	2.36485			0.105444			0.0527218	−	0.998609i	$-0.483210\pi$
$503$	2.36485			0.105444			0.0527218	+	0.998609i	$0.483210\pi$
$504$	−2.33813	−	1.76835i	−0.104149	−	0.0787688i
$505$	−7.94898			−0.353725
$506$	20.5034	−	35.5129i	0.911486	−	1.57874i
$507$	−5.58206	−	9.66841i	−0.247908	−	0.429389i
$508$	−20.7214	−	35.8905i	−0.919363	−	1.59238i
$509$	17.7027	−	30.6620i	0.784660	−	1.35907i	−0.144542	−	0.989499i	$-0.546171\pi$
$509$	17.7027	−	30.6620i	0.784660	−	1.35907i	0.929202	−	0.369572i	$-0.120496\pi$
$510$	74.4756			3.29783
$511$	−14.7937	+	6.24893i	−0.654435	+	0.276437i
$512$	−20.1049			−0.888518
$513$	−1.51691	+	2.62737i	−0.0669734	+	0.116001i
$514$	28.5489	+	49.4481i	1.25924	+	2.18106i
$515$	39.5243	+	68.4580i	1.74165	+	3.01662i
$516$	6.65344	−	11.5241i	0.292902	−	0.507320i
$517$	−7.02956			−0.309160
$518$	−49.9466	+	21.0977i	−2.19453	+	0.926978i
$519$	−33.4838			−1.46978
$520$	19.2218	−	33.2931i	0.842931	−	1.46000i
$521$	0.973146	+	1.68554i	0.0426343	+	0.0738448i	0.886555	−	0.462623i	$-0.153092\pi$
$521$	0.973146	+	1.68554i	0.0426343	+	0.0738448i	−0.843921	+	0.536468i	$0.819758\pi$
$522$	0.457741	+	0.792830i	0.0200348	+	0.0347012i
$523$	−11.4102	+	19.7630i	−0.498933	+	0.864177i	−0.999999	−	0.00123182i	$-0.999608\pi$
$523$	−11.4102	+	19.7630i	−0.498933	+	0.864177i	0.501066	+	0.865409i	$0.332941\pi$
$524$	−6.33253			−0.276638
$525$	−39.0447	−	29.5299i	−1.70405	−	1.28879i
$526$	7.83916			0.341804
$527$	−9.91916	+	17.1805i	−0.432085	+	0.748394i
$528$	−3.32315	−	5.75586i	−0.144621	−	0.250492i
$529$	−19.4596	−	33.7051i	−0.846071	−	1.46544i
$530$	−65.5587	+	113.551i	−2.84769	+	4.93234i
$531$	4.10285			0.178048
$532$	0.662193	−	5.31597i	0.0287097	−	0.230477i
$533$	2.49374			0.108016
$534$	10.8773	−	18.8401i	0.470708	−	0.815290i
$535$	7.20238	+	12.4749i	0.311386	+	0.539337i
$536$	−1.33796	−	2.31742i	−0.0577912	−	0.100097i
$537$	13.4017	−	23.2125i	0.578327	−	1.00169i
$538$	27.5479			1.18767
$539$	−4.19151	−	14.8136i	−0.180541	−	0.638067i
$540$	−78.8840			−3.39463
$541$	−5.18187	+	8.97527i	−0.222786	+	0.385877i	−0.955653	−	0.294495i	$-0.904849\pi$
$541$	−5.18187	+	8.97527i	−0.222786	+	0.385877i	0.732867	+	0.680372i	$0.238182\pi$
$542$	32.3665	+	56.0604i	1.39026	+	2.40800i
$543$	−8.41180	−	14.5697i	−0.360985	−	0.625244i
$544$	7.82104	−	13.5464i	0.335324	−	0.580799i
$545$	−38.0317			−1.62910
$546$	−3.18147	+	25.5403i	−0.136154	+	1.09302i
$547$	−34.3321			−1.46793			−0.733967	−	0.679186i	$-0.762333\pi$
$547$	−34.3321			−1.46793			−0.733967	+	0.679186i	$0.762333\pi$
$548$	−22.9562	+	39.7613i	−0.980640	+	1.69852i
$549$	−0.928257	−	1.60779i	−0.0396171	−	0.0686188i
$550$	29.2846	+	50.7224i	1.24870	+	2.16281i
$551$	−0.373627	+	0.647142i	−0.0159171	+	0.0275692i
$552$	−49.5587			−2.10936
$553$	0.528300	+	0.399559i	0.0224656	+	0.0169910i
$554$	−58.8680			−2.50106
$555$	−28.6890	+	49.6908i	−1.21778	+	2.10926i
$556$	−5.66214	−	9.80712i	−0.240128	−	0.415914i
$557$	−17.0296	−	29.4962i	−0.721568	−	1.24979i	−0.960371	−	0.278725i	$-0.910088\pi$
$557$	−17.0296	−	29.4962i	−0.721568	−	1.24979i	0.238803	−	0.971068i	$-0.423245\pi$
$558$	1.43688	−	2.48874i	0.0608278	−	0.105357i
$559$	5.57655			0.235863
$560$	18.0284	−	7.61526i	0.761837	−	0.321804i
$561$	17.1540			0.724243
$562$	10.6991	−	18.5313i	0.451313	−	0.781696i
$563$	−14.6461	−	25.3679i	−0.617261	−	1.06913i	−0.989983	−	0.141185i	$-0.954909\pi$
$563$	−14.6461	−	25.3679i	−0.617261	−	1.06913i	0.372722	−	0.927943i	$-0.378425\pi$
$564$	9.50983	+	16.4715i	0.400436	+	0.693576i
$565$	13.1333	−	22.7476i	0.552523	−	0.956997i
$566$	−38.8441			−1.63274
$567$	19.6129	−	8.28460i	0.823666	−	0.347920i
$568$	−21.0026			−0.881248
$569$	12.5078	−	21.6641i	0.524353	−	0.908206i	−0.475245	−	0.879853i	$-0.657641\pi$
$569$	12.5078	−	21.6641i	0.524353	−	0.908206i	0.999598	−	0.0283524i	$-0.00902606\pi$
$570$	−4.40299	−	7.62620i	−0.184421	−	0.319426i
$571$	−21.9646	−	38.0437i	−0.919188	−	1.59208i	−0.800651	−	0.599131i	$-0.795513\pi$
$571$	−21.9646	−	38.0437i	−0.919188	−	1.59208i	−0.118537	−	0.992950i	$-0.537820\pi$
$572$	9.91188	−	17.1679i	0.414436	−	0.717825i
$573$	18.1722			0.759156
$574$	5.00009	+	3.78162i	0.208700	+	0.157842i
$575$	88.4381			3.68813
$576$	−1.66460	+	2.88318i	−0.0693585	+	0.120132i
$577$	−9.52253	−	16.4935i	−0.396428	−	0.686633i	0.596854	−	0.802350i	$-0.296417\pi$
$577$	−9.52253	−	16.4935i	−0.396428	−	0.686633i	−0.993282	+	0.115716i	$0.963084\pi$
$578$	−6.45161	−	11.1745i	−0.268351	−	0.464798i
$579$	16.8646	−	29.2104i	0.700870	−	1.21394i
$580$	−19.4297			−0.806776
$581$	2.59532	−	20.8348i	0.107672	−	0.864373i
$582$	−38.8907			−1.61207
$583$	−15.1002	+	26.1543i	−0.625386	+	1.08320i
$584$	−11.6103	−	20.1096i	−0.480436	−	0.832140i
$585$	−1.45531	−	2.52067i	−0.0601695	−	0.104217i
$586$	−20.8262	+	36.0720i	−0.860321	+	1.49012i
$587$	−17.0503			−0.703740			−0.351870	−	0.936049i	$-0.614454\pi$
$587$	−17.0503			−0.703740			−0.351870	+	0.936049i	$0.614454\pi$
$588$	−29.0405	+	29.8618i	−1.19761	+	1.23148i
$589$	2.34568			0.0966520
$590$	−67.6294	+	117.138i	−2.78426	+	4.82248i
$591$	−1.99969	−	3.46356i	−0.0822562	−	0.142472i
$592$	−7.93782	−	13.7487i	−0.326242	−	0.565068i
$593$	−3.24688	+	5.62376i	−0.133333	+	0.230940i	−0.924960	−	0.380065i	$-0.875901\pi$
$593$	−3.24688	+	5.62376i	−0.133333	+	0.230940i	0.791626	+	0.611006i	$0.209235\pi$
$594$	−28.2231			−1.15801
$595$	−6.24384	+	50.1245i	−0.255973	+	2.05490i
$596$	36.2191			1.48359
$597$	−1.49438	+	2.58834i	−0.0611608	+	0.105934i
$598$	−23.2482	−	40.2671i	−0.950690	−	1.64664i
$599$	20.2847	+	35.1341i	0.828810	+	1.43554i	0.898973	+	0.438005i	$0.144315\pi$
$599$	20.2847	+	35.1341i	0.828810	+	1.43554i	−0.0701630	+	0.997536i	$0.522352\pi$
$600$	35.3919	−	61.3005i	1.44487	−	2.50258i
$601$	5.64601			0.230305			0.115153	−	0.993348i	$-0.463264\pi$
$601$	5.64601			0.230305			0.115153	+	0.993348i	$0.463264\pi$
$602$	11.1813	+	8.45653i	0.455716	+	0.344662i
$603$	−0.202598			−0.00825043
$604$	−21.6893	+	37.5670i	−0.882526	+	1.52858i
$605$	−12.4178	−	21.5082i	−0.504854	−	0.874433i
$606$	3.84744	+	6.66396i	0.156291	+	0.270705i
$607$	−1.77418	+	3.07298i	−0.0720119	+	0.124728i	−0.899783	−	0.436338i	$-0.856275\pi$
$607$	−1.77418	+	3.07298i	−0.0720119	+	0.124728i	0.827771	+	0.561066i	$0.189609\pi$
$608$	−1.84952			−0.0750078
$609$	5.35243	−	2.26089i	0.216892	−	0.0916160i
$610$	61.2039			2.47807
$611$	−3.98531	+	6.90276i	−0.161228	+	0.279256i
$612$	2.47992	+	4.29535i	0.100245	+	0.173629i
$613$	8.73172	+	15.1238i	0.352671	+	0.610844i	0.986716	−	0.162452i	$-0.0519402\pi$
$613$	8.73172	+	15.1238i	0.352671	+	0.610844i	−0.634046	+	0.773296i	$0.718607\pi$
$614$	−19.5394	+	33.8432i	−0.788544	+	1.36580i
$615$	6.63427			0.267520
$616$	20.5059	−	8.66177i	0.826205	−	0.348993i
$617$	13.6489			0.549485			0.274742	−	0.961518i	$-0.411407\pi$
$617$	13.6489			0.549485			0.274742	+	0.961518i	$0.411407\pi$
$618$	38.2608	−	66.2696i	1.53907	−	2.66575i
$619$	−3.63785	−	6.30094i	−0.146217	−	0.253256i	0.783609	−	0.621254i	$-0.213377\pi$
$619$	−3.63785	−	6.30094i	−0.146217	−	0.253256i	−0.929827	+	0.367998i	$0.880043\pi$
$620$	30.4956	+	52.8199i	1.22473	+	2.12130i
$621$	−21.3081	+	36.9067i	−0.855064	+	1.48101i
$622$	−58.3396			−2.33920
$623$	11.7681	+	8.90030i	0.471478	+	0.356583i
$624$	−7.53605			−0.301683
$625$	−22.5599	+	39.0748i	−0.902394	+	1.56299i
$626$	−3.55258	−	6.15326i	−0.141990	−	0.245934i
$627$	−1.01414	−	1.75655i	−0.0405010	−	0.0701498i
$628$	25.7619	−	44.6209i	1.02801	−	1.78057i
$629$	40.9749			1.63377
$630$	0.904475	−	7.26097i	0.0360352	−	0.289284i
$631$	18.3434			0.730240			0.365120	−	0.930960i	$-0.381028\pi$
$631$	18.3434			0.730240			0.365120	+	0.930960i	$0.381028\pi$
$632$	−0.478875	+	0.829435i	−0.0190486	+	0.0329932i
$633$	14.1090	+	24.4375i	0.560783	+	0.971304i
$634$	−10.8802	−	18.8451i	−0.432109	−	0.748435i
$635$	23.1020	−	40.0139i	0.916776	−	1.58790i
$636$	81.7123			3.24010
$637$	−16.9227	−	4.28247i	−0.670503	−	0.169678i
$638$	−6.95155			−0.275215
$639$	−0.795066	+	1.37710i	−0.0314523	+	0.0544770i
$640$	−41.5724	−	72.0054i	−1.64329	−	2.84626i
$641$	−8.91900	−	15.4482i	−0.352279	−	0.610166i	0.634369	−	0.773030i	$-0.281260\pi$
$641$	−8.91900	−	15.4482i	−0.352279	−	0.610166i	−0.986648	+	0.162865i	$0.947927\pi$
$642$	6.97214	−	12.0761i	0.275168	−	0.476606i
$643$	−9.75440			−0.384676			−0.192338	−	0.981329i	$-0.561607\pi$
$643$	−9.75440			−0.384676			−0.192338	+	0.981329i	$0.561607\pi$
$644$	9.30183	−	74.6735i	0.366544	−	2.94255i
$645$	14.8357			0.584155
$646$	−3.14427	+	5.44604i	−0.123710	+	0.214271i
$647$	4.23471	+	7.33473i	0.166484	+	0.288358i	0.937181	−	0.348843i	$-0.113425\pi$
$647$	4.23471	+	7.33473i	0.166484	+	0.288358i	−0.770698	+	0.637201i	$0.780092\pi$
$648$	15.3925	+	26.6605i	0.604673	+	1.04732i
$649$	−15.5771	+	26.9804i	−0.611456	+	1.05907i
$650$	66.4100			2.60481
$651$	−14.5471	−	11.0021i	−0.570144	−	0.431206i
$652$	−26.2514			−1.02808
$653$	4.46961	−	7.74159i	0.174909	−	0.302952i	−0.765221	−	0.643768i	$-0.777370\pi$
$653$	4.46961	−	7.74159i	0.174909	−	0.302952i	0.940130	+	0.340816i	$0.110703\pi$
$654$	18.4080	+	31.8835i	0.719808	+	1.24674i
$655$	−3.53003	−	6.11420i	−0.137930	−	0.238901i
$656$	−0.917802	+	1.58968i	−0.0358341	+	0.0620666i
$657$	−1.75806			−0.0685884
$658$	−18.4584	+	7.79692i	−0.719584	+	0.303956i
$659$	41.0753			1.60006			0.800032	−	0.599957i	$-0.204816\pi$
$659$	41.0753			1.60006			0.800032	+	0.599957i	$0.204816\pi$
$660$	26.3693	−	45.6729i	1.02642	−	1.77782i
$661$	1.44504	+	2.50288i	0.0562055	+	0.0973509i	0.892759	−	0.450534i	$-0.148766\pi$
$661$	1.44504	+	2.50288i	0.0562055	+	0.0973509i	−0.836554	+	0.547885i	$0.815433\pi$
$662$	−35.4232	−	61.3548i	−1.37676	−	2.38462i
$663$	9.72523	−	16.8446i	0.377697	−	0.654190i
$664$	30.3583			1.17813
$665$	5.50182	−	2.32399i	0.213351	−	0.0901207i
$666$	−5.93556			−0.229998
$667$	−5.24835	+	9.09040i	−0.203217	+	0.351982i
$668$	5.36645	+	9.29497i	0.207634	+	0.359633i
$669$	−10.9969	−	19.0472i	−0.425165	−	0.736408i
$670$	3.33953	−	5.78424i	0.129017	−	0.223465i
$671$	14.0971			0.544214
$672$	11.4700	+	8.67491i	0.442467	+	0.334642i
$673$	2.39313			0.0922482			0.0461241	−	0.998936i	$-0.485313\pi$
$673$	2.39313			0.0922482			0.0461241	+	0.998936i	$0.485313\pi$
$674$	21.1605	−	36.6510i	0.815070	−	1.41174i
$675$	−30.4340	−	52.7132i	−1.17140	−	2.02893i
$676$	12.2554	+	21.2270i	0.471363	+	0.816425i
$677$	20.4265	−	35.3797i	0.785054	−	1.35975i	−0.143913	−	0.989590i	$-0.545969\pi$
$677$	20.4265	−	35.3797i	0.785054	−	1.35975i	0.928967	−	0.370163i	$-0.120698\pi$
$678$	−25.4269			−0.976516
$679$	3.26050	−	26.1747i	0.125126	−	1.00449i
$680$	−73.0361			−2.80081
$681$	9.21130	−	15.9544i	0.352978	−	0.611375i
$682$	10.9107	+	18.8979i	0.417792	+	0.723636i
$683$	−2.09876	−	3.63516i	−0.0803067	−	0.139095i	0.823075	−	0.567933i	$-0.192257\pi$
$683$	−2.09876	−	3.63516i	−0.0803067	−	0.139095i	−0.903382	+	0.428837i	$0.858923\pi$
$684$	0.293225	−	0.507881i	0.0112117	−	0.0194193i
$685$	−51.1872			−1.95576
$686$	−27.4369	−	34.2489i	−1.04755	−	1.30763i
$687$	−1.63719			−0.0624625
$688$	−2.05241	+	3.55487i	−0.0782473	+	0.135528i
$689$	17.1217	+	29.6556i	0.652284	+	1.12979i
$690$	−61.8488	−	107.125i	−2.35454	−	4.07819i
$691$	15.3515	−	26.5896i	0.583999	−	1.01152i	−0.411001	−	0.911635i	$-0.634821\pi$
$691$	15.3515	−	26.5896i	0.583999	−	1.01152i	0.994999	−	0.0998802i	$-0.0318460\pi$
$692$	73.5139			2.79458
$693$	0.208328	−	1.67242i	0.00791374	−	0.0635302i
$694$	26.2843			0.997739
$695$	6.31265	−	10.9338i	0.239453	−	0.414744i
$696$	4.20065	+	7.27574i	0.159225	+	0.275786i
$697$	−2.36884	−	4.10295i	−0.0897261	−	0.155410i
$698$	−41.1055	+	71.1969i	−1.55587	+	2.69484i
$699$	−36.1622			−1.36778
$700$	85.7229	+	64.8331i	3.24002	+	2.45046i
$701$	−42.2453			−1.59558			−0.797792	−	0.602933i	$-0.793999\pi$
$701$	−42.2453			−1.59558			−0.797792	+	0.602933i	$0.793999\pi$
$702$	−16.0007	+	27.7140i	−0.603906	+	1.04600i
$703$	−2.42243	−	4.19577i	−0.0913637	−	0.158247i
$704$	−12.6399	−	21.8930i	−0.476384	−	0.825122i
$705$	−10.6024	+	18.3639i	−0.399309	+	0.691624i
$706$	−73.4318			−2.76364
$707$	−4.80762	+	2.03076i	−0.180809	+	0.0763747i
$708$	84.2933			3.16793
$709$	24.7223	−	42.8202i	0.928464	−	1.60815i	0.142572	−	0.989784i	$-0.454463\pi$
$709$	24.7223	−	42.8202i	0.928464	−	1.60815i	0.785892	−	0.618363i	$-0.212204\pi$
$710$	−26.2110	−	45.3988i	−0.983682	−	1.70379i
$711$	0.0362562	+	0.0627977i	0.00135972	+	0.00235510i
$712$	−10.6671	+	18.4759i	−0.399766	+	0.692415i
$713$	32.9498			1.23398
$714$	45.0435	−	19.0266i	1.68571	−	0.712052i
$715$	22.1013			0.826541
$716$	−29.4236	+	50.9631i	−1.09961	+	1.90458i
$717$	−13.4320	−	23.2650i	−0.501629	−	0.868847i
$718$	0.916619	+	1.58763i	0.0342079	+	0.0592499i
$719$	−16.9382	+	29.3379i	−0.631690	+	1.09412i	0.355516	+	0.934670i	$0.384305\pi$
$719$	−16.9382	+	29.3379i	−0.631690	+	1.09412i	−0.987206	+	0.159449i	$0.949028\pi$
$720$	2.14246			0.0798447
$721$	41.3939	+	31.3066i	1.54159	+	1.16592i
$722$	−44.2768			−1.64781
$723$	1.37026	−	2.37336i	0.0509605	−	0.0882661i
$724$	18.4681	+	31.9878i	0.686363	+	1.18882i
$725$	−7.49612	−	12.9837i	−0.278399	−	0.482201i
$726$	−12.0208	+	20.8206i	−0.446134	+	0.772726i
$727$	19.3374			0.717186			0.358593	−	0.933494i	$-0.383257\pi$
$727$	19.3374			0.717186			0.358593	+	0.933494i	$0.383257\pi$
$728$	3.11998	−	25.0467i	0.115634	−	0.928291i
$729$	29.0791			1.07700
$730$	28.9790	−	50.1932i	1.07256	−	1.85773i
$731$	−5.29724	−	9.17509i	−0.195926	−	0.339353i
$732$	−19.0711	−	33.0321i	−0.704889	−	1.22090i
$733$	12.9613	−	22.4496i	0.478736	−	0.829196i	−0.520966	−	0.853577i	$-0.674428\pi$
$733$	12.9613	−	22.4496i	0.478736	−	0.829196i	0.999703	+	0.0243813i	$0.00776159\pi$
$734$	52.5148			1.93836
$735$	−45.0207	−	11.3929i	−1.66061	−	0.420235i
$736$	−25.9802			−0.957642
$737$	0.769197	−	1.33229i	0.0283337	−	0.0490755i
$738$	0.343147	+	0.594347i	0.0126314	+	0.0218782i
$739$	2.14696	+	3.71864i	0.0789771	+	0.136792i	0.902809	−	0.430042i	$-0.141501\pi$
$739$	2.14696	+	3.71864i	0.0789771	+	0.136792i	−0.823832	+	0.566834i	$0.808168\pi$
$740$	62.9868	−	109.096i	2.31544	−	4.01046i
$741$	−2.29982			−0.0844860
$742$	−10.6411	+	85.4253i	−0.390649	+	3.13606i
$743$	−3.57081			−0.131000			−0.0655002	−	0.997853i	$-0.520864\pi$
$743$	−3.57081			−0.131000			−0.0655002	+	0.997853i	$0.520864\pi$
$744$	13.1861	−	22.8390i	0.483426	−	0.837318i
$745$	20.1901	+	34.9704i	0.739710	+	1.28121i
$746$	−11.5899	−	20.0743i	−0.424336	−	0.734972i
$747$	1.14923	−	1.99053i	0.0420482	−	0.0728296i
$748$	−37.6617			−1.37705
$749$	7.54308	+	5.70491i	0.275618	+	0.208453i
$750$	98.0758			3.58122
$751$	−21.4992	+	37.2377i	−0.784518	+	1.35882i	0.144769	+	0.989465i	$0.453756\pi$
$751$	−21.4992	+	37.2377i	−0.784518	+	1.35882i	−0.929287	+	0.369359i	$0.879577\pi$
$752$	−2.93353	−	5.08102i	−0.106975	−	0.185286i
$753$	−14.0486	−	24.3329i	−0.511959	−	0.886739i
$754$	−3.94109	+	6.82616i	−0.143526	+	0.248594i
$755$	−48.3623			−1.76009
$756$	−47.7098	+	20.1529i	−1.73519	+	0.732952i
$757$	−11.1293			−0.404501			−0.202251	−	0.979334i	$-0.564826\pi$
$757$	−11.1293			−0.404501			−0.202251	+	0.979334i	$0.564826\pi$
$758$	−27.9107	+	48.3427i	−1.01376	+	1.75589i
$759$	−14.2457	−	24.6743i	−0.517086	−	0.895619i
$760$	4.31789	+	7.47881i	0.156626	+	0.271285i
$761$	3.70112	−	6.41053i	0.134165	−	0.232381i	−0.791113	−	0.611670i	$-0.790498\pi$
$761$	3.70112	−	6.41053i	0.134165	−	0.232381i	0.925278	+	0.379289i	$0.123831\pi$
$762$	−44.7270			−1.62029
$763$	−23.0019	+	9.71613i	−0.832726	+	0.351747i
$764$	−39.8972			−1.44343
$765$	−2.76483	+	4.78883i	−0.0999627	+	0.173141i
$766$	−19.5128	−	33.7972i	−0.705026	−	1.22114i
$767$	17.6625	+	30.5923i	0.637756	+	1.10463i
$768$	−21.3199	+	36.9272i	−0.769317	+	1.33250i
$769$	−6.22010			−0.224302			−0.112151	−	0.993691i	$-0.535774\pi$
$769$	−6.22010			−0.224302			−0.112151	+	0.993691i	$0.535774\pi$
$770$	44.3143	+	33.5153i	1.59698	+	1.20781i
$771$	39.6714			1.42873
$772$	−37.0264	+	64.1316i	−1.33261	+	2.30815i
$773$	0.562714	+	0.974649i	0.0202394	+	0.0350557i	0.875968	−	0.482370i	$-0.160224\pi$
$773$	0.562714	+	0.974649i	0.0202394	+	0.0350557i	−0.855728	+	0.517425i	$0.826890\pi$
$774$	0.767352	+	1.32909i	0.0275819	+	0.0477732i
$775$	−23.5308	+	40.7565i	−0.845250	+	1.46402i
$776$	38.1390			1.36911
$777$	−4.65665	+	37.3828i	−0.167056	+	1.34110i
$778$	1.88997			0.0677585
$779$	−0.280091	+	0.485132i	−0.0100353	+	0.0173817i
$780$	−29.8994	−	51.7872i	−1.07057	−	1.85428i
$781$	−6.03721	−	10.4567i	−0.216028	−	0.374172i
$782$	−44.1676	+	76.5005i	−1.57943	+	2.73565i
$783$	7.22439			0.258179
$784$	8.95822	−	9.21157i	0.319936	−	0.328985i
$785$	57.4432			2.05024
$786$	−3.41719	+	5.91874i	−0.121887	+	0.211114i
$787$	5.65092	+	9.78767i	0.201433	+	0.348893i	0.948990	−	0.315305i	$-0.102107\pi$
$787$	5.65092	+	9.78767i	0.201433	+	0.348893i	−0.747557	+	0.664198i	$0.768773\pi$
$788$	4.39033	+	7.60427i	0.156399	+	0.270891i
$789$	2.72331	−	4.71692i	0.0969525	−	0.167927i
$790$	−2.39053			−0.0850511
$791$	2.13173	−	17.1132i	0.0757956	−	0.608474i
$792$	2.43688			0.0865908
$793$	7.99218	−	13.8429i	0.283811	−	0.491574i
$794$	−20.1583	−	34.9153i	−0.715393	−	1.23910i
$795$	45.5500	+	78.8949i	1.61549	+	2.79812i
$796$	3.28091	−	5.68271i	0.116289	−	0.201418i
$797$	−2.55391			−0.0904642			−0.0452321	−	0.998977i	$-0.514403\pi$
$797$	−2.55391			−0.0904642			−0.0452321	+	0.998977i	$0.514403\pi$
$798$	−4.61127	−	3.48755i	−0.163237	−	0.123458i
$799$	15.1428			0.535714
$800$	18.5535	−	32.1356i	0.655966	−	1.13617i
$801$	0.807620	+	1.39884i	0.0285359	+	0.0494256i
$802$	29.2950	+	50.7405i	1.03444	+	1.79171i
$803$	6.67477	−	11.5610i	0.235547	−	0.407980i
$804$	−4.16239			−0.146796
$805$	77.2841	−	32.6452i	2.72391	−	1.15059i
$806$	24.7426			0.871522
$807$	9.57009	−	16.5759i	0.336883	−	0.583499i
$808$	−3.77308	−	6.53516i	−0.132736	−	0.229906i
$809$	26.8368	+	46.4828i	0.943533	+	1.63425i	0.758662	+	0.651484i	$0.225853\pi$
$809$	26.8368	+	46.4828i	0.943533	+	1.63425i	0.184871	+	0.982763i	$0.440813\pi$
$810$	−38.4193	+	66.5442i	−1.34992	+	2.33812i
$811$	3.54969			0.124646			0.0623232	−	0.998056i	$-0.480149\pi$
$811$	3.54969			0.124646			0.0623232	+	0.998056i	$0.480149\pi$
$812$	−11.7513	+	4.96380i	−0.412389	+	0.174195i
$813$	44.9763			1.57739
$814$	22.5354	−	39.0324i	0.789864	−	1.36808i
$815$	−14.6337	−	25.3463i	−0.512596	−	0.887841i
$816$	7.15860	+	12.3991i	0.250601	+	0.434054i
$817$	−0.626345	+	1.08486i	−0.0219130	+	0.0379545i
$818$	18.1542			0.634747
$819$	−1.52415	−	1.15273i	−0.0532581	−	0.0402796i
$820$	−14.5656			−0.508652
$821$	13.6125	−	23.5775i	0.475080	−	0.822862i	−0.524513	−	0.851402i	$-0.675753\pi$
$821$	13.6125	−	23.5775i	0.475080	−	0.822862i	0.999593	+	0.0285404i	$0.00908592\pi$
$822$	24.7754	+	42.9123i	0.864142	+	1.49674i
$823$	−4.96824	−	8.60524i	−0.173182	−	0.299960i	0.766349	−	0.642425i	$-0.222072\pi$
$823$	−4.96824	−	8.60524i	−0.173182	−	0.299960i	−0.939531	+	0.342465i	$0.888738\pi$
$824$	−37.5213	+	64.9888i	−1.30712	+	2.26399i
$825$	40.6937			1.41677
$826$	−10.9773	+	88.1235i	−0.381948	+	3.06621i
$827$	−52.7777			−1.83526			−0.917631	−	0.397434i	$-0.869901\pi$
$827$	−52.7777			−1.83526			−0.917631	+	0.397434i	$0.869901\pi$
$828$	4.11894	−	7.13421i	0.143143	−	0.247931i
$829$	14.3410	+	24.8393i	0.498082	+	0.862704i	0.999998	−	0.00221297i	$-0.000704412\pi$
$829$	14.3410	+	24.8393i	0.498082	+	0.862704i	−0.501915	+	0.864917i	$0.667371\pi$
$830$	37.8868	+	65.6219i	1.31507	+	2.27777i
$831$	−20.4507	+	35.4216i	−0.709426	+	1.22876i
$832$	−28.6641			−0.993748
$833$	9.02919	+	31.9109i	0.312843	+	1.10565i
$834$	−12.2217			−0.423203
$835$	−5.98299	+	10.3628i	−0.207050	+	0.358621i
$836$	2.22656	+	3.85651i	0.0770071	+	0.133380i
$837$	−11.3389	−	19.6396i	−0.391930	−	0.678843i
$838$	16.1640	−	27.9968i	0.558376	−	0.967135i
$839$	−13.8280			−0.477396			−0.238698	−	0.971094i	$-0.576721\pi$
$839$	−13.8280			−0.477396			−0.238698	+	0.971094i	$0.576721\pi$
$840$	8.30030	−	66.6334i	0.286388	−	2.29907i
$841$	−27.2206			−0.938641
$842$	42.7702	−	74.0801i	1.47396	−	2.55297i
$843$	−7.43368	−	12.8755i	−0.256029	−	0.443456i
$844$	−30.9764	−	53.6527i	−1.06625	−	1.84680i
$845$	−13.6634	+	23.6658i	−0.470037	+	0.814127i
$846$	−2.19357			−0.0754164
$847$	−13.0052	−	9.83594i	−0.446863	−	0.337967i
$848$	−25.2060			−0.865578
$849$	−13.4944	+	23.3730i	−0.463127	+	0.802159i
$850$	−63.0837	−	109.264i	−2.16375	−	3.74773i
$851$	−34.0279	−	58.9380i	−1.16646	−	2.02037i
$852$	−16.3347	+	28.2925i	−0.559617	+	0.969286i
$853$	7.82689			0.267988			0.133994	−	0.990982i	$-0.457220\pi$
$853$	7.82689			0.267988			0.133994	+	0.990982i	$0.457220\pi$
$854$	37.0167	−	15.6360i	1.26669	−	0.535054i
$855$	0.653827			0.0223604
$856$	−6.83738	+	11.8427i	−0.233697	+	0.404775i
$857$	−11.3089	−	19.5875i	−0.386304	−	0.669097i	0.605646	−	0.795735i	$-0.292915\pi$
$857$	−11.3089	−	19.5875i	−0.386304	−	0.669097i	−0.991949	+	0.126637i	$0.959582\pi$
$858$	−10.6974	−	18.5284i	−0.365202	−	0.632549i
$859$	1.80805	−	3.13164i	0.0616899	−	0.106850i	−0.833531	−	0.552473i	$-0.813684\pi$
$859$	1.80805	−	3.13164i	0.0616899	−	0.106850i	0.895221	+	0.445623i	$0.147018\pi$
$860$	−32.5718			−1.11069
$861$	4.01247	−	1.69489i	0.136745	−	0.0577615i
$862$	14.4075			0.490720
$863$	−2.96842	+	5.14146i	−0.101046	+	0.175017i	−0.912116	−	0.409932i	$-0.865552\pi$
$863$	−2.96842	+	5.14146i	−0.101046	+	0.175017i	0.811070	+	0.584950i	$0.198886\pi$
$864$	8.94049	+	15.4854i	0.304161	+	0.526823i
$865$	40.9799	+	70.9793i	1.39336	+	2.41337i
$866$	16.1432	−	27.9608i	0.548568	−	0.950148i
$867$	−8.96512			−0.304471
$868$	31.9381	+	24.1551i	1.08405	+	0.819879i
$869$	−0.550612			−0.0186782
$870$	−10.4848	+	18.1601i	−0.355466	+	0.615686i
$871$	−0.872172	−	1.51065i	−0.0295524	−	0.0511863i
$872$	−18.0522	−	31.2673i	−0.611324	−	1.05884i
$873$	1.44378	−	2.50070i	0.0488645	−	0.0846357i
$874$	10.4447			0.353298
$875$	−8.22243	+	66.0082i	−0.277969	+	2.23149i
$876$	−36.1194			−1.22036
$877$	2.71066	−	4.69500i	0.0915324	−	0.158539i	−0.816624	−	0.577170i	$-0.804157\pi$
$877$	2.71066	−	4.69500i	0.0915324	−	0.158539i	0.908156	+	0.418632i	$0.137490\pi$
$878$	−29.5240	−	51.1371i	−0.996388	−	1.72579i
$879$	14.4700	+	25.0627i	0.488060	+	0.845345i
$880$	−8.13420	+	14.0889i	−0.274204	+	0.474935i
$881$	30.2288			1.01843			0.509217	−	0.860638i	$-0.329935\pi$
$881$	30.2288			1.01843			0.509217	+	0.860638i	$0.329935\pi$
$882$	−1.30796	−	4.62257i	−0.0440412	−	0.155650i
$883$	0.723881			0.0243605			0.0121803	−	0.999926i	$-0.496123\pi$
$883$	0.723881			0.0243605			0.0121803	+	0.999926i	$0.496123\pi$
$884$	−21.3518	+	36.9824i	−0.718138	+	1.24385i
$885$	46.9888	+	81.3869i	1.57951	+	2.73579i
$886$	−22.4381	−	38.8639i	−0.753822	−	1.30566i
$887$	−15.1711	+	26.2771i	−0.509396	+	0.882300i	0.490545	+	0.871416i	$0.336798\pi$
$887$	−15.1711	+	26.2771i	−0.509396	+	0.882300i	−0.999941	+	0.0108837i	$0.996536\pi$
$888$	−54.4702			−1.82790
$889$	3.74980	−	30.1028i	0.125764	−	1.00961i
$890$	−53.2498			−1.78494
$891$	−8.84915	+	15.3272i	−0.296458	+	0.513480i
$892$	24.1438	+	41.8182i	0.808393	+	1.40018i
$893$	−0.895242	−	1.55060i	−0.0299581	−	0.0518890i
$894$	19.5447	−	33.8524i	0.653673	−	1.13220i
$895$	−65.6079			−2.19303
$896$	−43.5389	−	32.9289i	−1.45453	−	1.10008i
$897$	−32.3056			−1.07865
$898$	13.1180	−	22.7211i	0.437754	−	0.758212i
$899$	−2.79286	−	4.83737i	−0.0931471	−	0.161335i
$900$	5.88300	+	10.1897i	0.196100	+	0.339655i
$901$	32.5282	−	56.3406i	1.08367	−	1.87698i
$902$	−5.21126			−0.173516
$903$	8.97277	−	3.79014i	0.298595	−	0.126128i
$904$	24.9355			0.829342
$905$	−20.5899	+	35.6628i	−0.684432	+	1.18547i
$906$	23.4082	+	40.5441i	0.777684	+	1.34699i
$907$	7.10362	+	12.3038i	0.235872	+	0.408542i	0.959526	−	0.281621i	$-0.0908721\pi$
$907$	7.10362	+	12.3038i	0.235872	+	0.408542i	−0.723654	+	0.690163i	$0.757539\pi$
$908$	−20.2234	+	35.0280i	−0.671139	+	1.16245i
$909$	−0.571329			−0.0189498
$910$	58.0342	−	24.5139i	1.92381	−	0.812628i
$911$	−1.26559			−0.0419309			−0.0209655	−	0.999780i	$-0.506674\pi$
$911$	−1.26559			−0.0419309			−0.0209655	+	0.999780i	$0.506674\pi$
$912$	0.846431	−	1.46606i	0.0280281	−	0.0485462i
$913$	8.72651	+	15.1148i	0.288805	+	0.500225i
$914$	24.3851	+	42.2362i	0.806587	+	1.39705i
$915$	21.2622	−	36.8271i	0.702905	−	1.21747i
$916$	3.59445			0.118764
$917$	−3.69702	−	2.79609i	−0.122086	−	0.0923350i
$918$	60.7970			2.00660
$919$	4.31707	−	7.47739i	0.142407	−	0.246656i	−0.785995	−	0.618232i	$-0.787849\pi$
$919$	4.31707	−	7.47739i	0.142407	−	0.246656i	0.928403	+	0.371576i	$0.121182\pi$
$920$	60.6534	+	105.055i	1.99968	+	3.46356i
$921$	13.5759	+	23.5141i	0.447341	+	0.774817i
$922$	7.46222	−	12.9249i	0.245755	−	0.425660i
$923$	−13.6908			−0.450639
$924$	4.28012	−	34.3601i	0.140806	−	1.13036i
$925$	97.2028			3.19601
$926$	−23.2043	+	40.1911i	−0.762542	+	1.32076i
$927$	2.84079	+	4.92039i	0.0933037	+	0.161607i
$928$	2.20211	+	3.81417i	0.0722878	+	0.125206i
$929$	7.74753	−	13.4191i	0.254188	−	0.440267i	−0.710487	−	0.703711i	$-0.751525\pi$
$929$	7.74753	−	13.4191i	0.254188	−	0.440267i	0.964675	+	0.263444i	$0.0848584\pi$
$930$	65.8246			2.15847
$931$	2.73383	−	2.81115i	0.0895977	−	0.0921317i
$932$	79.3942			2.60064
$933$	−20.2671	+	35.1036i	−0.663515	+	1.14924i
$934$	40.1166	+	69.4840i	1.31266	+	2.27359i
$935$	−20.9943	−	36.3632i	−0.686587	−	1.18920i
$936$	1.38156	−	2.39292i	0.0451576	−	0.0782152i
$937$	19.9639			0.652192			0.326096	−	0.945337i	$-0.394267\pi$
$937$	19.9639			0.652192			0.326096	+	0.945337i	$0.394267\pi$
$938$	0.542056	−	4.35153i	0.0176987	−	0.142082i
$939$	−4.93665			−0.161102
$940$	23.2776	−	40.3180i	0.759232	−	1.31503i
$941$	−0.422204	−	0.731278i	−0.0137635	−	0.0238390i	0.859062	−	0.511872i	$-0.171048\pi$
$941$	−0.422204	−	0.731278i	−0.0137635	−	0.0238390i	−0.872825	+	0.488033i	$0.837715\pi$
$942$	−27.8034	−	48.1570i	−0.905885	−	1.56904i
$943$	−3.93444	+	6.81465i	−0.128123	+	0.221915i
$944$	−26.0022			−0.846299
$945$	−46.0536	−	34.8308i	−1.49812	−	1.13304i
$946$	−11.6535			−0.378889
$947$	15.0274	−	26.0282i	0.488325	−	0.845804i	−0.511585	−	0.859233i	$-0.670941\pi$
$947$	15.0274	−	26.0282i	0.488325	−	0.845804i	0.999910	+	0.0134292i	$0.00427477\pi$
$948$	0.744887	+	1.29018i	0.0241928	+	0.0419032i
$949$	−7.56833	−	13.1087i	−0.245678	−	0.425528i
$950$	−7.45901	+	12.9194i	−0.242002	+	0.419160i
$951$	−15.1191			−0.490271
$952$	−44.1729	+	18.6589i	−1.43165	+	0.604737i
$953$	25.3832			0.822243			0.411122	−	0.911581i	$-0.365137\pi$
$953$	25.3832			0.822243			0.411122	+	0.911581i	$0.365137\pi$
$954$	−4.71200	+	8.16142i	−0.152557	+	0.264236i
$955$	−22.2405	−	38.5216i	−0.719685	−	1.24653i
$956$	29.4901	+	51.0784i	0.953779	+	1.65199i
$957$	−2.41496	+	4.18284i	−0.0780646	+	0.135212i
$958$	8.79114			0.284029
$959$	−30.9585	+	13.0770i	−0.999702	+	0.422279i
$960$	−76.2570			−2.46119
$961$	6.73304	−	11.6620i	0.217195	−	0.376193i
$962$	−25.5522	−	44.2577i	−0.823837	−	1.42693i
$963$	0.517668	+	0.896627i	0.0166816	+	0.0288934i
$964$	−3.00841	+	5.21072i	−0.0968943	+	0.167826i
$965$	−82.5606			−2.65772
$966$	−64.7745	−	48.9896i	−2.08409	−	1.57621i
$967$	24.4940			0.787675			0.393838	−	0.919180i	$-0.371147\pi$
$967$	24.4940			0.787675			0.393838	+	0.919180i	$0.371147\pi$
$968$	11.7885	−	20.4182i	0.378896	−	0.656266i
$969$	2.18463	+	3.78389i	0.0701805	+	0.121556i
$970$	47.5971	+	82.4407i	1.52825	+	2.64701i
$971$	−9.78180	+	16.9426i	−0.313913	+	0.543713i	−0.979206	−	0.202869i	$-0.934973\pi$
$971$	−9.78180	+	16.9426i	−0.313913	+	0.543713i	0.665293	+	0.746582i	$0.268307\pi$
$972$	−10.8403			−0.347703
$973$	1.02464	−	8.22561i	0.0328484	−	0.263701i
$974$	6.60706			0.211704
$975$	23.0707	−	39.9597i	0.738855	−	1.27973i
$976$	5.88292	+	10.1895i	0.188308	+	0.326159i
$977$	22.0882	+	38.2579i	0.706665	+	1.22398i	0.966087	+	0.258216i	$0.0831345\pi$
$977$	22.0882	+	38.2579i	0.706665	+	1.22398i	−0.259422	+	0.965764i	$0.583532\pi$
$978$	−14.1659	+	24.5360i	−0.452975	+	0.784575i
$979$	−12.2651			−0.391993
$980$	98.8432	+	25.0133i	3.15743	+	0.799020i
$981$	−2.73351			−0.0872743
$982$	19.3426	−	33.5024i	0.617248	−	1.06910i
$983$	−5.94766	−	10.3017i	−0.189701	−	0.328572i	0.755450	−	0.655207i	$-0.227419\pi$
$983$	−5.94766	−	10.3017i	−0.189701	−	0.328572i	−0.945151	+	0.326635i	$0.894085\pi$
$984$	3.14903	+	5.45428i	0.100387	+	0.173876i
$985$	−4.89472	+	8.47791i	−0.155959	+	0.270129i
$986$	14.9748			0.476894
$987$	−1.72093	+	13.8153i	−0.0547777	+	0.439746i
$988$	5.04927			0.160639
$989$	−8.79828	+	15.2391i	−0.279769	+	0.484574i
$990$	3.04121	+	5.26752i	0.0966559	+	0.167413i
$991$	−15.8520	−	27.4565i	−0.503557	−	0.872186i	−0.999992	−	0.00411185i	$-0.998691\pi$
$991$	−15.8520	−	27.4565i	−0.503557	−	0.872186i	0.496435	−	0.868074i	$-0.334642\pi$
$992$	6.91256	−	11.9729i	0.219474	−	0.380140i
$993$	−49.2239			−1.56207
$994$	−27.4509	−	20.7614i	−0.870690	−	0.658511i
$995$	7.31570			0.231923
$996$	23.6111	−	40.8956i	0.748145	−	1.29583i
$997$	−13.5061	−	23.3932i	−0.427741	−	0.740869i	0.568931	−	0.822385i	$-0.307357\pi$
$997$	−13.5061	−	23.3932i	−0.427741	−	0.740869i	−0.996672	+	0.0815159i	$0.974024\pi$
$998$	−4.10153	−	7.10405i	−0.129832	−	0.224875i
$999$	−23.4198	+	40.5644i	−0.740971	+	1.28340i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	287.2.e.d.247.4	yes	34
7.2	even	3		2009.2.a.s.1.14		17
7.4	even	3	inner	287.2.e.d.165.4	✓	34
7.5	odd	6		2009.2.a.r.1.14		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
287.2.e.d.165.4	✓	34	7.4	even	3	inner
287.2.e.d.247.4	yes	34	1.1	even	1	trivial
2009.2.a.r.1.14		17	7.5	odd	6
2009.2.a.s.1.14		17	7.2	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:	\( N \)	\(=\)	\( 287 = 7 \cdot 41 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	287.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.18475 + 2.05204i) q^{2} +(0.823159 + 1.42575i) q^{3} +(-1.80725 - 3.13025i) q^{4} +(2.01488 - 3.48988i) q^{5} -3.90094 q^{6} +(0.327045 - 2.62546i) q^{7} +3.82554 q^{8} +(0.144819 - 0.250833i) q^{9} +O(q^{10})\)	\(q+(-1.18475 + 2.05204i) q^{2} +(0.823159 + 1.42575i) q^{3} +(-1.80725 - 3.13025i) q^{4} +(2.01488 - 3.48988i) q^{5} -3.90094 q^{6} +(0.327045 - 2.62546i) q^{7} +3.82554 q^{8} +(0.144819 - 0.250833i) q^{9} +(4.77425 + 8.26924i) q^{10} +(1.09966 + 1.90466i) q^{11} +(2.97531 - 5.15338i) q^{12} +2.49374 q^{13} +(5.00009 + 3.78162i) q^{14} +6.63427 q^{15} +(-0.917802 + 1.58968i) q^{16} +(-2.36884 - 4.10295i) q^{17} +(0.343147 + 0.594347i) q^{18} +(-0.280091 + 0.485132i) q^{19} -14.5656 q^{20} +(4.01247 - 1.69489i) q^{21} -5.21126 q^{22} +(-3.93444 + 6.81465i) q^{23} +(3.14903 + 5.45428i) q^{24} +(-5.61949 - 9.73324i) q^{25} +(-2.95445 + 5.11726i) q^{26} +5.41579 q^{27} +(-8.80939 + 3.72113i) q^{28} +1.33395 q^{29} +(-7.85993 + 13.6138i) q^{30} +(-2.09368 - 3.62635i) q^{31} +(1.65082 + 2.85930i) q^{32} +(-1.81038 + 3.13568i) q^{33} +11.2259 q^{34} +(-8.50357 - 6.43134i) q^{35} -1.04689 q^{36} +(-4.32436 + 7.49002i) q^{37} +(-0.663674 - 1.14952i) q^{38} +(2.05274 + 3.55546i) q^{39} +(7.70801 - 13.3507i) q^{40} +1.00000 q^{41} +(-1.27578 + 10.2418i) q^{42} +2.23622 q^{43} +(3.97471 - 6.88439i) q^{44} +(-0.583584 - 1.01080i) q^{45} +(-9.32263 - 16.1473i) q^{46} +(-1.59813 + 2.76804i) q^{47} -3.02199 q^{48} +(-6.78608 - 1.71729i) q^{49} +26.6307 q^{50} +(3.89986 - 6.75475i) q^{51} +(-4.50681 - 7.80602i) q^{52} +(6.86587 + 11.8920i) q^{53} +(-6.41634 + 11.1134i) q^{54} +8.86270 q^{55} +(1.25113 - 10.0438i) q^{56} -0.922238 q^{57} +(-1.58039 + 2.73732i) q^{58} +(7.08274 + 12.2677i) q^{59} +(-11.9898 - 20.7669i) q^{60} +(3.20490 - 5.55105i) q^{61} +9.92190 q^{62} +(-0.611190 - 0.462249i) q^{63} -11.4944 q^{64} +(5.02459 - 8.70284i) q^{65} +(-4.28969 - 7.42996i) q^{66} +(-0.349745 - 0.605775i) q^{67} +(-8.56216 + 14.8301i) q^{68} -12.9547 q^{69} +(23.2719 - 9.83018i) q^{70} -5.49009 q^{71} +(0.554010 - 0.959573i) q^{72} +(-3.03493 - 5.25666i) q^{73} +(-10.2466 - 17.7475i) q^{74} +(9.25146 - 16.0240i) q^{75} +2.02478 q^{76} +(5.36025 - 2.26419i) q^{77} -9.72793 q^{78} +(-0.125178 + 0.216815i) q^{79} +(3.69852 + 6.40603i) q^{80} +(4.02360 + 6.96908i) q^{81} +(-1.18475 + 2.05204i) q^{82} +7.93567 q^{83} +(-12.5569 - 9.49694i) q^{84} -19.0917 q^{85} +(-2.64936 + 4.58882i) q^{86} +(1.09805 + 1.90188i) q^{87} +(4.20678 + 7.28636i) q^{88} +(-2.78839 + 4.82963i) q^{89} +2.76560 q^{90} +(0.815565 - 6.54721i) q^{91} +28.4421 q^{92} +(3.44686 - 5.97013i) q^{93} +(-3.78675 - 6.55884i) q^{94} +(1.12870 + 1.95497i) q^{95} +(-2.71777 + 4.70732i) q^{96} +9.96956 q^{97} +(11.5637 - 11.8908i) q^{98} +0.637002 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 34 q - 3 q^{2} - q^{3} - 25 q^{4} + q^{5} + 4 q^{6} - 2 q^{7} + 18 q^{8} - 26 q^{9}+O(q^{10}) \) 34 * q - 3 * q^2 - q^3 - 25 * q^4 + q^5 + 4 * q^6 - 2 * q^7 + 18 * q^8 - 26 * q^9	\( 34 q - 3 q^{2} - q^{3} - 25 q^{4} + q^{5} + 4 q^{6} - 2 q^{7} + 18 q^{8} - 26 q^{9} + 2 q^{10} - 15 q^{11} - 4 q^{12} - 10 q^{13} + 21 q^{14} + 48 q^{15} - 33 q^{16} - 4 q^{17} - 10 q^{18} - 5 q^{19} - 52 q^{20} + 12 q^{21} + 32 q^{22} - 12 q^{23} - 16 q^{24} - 24 q^{25} - 31 q^{26} - 22 q^{27} + 60 q^{28} + 28 q^{29} + 33 q^{30} + 3 q^{31} - 16 q^{32} - 4 q^{33} - 48 q^{34} + 45 q^{35} + 114 q^{36} - 24 q^{37} - 45 q^{39} - 36 q^{40} + 34 q^{41} + 65 q^{42} + 28 q^{43} + 9 q^{44} + 21 q^{45} - 44 q^{46} - 19 q^{47} - 120 q^{48} - 10 q^{49} - 8 q^{50} - 2 q^{51} + 25 q^{52} - 4 q^{53} - 68 q^{54} + 18 q^{55} + 25 q^{56} - 24 q^{57} + q^{58} + 27 q^{59} - 66 q^{60} + q^{61} - 46 q^{62} + 37 q^{63} + 150 q^{64} - 22 q^{65} + 16 q^{66} - 49 q^{67} - 45 q^{68} + 24 q^{69} + 73 q^{70} + 80 q^{71} + 23 q^{72} + 14 q^{73} - 33 q^{74} - 27 q^{75} - 18 q^{76} - 20 q^{77} - 24 q^{78} - 61 q^{79} + 82 q^{80} - 53 q^{81} - 3 q^{82} - 36 q^{83} + 188 q^{84} - 26 q^{85} + 4 q^{86} + 17 q^{87} - 74 q^{88} - 18 q^{89} - 40 q^{90} + 7 q^{91} + 56 q^{92} + 36 q^{93} + 5 q^{94} - 20 q^{95} - 148 q^{96} + 52 q^{97} + 142 q^{98} + 76 q^{99}+O(q^{100}) \) 34 * q - 3 * q^2 - q^3 - 25 * q^4 + q^5 + 4 * q^6 - 2 * q^7 + 18 * q^8 - 26 * q^9 + 2 * q^10 - 15 * q^11 - 4 * q^12 - 10 * q^13 + 21 * q^14 + 48 * q^15 - 33 * q^16 - 4 * q^17 - 10 * q^18 - 5 * q^19 - 52 * q^20 + 12 * q^21 + 32 * q^22 - 12 * q^23 - 16 * q^24 - 24 * q^25 - 31 * q^26 - 22 * q^27 + 60 * q^28 + 28 * q^29 + 33 * q^30 + 3 * q^31 - 16 * q^32 - 4 * q^33 - 48 * q^34 + 45 * q^35 + 114 * q^36 - 24 * q^37 - 45 * q^39 - 36 * q^40 + 34 * q^41 + 65 * q^42 + 28 * q^43 + 9 * q^44 + 21 * q^45 - 44 * q^46 - 19 * q^47 - 120 * q^48 - 10 * q^49 - 8 * q^50 - 2 * q^51 + 25 * q^52 - 4 * q^53 - 68 * q^54 + 18 * q^55 + 25 * q^56 - 24 * q^57 + q^58 + 27 * q^59 - 66 * q^60 + q^61 - 46 * q^62 + 37 * q^63 + 150 * q^64 - 22 * q^65 + 16 * q^66 - 49 * q^67 - 45 * q^68 + 24 * q^69 + 73 * q^70 + 80 * q^71 + 23 * q^72 + 14 * q^73 - 33 * q^74 - 27 * q^75 - 18 * q^76 - 20 * q^77 - 24 * q^78 - 61 * q^79 + 82 * q^80 - 53 * q^81 - 3 * q^82 - 36 * q^83 + 188 * q^84 - 26 * q^85 + 4 * q^86 + 17 * q^87 - 74 * q^88 - 18 * q^89 - 40 * q^90 + 7 * q^91 + 56 * q^92 + 36 * q^93 + 5 * q^94 - 20 * q^95 - 148 * q^96 + 52 * q^97 + 142 * q^98 + 76 * q^99

Introduction

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