LMFDB - Embedded newform 143.2.e.a.100.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [143,2,Mod(100,143)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(143, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("143.100");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 143 = 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	143.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:	$1.14186074890$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.1714608.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 12x^{4} - 19x^{3} + 30x^{2} - 21x + 7 $ x^6 - 3x^5 + 12x^4 - 19x^3 + 30x^2 - 21*x + 7
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			100.1
Root			$0.500000 + 0.385124i$ of defining polynomial
Character	$\chi$	$=$	143.100
Dual form			143.2.e.a.133.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-1.30084 + 2.25312i) q^{3} +(0.500000 + 0.866025i) q^{4} +3.76873 q^{5} +(-1.30084 - 2.25312i) q^{6} +(-0.0835276 - 0.144674i) q^{7} -3.00000 q^{8} +(-1.88437 - 3.26382i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.30084 + 2.25312i) q^{3} +(0.500000 + 0.866025i) q^{4} +3.76873 q^{5} +(-1.30084 - 2.25312i) q^{6} +(-0.0835276 - 0.144674i) q^{7} -3.00000 q^{8} +(-1.88437 - 3.26382i) q^{9} +(-1.88437 + 3.26382i) q^{10} +(-0.500000 + 0.866025i) q^{11} -2.60168 q^{12} +(0.199160 - 3.60005i) q^{13} +0.167055 q^{14} +(-4.90252 + 8.49141i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-2.18521 - 3.78489i) q^{17} +3.76873 q^{18} +(1.68521 + 2.91886i) q^{19} +(1.88437 + 3.26382i) q^{20} +0.434624 q^{21} +(-0.500000 - 0.866025i) q^{22} +(2.60168 - 4.50624i) q^{23} +(3.90252 - 6.75936i) q^{24} +9.20336 q^{25} +(3.01815 + 1.97250i) q^{26} +2.00000 q^{27} +(0.0835276 - 0.144674i) q^{28} +(-0.967895 + 1.67644i) q^{29} +(-4.90252 - 8.49141i) q^{30} +6.86925 q^{31} +(-2.50000 - 4.33013i) q^{32} +(-1.30084 - 2.25312i) q^{33} +4.37041 q^{34} +(-0.314793 - 0.545238i) q^{35} +(1.88437 - 3.26382i) q^{36} +(-4.31899 + 7.48071i) q^{37} -3.37041 q^{38} +(7.85226 + 5.13182i) q^{39} -11.3062 q^{40} +(0.633784 - 1.09775i) q^{41} +(-0.217312 + 0.376395i) q^{42} +(3.60168 + 6.23829i) q^{43} -1.00000 q^{44} +(-7.10168 - 12.3005i) q^{45} +(2.60168 + 4.50624i) q^{46} -10.1391 q^{47} +(1.30084 + 2.25312i) q^{48} +(3.48605 - 6.03801i) q^{49} +(-4.60168 + 7.97034i) q^{50} +11.3704 q^{51} +(3.21731 - 1.62755i) q^{52} +1.33411 q^{53} +(-1.00000 + 1.73205i) q^{54} +(-1.88437 + 3.26382i) q^{55} +(0.250583 + 0.434022i) q^{56} -8.76873 q^{57} +(-0.967895 - 1.67644i) q^{58} +(-1.06957 - 1.85256i) q^{59} -9.80504 q^{60} +(2.40252 + 4.16128i) q^{61} +(-3.43462 + 5.94894i) q^{62} +(-0.314793 + 0.545238i) q^{63} +7.00000 q^{64} +(0.750583 - 13.5676i) q^{65} +2.60168 q^{66} +(2.06957 - 3.58461i) q^{67} +(2.18521 - 3.78489i) q^{68} +(6.76873 + 11.7238i) q^{69} +0.629587 q^{70} +(-3.00000 - 5.19615i) q^{71} +(5.65310 + 9.79146i) q^{72} +14.2420 q^{73} +(-4.31899 - 7.48071i) q^{74} +(-11.9721 + 20.7363i) q^{75} +(-1.68521 + 2.91886i) q^{76} +0.167055 q^{77} +(-8.37041 + 4.23435i) q^{78} -14.5738 q^{79} +(1.88437 - 3.26382i) q^{80} +(3.05142 - 5.28522i) q^{81} +(0.633784 + 1.09775i) q^{82} -10.5738 q^{83} +(0.217312 + 0.376395i) q^{84} +(-8.23546 - 14.2642i) q^{85} -7.20336 q^{86} +(-2.51815 - 4.36157i) q^{87} +(1.50000 - 2.59808i) q^{88} +(-7.15310 + 12.3895i) q^{89} +14.2034 q^{90} +(-0.537469 + 0.271890i) q^{91} +5.20336 q^{92} +(-8.93579 + 15.4772i) q^{93} +(5.06957 - 8.78076i) q^{94} +(6.35110 + 11.0004i) q^{95} +13.0084 q^{96} +(-1.78269 - 3.08771i) q^{97} +(3.48605 + 6.03801i) q^{98} +3.76873 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 3 q^{2} + 3 q^{4} + 6 q^{5} - 18 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q - 3 * q^2 + 3 * q^4 + 6 * q^5 - 18 * q^8 - 3 * q^9	$ 6 q - 3 q^{2} + 3 q^{4} + 6 q^{5} - 18 q^{8} - 3 q^{9} - 3 q^{10} - 3 q^{11} + 9 q^{13} - 6 q^{15} + 3 q^{16} + 3 q^{17} + 6 q^{18} - 6 q^{19} + 3 q^{20} - 12 q^{21} - 3 q^{22} + 24 q^{25} + 3 q^{26} + 12 q^{27} + 3 q^{29} - 6 q^{30} + 12 q^{31} - 15 q^{32} - 6 q^{34} - 18 q^{35} + 3 q^{36} - 3 q^{37} + 12 q^{38} + 30 q^{39} - 18 q^{40} - 3 q^{41} + 6 q^{42} + 6 q^{43} - 6 q^{44} - 27 q^{45} - 12 q^{47} - 3 q^{49} - 12 q^{50} + 36 q^{51} + 12 q^{52} + 6 q^{53} - 6 q^{54} - 3 q^{55} - 36 q^{57} + 3 q^{58} + 18 q^{59} - 12 q^{60} - 9 q^{61} - 6 q^{62} - 18 q^{63} + 42 q^{64} + 3 q^{65} - 12 q^{67} - 3 q^{68} + 24 q^{69} + 36 q^{70} - 18 q^{71} + 9 q^{72} + 18 q^{73} - 3 q^{74} - 24 q^{75} + 6 q^{76} - 18 q^{78} - 24 q^{79} + 3 q^{80} + 9 q^{81} - 3 q^{82} - 6 q^{84} - 27 q^{85} - 12 q^{86} + 9 q^{88} - 18 q^{89} + 54 q^{90} + 30 q^{91} - 36 q^{93} + 6 q^{94} + 24 q^{95} - 18 q^{97} - 3 q^{98} + 6 q^{99}+O(q^{100}) $ 6 * q - 3 * q^2 + 3 * q^4 + 6 * q^5 - 18 * q^8 - 3 * q^9 - 3 * q^10 - 3 * q^11 + 9 * q^13 - 6 * q^15 + 3 * q^16 + 3 * q^17 + 6 * q^18 - 6 * q^19 + 3 * q^20 - 12 * q^21 - 3 * q^22 + 24 * q^25 + 3 * q^26 + 12 * q^27 + 3 * q^29 - 6 * q^30 + 12 * q^31 - 15 * q^32 - 6 * q^34 - 18 * q^35 + 3 * q^36 - 3 * q^37 + 12 * q^38 + 30 * q^39 - 18 * q^40 - 3 * q^41 + 6 * q^42 + 6 * q^43 - 6 * q^44 - 27 * q^45 - 12 * q^47 - 3 * q^49 - 12 * q^50 + 36 * q^51 + 12 * q^52 + 6 * q^53 - 6 * q^54 - 3 * q^55 - 36 * q^57 + 3 * q^58 + 18 * q^59 - 12 * q^60 - 9 * q^61 - 6 * q^62 - 18 * q^63 + 42 * q^64 + 3 * q^65 - 12 * q^67 - 3 * q^68 + 24 * q^69 + 36 * q^70 - 18 * q^71 + 9 * q^72 + 18 * q^73 - 3 * q^74 - 24 * q^75 + 6 * q^76 - 18 * q^78 - 24 * q^79 + 3 * q^80 + 9 * q^81 - 3 * q^82 - 6 * q^84 - 27 * q^85 - 12 * q^86 + 9 * q^88 - 18 * q^89 + 54 * q^90 + 30 * q^91 - 36 * q^93 + 6 * q^94 + 24 * q^95 - 18 * q^97 - 3 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/143\mathbb{Z}\right)^\times$.

$n$	$67$	$79$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i	−0.986869	−	0.161521i	$-0.948360\pi$
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i	0.633316	+	0.773893i	$0.281693\pi$
$3$	−1.30084	+	2.25312i	−0.751040	+	1.30084i	0.196279	+	0.980548i	$0.437114\pi$
$3$	−1.30084	+	2.25312i	−0.751040	+	1.30084i	−0.947319	+	0.320291i	$0.896219\pi$
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	3.76873			1.68543			0.842715	−	0.538361i	$-0.180956\pi$
$5$	3.76873			1.68543			0.842715	+	0.538361i	$0.180956\pi$
$6$	−1.30084	−	2.25312i	−0.531066	−	0.919832i
$7$	−0.0835276	−	0.144674i	−0.0315705	−	0.0546816i	0.849808	−	0.527092i	$-0.176718\pi$
$7$	−0.0835276	−	0.144674i	−0.0315705	−	0.0546816i	−0.881379	+	0.472410i	$0.843384\pi$
$8$	−3.00000			−1.06066
$9$	−1.88437	−	3.26382i	−0.628122	−	1.08794i
$10$	−1.88437	+	3.26382i	−0.595889	+	1.03211i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	−2.60168			−0.751040
$13$	0.199160	−	3.60005i	0.0552372	−	0.998473i
$13$	0.199160	−	3.60005i	0.0552372	−	0.998473i
$14$	0.167055			0.0446474
$15$	−4.90252	+	8.49141i	−1.26582	+	2.19247i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−2.18521	−	3.78489i	−0.529990	−	0.917970i	−0.999388	−	0.0349834i	$-0.988862\pi$
$17$	−2.18521	−	3.78489i	−0.529990	−	0.917970i	0.469397	−	0.882987i	$-0.344471\pi$
$18$	3.76873			0.888299
$19$	1.68521	+	2.91886i	0.386613	+	0.669633i	0.991992	−	0.126304i	$-0.0403116\pi$
$19$	1.68521	+	2.91886i	0.386613	+	0.669633i	−0.605379	+	0.795938i	$0.706978\pi$
$20$	1.88437	+	3.26382i	0.421357	+	0.729812i
$21$	0.434624			0.0948427
$22$	−0.500000	−	0.866025i	−0.106600	−	0.184637i
$23$	2.60168	−	4.50624i	0.542488	−	0.939616i	−0.456273	−	0.889840i	$-0.650816\pi$
$23$	2.60168	−	4.50624i	0.542488	−	0.939616i	0.998760	−	0.0497761i	$-0.0158508\pi$
$24$	3.90252	−	6.75936i	0.796598	−	1.37975i
$25$	9.20336			1.84067
$26$	3.01815	+	1.97250i	0.591908	+	0.386839i
$27$	2.00000			0.384900
$28$	0.0835276	−	0.144674i	0.0157852	−	0.0273408i
$29$	−0.967895	+	1.67644i	−0.179734	+	0.311308i	−0.941789	−	0.336204i	$-0.890857\pi$
$29$	−0.967895	+	1.67644i	−0.179734	+	0.311308i	0.762056	+	0.647511i	$0.224190\pi$
$30$	−4.90252	−	8.49141i	−0.895073	−	1.55031i
$31$	6.86925			1.23375			0.616877	−	0.787060i	$-0.288398\pi$
$31$	6.86925			1.23375			0.616877	+	0.787060i	$0.288398\pi$
$32$	−2.50000	−	4.33013i	−0.441942	−	0.765466i
$33$	−1.30084	−	2.25312i	−0.226447	−	0.392218i
$34$	4.37041			0.749520
$35$	−0.314793	−	0.545238i	−0.0532098	−	0.0921620i
$36$	1.88437	−	3.26382i	0.314061	−	0.543970i
$37$	−4.31899	+	7.48071i	−0.710038	+	1.22982i	0.254805	+	0.966993i	$0.417989\pi$
$37$	−4.31899	+	7.48071i	−0.710038	+	1.22982i	−0.964842	+	0.262829i	$0.915345\pi$
$38$	−3.37041			−0.546753
$39$	7.85226	+	5.13182i	1.25737	+	0.821748i
$40$	−11.3062			−1.78767
$41$	0.633784	−	1.09775i	0.0989805	−	0.171439i	−0.812282	−	0.583264i	$-0.801775\pi$
$41$	0.633784	−	1.09775i	0.0989805	−	0.171439i	0.911263	+	0.411825i	$0.135109\pi$
$42$	−0.217312	+	0.376395i	−0.0335320	+	0.0580791i
$43$	3.60168	+	6.23829i	0.549251	+	0.951330i	0.998326	+	0.0578365i	$0.0184202\pi$
$43$	3.60168	+	6.23829i	0.549251	+	0.951330i	−0.449075	+	0.893494i	$0.648246\pi$
$44$	−1.00000			−0.150756
$45$	−7.10168	−	12.3005i	−1.05866	−	1.83365i
$46$	2.60168	+	4.50624i	0.383597	+	0.664409i
$47$	−10.1391			−1.47895			−0.739473	−	0.673186i	$-0.764925\pi$
$47$	−10.1391			−1.47895			−0.739473	+	0.673186i	$0.764925\pi$
$48$	1.30084	+	2.25312i	0.187760	+	0.325210i
$49$	3.48605	−	6.03801i	0.498007	−	0.862573i
$50$	−4.60168	+	7.97034i	−0.650776	+	1.12718i
$51$	11.3704			1.59218
$52$	3.21731	−	1.62755i	0.446161	−	0.225700i
$53$	1.33411			0.183254			0.0916271	−	0.995793i	$-0.470793\pi$
$53$	1.33411			0.183254			0.0916271	+	0.995793i	$0.470793\pi$
$54$	−1.00000	+	1.73205i	−0.136083	+	0.235702i
$55$	−1.88437	+	3.26382i	−0.254088	+	0.440093i
$56$	0.250583	+	0.434022i	0.0334855	+	0.0579986i
$57$	−8.76873			−1.16145
$58$	−0.967895	−	1.67644i	−0.127091	−	0.220128i
$59$	−1.06957	−	1.85256i	−0.139247	−	0.241182i	0.787965	−	0.615720i	$-0.211135\pi$
$59$	−1.06957	−	1.85256i	−0.139247	−	0.241182i	−0.927212	+	0.374538i	$0.877801\pi$
$60$	−9.80504			−1.26582
$61$	2.40252	+	4.16128i	0.307611	+	0.532798i	0.977839	−	0.209357i	$-0.0671371\pi$
$61$	2.40252	+	4.16128i	0.307611	+	0.532798i	−0.670228	+	0.742155i	$0.733804\pi$
$62$	−3.43462	+	5.94894i	−0.436198	+	0.755517i
$63$	−0.314793	+	0.545238i	−0.0396602	+	0.0686935i
$64$	7.00000			0.875000
$65$	0.750583	−	13.5676i	0.0930983	−	1.68286i
$66$	2.60168			0.320245
$67$	2.06957	−	3.58461i	0.252839	−	0.437929i	−0.711468	−	0.702719i	$-0.751969\pi$
$67$	2.06957	−	3.58461i	0.252839	−	0.437929i	0.964306	+	0.264789i	$0.0853025\pi$
$68$	2.18521	−	3.78489i	0.264995	−	0.458985i
$69$	6.76873	+	11.7238i	0.814860	+	1.41138i
$70$	0.629587			0.0752500
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	0.631260	−	0.775571i	$-0.282538\pi$
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	−0.987294	+	0.158901i	$0.949205\pi$
$72$	5.65310	+	9.79146i	0.666224	+	1.15393i
$73$	14.2420			1.66690			0.833450	−	0.552596i	$-0.186363\pi$
$73$	14.2420			1.66690			0.833450	+	0.552596i	$0.186363\pi$
$74$	−4.31899	−	7.48071i	−0.502073	−	0.869615i
$75$	−11.9721	+	20.7363i	−1.38242	+	2.39442i
$76$	−1.68521	+	2.91886i	−0.193306	+	0.334817i
$77$	0.167055			0.0190377
$78$	−8.37041	+	4.23435i	−0.947763	+	0.479446i
$79$	−14.5738			−1.63968			−0.819839	−	0.572595i	$-0.805937\pi$
$79$	−14.5738			−1.63968			−0.819839	+	0.572595i	$0.805937\pi$
$80$	1.88437	−	3.26382i	0.210679	−	0.364906i
$81$	3.05142	−	5.28522i	0.339047	−	0.587247i
$82$	0.633784	+	1.09775i	0.0699898	+	0.121226i
$83$	−10.5738			−1.16062			−0.580311	−	0.814395i	$-0.697069\pi$
$83$	−10.5738			−1.16062			−0.580311	+	0.814395i	$0.697069\pi$
$84$	0.217312	+	0.376395i	0.0237107	+	0.0410681i
$85$	−8.23546	−	14.2642i	−0.893261	−	1.54717i
$86$	−7.20336			−0.776758
$87$	−2.51815	−	4.36157i	−0.269974	−	0.467609i
$88$	1.50000	−	2.59808i	0.159901	−	0.276956i
$89$	−7.15310	+	12.3895i	−0.758227	+	1.31329i	0.185527	+	0.982639i	$0.440601\pi$
$89$	−7.15310	+	12.3895i	−0.758227	+	1.31329i	−0.943754	+	0.330649i	$0.892732\pi$
$90$	14.2034			1.49717
$91$	−0.537469	+	0.271890i	−0.0563420	+	0.0285018i
$92$	5.20336			0.542488
$93$	−8.93579	+	15.4772i	−0.926598	+	1.60492i
$94$	5.06957	−	8.78076i	0.522887	−	0.905666i
$95$	6.35110	+	11.0004i	0.651609	+	1.12862i
$96$	13.0084			1.32766
$97$	−1.78269	−	3.08771i	−0.181005	−	0.313509i	0.761218	−	0.648496i	$-0.224602\pi$
$97$	−1.78269	−	3.08771i	−0.181005	−	0.313509i	−0.942223	+	0.334987i	$0.891268\pi$
$98$	3.48605	+	6.03801i	0.352144	+	0.609931i
$99$	3.76873			0.378772
$100$	4.60168	+	7.97034i	0.460168	+	0.797034i
$101$	6.01815	−	10.4237i	0.598828	−	1.03720i	−0.394166	−	0.919039i	$-0.628966\pi$
$101$	6.01815	−	10.4237i	0.598828	−	1.03720i	0.992994	−	0.118162i	$-0.0377002\pi$
$102$	−5.68521	+	9.84707i	−0.562919	+	0.975005i
$103$	−6.40672			−0.631273			−0.315636	−	0.948880i	$-0.602218\pi$
$103$	−6.40672			−0.631273			−0.315636	+	0.948880i	$0.602218\pi$
$104$	−0.597481	+	10.8001i	−0.0585879	+	1.05904i
$105$	1.63798			0.159851
$106$	−0.667055	+	1.15537i	−0.0647901	+	0.112220i
$107$	6.85226	−	11.8685i	0.662433	−	1.14737i	−0.317541	−	0.948244i	$-0.602857\pi$
$107$	6.85226	−	11.8685i	0.662433	−	1.14737i	0.979974	−	0.199123i	$-0.0638095\pi$
$108$	1.00000	+	1.73205i	0.0962250	+	0.166667i
$109$	−8.84134			−0.846847			−0.423423	−	0.905932i	$-0.639172\pi$
$109$	−8.84134			−0.846847			−0.423423	+	0.905932i	$0.639172\pi$
$110$	−1.88437	−	3.26382i	−0.179667	−	0.311193i
$111$	−11.2366	−	19.4624i	−1.06653	−	1.84729i
$112$	−0.167055			−0.0157852
$113$	−2.28269	−	3.95373i	−0.214737	−	0.371936i	0.738454	−	0.674304i	$-0.235556\pi$
$113$	−2.28269	−	3.95373i	−0.214737	−	0.371936i	−0.953191	+	0.302368i	$0.902223\pi$
$114$	4.38437	−	7.59395i	0.410634	−	0.711238i
$115$	9.80504	−	16.9828i	0.914324	−	1.58366i
$116$	−1.93579			−0.179734
$117$	−12.1252	+	6.13379i	−1.12097	+	0.567069i
$118$	2.13915			0.196925
$119$	−0.365050	+	0.632285i	−0.0334641	+	0.0579615i
$120$	14.7076	−	25.4742i	1.34261	−	2.32547i
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	−4.80504			−0.435028
$123$	1.64890	+	2.85598i	0.148677	+	0.257515i
$124$	3.43462	+	5.94894i	0.308438	+	0.534231i
$125$	15.8413			1.41689
$126$	−0.314793	−	0.545238i	−0.0280440	−	0.0485737i
$127$	0.665890	−	1.15335i	0.0590882	−	0.102344i	−0.834968	−	0.550298i	$-0.814514\pi$
$127$	0.665890	−	1.15335i	0.0590882	−	0.102344i	0.894056	+	0.447955i	$0.147847\pi$
$128$	1.50000	−	2.59808i	0.132583	−	0.229640i
$129$	−18.7408			−1.65004
$130$	11.3746	+	7.43383i	0.997619	+	0.651990i
$131$	13.7045			1.19737			0.598685	−	0.800985i	$-0.295690\pi$
$131$	13.7045			1.19737			0.598685	+	0.800985i	$0.295690\pi$
$132$	1.30084	−	2.25312i	0.113224	−	0.196109i
$133$	0.281523	−	0.487611i	0.0244111	−	0.0422813i
$134$	2.06957	+	3.58461i	0.178784	+	0.309663i
$135$	7.53747			0.648722
$136$	6.55562	+	11.3547i	0.562140	+	0.973655i
$137$	6.82016	+	11.8129i	0.582685	+	1.00924i	0.995160	+	0.0982713i	$0.0313313\pi$
$137$	6.82016	+	11.8129i	0.582685	+	1.00924i	−0.412474	+	0.910969i	$0.635335\pi$
$138$	−13.5375			−1.15239
$139$	−0.434624	−	0.752791i	−0.0368643	−	0.0638509i	0.847005	−	0.531586i	$-0.178404\pi$
$139$	−0.434624	−	0.752791i	−0.0368643	−	0.0638509i	−0.883869	+	0.467735i	$0.845070\pi$
$140$	0.314793	−	0.545238i	0.0266049	−	0.0460810i
$141$	13.1894	−	22.8447i	1.11075	−	1.92387i
$142$	6.00000			0.503509
$143$	3.01815	+	1.97250i	0.252391	+	0.164949i
$144$	−3.76873			−0.314061
$145$	−3.64774	+	6.31807i	−0.302928	+	0.524687i
$146$	−7.12100	+	12.3339i	−0.589338	+	1.02076i
$147$	9.06957	+	15.7090i	0.748046	+	1.29565i
$148$	−8.63798			−0.710038
$149$	−0.583528	−	1.01070i	−0.0478044	−	0.0827997i	0.841133	−	0.540828i	$-0.181889\pi$
$149$	−0.583528	−	1.01070i	−0.0478044	−	0.0827997i	−0.888938	+	0.458028i	$0.848556\pi$
$150$	−11.9721	−	20.7363i	−0.977517	−	1.69311i
$151$	−10.7408			−0.874076			−0.437038	−	0.899443i	$-0.643972\pi$
$151$	−10.7408			−0.874076			−0.437038	+	0.899443i	$0.643972\pi$
$152$	−5.05562	−	8.75659i	−0.410065	−	0.710253i
$153$	−8.23546	+	14.2642i	−0.665798	+	1.15320i
$154$	−0.0835276	+	0.144674i	−0.00673084	+	0.0116582i
$155$	25.8884			2.07940
$156$	−0.518152	+	9.36617i	−0.0414853	+	0.749893i
$157$	−4.59328			−0.366584			−0.183292	−	0.983059i	$-0.558675\pi$
$157$	−4.59328			−0.366584			−0.183292	+	0.983059i	$0.558675\pi$
$158$	7.28689	−	12.6213i	0.579714	−	1.00409i
$159$	−1.73546	+	3.00591i	−0.137631	+	0.238384i
$160$	−9.42184	−	16.3191i	−0.744862	−	1.29014i
$161$	−0.869248			−0.0685063
$162$	3.05142	+	5.28522i	0.239742	+	0.415246i
$163$	−5.67125	−	9.82290i	−0.444207	−	0.769389i	0.553790	−	0.832657i	$-0.313181\pi$
$163$	−5.67125	−	9.82290i	−0.444207	−	0.769389i	−0.997997	+	0.0632677i	$0.979848\pi$
$164$	1.26757			0.0989805
$165$	−4.90252	−	8.49141i	−0.381661	−	0.661055i
$166$	5.28689	−	9.15715i	0.410342	−	0.710733i
$167$	−8.63798	+	14.9614i	−0.668427	+	1.15775i	0.309917	+	0.950764i	$0.399699\pi$
$167$	−8.63798	+	14.9614i	−0.668427	+	1.15775i	−0.978344	+	0.206986i	$0.933635\pi$
$168$	−1.30387			−0.100596
$169$	−12.9207	−	1.43397i	−0.993898	−	0.110306i
$170$	16.4709			1.26326
$171$	6.35110	−	11.0004i	0.485680	−	0.841223i
$172$	−3.60168	+	6.23829i	−0.274625	+	0.475665i
$173$	6.42067	+	11.1209i	0.488155	+	0.845508i	0.999907	−	0.0136244i	$-0.00433691\pi$
$173$	6.42067	+	11.1209i	0.488155	+	0.845508i	−0.511753	+	0.859133i	$0.671004\pi$
$174$	5.03630			0.381801
$175$	−0.768734	−	1.33149i	−0.0581109	−	0.100651i
$176$	0.500000	+	0.866025i	0.0376889	+	0.0652791i
$177$	5.56538			0.418319
$178$	−7.15310	−	12.3895i	−0.536148	−	0.928635i
$179$	2.46789	−	4.27452i	0.184459	−	0.319493i	−0.758935	−	0.651166i	$-0.774280\pi$
$179$	2.46789	−	4.27452i	0.184459	−	0.319493i	0.943394	+	0.331674i	$0.107613\pi$
$180$	7.10168	−	12.3005i	0.529328	−	0.916823i
$181$	0.637982			0.0474208			0.0237104	−	0.999719i	$-0.492452\pi$
$181$	0.637982			0.0474208			0.0237104	+	0.999719i	$0.492452\pi$
$182$	0.0332708	−	0.601406i	0.00246619	−	0.0445792i
$183$	−12.5012			−0.924113
$184$	−7.80504	+	13.5187i	−0.575395	+	0.996613i
$185$	−16.2771	+	28.1928i	−1.19672	+	2.07278i
$186$	−8.93579	−	15.4772i	−0.655204	−	1.13485i
$187$	4.37041			0.319596
$188$	−5.06957	−	8.78076i	−0.369737	−	0.640403i
$189$	−0.167055	−	0.289348i	−0.0121515	−	0.0210470i
$190$	−12.7022			−0.921514
$191$	−13.0696	−	22.6372i	−0.945681	−	1.63797i	−0.754382	−	0.656436i	$-0.772063\pi$
$191$	−13.0696	−	22.6372i	−0.945681	−	1.63797i	−0.191300	−	0.981532i	$-0.561270\pi$
$192$	−9.10588	+	15.7718i	−0.657160	+	1.13823i
$193$	5.56957	−	9.64678i	0.400907	−	0.694391i	−0.592929	−	0.805255i	$-0.702028\pi$
$193$	5.56957	−	9.64678i	0.400907	−	0.694391i	0.993836	+	0.110864i	$0.0353618\pi$
$194$	3.56538			0.255979
$195$	29.5931	+	19.3404i	2.11921	+	1.38500i
$196$	6.97209			0.498007
$197$	−7.76873	+	13.4558i	−0.553499	+	0.958689i	0.444519	+	0.895769i	$0.353375\pi$
$197$	−7.76873	+	13.4558i	−0.553499	+	0.958689i	−0.998019	+	0.0629198i	$0.979959\pi$
$198$	−1.88437	+	3.26382i	−0.133916	+	0.231950i
$199$	5.83831	+	10.1122i	0.413867	+	0.716838i	0.995309	−	0.0967497i	$-0.0308446\pi$
$199$	5.83831	+	10.1122i	0.413867	+	0.716838i	−0.581442	+	0.813588i	$0.697511\pi$
$200$	−27.6101			−1.95233
$201$	5.38437	+	9.32600i	0.379784	+	0.657805i
$202$	6.01815	+	10.4237i	0.423436	+	0.733412i
$203$	0.323384			0.0226971
$204$	5.68521	+	9.84707i	0.398044	+	0.689433i
$205$	2.38856	−	4.13712i	0.166825	−	0.288949i
$206$	3.20336	−	5.54838i	0.223189	−	0.386574i
$207$	−19.6101			−1.36299
$208$	−3.01815	−	1.97250i	−0.209271	−	0.136768i
$209$	−3.37041			−0.233136
$210$	−0.818991	+	1.41853i	−0.0565158	+	0.0978882i
$211$	2.28689	−	3.96100i	0.157436	−	0.272687i	−0.776508	−	0.630108i	$-0.783011\pi$
$211$	2.28689	−	3.96100i	0.157436	−	0.272687i	0.933943	+	0.357421i	$0.116344\pi$
$212$	0.667055	+	1.15537i	0.0458135	+	0.0793514i
$213$	15.6101			1.06958
$214$	6.85226	+	11.8685i	0.468411	+	0.811312i
$215$	13.5738	+	23.5105i	0.925724	+	1.60340i
$216$	−6.00000			−0.408248
$217$	−0.573772	−	0.993802i	−0.0389502	−	0.0674637i
$218$	4.42067	−	7.65683i	0.299406	−	0.518586i
$219$	−18.5265	+	32.0889i	−1.25191	+	2.16837i
$220$	−3.76873			−0.254088
$221$	−14.0610	+	7.11305i	−0.945844	+	0.478475i
$222$	22.4733			1.50831
$223$	4.53211	−	7.84984i	0.303492	−	0.525664i	−0.673432	−	0.739249i	$-0.735181\pi$
$223$	4.53211	−	7.84984i	0.303492	−	0.525664i	0.976924	+	0.213585i	$0.0685140\pi$
$224$	−0.417638	+	0.723370i	−0.0279046	+	0.0483322i
$225$	−17.3425	−	30.0381i	−1.15617	−	2.00254i
$226$	4.56538			0.303684
$227$	6.60168	+	11.4344i	0.438169	+	0.758931i	0.997548	−	0.0699810i	$-0.0222939\pi$
$227$	6.60168	+	11.4344i	0.438169	+	0.758931i	−0.559379	+	0.828912i	$0.688961\pi$
$228$	−4.38437	−	7.59395i	−0.290362	−	0.502921i
$229$	2.02791			0.134008			0.0670039	−	0.997753i	$-0.478656\pi$
$229$	2.02791			0.134008			0.0670039	+	0.997753i	$0.478656\pi$
$230$	9.80504	+	16.9828i	0.646525	+	1.11981i
$231$	−0.217312	+	0.376395i	−0.0142981	+	0.0247650i
$232$	2.90368	−	5.02933i	0.190636	−	0.330192i
$233$	−12.7408			−0.834679			−0.417340	−	0.908751i	$-0.637037\pi$
$233$	−12.7408			−0.834679			−0.417340	+	0.908751i	$0.637037\pi$
$234$	0.750583	−	13.5676i	0.0490671	−	0.886943i
$235$	−38.2118			−2.49266
$236$	1.06957	−	1.85256i	0.0696233	−	0.120591i
$237$	18.9581	−	32.8365i	1.23146	−	2.13296i
$238$	−0.365050	−	0.632285i	−0.0236627	−	0.0409850i
$239$	4.07261			0.263435			0.131717	−	0.991287i	$-0.457951\pi$
$239$	4.07261			0.263435			0.131717	+	0.991287i	$0.457951\pi$
$240$	4.90252	+	8.49141i	0.316456	+	0.548118i
$241$	9.49141	+	16.4396i	0.611395	+	1.05897i	0.991005	+	0.133821i	$0.0427248\pi$
$241$	9.49141	+	16.4396i	0.611395	+	1.05897i	−0.379610	+	0.925147i	$0.623942\pi$
$242$	1.00000			0.0642824
$243$	10.9388	+	18.9466i	0.701726	+	1.21542i
$244$	−2.40252	+	4.16128i	−0.153805	+	0.266399i
$245$	13.1380	−	22.7557i	0.839355	−	1.45381i
$246$	−3.29781			−0.210261
$247$	10.8437	−	5.48550i	0.689966	−	0.349034i
$248$	−20.6077			−1.30859
$249$	13.7548	−	23.8240i	0.871674	−	1.50978i
$250$	−7.92067	+	13.7190i	−0.500947	+	0.867666i
$251$	−5.17009	−	8.95485i	−0.326333	−	0.565225i	0.655448	−	0.755240i	$-0.272480\pi$
$251$	−5.17009	−	8.95485i	−0.326333	−	0.565225i	−0.981781	+	0.190015i	$0.939146\pi$
$252$	−0.629587			−0.0396602
$253$	2.60168	+	4.50624i	0.163566	+	0.283305i
$254$	0.665890	+	1.15335i	0.0417816	+	0.0723679i
$255$	42.8521			2.68350
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	−12.0877	+	20.9366i	−0.754012	+	1.30599i	0.191853	+	0.981424i	$0.438550\pi$
$257$	−12.0877	+	20.9366i	−0.754012	+	1.30599i	−0.945864	+	0.324563i	$0.894783\pi$
$258$	9.37041	−	16.2300i	0.583376	−	1.01044i
$259$	1.44302			0.0896649
$260$	12.1252	−	6.13379i	0.751973	−	0.380401i
$261$	7.29548			0.451579
$262$	−6.85226	+	11.8685i	−0.423334	+	0.733236i
$263$	5.37041	−	9.30183i	0.331154	−	0.573575i	−0.651585	−	0.758576i	$-0.725895\pi$
$263$	5.37041	−	9.30183i	0.331154	−	0.573575i	0.982738	+	0.185001i	$0.0592287\pi$
$264$	3.90252	+	6.75936i	0.240183	+	0.416010i
$265$	5.02791			0.308862
$266$	0.281523	+	0.487611i	0.0172613	+	0.0298974i
$267$	−18.6101	−	32.2336i	−1.13892	−	1.97266i
$268$	4.13915			0.252839
$269$	−8.83294	−	15.2991i	−0.538554	−	0.932803i	−0.998982	−	0.0451061i	$-0.985637\pi$
$269$	−8.83294	−	15.2991i	−0.538554	−	0.932803i	0.460428	−	0.887697i	$-0.347696\pi$
$270$	−3.76873	+	6.52764i	−0.229358	+	0.397259i
$271$	−4.37041	+	7.56978i	−0.265484	+	0.459831i	−0.967690	−	0.252142i	$-0.918865\pi$
$271$	−4.37041	+	7.56978i	−0.265484	+	0.459831i	0.702207	+	0.711973i	$0.252198\pi$
$272$	−4.37041			−0.264995
$273$	0.0865599	−	1.56467i	0.00523884	−	0.0946979i
$274$	−13.6403			−0.824041
$275$	−4.60168	+	7.97034i	−0.277492	+	0.480630i
$276$	−6.76873	+	11.7238i	−0.407430	+	0.705689i
$277$	−14.6059	−	25.2981i	−0.877582	−	1.52002i	−0.853986	−	0.520295i	$-0.825822\pi$
$277$	−14.6059	−	25.2981i	−0.877582	−	1.52002i	−0.0235956	−	0.999722i	$-0.507511\pi$
$278$	0.869248			0.0521340
$279$	−12.9442	−	22.4200i	−0.774948	−	1.34225i
$280$	0.944380	+	1.63571i	0.0564375	+	0.0977526i
$281$	−10.8050			−0.644574			−0.322287	−	0.946642i	$-0.604452\pi$
$281$	−10.8050			−0.644574			−0.322287	+	0.946642i	$0.604452\pi$
$282$	13.1894	+	22.8447i	0.785418	+	1.36038i
$283$	−5.11983	+	8.86781i	−0.304342	+	0.527136i	−0.977115	−	0.212713i	$-0.931770\pi$
$283$	−5.11983	+	8.86781i	−0.304342	+	0.527136i	0.672772	+	0.739850i	$0.265103\pi$
$284$	3.00000	−	5.19615i	0.178017	−	0.308335i
$285$	−33.0470			−1.95754
$286$	−3.21731	+	1.62755i	−0.190244	+	0.0962388i
$287$	−0.211754			−0.0124994
$288$	−9.42184	+	16.3191i	−0.555187	+	0.961612i
$289$	−1.05026	+	1.81910i	−0.0617798	+	0.107006i
$290$	−3.64774	−	6.31807i	−0.214203	−	0.371010i
$291$	9.27596			0.543767
$292$	7.12100	+	12.3339i	0.416725	+	0.721788i
$293$	−1.98185	−	3.43266i	−0.115781	−	0.200538i	0.802311	−	0.596907i	$-0.203604\pi$
$293$	−1.98185	−	3.43266i	−0.115781	−	0.200538i	−0.918092	+	0.396368i	$0.870270\pi$
$294$	−18.1391			−1.05790
$295$	−4.03094	−	6.98179i	−0.234690	−	0.406496i
$296$	12.9570	−	22.4421i	0.753109	−	1.30442i
$297$	−1.00000	+	1.73205i	−0.0580259	+	0.100504i
$298$	1.16706			0.0676057
$299$	−15.7045	−	10.2636i	−0.908216	−	0.593561i
$300$	−23.9442			−1.38242
$301$	0.601679	−	1.04214i	0.0346802	−	0.0600679i
$302$	5.37041	−	9.30183i	0.309033	−	0.535260i
$303$	15.6573	+	27.1192i	0.899488	+	1.55796i
$304$	3.37041			0.193306
$305$	9.05445	+	15.6828i	0.518457	+	0.897993i
$306$	−8.23546	−	14.2642i	−0.470790	−	0.815432i
$307$	14.2397			0.812700			0.406350	−	0.913717i	$-0.366801\pi$
$307$	14.2397			0.812700			0.406350	+	0.913717i	$0.366801\pi$
$308$	0.0835276	+	0.144674i	0.00475943	+	0.00824357i
$309$	8.33411	−	14.4351i	0.474111	−	0.821184i
$310$	−12.9442	+	22.4200i	−0.735180	+	1.27337i
$311$	11.8776			0.673519			0.336760	−	0.941591i	$-0.390669\pi$
$311$	11.8776			0.673519			0.336760	+	0.941591i	$0.390669\pi$
$312$	−23.5568	−	15.3954i	−1.33364	−	0.871596i
$313$	7.89949			0.446505			0.223253	−	0.974761i	$-0.428332\pi$
$313$	7.89949			0.446505			0.223253	+	0.974761i	$0.428332\pi$
$314$	2.29664	−	3.97790i	0.129607	−	0.224486i
$315$	−1.18637	+	2.05486i	−0.0668445	+	0.115778i
$316$	−7.28689	−	12.6213i	−0.409919	−	0.710001i
$317$	27.3230			1.53461			0.767306	−	0.641281i	$-0.221597\pi$
$317$	27.3230			1.53461			0.767306	+	0.641281i	$0.221597\pi$
$318$	−1.73546	−	3.00591i	−0.0973200	−	0.168563i
$319$	−0.967895	−	1.67644i	−0.0541917	−	0.0938628i
$320$	26.3811			1.47475
$321$	17.8274	+	30.8779i	0.995028	+	1.72344i
$322$	0.434624	−	0.752791i	0.0242206	−	0.0419514i
$323$	7.36505	−	12.7566i	0.409802	−	0.709798i
$324$	6.10284			0.339047
$325$	1.83294	−	33.1325i	0.101673	−	1.83786i
$326$	11.3425			0.628203
$327$	11.5012	−	19.9206i	0.636016	−	1.10161i
$328$	−1.90135	+	3.29324i	−0.104985	+	0.181839i
$329$	0.846899	+	1.46687i	0.0466910	+	0.0808712i
$330$	9.80504			0.539750
$331$	−2.37041	−	4.10568i	−0.130290	−	0.225668i	0.793499	−	0.608572i	$-0.208257\pi$
$331$	−2.37041	−	4.10568i	−0.130290	−	0.225668i	−0.923788	+	0.382904i	$0.874924\pi$
$332$	−5.28689	−	9.15715i	−0.290156	−	0.502564i
$333$	32.5543			1.78396
$334$	−8.63798	−	14.9614i	−0.472649	−	0.818653i
$335$	7.79967	−	13.5094i	0.426142	−	0.738099i
$336$	0.217312	−	0.376395i	0.0118553	−	0.0205341i
$337$	−32.4430			−1.76728			−0.883642	−	0.468163i	$-0.844916\pi$
$337$	−32.4430			−1.76728			−0.883642	+	0.468163i	$0.844916\pi$
$338$	7.70219	−	10.4726i	0.418944	−	0.569637i
$339$	11.8776			0.645105
$340$	8.23546	−	14.2642i	0.446631	−	0.773587i
$341$	−3.43462	+	5.94894i	−0.185995	+	0.322153i
$342$	6.35110	+	11.0004i	0.343428	+	0.594835i
$343$	−2.33411			−0.126030
$344$	−10.8050	−	18.7149i	−0.582569	−	1.00904i
$345$	25.5096	+	44.1839i	1.37339	+	2.37878i
$346$	−12.8413			−0.690355
$347$	5.91647	+	10.2476i	0.317613	+	0.550122i	0.979989	−	0.199049i	$-0.0637854\pi$
$347$	5.91647	+	10.2476i	0.317613	+	0.550122i	−0.662377	+	0.749171i	$0.730452\pi$
$348$	2.51815	−	4.36157i	0.134987	−	0.233805i
$349$	−15.0000	+	25.9808i	−0.802932	+	1.39072i	0.114747	+	0.993395i	$0.463394\pi$
$349$	−15.0000	+	25.9808i	−0.802932	+	1.39072i	−0.917679	+	0.397324i	$0.869939\pi$
$350$	1.53747			0.0821812
$351$	0.398321	−	7.20009i	0.0212608	−	0.384313i
$352$	5.00000			0.266501
$353$	5.10168	−	8.83637i	0.271535	−	0.470312i	−0.697720	−	0.716370i	$-0.745802\pi$
$353$	5.10168	−	8.83637i	0.271535	−	0.470312i	0.969255	+	0.246058i	$0.0791354\pi$
$354$	−2.78269	+	4.81976i	−0.147898	+	0.256167i
$355$	−11.3062	−	19.5829i	−0.600071	−	1.03935i
$356$	−14.3062			−0.758227
$357$	−0.949743	−	1.64500i	−0.0502657	−	0.0870628i
$358$	2.46789	+	4.27452i	0.130432	+	0.225915i
$359$	−13.5375			−0.714480			−0.357240	−	0.934013i	$-0.616282\pi$
$359$	−13.5375			−0.714480			−0.357240	+	0.934013i	$0.616282\pi$
$360$	21.3050	+	36.9014i	1.12287	+	1.94487i
$361$	3.82016	−	6.61671i	0.201061	−	0.348248i
$362$	−0.318991	+	0.552509i	−0.0167658	+	0.0290392i
$363$	2.60168			0.136553
$364$	−0.504198	−	0.329517i	−0.0264271	−	0.0172714i
$365$	53.6743			2.80944
$366$	6.25058	−	10.8263i	0.326723	−	0.565901i
$367$	5.57377	−	9.65406i	0.290949	−	0.503938i	−0.683086	−	0.730338i	$-0.739362\pi$
$367$	5.57377	−	9.65406i	0.290949	−	0.503938i	0.974034	+	0.226401i	$0.0726958\pi$
$368$	−2.60168	−	4.50624i	−0.135622	−	0.234904i
$369$	−4.77713			−0.248687
$370$	−16.2771	−	28.1928i	−0.846208	−	1.46567i
$371$	−0.111435	−	0.193011i	−0.00578542	−	0.0100206i
$372$	−17.8716			−0.926598
$373$	13.6561	+	23.6531i	0.707088	+	1.22471i	0.965933	+	0.258793i	$0.0833248\pi$
$373$	13.6561	+	23.6531i	0.707088	+	1.22471i	−0.258845	+	0.965919i	$0.583342\pi$
$374$	−2.18521	+	3.78489i	−0.112994	+	0.195712i
$375$	−20.6070	+	35.6924i	−1.06414	+	1.84315i
$376$	30.4174			1.56866
$377$	5.84251	+	3.81835i	0.300904	+	0.196655i
$378$	0.334110			0.0171848
$379$	−9.20336	+	15.9407i	−0.472745	+	0.818818i	−0.999513	−	0.0311907i	$-0.990070\pi$
$379$	−9.20336	+	15.9407i	−0.472745	+	0.818818i	0.526769	+	0.850009i	$0.323403\pi$
$380$	−6.35110	+	11.0004i	−0.325804	+	0.564310i
$381$	1.73243	+	3.00066i	0.0887551	+	0.153728i
$382$	26.1391			1.33740
$383$	12.9358	+	22.4054i	0.660988	+	1.14486i	0.980356	+	0.197234i	$0.0631959\pi$
$383$	12.9358	+	22.4054i	0.660988	+	1.14486i	−0.319368	+	0.947631i	$0.603471\pi$
$384$	3.90252	+	6.75936i	0.199150	+	0.344937i
$385$	0.629587			0.0320867
$386$	5.56957	+	9.64678i	0.283484	+	0.491008i
$387$	13.5738	−	23.5105i	0.689994	−	1.19510i
$388$	1.78269	−	3.08771i	0.0905023	−	0.156755i
$389$	20.7153			1.05030			0.525152	−	0.851008i	$-0.324008\pi$
$389$	20.7153			1.05030			0.525152	+	0.851008i	$0.324008\pi$
$390$	−31.5459	+	15.9581i	−1.59739	+	0.808072i
$391$	−22.7408			−1.15005
$392$	−10.4581	+	18.1140i	−0.528216	+	0.914897i
$393$	−17.8274	+	30.8779i	−0.899273	+	1.55759i
$394$	−7.76873	−	13.4558i	−0.391383	−	0.677896i
$395$	−54.9247			−2.76356
$396$	1.88437	+	3.26382i	0.0946930	+	0.164013i
$397$	10.7911	+	18.6907i	0.541589	+	0.938060i	0.998813	+	0.0487081i	$0.0155104\pi$
$397$	10.7911	+	18.6907i	0.541589	+	0.938060i	−0.457224	+	0.889352i	$0.651156\pi$
$398$	−11.6766			−0.585296
$399$	0.732431	+	1.26861i	0.0366674	+	0.0635098i
$400$	4.60168	−	7.97034i	0.230084	−	0.398517i
$401$	−0.101679	+	0.176113i	−0.00507761	+	0.00879468i	−0.868553	−	0.495596i	$-0.834950\pi$
$401$	−0.101679	+	0.176113i	−0.00507761	+	0.00879468i	0.863475	+	0.504391i	$0.168283\pi$
$402$	−10.7687			−0.537096
$403$	1.36808	−	24.7296i	0.0681490	−	1.23187i
$404$	12.0363			0.598828
$405$	11.5000	−	19.9186i	0.571440	−	0.989762i
$406$	−0.161692	+	0.280058i	−0.00802463	+	0.0138991i
$407$	−4.31899	−	7.48071i	−0.214084	−	0.370805i
$408$	−34.1112			−1.68876
$409$	−0.0460590	−	0.0797765i	−0.00227747	−	0.00394469i	0.864884	−	0.501971i	$-0.167392\pi$
$409$	−0.0460590	−	0.0797765i	−0.00227747	−	0.00394469i	−0.867162	+	0.498026i	$0.834058\pi$
$410$	2.38856	+	4.13712i	0.117963	+	0.204318i
$411$	−35.4877			−1.75048
$412$	−3.20336	−	5.54838i	−0.157818	−	0.273349i
$413$	−0.178678	+	0.309479i	−0.00879216	+	0.0152285i
$414$	9.80504	−	16.9828i	0.481891	−	0.834660i
$415$	−39.8497			−1.95615
$416$	−16.0866	+	8.13773i	−0.788708	+	0.398985i
$417$	2.26150			0.110746
$418$	1.68521	−	2.91886i	0.0824262	−	0.142766i
$419$	−5.06421	+	8.77147i	−0.247403	+	0.428514i	−0.962804	−	0.270199i	$-0.912910\pi$
$419$	−5.06421	+	8.77147i	−0.247403	+	0.428514i	0.715402	+	0.698714i	$0.246244\pi$
$420$	0.818991	+	1.41853i	0.0399627	+	0.0692174i
$421$	−6.58217			−0.320795			−0.160398	−	0.987052i	$-0.551278\pi$
$421$	−6.58217			−0.320795			−0.160398	+	0.987052i	$0.551278\pi$
$422$	2.28689	+	3.96100i	0.111324	+	0.192819i
$423$	19.1059	+	33.0923i	0.928960	+	1.60901i
$424$	−4.00233			−0.194370
$425$	−20.1112	−	34.8337i	−0.975538	−	1.68968i
$426$	−7.80504	+	13.5187i	−0.378155	+	0.654984i
$427$	0.401353	−	0.695164i	0.0194228	−	0.0336413i
$428$	13.7045			0.662433
$429$	−8.37041	+	4.23435i	−0.404127	+	0.204436i
$430$	−27.1475			−1.30917
$431$	−8.74942	+	15.1544i	−0.421445	+	0.729963i	−0.996081	−	0.0884453i	$-0.971810\pi$
$431$	−8.74942	+	15.1544i	−0.421445	+	0.729963i	0.574636	+	0.818409i	$0.305143\pi$
$432$	1.00000	−	1.73205i	0.0481125	−	0.0833333i
$433$	4.34690	+	7.52905i	0.208899	+	0.361823i	0.951368	−	0.308057i	$-0.0996788\pi$
$433$	4.34690	+	7.52905i	0.208899	+	0.361823i	−0.742469	+	0.669880i	$0.766345\pi$
$434$	1.14754			0.0550838
$435$	−9.49024	−	16.4376i	−0.455022	−	0.788122i
$436$	−4.42067	−	7.65683i	−0.211712	−	0.366695i
$437$	17.5375			0.838931
$438$	−18.5265	−	32.0889i	−0.885233	−	1.53327i
$439$	12.2869	−	21.2815i	0.586421	−	1.01571i	−0.408276	−	0.912859i	$-0.633870\pi$
$439$	12.2869	−	21.2815i	0.586421	−	1.01571i	0.994697	−	0.102852i	$-0.0327969\pi$
$440$	5.65310	−	9.79146i	0.269501	−	0.466789i
$441$	−26.2760			−1.25124
$442$	0.870413	−	15.7337i	0.0414013	−	0.748375i
$443$	−17.2699			−0.820518			−0.410259	−	0.911969i	$-0.634562\pi$
$443$	−17.2699			−0.820518			−0.410259	+	0.911969i	$0.634562\pi$
$444$	11.2366	−	19.4624i	0.533267	−	0.923645i
$445$	−26.9581	+	46.6929i	−1.27794	+	2.21345i
$446$	4.53211	+	7.84984i	0.214601	+	0.371701i
$447$	3.03630			0.143612
$448$	−0.584693	−	1.01272i	−0.0276242	−	0.0478464i
$449$	−8.16150	−	14.1361i	−0.385165	−	0.667125i	0.606627	−	0.794986i	$-0.292522\pi$
$449$	−8.16150	−	14.1361i	−0.385165	−	0.667125i	−0.991792	+	0.127861i	$0.959189\pi$
$450$	34.6850			1.63507
$451$	0.633784	+	1.09775i	0.0298437	+	0.0516909i
$452$	2.28269	−	3.95373i	0.107369	−	0.185968i
$453$	13.9721	−	24.2004i	0.656466	−	1.13703i
$454$	−13.2034			−0.619664
$455$	−2.02558	+	1.02468i	−0.0949605	+	0.0480378i
$456$	26.3062			1.23190
$457$	−10.7087	+	18.5480i	−0.500933	+	0.867641i	0.499067	+	0.866564i	$0.333676\pi$
$457$	−10.7087	+	18.5480i	−0.500933	+	0.867641i	−0.999999	+	0.00107752i	$0.999657\pi$
$458$	−1.01395	+	1.75622i	−0.0473789	+	0.0820627i
$459$	−4.37041	−	7.56978i	−0.203993	−	0.353327i
$460$	19.6101			0.914324
$461$	8.90368	+	15.4216i	0.414686	+	0.718257i	0.995395	−	0.0958538i	$-0.0305581\pi$
$461$	8.90368	+	15.4216i	0.414686	+	0.718257i	−0.580710	+	0.814111i	$0.697225\pi$
$462$	−0.217312	−	0.376395i	−0.0101103	−	0.0175115i
$463$	4.80271			0.223201			0.111600	−	0.993753i	$-0.464402\pi$
$463$	4.80271			0.223201			0.111600	+	0.993753i	$0.464402\pi$
$464$	0.967895	+	1.67644i	0.0449334	+	0.0778269i
$465$	−33.6766	+	58.3296i	−1.56172	+	2.70497i
$466$	6.37041	−	11.0339i	0.295104	−	0.511135i
$467$	−2.80737			−0.129910			−0.0649548	−	0.997888i	$-0.520690\pi$
$467$	−2.80737			−0.129910			−0.0649548	+	0.997888i	$0.520690\pi$
$468$	−11.3746	−	7.43383i	−0.525792	−	0.343629i
$469$	−0.691466			−0.0319289
$470$	19.1059	−	33.0923i	0.881288	−	1.52644i
$471$	5.97512	−	10.3492i	0.275319	−	0.476867i
$472$	3.20872	+	5.55767i	0.147693	+	0.255812i
$473$	−7.20336			−0.331211
$474$	18.9581	+	32.8365i	0.870776	+	1.50823i
$475$	15.5096	+	26.8633i	0.711627	+	1.23257i
$476$	−0.730100			−0.0334641
$477$	−2.51395	−	4.35430i	−0.115106	−	0.199369i
$478$	−2.03630	+	3.52698i	−0.0931383	+	0.161320i
$479$	−5.91647	+	10.2476i	−0.270331	+	0.468226i	−0.968946	−	0.247271i	$-0.920466\pi$
$479$	−5.91647	+	10.2476i	−0.270331	+	0.468226i	0.698616	+	0.715497i	$0.253800\pi$
$480$	49.0252			2.23768
$481$	26.0707	+	17.0384i	1.18872	+	0.776886i
$482$	−18.9828			−0.864644
$483$	1.13075	−	1.95852i	0.0514510	−	0.0891157i
$484$	0.500000	−	0.866025i	0.0227273	−	0.0393648i
$485$	−6.71848	−	11.6367i	−0.305070	−	0.528397i
$486$	−21.8776			−0.992390
$487$	8.20872	+	14.2179i	0.371973	+	0.644276i	0.989869	−	0.141984i	$-0.0453482\pi$
$487$	8.20872	+	14.2179i	0.371973	+	0.644276i	−0.617896	+	0.786260i	$0.712015\pi$
$488$	−7.20756	−	12.4839i	−0.326271	−	0.565117i
$489$	29.5096			1.33447
$490$	13.1380	+	22.7557i	0.593514	+	1.02800i
$491$	−3.91647	+	6.78353i	−0.176748	+	0.306136i	−0.940765	−	0.339060i	$-0.889891\pi$
$491$	−3.91647	+	6.78353i	−0.176748	+	0.306136i	0.764017	+	0.645196i	$0.223224\pi$
$492$	−1.64890	+	2.85598i	−0.0743383	+	0.128758i
$493$	8.46020			0.381028
$494$	−0.671253	+	12.1336i	−0.0302011	+	0.545919i
$495$	14.2034			0.638393
$496$	3.43462	−	5.94894i	0.154219	−	0.267115i
$497$	−0.501166	+	0.868044i	−0.0224803	+	0.0389371i
$498$	13.7548	+	23.8240i	0.616366	+	1.06758i
$499$	12.2722			0.549381			0.274690	−	0.961533i	$-0.411425\pi$
$499$	12.2722			0.549381			0.274690	+	0.961533i	$0.411425\pi$
$500$	7.92067	+	13.7190i	0.354223	+	0.613532i
$501$	−22.4733	−	38.9248i	−1.00403	−	1.73903i
$502$	10.3402			0.461505
$503$	−0.554455	−	0.960344i	−0.0247219	−	0.0428196i	0.853400	−	0.521257i	$-0.174537\pi$
$503$	−0.554455	−	0.960344i	−0.0247219	−	0.0428196i	−0.878122	+	0.478437i	$0.841203\pi$
$504$	0.944380	−	1.63571i	0.0420660	−	0.0728605i
$505$	22.6808	−	39.2843i	1.00928	−	1.74813i
$506$	−5.20336			−0.231317
$507$	20.0386	−	27.2465i	0.889947	−	1.21006i
$508$	1.33178			0.0590882
$509$	11.9346	−	20.6714i	0.528993	−	0.916243i	−0.470435	−	0.882434i	$-0.655903\pi$
$509$	11.9346	−	20.6714i	0.528993	−	0.916243i	0.999428	−	0.0338082i	$-0.0107635\pi$
$510$	−21.4260	+	37.1110i	−0.948761	+	1.64330i
$511$	−1.18960	−	2.06045i	−0.0526248	−	0.0911488i
$512$	−11.0000			−0.486136
$513$	3.37041	+	5.83773i	0.148807	+	0.257742i
$514$	−12.0877	−	20.9366i	−0.533167	−	0.923472i
$515$	−24.1452			−1.06397
$516$	−9.37041	−	16.2300i	−0.412509	−	0.714487i
$517$	5.06957	−	8.78076i	0.222960	−	0.386177i
$518$	−0.721510	+	1.24969i	−0.0317013	+	0.0549083i
$519$	−33.4090			−1.46649
$520$	−2.25175	+	40.7029i	−0.0987457	+	1.78494i
$521$	18.3318			0.803130			0.401565	−	0.915831i	$-0.368466\pi$
$521$	18.3318			0.803130			0.401565	+	0.915831i	$0.368466\pi$
$522$	−3.64774	+	6.31807i	−0.159657	+	0.276534i
$523$	5.22034	−	9.04190i	0.228270	−	0.395375i	−0.729026	−	0.684486i	$-0.760027\pi$
$523$	5.22034	−	9.04190i	0.228270	−	0.395375i	0.957295	+	0.289112i	$0.0933599\pi$
$524$	6.85226	+	11.8685i	0.299342	+	0.518476i
$525$	4.00000			0.174574
$526$	5.37041	+	9.30183i	0.234161	+	0.405579i
$527$	−15.0107	−	25.9993i	−0.653878	−	1.13255i
$528$	−2.60168			−0.113224
$529$	−2.03747	−	3.52900i	−0.0885856	−	0.153435i
$530$	−2.51395	+	4.35430i	−0.109199	+	0.189139i
$531$	−4.03094	+	6.98179i	−0.174928	+	0.302984i
$532$	0.563045			0.0244111
$533$	−3.82571	−	2.50028i	−0.165710	−	0.108299i
$534$	37.2201			1.61067
$535$	25.8244	−	44.7291i	1.11648	−	1.93381i
$536$	−6.20872	+	10.7538i	−0.268176	+	0.464494i
$537$	6.42067	+	11.1209i	0.277072	+	0.479903i
$538$	17.6659			0.761631
$539$	3.48605	+	6.03801i	0.150155	+	0.260075i
$540$	3.76873	+	6.52764i	0.162181	+	0.280905i
$541$	−11.0554			−0.475310			−0.237655	−	0.971350i	$-0.576379\pi$
$541$	−11.0554			−0.475310			−0.237655	+	0.971350i	$0.576379\pi$
$542$	−4.37041	−	7.56978i	−0.187725	−	0.325150i
$543$	−0.829913	+	1.43745i	−0.0356150	+	0.0616869i
$544$	−10.9260	+	18.9244i	−0.468450	+	0.811379i
$545$	−33.3207			−1.42730
$546$	1.31176	+	0.857296i	0.0561382	+	0.0366889i
$547$	25.3532			1.08403			0.542013	−	0.840370i	$-0.317662\pi$
$547$	25.3532			1.08403			0.542013	+	0.840370i	$0.317662\pi$
$548$	−6.82016	+	11.8129i	−0.291343	+	0.504620i
$549$	9.05445	−	15.6828i	0.386435	−	0.669325i
$550$	−4.60168	−	7.97034i	−0.196216	−	0.339857i
$551$	−6.52441			−0.277949
$552$	−20.3062	−	35.1714i	−0.864289	−	1.49699i
$553$	1.21731	+	2.10845i	0.0517654	+	0.0896603i
$554$	29.2118			1.24109
$555$	−42.3479	−	73.3487i	−1.79757	−	3.11348i
$556$	0.434624	−	0.752791i	0.0184322	−	0.0319254i
$557$	−10.1713	+	17.6171i	−0.430970	+	0.746462i	−0.996957	−	0.0779524i	$-0.975162\pi$
$557$	−10.1713	+	17.6171i	−0.430970	+	0.746462i	0.565987	+	0.824414i	$0.308495\pi$
$558$	25.8884			1.09594
$559$	23.1755	−	11.7238i	0.980217	−	0.495864i
$560$	−0.629587			−0.0266049
$561$	−5.68521	+	9.84707i	−0.240030	+	0.415743i
$562$	5.40252	−	9.35744i	0.227891	−	0.394720i
$563$	3.38740	+	5.86715i	0.142762	+	0.247271i	0.928536	−	0.371243i	$-0.121068\pi$
$563$	3.38740	+	5.86715i	0.142762	+	0.247271i	−0.785774	+	0.618514i	$0.787735\pi$
$564$	26.3788			1.11075
$565$	−8.60284	−	14.9006i	−0.361924	−	0.626871i
$566$	−5.11983	−	8.86781i	−0.215203	−	0.372742i
$567$	−1.01951			−0.0428155
$568$	9.00000	+	15.5885i	0.377632	+	0.654077i
$569$	−8.43695	+	14.6132i	−0.353696	+	0.612619i	−0.986894	−	0.161371i	$-0.948408\pi$
$569$	−8.43695	+	14.6132i	−0.353696	+	0.612619i	0.633198	+	0.773990i	$0.281742\pi$
$570$	16.5235	−	28.6196i	0.692094	−	1.19874i
$571$	44.9973			1.88308			0.941539	−	0.336905i	$-0.109380\pi$
$571$	44.9973			1.88308			0.941539	+	0.336905i	$0.109380\pi$
$572$	−0.199160	+	3.60005i	−0.00832732	+	0.150526i
$573$	68.0057			2.84098
$574$	0.105877	−	0.183384i	0.00441922	−	0.00765431i
$575$	23.9442	−	41.4725i	0.998542	−	1.72952i
$576$	−13.1906	−	22.8467i	−0.549607	−	0.951947i
$577$	−19.5119			−0.812291			−0.406145	−	0.913808i	$-0.633127\pi$
$577$	−19.5119			−0.812291			−0.406145	+	0.913808i	$0.633127\pi$
$578$	−1.05026	−	1.81910i	−0.0436849	−	0.0756645i
$579$	14.4902	+	25.0978i	0.602194	+	1.04303i
$580$	−7.29548			−0.302928
$581$	0.883202	+	1.52975i	0.0366414	+	0.0634647i
$582$	−4.63798	+	8.03322i	−0.192251	+	0.332988i
$583$	−0.667055	+	1.15537i	−0.0276266	+	0.0478507i
$584$	−42.7260			−1.76801
$585$	−45.6966	+	23.1166i	−1.88932	+	0.955754i
$586$	3.96370			0.163739
$587$	−8.33947	+	14.4444i	−0.344207	+	0.596184i	−0.985209	−	0.171355i	$-0.945186\pi$
$587$	−8.33947	+	14.4444i	−0.344207	+	0.596184i	0.641002	+	0.767539i	$0.278519\pi$
$588$	−9.06957	+	15.7090i	−0.374023	+	0.647827i
$589$	11.5761	+	20.0504i	0.476985	+	0.826162i
$590$	8.06188			0.331902
$591$	−20.2118	−	35.0078i	−0.831400	−	1.44003i
$592$	4.31899	+	7.48071i	0.177509	+	0.307455i
$593$	−29.4128			−1.20784			−0.603919	−	0.797046i	$-0.706395\pi$
$593$	−29.4128			−1.20784			−0.603919	+	0.797046i	$0.706395\pi$
$594$	−1.00000	−	1.73205i	−0.0410305	−	0.0710669i
$595$	−1.37578	+	2.38292i	−0.0564013	+	0.0976900i
$596$	0.583528	−	1.01070i	0.0239022	−	0.0413999i
$597$	−30.3788			−1.24332
$598$	16.7408	−	8.46870i	0.684583	−	0.346311i
$599$	6.12842			0.250400			0.125200	−	0.992131i	$-0.460043\pi$
$599$	6.12842			0.250400			0.125200	+	0.992131i	$0.460043\pi$
$600$	35.9163	−	62.2088i	1.46628	−	2.53966i
$601$	−12.5030	+	21.6559i	−0.510009	+	0.883362i	0.489923	+	0.871765i	$0.337025\pi$
$601$	−12.5030	+	21.6559i	−0.510009	+	0.883362i	−0.999933	+	0.0115966i	$0.996309\pi$
$602$	0.601679	+	1.04214i	0.0245226	+	0.0424744i
$603$	−15.5993			−0.635255
$604$	−5.37041	−	9.30183i	−0.218519	−	0.378486i
$605$	−1.88437	−	3.26382i	−0.0766104	−	0.132693i
$606$	−31.3146			−1.27207
$607$	−16.2203	−	28.0945i	−0.658363	−	1.14032i	−0.981039	−	0.193809i	$-0.937916\pi$
$607$	−16.2203	−	28.0945i	−0.658363	−	1.14032i	0.322676	−	0.946510i	$-0.395418\pi$
$608$	8.42603	−	14.5943i	0.341721	−	0.591878i
$609$	−0.420670	+	0.728622i	−0.0170464	+	0.0295253i
$610$	−18.1089			−0.733208
$611$	−2.01932	+	36.5014i	−0.0816928	+	1.47669i
$612$	−16.4709			−0.665798
$613$	8.28572	−	14.3513i	0.334657	−	0.579643i	−0.648762	−	0.760992i	$-0.724713\pi$
$613$	8.28572	−	14.3513i	0.334657	−	0.579643i	0.983419	+	0.181348i	$0.0580462\pi$
$614$	−7.11983	+	12.3319i	−0.287333	+	0.497675i
$615$	6.21428	+	10.7634i	0.250584	+	0.434024i
$616$	−0.501166			−0.0201925
$617$	8.93462	+	15.4752i	0.359694	+	0.623009i	0.987910	−	0.155031i	$-0.0495476\pi$
$617$	8.93462	+	15.4752i	0.359694	+	0.623009i	−0.628215	+	0.778040i	$0.716214\pi$
$618$	8.33411	+	14.4351i	0.335247	+	0.580665i
$619$	−27.4151			−1.10191			−0.550953	−	0.834536i	$-0.685736\pi$
$619$	−27.4151			−1.10191			−0.550953	+	0.834536i	$0.685736\pi$
$620$	12.9442	+	22.4200i	0.519851	+	0.900408i
$621$	5.20336	−	9.01248i	0.208804	−	0.361658i
$622$	−5.93882	+	10.2863i	−0.238125	+	0.412445i
$623$	2.38993			0.0957503
$624$	8.37041	−	4.23435i	0.335085	−	0.169510i
$625$	13.6850			0.547400
$626$	−3.94974	+	6.84116i	−0.157863	+	0.273428i
$627$	4.38437	−	7.59395i	0.175095	−	0.303273i
$628$	−2.29664	−	3.97790i	−0.0916460	−	0.158735i
$629$	37.7516			1.50525
$630$	−1.18637	−	2.05486i	−0.0472662	−	0.0818675i
$631$	−3.27293	−	5.66888i	−0.130293	−	0.225675i	0.793496	−	0.608575i	$-0.208259\pi$
$631$	−3.27293	−	5.66888i	−0.130293	−	0.225675i	−0.923790	+	0.382900i	$0.874925\pi$
$632$	43.7213			1.73914
$633$	5.94974	+	10.3053i	0.236481	+	0.409597i
$634$	−13.6615	+	23.6624i	−0.542567	+	0.939754i
$635$	2.50956	−	4.34669i	0.0995889	−	0.172493i
$636$	−3.47093			−0.137631
$637$	−21.0428	−	13.7525i	−0.833747	−	0.544892i
$638$	1.93579			0.0766386
$639$	−11.3062	+	19.5829i	−0.447266	+	0.774688i
$640$	5.65310	−	9.79146i	0.223458	−	0.387041i
$641$	−1.03747	−	1.79695i	−0.0409775	−	0.0709752i	0.844809	−	0.535068i	$-0.179714\pi$
$641$	−1.03747	−	1.79695i	−0.0409775	−	0.0709752i	−0.885787	+	0.464092i	$0.846381\pi$
$642$	−35.6548			−1.40718
$643$	6.13378	+	10.6240i	0.241893	+	0.418971i	0.961253	−	0.275666i	$-0.0888984\pi$
$643$	6.13378	+	10.6240i	0.241893	+	0.418971i	−0.719361	+	0.694637i	$0.755565\pi$
$644$	−0.434624	−	0.752791i	−0.0171266	−	0.0296641i
$645$	−70.6292			−2.78102
$646$	7.36505	+	12.7566i	0.289774	+	0.501903i
$647$	−23.5435	+	40.7786i	−0.925592	+	1.60317i	−0.134985	+	0.990848i	$0.543099\pi$
$647$	−23.5435	+	40.7786i	−0.925592	+	1.60317i	−0.790607	+	0.612324i	$0.790235\pi$
$648$	−9.15427	+	15.8557i	−0.359614	+	0.622869i
$649$	2.13915			0.0839689
$650$	27.7771	+	18.1536i	1.08951	+	0.712044i
$651$	2.98554			0.117013
$652$	5.67125	−	9.82290i	0.222103	−	0.384694i
$653$	10.5514	−	18.2756i	0.412909	−	0.715179i	−0.582297	−	0.812976i	$-0.697846\pi$
$653$	10.5514	−	18.2756i	0.412909	−	0.715179i	0.995206	+	0.0977964i	$0.0311794\pi$
$654$	11.5012	+	19.9206i	0.449731	+	0.778957i
$655$	51.6487			2.01808
$656$	−0.633784	−	1.09775i	−0.0247451	−	0.0428598i
$657$	−26.8371	−	46.4833i	−1.04702	−	1.81349i
$658$	−1.69380			−0.0660311
$659$	9.19477	+	15.9258i	0.358177	+	0.620381i	0.987656	−	0.156636i	$-0.0500650\pi$
$659$	9.19477	+	15.9258i	0.358177	+	0.620381i	−0.629479	+	0.777017i	$0.716732\pi$
$660$	4.90252	−	8.49141i	0.190830	−	0.330528i
$661$	−8.34690	+	14.4573i	−0.324657	+	0.562322i	−0.981443	−	0.191755i	$-0.938582\pi$
$661$	−8.34690	+	14.4573i	−0.324657	+	0.562322i	0.656786	+	0.754077i	$0.271915\pi$
$662$	4.74083			0.184257
$663$	2.26454	−	40.9340i	0.0879473	−	1.58975i
$664$	31.7213			1.23103
$665$	1.06098	−	1.83768i	0.0411432	−	0.0712621i
$666$	−16.2771	+	28.1928i	−0.630726	+	1.09245i
$667$	5.03630	+	8.72313i	0.195006	+	0.337761i
$668$	−17.2760			−0.668427
$669$	11.7911	+	20.4228i	0.455870	+	0.789589i
$670$	7.79967	+	13.5094i	0.301328	+	0.521915i
$671$	−4.80504			−0.185496
$672$	−1.08656	−	1.88198i	−0.0419150	−	0.0725988i
$673$	−14.8092	+	25.6503i	−0.570854	+	0.988748i	0.425624	+	0.904900i	$0.360054\pi$
$673$	−14.8092	+	25.6503i	−0.570854	+	0.988748i	−0.996479	+	0.0838484i	$0.973279\pi$
$674$	16.2215	−	28.0965i	0.624829	−	1.08224i
$675$	18.4067			0.708475
$676$	−5.21848	−	11.9066i	−0.200711	−	0.457947i
$677$	−22.6124			−0.869065			−0.434533	−	0.900656i	$-0.643086\pi$
$677$	−22.6124			−0.869065			−0.434533	+	0.900656i	$0.643086\pi$
$678$	−5.93882	+	10.2863i	−0.228079	+	0.395045i
$679$	−0.297807	+	0.515817i	−0.0114288	+	0.0197953i
$680$	24.7064	+	42.7927i	0.947447	+	1.64103i
$681$	−34.3509			−1.31633
$682$	−3.43462	−	5.94894i	−0.131519	−	0.227797i
$683$	−16.5714	−	28.7026i	−0.634089	−	1.09827i	−0.986707	−	0.162507i	$-0.948042\pi$
$683$	−16.5714	−	28.7026i	−0.634089	−	1.09827i	0.352619	−	0.935767i	$-0.385291\pi$
$684$	12.7022			0.485680
$685$	25.7034	+	44.5195i	0.982075	+	1.70100i
$686$	1.16706	−	2.02140i	0.0445584	−	0.0771774i
$687$	−2.63798	+	4.56912i	−0.100645	+	0.174323i
$688$	7.20336			0.274625
$689$	0.265702	−	4.80286i	0.0101224	−	0.182974i
$690$	−51.0191			−1.94226
$691$	−8.10284	+	14.0345i	−0.308247	+	0.533899i	−0.977979	−	0.208704i	$-0.933076\pi$
$691$	−8.10284	+	14.0345i	−0.308247	+	0.533899i	0.669732	+	0.742603i	$0.266409\pi$
$692$	−6.42067	+	11.1209i	−0.244077	+	0.422754i
$693$	−0.314793	−	0.545238i	−0.0119580	−	0.0207119i
$694$	−11.8329			−0.449172
$695$	−1.63798	−	2.83707i	−0.0621322	−	0.107616i
$696$	7.55445	+	13.0847i	0.286351	+	0.495974i
$697$	−5.53980			−0.209835
$698$	−15.0000	−	25.9808i	−0.567758	−	0.983386i
$699$	16.5738	−	28.7066i	0.626878	−	1.08578i
$700$	0.768734	−	1.33149i	0.0290554	−	0.0503255i
$701$	16.7855			0.633981			0.316990	−	0.948429i	$-0.397328\pi$
$701$	16.7855			0.633981			0.316990	+	0.948429i	$0.397328\pi$
$702$	6.03630	+	3.94500i	0.227826	+	0.148895i
$703$	−29.1136			−1.09804
$704$	−3.50000	+	6.06218i	−0.131911	+	0.228477i
$705$	49.7074	−	86.0957i	1.87209	−	3.24255i
$706$	5.10168	+	8.83637i	0.192004	+	0.332561i
$707$	−2.01073			−0.0756212
$708$	2.78269	+	4.81976i	0.104580	+	0.181138i
$709$	−13.8146	−	23.9276i	−0.518818	−	0.898619i	−0.999761	−	0.0218674i	$-0.993039\pi$
$709$	−13.8146	−	23.9276i	−0.518818	−	0.898619i	0.480943	−	0.876752i	$-0.340294\pi$
$710$	22.6124			0.848628
$711$	27.4623	+	47.5662i	1.02992	+	1.78387i
$712$	21.4593	−	37.1686i	0.804221	−	1.39295i
$713$	17.8716	−	30.9545i	0.669296	−	1.15925i
$714$	1.89949			0.0710865
$715$	11.3746	+	7.43383i	0.425386	+	0.278010i
$716$	4.93579			0.184459
$717$	−5.29781	+	9.17607i	−0.197850	+	0.342687i
$718$	6.76873	−	11.7238i	0.252607	−	0.437528i
$719$	−4.70452	−	8.14847i	−0.175449	−	0.303887i	0.764867	−	0.644188i	$-0.222804\pi$
$719$	−4.70452	−	8.14847i	−0.175449	−	0.303887i	−0.940317	+	0.340301i	$0.889471\pi$
$720$	−14.2034			−0.529328
$721$	0.535138	+	0.926885i	0.0199296	+	0.0345190i
$722$	3.82016	+	6.61671i	0.142172	+	0.246248i
$723$	−49.3872			−1.83673
$724$	0.318991	+	0.552509i	0.0118552	+	0.0205338i
$725$	−8.90788	+	15.4289i	−0.330830	+	0.573015i
$726$	−1.30084	+	2.25312i	−0.0482787	+	0.0836211i
$727$	20.6682			0.766542			0.383271	−	0.923636i	$-0.374798\pi$
$727$	20.6682			0.766542			0.383271	+	0.923636i	$0.374798\pi$
$728$	1.61241	−	0.815670i	0.0597597	−	0.0302307i
$729$	−38.6101			−1.43000
$730$	−26.8371	+	46.4833i	−0.993287	+	1.72042i
$731$	15.7408	−	27.2639i	0.582196	−	1.00839i
$732$	−6.25058	−	10.8263i	−0.231028	−	0.400153i
$733$	26.1368			0.965385			0.482693	−	0.875790i	$-0.339659\pi$
$733$	26.1368			0.965385			0.482693	+	0.875790i	$0.339659\pi$
$734$	5.57377	+	9.65406i	0.205732	+	0.356338i
$735$	34.1808	+	59.2029i	1.26078	+	2.18373i
$736$	−26.0168			−0.958992
$737$	2.06957	+	3.58461i	0.0762337	+	0.132041i
$738$	2.38856	−	4.13712i	0.0879243	−	0.152289i
$739$	8.23966	−	14.2715i	0.303101	−	0.524986i	−0.673736	−	0.738972i	$-0.735311\pi$
$739$	8.23966	−	14.2715i	0.303101	−	0.524986i	0.976837	+	0.213986i	$0.0686448\pi$
$740$	−32.5543			−1.19672
$741$	−1.74638	+	31.5679i	−0.0641551	+	1.15967i
$742$	0.222870			0.00818182
$743$	−14.8220	+	25.6725i	−0.543767	+	0.941833i	0.454916	+	0.890534i	$0.349669\pi$
$743$	−14.8220	+	25.6725i	−0.543767	+	0.941833i	−0.998683	+	0.0512983i	$0.983664\pi$
$744$	26.8074	−	46.4317i	0.982806	−	1.70227i
$745$	−2.19916	−	3.80906i	−0.0805710	−	0.139553i
$746$	−27.3123			−0.999973
$747$	19.9249	+	34.5109i	0.729013	+	1.26269i
$748$	2.18521	+	3.78489i	0.0798991	+	0.138389i
$749$	−2.28941			−0.0836533
$750$	−20.6070	−	35.6924i	−0.752463	−	1.30330i
$751$	−12.6743	+	21.9525i	−0.462491	+	0.801058i	−0.999084	−	0.0427828i	$-0.986378\pi$
$751$	−12.6743	+	21.9525i	−0.462491	+	0.801058i	0.536593	+	0.843841i	$0.319711\pi$
$752$	−5.06957	+	8.78076i	−0.184868	+	0.320201i
$753$	26.9018			0.980357
$754$	−6.22804	+	3.15059i	−0.226812	+	0.114738i
$755$	−40.4793			−1.47319
$756$	0.167055	−	0.289348i	0.00607574	−	0.0105235i
$757$	−15.8660	+	27.4808i	−0.576660	+	0.998805i	0.419199	+	0.907895i	$0.362311\pi$
$757$	−15.8660	+	27.4808i	−0.576660	+	0.998805i	−0.995859	+	0.0909105i	$0.971022\pi$
$758$	−9.20336	−	15.9407i	−0.334281	−	0.578992i
$759$	−13.5375			−0.491379
$760$	−19.0533	−	33.0013i	−0.691135	−	1.19708i
$761$	21.9419	+	38.0044i	0.795392	+	1.37766i	0.922590	+	0.385781i	$0.126068\pi$
$761$	21.9419	+	38.0044i	0.795392	+	1.37766i	−0.127199	+	0.991877i	$0.540599\pi$
$762$	−3.46486			−0.125519
$763$	0.738496	+	1.27911i	0.0267353	+	0.0463070i
$764$	13.0696	−	22.6372i	0.472841	−	0.818984i
$765$	−31.0373	+	53.7581i	−1.12216	+	1.94363i
$766$	−25.8716			−0.934778
$767$	−6.88231	+	3.48156i	−0.248506	+	0.125712i
$768$	−44.2285			−1.59596
$769$	7.80737	−	13.5228i	0.281541	−	0.487643i	−0.690224	−	0.723596i	$-0.742488\pi$
$769$	7.80737	−	13.5228i	0.281541	−	0.487643i	0.971764	+	0.235953i	$0.0758212\pi$
$770$	−0.314793	+	0.545238i	−0.0113444	+	0.0196490i
$771$	−31.4484	−	54.4702i	−1.13259	−	1.96170i
$772$	11.1391			0.400907
$773$	11.1252	+	19.2694i	0.400145	+	0.693072i	0.993743	−	0.111690i	$-0.0356263\pi$
$773$	11.1252	+	19.2694i	0.400145	+	0.693072i	−0.593598	+	0.804762i	$0.702293\pi$
$774$	13.5738	+	23.5105i	0.487899	+	0.845066i
$775$	63.2201			2.27093
$776$	5.34806	+	9.26312i	0.191984	+	0.332527i
$777$	−1.87714	+	3.25130i	−0.0673419	+	0.116640i
$778$	−10.3576	+	17.9399i	−0.371339	+	0.643178i
$779$	4.27223			0.153069
$780$	−1.95278	+	35.2986i	−0.0699206	+	1.26389i
$781$	6.00000			0.214697
$782$	11.3704	−	19.6941i	0.406605	−	0.704261i
$783$	−1.93579	+	3.35289i	−0.0691795	+	0.119822i
$784$	−3.48605	−	6.03801i	−0.124502	−	0.215643i
$785$	−17.3109			−0.617851
$786$	−17.8274	−	30.8779i	−0.635882	−	1.10138i
$787$	−26.9914	−	46.7505i	−0.962140	−	1.66648i	−0.717111	−	0.696959i	$-0.754536\pi$
$787$	−26.9914	−	46.7505i	−0.962140	−	1.66648i	−0.245029	−	0.969516i	$-0.578798\pi$
$788$	−15.5375			−0.553499
$789$	13.9721	+	24.2004i	0.497420	+	0.861556i
$790$	27.4623	−	47.5662i	0.977066	−	1.69233i
$791$	−0.381335	+	0.660491i	−0.0135587	+	0.0234844i
$792$	−11.3062			−0.401748
$793$	15.4593	−	7.82042i	0.548976	−	0.277711i
$794$	−21.5822			−0.765922
$795$	−6.54050	+	11.3285i	−0.231968	+	0.401780i
$796$	−5.83831	+	10.1122i	−0.206933	+	0.358419i
$797$	16.4956	+	28.5712i	0.584304	+	1.01204i	0.994962	+	0.100255i	$0.0319659\pi$
$797$	16.4956	+	28.5712i	0.584304	+	1.01204i	−0.410657	+	0.911790i	$0.634701\pi$
$798$	−1.46486			−0.0518556
$799$	22.1561	+	38.3755i	0.783828	+	1.35763i
$800$	−23.0084	−	39.8517i	−0.813470	−	1.40897i
$801$	53.9163			1.90504
$802$	−0.101679	−	0.176113i	−0.00359041	−	0.00621878i
$803$	−7.12100	+	12.3339i	−0.251294	+	0.435255i
$804$	−5.38437	+	9.32600i	−0.189892	+	0.328903i
$805$	−3.27596			−0.115463
$806$	20.7324	+	13.5496i	0.730269	+	0.477264i
$807$	45.9610			1.61790
$808$	−18.0545	+	31.2712i	−0.635153	+	1.10012i
$809$	16.3886	−	28.3858i	0.576191	−	0.997993i	−0.419720	−	0.907654i	$-0.637872\pi$
$809$	16.3886	−	28.3858i	0.576191	−	0.997993i	0.995911	−	0.0903388i	$-0.0287950\pi$
$810$	11.5000	+	19.9186i	0.404069	+	0.699868i
$811$	4.94185			0.173532			0.0867660	−	0.996229i	$-0.472347\pi$
$811$	4.94185			0.173532			0.0867660	+	0.996229i	$0.472347\pi$
$812$	0.161692	+	0.280058i	0.00567427	+	0.00982813i
$813$	−11.3704	−	19.6941i	−0.398778	−	0.690703i
$814$	8.63798			0.302761
$815$	−21.3734	−	37.0199i	−0.748679	−	1.29675i
$816$	5.68521	−	9.84707i	0.199022	−	0.344716i
$817$	−12.1391	+	21.0256i	−0.424695	+	0.735593i
$818$	0.0921180			0.00322083
$819$	1.90019	+	1.24186i	0.0663979	+	0.0433941i
$820$	4.77713			0.166825
$821$	9.90788	−	17.1610i	0.345787	−	0.598921i	−0.639709	−	0.768617i	$-0.720945\pi$
$821$	9.90788	−	17.1610i	0.345787	−	0.598921i	0.985497	+	0.169696i	$0.0542785\pi$
$822$	17.7439	−	30.7333i	0.618888	−	1.07195i
$823$	−14.0749	−	24.3785i	−0.490621	−	0.849781i	0.509320	−	0.860577i	$-0.329897\pi$
$823$	−14.0749	−	24.3785i	−0.490621	−	0.849781i	−0.999942	+	0.0107957i	$0.996564\pi$
$824$	19.2201			0.669566
$825$	−11.9721	−	20.7363i	−0.416815	−	0.721944i
$826$	−0.178678	−	0.309479i	−0.00621700	−	0.0107682i
$827$	33.0578			1.14953			0.574765	−	0.818318i	$-0.305093\pi$
$827$	33.0578			1.14953			0.574765	+	0.818318i	$0.305093\pi$
$828$	−9.80504	−	16.9828i	−0.340749	−	0.590194i
$829$	7.48605	−	12.9662i	0.260001	−	0.450335i	−0.706241	−	0.707972i	$-0.749610\pi$
$829$	7.48605	−	12.9662i	0.260001	−	0.450335i	0.966242	+	0.257637i	$0.0829437\pi$
$830$	19.9249	−	34.5109i	0.691602	−	1.19789i
$831$	75.9996			2.63640
$832$	1.39412	−	25.2003i	0.0483325	−	0.873664i
$833$	−30.4709			−1.05576
$834$	−1.13075	+	1.95852i	−0.0391547	+	0.0678180i
$835$	−32.5543	+	56.3856i	−1.12659	+	1.95131i
$836$	−1.68521	−	2.91886i	−0.0582841	−	0.100951i
$837$	13.7385			0.474872
$838$	−5.06421	−	8.77147i	−0.174940	−	0.303005i
$839$	6.50653	+	11.2696i	0.224630	+	0.389071i	0.956208	−	0.292686i	$-0.0945492\pi$
$839$	6.50653	+	11.2696i	0.224630	+	0.389071i	−0.731578	+	0.681758i	$0.761216\pi$
$840$	−4.91395			−0.169547
$841$	12.6264	+	21.8695i	0.435392	+	0.754121i
$842$	3.29108	−	5.70032i	0.113418	−	0.196446i
$843$	14.0556	−	24.3450i	0.484101	−	0.838488i
$844$	4.57377			0.157436
$845$	−48.6946	−	5.40427i	−1.67514	−	0.185912i
$846$	−38.2118			−1.31375
$847$	−0.0835276	+	0.144674i	−0.00287004	+	0.00497106i
$848$	0.667055	−	1.15537i	0.0229068	−	0.0396757i
$849$	−13.3202	−	23.0712i	−0.457147	−	0.791801i
$850$	40.2225			1.37962
$851$	22.4733	+	38.9248i	0.770373	+	1.33433i
$852$	7.80504	+	13.5187i	0.267396	+	0.463144i
$853$	25.3448			0.867791			0.433895	−	0.900963i	$-0.357139\pi$
$853$	25.3448			0.867791			0.433895	+	0.900963i	$0.357139\pi$
$854$	0.401353	+	0.695164i	0.0137340	+	0.0237880i
$855$	23.9356	−	41.4577i	0.818580	−	1.41782i
$856$	−20.5568	+	35.6054i	−0.702616	+	1.21697i
$857$	49.5627			1.69303			0.846514	−	0.532366i	$-0.178697\pi$
$857$	49.5627			1.69303			0.846514	+	0.532366i	$0.178697\pi$
$858$	0.518152	−	9.36617i	0.0176894	−	0.319756i
$859$	−55.6208			−1.89776			−0.948879	−	0.315641i	$-0.897780\pi$
$859$	−55.6208			−1.89776			−0.948879	+	0.315641i	$0.897780\pi$
$860$	−13.5738	+	23.5105i	−0.462862	+	0.801700i
$861$	0.275458	−	0.477107i	0.00938758	−	0.0162598i
$862$	−8.74942	−	15.1544i	−0.298006	−	0.516162i
$863$	10.6124			0.361250			0.180625	−	0.983552i	$-0.442188\pi$
$863$	10.6124			0.361250			0.180625	+	0.983552i	$0.442188\pi$
$864$	−5.00000	−	8.66025i	−0.170103	−	0.294628i
$865$	24.1978	+	41.9118i	0.822750	+	1.42504i
$866$	−8.69380			−0.295427
$867$	−2.73243	−	4.73271i	−0.0927982	−	0.160731i
$868$	0.573772	−	0.993802i	0.0194751	−	0.0337318i
$869$	7.28689	−	12.6213i	0.247191	−	0.428147i
$870$	18.9805			0.643499
$871$	−12.4926	−	8.16447i	−0.423295	−	0.276643i
$872$	26.5240			0.898217
$873$	−6.71848	+	11.6367i	−0.227386	+	0.393844i
$874$	−8.76873	+	15.1879i	−0.296607	+	0.513738i
$875$	−1.32319	−	2.29183i	−0.0447320	−	0.0774780i
$876$	−37.0531			−1.25191
$877$	−26.9237	−	46.6332i	−0.909149	−	1.57469i	−0.815249	−	0.579110i	$-0.803400\pi$
$877$	−26.9237	−	46.6332i	−0.909149	−	1.57469i	−0.0938996	−	0.995582i	$-0.529933\pi$
$878$	12.2869	+	21.2815i	0.414662	+	0.718216i
$879$	10.3123			0.347824
$880$	1.88437	+	3.26382i	0.0635220	+	0.110023i
$881$	0.600514	−	1.04012i	0.0202318	−	0.0350425i	−0.855732	−	0.517419i	$-0.826893\pi$
$881$	0.600514	−	1.04012i	0.0202318	−	0.0350425i	0.875964	+	0.482376i	$0.160226\pi$
$882$	13.1380	−	22.7557i	0.442379	−	0.766223i
$883$	58.4793			1.96799			0.983993	−	0.178207i	$-0.0570298\pi$
$883$	58.4793			1.96799			0.983993	+	0.178207i	$0.0570298\pi$
$884$	−13.1906	−	8.62065i	−0.443647	−	0.289944i
$885$	20.9744			0.705048
$886$	8.63495	−	14.9562i	0.290097	−	0.502462i
$887$	13.6682	−	23.6741i	0.458934	−	0.794897i	−0.539971	−	0.841684i	$-0.681565\pi$
$887$	13.6682	−	23.6741i	0.458934	−	0.794897i	0.998905	+	0.0467868i	$0.0148981\pi$
$888$	33.7099	+	58.3872i	1.13123	+	1.95935i
$889$	−0.222481			−0.00746176
$890$	−26.9581	−	46.6929i	−0.903639	−	1.56515i
$891$	3.05142	+	5.28522i	0.102226	+	0.177061i
$892$	9.06421			0.303492
$893$	−17.0866	−	29.5948i	−0.571780	−	0.990352i
$894$	−1.51815	+	2.62952i	−0.0507746	+	0.0879442i
$895$	9.30084	−	16.1095i	0.310893	−	0.538482i
$896$	−0.501166			−0.0167428
$897$	43.5543	−	22.0328i	1.45423	−	0.735655i
$898$	16.3230			0.544705
$899$	−6.64871	+	11.5159i	−0.221747	+	0.384077i
$900$	17.3425	−	30.0381i	0.578084	−	1.00127i
$901$	−2.91531	−	5.04946i	−0.0971230	−	0.168222i
$902$	−1.26757			−0.0422054
$903$	1.56538	+	2.71131i	0.0520925	+	0.0902268i
$904$	6.84806	+	11.8612i	0.227763	+	0.394497i
$905$	2.40439			0.0799245
$906$	13.9721	+	24.2004i	0.464192	+	0.804004i
$907$	8.82991	−	15.2939i	0.293192	−	0.507824i	−0.681370	−	0.731939i	$-0.738616\pi$
$907$	8.82991	−	15.2939i	0.293192	−	0.507824i	0.974563	+	0.224115i	$0.0719490\pi$
$908$	−6.60168	+	11.4344i	−0.219084	+	0.379465i
$909$	−45.3616			−1.50455
$910$	0.125389	−	2.26654i	0.00415660	−	0.0751351i
$911$	−20.8074			−0.689379			−0.344689	−	0.938717i	$-0.612016\pi$
$911$	−20.8074			−0.689379			−0.344689	+	0.938717i	$0.612016\pi$
$912$	−4.38437	+	7.59395i	−0.145181	+	0.251461i
$913$	5.28689	−	9.15715i	0.174970	−	0.303058i
$914$	−10.7087	−	18.5480i	−0.354213	−	0.613515i
$915$	−47.1136			−1.55753
$916$	1.01395	+	1.75622i	0.0335020	+	0.0580271i
$917$	−1.14471	−	1.98269i	−0.0378015	−	0.0654741i
$918$	8.74083			0.288490
$919$	−28.6850	−	49.6839i	−0.946231	−	1.63892i	−0.753267	−	0.657715i	$-0.771523\pi$
$919$	−28.6850	−	49.6839i	−0.946231	−	1.63892i	−0.192964	−	0.981206i	$-0.561810\pi$
$920$	−29.4151	+	50.9485i	−0.969788	+	1.67972i
$921$	−18.5235	+	32.0837i	−0.610371	+	1.05719i
$922$	−17.8074			−0.586454
$923$	−19.3039	+	9.76527i	−0.635395	+	0.321428i
$924$	−0.434624			−0.0142981
$925$	−39.7492	+	68.8477i	−1.30695	+	2.26370i
$926$	−2.40135	+	4.15927i	−0.0789134	+	0.136682i
$927$	12.0726	+	20.9104i	0.396516	+	0.686787i
$928$	9.67895			0.317727
$929$	−23.5726	−	40.8290i	−0.773392	−	1.33955i	−0.935694	−	0.352813i	$-0.885225\pi$
$929$	−23.5726	−	40.8290i	−0.773392	−	1.33955i	0.162302	−	0.986741i	$-0.448108\pi$
$930$	−33.6766	−	58.3296i	−1.10430	−	1.91270i
$931$	23.4988			0.770143
$932$	−6.37041	−	11.0339i	−0.208670	−	0.361427i
$933$	−15.4509	+	26.7618i	−0.505840	+	0.876141i
$934$	1.40368	−	2.43125i	0.0459300	−	0.0795530i
$935$	16.4709			0.538657
$936$	36.3756	−	18.4014i	1.18897	−	0.601467i
$937$	24.2820			0.793259			0.396630	−	0.917979i	$-0.370180\pi$
$937$	24.2820			0.793259			0.396630	+	0.917979i	$0.370180\pi$
$938$	0.345733	−	0.598827i	0.0112886	−	0.0195524i
$939$	−10.2760	+	17.7985i	−0.335343	+	0.580832i
$940$	−19.1059	−	33.0923i	−0.623165	−	1.07935i
$941$	12.7408			0.415339			0.207670	−	0.978199i	$-0.433412\pi$
$941$	12.7408			0.415339			0.207670	+	0.978199i	$0.433412\pi$
$942$	5.97512	+	10.3492i	0.194680	+	0.337196i
$943$	−3.29781	−	5.71197i	−0.107391	−	0.186007i
$944$	−2.13915			−0.0696233
$945$	−0.629587	−	1.09048i	−0.0204805	−	0.0354732i
$946$	3.60168	−	6.23829i	0.117101	−	0.202824i
$947$	5.53747	−	9.59118i	0.179944	−	0.311671i	−0.761917	−	0.647674i	$-0.775742\pi$
$947$	5.53747	−	9.59118i	0.179944	−	0.311671i	0.941861	+	0.336003i	$0.109075\pi$
$948$	37.9163			1.23146
$949$	2.83644	−	51.2718i	0.0920748	−	1.66435i
$950$	−31.0191			−1.00639
$951$	−35.5428	+	61.5620i	−1.15256	+	1.99628i
$952$	1.09515	−	1.89686i	0.0354940	−	0.0614775i
$953$	−25.1838	−	43.6197i	−0.815785	−	1.41298i	−0.908763	−	0.417313i	$-0.862972\pi$
$953$	−25.1838	−	43.6197i	−0.815785	−	1.41298i	0.0929782	−	0.995668i	$-0.470361\pi$
$954$	5.02791			0.162785
$955$	−49.2558	−	85.3135i	−1.59388	−	2.76068i
$956$	2.03630	+	3.52698i	0.0658587	+	0.114071i
$957$	5.03630			0.162801
$958$	−5.91647	−	10.2476i	−0.191153	−	0.331086i
$959$	1.13934	−	1.97340i	0.0367913	−	0.0637244i
$960$	−34.3176	+	59.4399i	−1.10760	+	1.91841i
$961$	16.1866			0.522147
$962$	−27.7911	+	14.0587i	−0.896020	+	0.453271i
$963$	−51.6487			−1.66436
$964$	−9.49141	+	16.4396i	−0.305698	+	0.529484i
$965$	20.9902	−	36.3562i	0.675700	−	1.17035i
$966$	1.13075	+	1.95852i	0.0363814	+	0.0630143i
$967$	47.7213			1.53461			0.767307	−	0.641280i	$-0.221596\pi$
$967$	47.7213			1.53461			0.767307	+	0.641280i	$0.221596\pi$
$968$	1.50000	+	2.59808i	0.0482118	+	0.0835053i
$969$	19.1615	+	33.1887i	0.615556	+	1.06617i
$970$	13.4370			0.431435
$971$	15.3734	+	26.6276i	0.493357	+	0.854520i	0.999971	−	0.00765336i	$-0.00243616\pi$
$971$	15.3734	+	26.6276i	0.493357	+	0.854520i	−0.506613	+	0.862173i	$0.669103\pi$
$972$	−10.9388	+	18.9466i	−0.350863	+	0.607712i
$973$	−0.0726062	+	0.125758i	−0.00232765	+	0.00403160i
$974$	−16.4174			−0.526049
$975$	72.2672	+	47.2299i	2.31440	+	1.51257i
$976$	4.80504			0.153805
$977$	11.3213	−	19.6091i	0.362201	−	0.627351i	−0.626122	−	0.779725i	$-0.715359\pi$
$977$	11.3213	−	19.6091i	0.362201	−	0.627351i	0.988323	+	0.152375i	$0.0486920\pi$
$978$	−14.7548	+	25.5560i	−0.471806	+	0.817192i
$979$	−7.15310	−	12.3895i	−0.228614	−	0.395971i
$980$	26.2760			0.839355
$981$	16.6603	+	28.8565i	0.531923	+	0.921318i
$982$	−3.91647	−	6.78353i	−0.124980	−	0.216471i
$983$	2.40672			0.0767623			0.0383812	−	0.999263i	$-0.487780\pi$
$983$	2.40672			0.0767623			0.0383812	+	0.999263i	$0.487780\pi$
$984$	−4.94671	−	8.56795i	−0.157695	−	0.273136i
$985$	−29.2783	+	50.7115i	−0.932884	+	1.61580i
$986$	−4.23010	+	7.32675i	−0.134714	+	0.233331i
$987$	−4.40672			−0.140267
$988$	10.1724	+	6.64814i	0.323628	+	0.211506i
$989$	37.4817			1.19185
$990$	−7.10168	+	12.3005i	−0.225706	+	0.390935i
$991$	−6.60471	+	11.4397i	−0.209806	+	0.363394i	−0.951653	−	0.307175i	$-0.900616\pi$
$991$	−6.60471	+	11.4397i	−0.209806	+	0.363394i	0.741848	+	0.670569i	$0.233950\pi$
$992$	−17.1731	−	29.7447i	−0.545247	−	0.944396i
$993$	12.3341			0.391411
$994$	−0.501166	−	0.868044i	−0.0158960	−	0.0275327i
$995$	22.0030	+	38.1104i	0.697543	+	1.20818i
$996$	27.5096			0.871674
$997$	−8.62823	−	14.9445i	−0.273259	−	0.473298i	0.696436	−	0.717619i	$-0.254768\pi$
$997$	−8.62823	−	14.9445i	−0.273259	−	0.473298i	−0.969694	+	0.244321i	$0.921435\pi$
$998$	−6.13612	+	10.6281i	−0.194235	+	0.336425i
$999$	−8.63798	+	14.9614i	−0.273294	+	0.473359i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	143.2.e.a.100.1	✓	6
13.3	even	3	inner	143.2.e.a.133.1	yes	6
13.4	even	6		1859.2.a.e.1.3		3
13.9	even	3		1859.2.a.h.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
143.2.e.a.100.1	✓	6	1.1	even	1	trivial
143.2.e.a.133.1	yes	6	13.3	even	3	inner
1859.2.a.e.1.3		3	13.4	even	6
1859.2.a.h.1.3		3	13.9	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:	\( N \)	\(=\)	\( 143 = 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	143.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.30084 + 2.25312i) q^{3} +(0.500000 + 0.866025i) q^{4} +3.76873 q^{5} +(-1.30084 - 2.25312i) q^{6} +(-0.0835276 - 0.144674i) q^{7} -3.00000 q^{8} +(-1.88437 - 3.26382i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-1.30084 + 2.25312i) q^{3} +(0.500000 + 0.866025i) q^{4} +3.76873 q^{5} +(-1.30084 - 2.25312i) q^{6} +(-0.0835276 - 0.144674i) q^{7} -3.00000 q^{8} +(-1.88437 - 3.26382i) q^{9} +(-1.88437 + 3.26382i) q^{10} +(-0.500000 + 0.866025i) q^{11} -2.60168 q^{12} +(0.199160 - 3.60005i) q^{13} +0.167055 q^{14} +(-4.90252 + 8.49141i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-2.18521 - 3.78489i) q^{17} +3.76873 q^{18} +(1.68521 + 2.91886i) q^{19} +(1.88437 + 3.26382i) q^{20} +0.434624 q^{21} +(-0.500000 - 0.866025i) q^{22} +(2.60168 - 4.50624i) q^{23} +(3.90252 - 6.75936i) q^{24} +9.20336 q^{25} +(3.01815 + 1.97250i) q^{26} +2.00000 q^{27} +(0.0835276 - 0.144674i) q^{28} +(-0.967895 + 1.67644i) q^{29} +(-4.90252 - 8.49141i) q^{30} +6.86925 q^{31} +(-2.50000 - 4.33013i) q^{32} +(-1.30084 - 2.25312i) q^{33} +4.37041 q^{34} +(-0.314793 - 0.545238i) q^{35} +(1.88437 - 3.26382i) q^{36} +(-4.31899 + 7.48071i) q^{37} -3.37041 q^{38} +(7.85226 + 5.13182i) q^{39} -11.3062 q^{40} +(0.633784 - 1.09775i) q^{41} +(-0.217312 + 0.376395i) q^{42} +(3.60168 + 6.23829i) q^{43} -1.00000 q^{44} +(-7.10168 - 12.3005i) q^{45} +(2.60168 + 4.50624i) q^{46} -10.1391 q^{47} +(1.30084 + 2.25312i) q^{48} +(3.48605 - 6.03801i) q^{49} +(-4.60168 + 7.97034i) q^{50} +11.3704 q^{51} +(3.21731 - 1.62755i) q^{52} +1.33411 q^{53} +(-1.00000 + 1.73205i) q^{54} +(-1.88437 + 3.26382i) q^{55} +(0.250583 + 0.434022i) q^{56} -8.76873 q^{57} +(-0.967895 - 1.67644i) q^{58} +(-1.06957 - 1.85256i) q^{59} -9.80504 q^{60} +(2.40252 + 4.16128i) q^{61} +(-3.43462 + 5.94894i) q^{62} +(-0.314793 + 0.545238i) q^{63} +7.00000 q^{64} +(0.750583 - 13.5676i) q^{65} +2.60168 q^{66} +(2.06957 - 3.58461i) q^{67} +(2.18521 - 3.78489i) q^{68} +(6.76873 + 11.7238i) q^{69} +0.629587 q^{70} +(-3.00000 - 5.19615i) q^{71} +(5.65310 + 9.79146i) q^{72} +14.2420 q^{73} +(-4.31899 - 7.48071i) q^{74} +(-11.9721 + 20.7363i) q^{75} +(-1.68521 + 2.91886i) q^{76} +0.167055 q^{77} +(-8.37041 + 4.23435i) q^{78} -14.5738 q^{79} +(1.88437 - 3.26382i) q^{80} +(3.05142 - 5.28522i) q^{81} +(0.633784 + 1.09775i) q^{82} -10.5738 q^{83} +(0.217312 + 0.376395i) q^{84} +(-8.23546 - 14.2642i) q^{85} -7.20336 q^{86} +(-2.51815 - 4.36157i) q^{87} +(1.50000 - 2.59808i) q^{88} +(-7.15310 + 12.3895i) q^{89} +14.2034 q^{90} +(-0.537469 + 0.271890i) q^{91} +5.20336 q^{92} +(-8.93579 + 15.4772i) q^{93} +(5.06957 - 8.78076i) q^{94} +(6.35110 + 11.0004i) q^{95} +13.0084 q^{96} +(-1.78269 - 3.08771i) q^{97} +(3.48605 + 6.03801i) q^{98} +3.76873 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 3 q^{2} + 3 q^{4} + 6 q^{5} - 18 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q - 3 * q^2 + 3 * q^4 + 6 * q^5 - 18 * q^8 - 3 * q^9	\( 6 q - 3 q^{2} + 3 q^{4} + 6 q^{5} - 18 q^{8} - 3 q^{9} - 3 q^{10} - 3 q^{11} + 9 q^{13} - 6 q^{15} + 3 q^{16} + 3 q^{17} + 6 q^{18} - 6 q^{19} + 3 q^{20} - 12 q^{21} - 3 q^{22} + 24 q^{25} + 3 q^{26} + 12 q^{27} + 3 q^{29} - 6 q^{30} + 12 q^{31} - 15 q^{32} - 6 q^{34} - 18 q^{35} + 3 q^{36} - 3 q^{37} + 12 q^{38} + 30 q^{39} - 18 q^{40} - 3 q^{41} + 6 q^{42} + 6 q^{43} - 6 q^{44} - 27 q^{45} - 12 q^{47} - 3 q^{49} - 12 q^{50} + 36 q^{51} + 12 q^{52} + 6 q^{53} - 6 q^{54} - 3 q^{55} - 36 q^{57} + 3 q^{58} + 18 q^{59} - 12 q^{60} - 9 q^{61} - 6 q^{62} - 18 q^{63} + 42 q^{64} + 3 q^{65} - 12 q^{67} - 3 q^{68} + 24 q^{69} + 36 q^{70} - 18 q^{71} + 9 q^{72} + 18 q^{73} - 3 q^{74} - 24 q^{75} + 6 q^{76} - 18 q^{78} - 24 q^{79} + 3 q^{80} + 9 q^{81} - 3 q^{82} - 6 q^{84} - 27 q^{85} - 12 q^{86} + 9 q^{88} - 18 q^{89} + 54 q^{90} + 30 q^{91} - 36 q^{93} + 6 q^{94} + 24 q^{95} - 18 q^{97} - 3 q^{98} + 6 q^{99}+O(q^{100}) \) 6 * q - 3 * q^2 + 3 * q^4 + 6 * q^5 - 18 * q^8 - 3 * q^9 - 3 * q^10 - 3 * q^11 + 9 * q^13 - 6 * q^15 + 3 * q^16 + 3 * q^17 + 6 * q^18 - 6 * q^19 + 3 * q^20 - 12 * q^21 - 3 * q^22 + 24 * q^25 + 3 * q^26 + 12 * q^27 + 3 * q^29 - 6 * q^30 + 12 * q^31 - 15 * q^32 - 6 * q^34 - 18 * q^35 + 3 * q^36 - 3 * q^37 + 12 * q^38 + 30 * q^39 - 18 * q^40 - 3 * q^41 + 6 * q^42 + 6 * q^43 - 6 * q^44 - 27 * q^45 - 12 * q^47 - 3 * q^49 - 12 * q^50 + 36 * q^51 + 12 * q^52 + 6 * q^53 - 6 * q^54 - 3 * q^55 - 36 * q^57 + 3 * q^58 + 18 * q^59 - 12 * q^60 - 9 * q^61 - 6 * q^62 - 18 * q^63 + 42 * q^64 + 3 * q^65 - 12 * q^67 - 3 * q^68 + 24 * q^69 + 36 * q^70 - 18 * q^71 + 9 * q^72 + 18 * q^73 - 3 * q^74 - 24 * q^75 + 6 * q^76 - 18 * q^78 - 24 * q^79 + 3 * q^80 + 9 * q^81 - 3 * q^82 - 6 * q^84 - 27 * q^85 - 12 * q^86 + 9 * q^88 - 18 * q^89 + 54 * q^90 + 30 * q^91 - 36 * q^93 + 6 * q^94 + 24 * q^95 - 18 * q^97 - 3 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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