LMFDB - Embedded newform 87.2.f.b.17.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [87,2,Mod(17,87)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("87.17"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(87, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	87.f (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [4,2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.694698497585$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(i)$
Coefficient field:	$\Q(\zeta_{12})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			17.1
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	87.17
Dual form			87.2.f.b.41.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.366025 - 0.366025i) q^{2} +(1.50000 + 0.866025i) q^{3} -1.73205i q^{4} -0.267949 q^{5} +(-0.232051 - 0.866025i) q^{6} +0.732051 q^{7} +(-1.36603 + 1.36603i) q^{8} +(1.50000 + 2.59808i) q^{9} +(0.0980762 + 0.0980762i) q^{10} +(-1.36603 - 1.36603i) q^{11} +(1.50000 - 2.59808i) q^{12} +2.26795i q^{13} +(-0.267949 - 0.267949i) q^{14} +(-0.401924 - 0.232051i) q^{15} -2.46410 q^{16} +(-2.73205 - 2.73205i) q^{17} +(0.401924 - 1.50000i) q^{18} +(-1.73205 + 1.73205i) q^{19} +0.464102i q^{20} +(1.09808 + 0.633975i) q^{21} +1.00000i q^{22} +5.46410i q^{23} +(-3.23205 + 0.866025i) q^{24} -4.92820 q^{25} +(0.830127 - 0.830127i) q^{26} +5.19615i q^{27} -1.26795i q^{28} +(-2.00000 - 5.00000i) q^{29} +(0.0621778 + 0.232051i) q^{30} +(2.36603 - 2.36603i) q^{31} +(3.63397 + 3.63397i) q^{32} +(-0.866025 - 3.23205i) q^{33} +2.00000i q^{34} -0.196152 q^{35} +(4.50000 - 2.59808i) q^{36} +(3.46410 + 3.46410i) q^{37} +1.26795 q^{38} +(-1.96410 + 3.40192i) q^{39} +(0.366025 - 0.366025i) q^{40} +(5.19615 - 5.19615i) q^{41} +(-0.169873 - 0.633975i) q^{42} +(8.56218 - 8.56218i) q^{43} +(-2.36603 + 2.36603i) q^{44} +(-0.401924 - 0.696152i) q^{45} +(2.00000 - 2.00000i) q^{46} +(7.83013 - 7.83013i) q^{47} +(-3.69615 - 2.13397i) q^{48} -6.46410 q^{49} +(1.80385 + 1.80385i) q^{50} +(-1.73205 - 6.46410i) q^{51} +3.92820 q^{52} +9.92820i q^{53} +(1.90192 - 1.90192i) q^{54} +(0.366025 + 0.366025i) q^{55} +(-1.00000 + 1.00000i) q^{56} +(-4.09808 + 1.09808i) q^{57} +(-1.09808 + 2.56218i) q^{58} +7.46410i q^{59} +(-0.401924 + 0.696152i) q^{60} +(-2.00000 + 2.00000i) q^{61} -1.73205 q^{62} +(1.09808 + 1.90192i) q^{63} +2.26795i q^{64} -0.607695i q^{65} +(-0.866025 + 1.50000i) q^{66} -4.92820i q^{67} +(-4.73205 + 4.73205i) q^{68} +(-4.73205 + 8.19615i) q^{69} +(0.0717968 + 0.0717968i) q^{70} +13.2679 q^{71} +(-5.59808 - 1.50000i) q^{72} +(-4.00000 - 4.00000i) q^{73} -2.53590i q^{74} +(-7.39230 - 4.26795i) q^{75} +(3.00000 + 3.00000i) q^{76} +(-1.00000 - 1.00000i) q^{77} +(1.96410 - 0.526279i) q^{78} +(-6.83013 + 6.83013i) q^{79} +0.660254 q^{80} +(-4.50000 + 7.79423i) q^{81} -3.80385 q^{82} -13.8564i q^{83} +(1.09808 - 1.90192i) q^{84} +(0.732051 + 0.732051i) q^{85} -6.26795 q^{86} +(1.33013 - 9.23205i) q^{87} +3.73205 q^{88} +(-5.00000 - 5.00000i) q^{89} +(-0.107695 + 0.401924i) q^{90} +1.66025i q^{91} +9.46410 q^{92} +(5.59808 - 1.50000i) q^{93} -5.73205 q^{94} +(0.464102 - 0.464102i) q^{95} +(2.30385 + 8.59808i) q^{96} +(-4.26795 - 4.26795i) q^{97} +(2.36603 + 2.36603i) q^{98} +(1.50000 - 5.59808i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{2} + 6 q^{3} - 8 q^{5} + 6 q^{6} - 4 q^{7} - 2 q^{8} + 6 q^{9} - 10 q^{10} - 2 q^{11} + 6 q^{12} - 8 q^{14} - 12 q^{15} + 4 q^{16} - 4 q^{17} + 12 q^{18} - 6 q^{21} - 6 q^{24} + 8 q^{25} - 14 q^{26}+ \cdots + 6 q^{99}+O(q^{100}) $ 4 * q + 2 * q^2 + 6 * q^3 - 8 * q^5 + 6 * q^6 - 4 * q^7 - 2 * q^8 + 6 * q^9 - 10 * q^10 - 2 * q^11 + 6 * q^12 - 8 * q^14 - 12 * q^15 + 4 * q^16 - 4 * q^17 + 12 * q^18 - 6 * q^21 - 6 * q^24 + 8 * q^25 - 14 * q^26 - 8 * q^29 - 24 * q^30 + 6 * q^31 + 18 * q^32 + 20 * q^35 + 18 * q^36 + 12 * q^38 + 6 * q^39 - 2 * q^40 - 18 * q^42 + 10 * q^43 - 6 * q^44 - 12 * q^45 + 8 * q^46 + 14 * q^47 + 6 * q^48 - 12 * q^49 + 28 * q^50 - 12 * q^52 + 18 * q^54 - 2 * q^55 - 4 * q^56 - 6 * q^57 + 6 * q^58 - 12 * q^60 - 8 * q^61 - 6 * q^63 - 12 * q^68 - 12 * q^69 + 28 * q^70 + 60 * q^71 - 12 * q^72 - 16 * q^73 + 12 * q^75 + 12 * q^76 - 4 * q^77 - 6 * q^78 - 10 * q^79 - 32 * q^80 - 18 * q^81 - 36 * q^82 - 6 * q^84 - 4 * q^85 - 32 * q^86 - 12 * q^87 + 8 * q^88 - 20 * q^89 - 42 * q^90 + 24 * q^92 + 12 * q^93 - 16 * q^94 - 12 * q^95 + 30 * q^96 - 24 * q^97 + 6 * q^98 + 6 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	−0.366025	−	0.366025i	−0.258819	−	0.258819i	0.565755	−	0.824574i	$-0.308585\pi$
$2$	−0.366025	−	0.366025i	−0.258819	−	0.258819i	−0.824574	+	0.565755i	$0.808585\pi$
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$3$	1.50000	+	0.866025i	0.866025	+	0.500000i
$4$		−	1.73205i		−	0.866025i
$5$	−0.267949			−0.119831			−0.0599153	−	0.998203i	$-0.519083\pi$
$5$	−0.267949			−0.119831			−0.0599153	+	0.998203i	$0.519083\pi$
$6$	−0.232051	−	0.866025i	−0.0947343	−	0.353553i
$7$	0.732051			0.276689			0.138345	−	0.990384i	$-0.455822\pi$
$7$	0.732051			0.276689			0.138345	+	0.990384i	$0.455822\pi$
$8$	−1.36603	+	1.36603i	−0.482963	+	0.482963i
$9$	1.50000	+	2.59808i	0.500000	+	0.866025i
$10$	0.0980762	+	0.0980762i	0.0310144	+	0.0310144i
$11$	−1.36603	−	1.36603i	−0.411872	−	0.411872i	0.470518	−	0.882390i	$-0.344067\pi$
$11$	−1.36603	−	1.36603i	−0.411872	−	0.411872i	−0.882390	+	0.470518i	$0.844067\pi$
$12$	1.50000	−	2.59808i	0.433013	−	0.750000i
$13$			2.26795i			0.629016i	0.949255	+	0.314508i	$0.101840\pi$
$13$			2.26795i			0.629016i	−0.949255	+	0.314508i	$0.898160\pi$
$14$	−0.267949	−	0.267949i	−0.0716124	−	0.0716124i
$15$	−0.401924	−	0.232051i	−0.103776	−	0.0599153i
$16$	−2.46410			−0.616025
$17$	−2.73205	−	2.73205i	−0.662620	−	0.662620i	0.293377	−	0.955997i	$-0.405221\pi$
$17$	−2.73205	−	2.73205i	−0.662620	−	0.662620i	−0.955997	+	0.293377i	$0.905221\pi$
$18$	0.401924	−	1.50000i	0.0947343	−	0.353553i
$19$	−1.73205	+	1.73205i	−0.397360	+	0.397360i	−0.877301	−	0.479941i	$-0.840658\pi$
$19$	−1.73205	+	1.73205i	−0.397360	+	0.397360i	0.479941	+	0.877301i	$0.340658\pi$
$20$			0.464102i			0.103776i
$21$	1.09808	+	0.633975i	0.239620	+	0.138345i
$22$			1.00000i			0.213201i
$23$			5.46410i			1.13934i	0.821872	+	0.569672i	$0.192930\pi$
$23$			5.46410i			1.13934i	−0.821872	+	0.569672i	$0.807070\pi$
$24$	−3.23205	+	0.866025i	−0.659740	+	0.176777i
$25$	−4.92820			−0.985641
$26$	0.830127	−	0.830127i	0.162801	−	0.162801i
$27$			5.19615i			1.00000i
$28$		−	1.26795i		−	0.239620i
$29$	−2.00000	−	5.00000i	−0.371391	−	0.928477i
$29$	−2.00000	−	5.00000i	−0.371391	−	0.928477i
$30$	0.0621778	+	0.232051i	0.0113521	+	0.0423665i
$31$	2.36603	−	2.36603i	0.424951	−	0.424951i	−0.461953	−	0.886904i	$-0.652851\pi$
$31$	2.36603	−	2.36603i	0.424951	−	0.424951i	0.886904	+	0.461953i	$0.152851\pi$
$32$	3.63397	+	3.63397i	0.642402	+	0.642402i
$33$	−0.866025	−	3.23205i	−0.150756	−	0.562628i
$34$			2.00000i			0.342997i
$35$	−0.196152			−0.0331558
$36$	4.50000	−	2.59808i	0.750000	−	0.433013i
$37$	3.46410	+	3.46410i	0.569495	+	0.569495i	0.931987	−	0.362492i	$-0.118074\pi$
$37$	3.46410	+	3.46410i	0.569495	+	0.569495i	−0.362492	+	0.931987i	$0.618074\pi$
$38$	1.26795			0.205689
$39$	−1.96410	+	3.40192i	−0.314508	+	0.544744i
$40$	0.366025	−	0.366025i	0.0578737	−	0.0578737i
$41$	5.19615	−	5.19615i	0.811503	−	0.811503i	−0.173356	−	0.984859i	$-0.555461\pi$
$41$	5.19615	−	5.19615i	0.811503	−	0.811503i	0.984859	+	0.173356i	$0.0554613\pi$
$42$	−0.169873	−	0.633975i	−0.0262120	−	0.0978244i
$43$	8.56218	−	8.56218i	1.30572	−	1.30572i	0.381246	−	0.924473i	$-0.375495\pi$
$43$	8.56218	−	8.56218i	1.30572	−	1.30572i	0.924473	−	0.381246i	$-0.124505\pi$
$44$	−2.36603	+	2.36603i	−0.356692	+	0.356692i
$45$	−0.401924	−	0.696152i	−0.0599153	−	0.103776i
$46$	2.00000	−	2.00000i	0.294884	−	0.294884i
$47$	7.83013	−	7.83013i	1.14214	−	1.14214i	0.154084	−	0.988058i	$-0.450757\pi$
$47$	7.83013	−	7.83013i	1.14214	−	1.14214i	0.988058	−	0.154084i	$-0.0492425\pi$
$48$	−3.69615	−	2.13397i	−0.533494	−	0.308013i
$49$	−6.46410			−0.923443
$50$	1.80385	+	1.80385i	0.255103	+	0.255103i
$51$	−1.73205	−	6.46410i	−0.242536	−	0.905155i
$52$	3.92820			0.544744
$53$			9.92820i			1.36374i	0.731472	+	0.681872i	$0.238834\pi$
$53$			9.92820i			1.36374i	−0.731472	+	0.681872i	$0.761166\pi$
$54$	1.90192	−	1.90192i	0.258819	−	0.258819i
$55$	0.366025	+	0.366025i	0.0493549	+	0.0493549i
$56$	−1.00000	+	1.00000i	−0.133631	+	0.133631i
$57$	−4.09808	+	1.09808i	−0.542803	+	0.145444i
$58$	−1.09808	+	2.56218i	−0.144184	+	0.336430i
$59$			7.46410i			0.971743i	0.874030	+	0.485872i	$0.161498\pi$
$59$			7.46410i			0.971743i	−0.874030	+	0.485872i	$0.838502\pi$
$60$	−0.401924	+	0.696152i	−0.0518881	+	0.0898729i
$61$	−2.00000	+	2.00000i	−0.256074	+	0.256074i	−0.823455	−	0.567381i	$-0.807957\pi$
$61$	−2.00000	+	2.00000i	−0.256074	+	0.256074i	0.567381	+	0.823455i	$0.307957\pi$
$62$	−1.73205			−0.219971
$63$	1.09808	+	1.90192i	0.138345	+	0.239620i
$64$			2.26795i			0.283494i
$65$		−	0.607695i		−	0.0753753i
$66$	−0.866025	+	1.50000i	−0.106600	+	0.184637i
$67$		−	4.92820i		−	0.602076i	−0.953612	−	0.301038i	$-0.902667\pi$
$67$		−	4.92820i		−	0.602076i	0.953612	−	0.301038i	$-0.0973331\pi$
$68$	−4.73205	+	4.73205i	−0.573845	+	0.573845i
$69$	−4.73205	+	8.19615i	−0.569672	+	0.986701i
$70$	0.0717968	+	0.0717968i	0.00858136	+	0.00858136i
$71$	13.2679			1.57462			0.787308	−	0.616560i	$-0.211474\pi$
$71$	13.2679			1.57462			0.787308	+	0.616560i	$0.211474\pi$
$72$	−5.59808	−	1.50000i	−0.659740	−	0.176777i
$73$	−4.00000	−	4.00000i	−0.468165	−	0.468165i	0.433155	−	0.901319i	$-0.357400\pi$
$73$	−4.00000	−	4.00000i	−0.468165	−	0.468165i	−0.901319	+	0.433155i	$0.857400\pi$
$74$		−	2.53590i		−	0.294792i
$75$	−7.39230	−	4.26795i	−0.853590	−	0.492820i
$76$	3.00000	+	3.00000i	0.344124	+	0.344124i
$77$	−1.00000	−	1.00000i	−0.113961	−	0.113961i
$78$	1.96410	−	0.526279i	0.222391	−	0.0595894i
$79$	−6.83013	+	6.83013i	−0.768449	+	0.768449i	−0.977833	−	0.209384i	$-0.932854\pi$
$79$	−6.83013	+	6.83013i	−0.768449	+	0.768449i	0.209384	+	0.977833i	$0.432854\pi$
$80$	0.660254			0.0738186
$81$	−4.50000	+	7.79423i	−0.500000	+	0.866025i
$82$	−3.80385			−0.420065
$83$		−	13.8564i		−	1.52094i	−0.649374	−	0.760469i	$-0.724969\pi$
$83$		−	13.8564i		−	1.52094i	0.649374	−	0.760469i	$-0.275031\pi$
$84$	1.09808	−	1.90192i	0.119810	−	0.207517i
$85$	0.732051	+	0.732051i	0.0794021	+	0.0794021i
$86$	−6.26795			−0.675890
$87$	1.33013	−	9.23205i	0.142605	−	0.989780i
$88$	3.73205			0.397838
$89$	−5.00000	−	5.00000i	−0.529999	−	0.529999i	0.390573	−	0.920572i	$-0.372277\pi$
$89$	−5.00000	−	5.00000i	−0.529999	−	0.529999i	−0.920572	+	0.390573i	$0.872277\pi$
$90$	−0.107695	+	0.401924i	−0.0113521	+	0.0423665i
$91$			1.66025i			0.174042i
$92$	9.46410			0.986701
$93$	5.59808	−	1.50000i	0.580493	−	0.155543i
$94$	−5.73205			−0.591216
$95$	0.464102	−	0.464102i	0.0476158	−	0.0476158i
$96$	2.30385	+	8.59808i	0.235135	+	0.877537i
$97$	−4.26795	−	4.26795i	−0.433345	−	0.433345i	0.456420	−	0.889764i	$-0.349131\pi$
$97$	−4.26795	−	4.26795i	−0.433345	−	0.433345i	−0.889764	+	0.456420i	$0.849131\pi$
$98$	2.36603	+	2.36603i	0.239005	+	0.239005i
$99$	1.50000	−	5.59808i	0.150756	−	0.562628i
$100$			8.53590i			0.853590i
$101$	−6.19615	−	6.19615i	−0.616540	−	0.616540i	0.328102	−	0.944642i	$-0.393591\pi$
$101$	−6.19615	−	6.19615i	−0.616540	−	0.616540i	−0.944642	+	0.328102i	$0.893591\pi$
$102$	−1.73205	+	3.00000i	−0.171499	+	0.297044i
$103$	7.26795			0.716132			0.358066	−	0.933696i	$-0.383436\pi$
$103$	7.26795			0.716132			0.358066	+	0.933696i	$0.383436\pi$
$104$	−3.09808	−	3.09808i	−0.303791	−	0.303791i
$105$	−0.294229	−	0.169873i	−0.0287138	−	0.0165779i
$106$	3.63397	−	3.63397i	0.352963	−	0.352963i
$107$			8.73205i			0.844159i	0.906559	+	0.422080i	$0.138700\pi$
$107$			8.73205i			0.844159i	−0.906559	+	0.422080i	$0.861300\pi$
$108$	9.00000			0.866025
$109$			7.00000i			0.670478i	0.942133	+	0.335239i	$0.108817\pi$
$109$			7.00000i			0.670478i	−0.942133	+	0.335239i	$0.891183\pi$
$110$		−	0.267949i		−	0.0255480i
$111$	2.19615	+	8.19615i	0.208450	+	0.777944i
$112$	−1.80385			−0.170448
$113$	−7.92820	+	7.92820i	−0.745823	+	0.745823i	−0.973692	−	0.227869i	$-0.926824\pi$
$113$	−7.92820	+	7.92820i	−0.745823	+	0.745823i	0.227869	+	0.973692i	$0.426824\pi$
$114$	1.90192	+	1.09808i	0.178131	+	0.102844i
$115$		−	1.46410i		−	0.136528i
$116$	−8.66025	+	3.46410i	−0.804084	+	0.321634i
$117$	−5.89230	+	3.40192i	−0.544744	+	0.314508i
$118$	2.73205	−	2.73205i	0.251506	−	0.251506i
$119$	−2.00000	−	2.00000i	−0.183340	−	0.183340i
$120$	0.866025	−	0.232051i	0.0790569	−	0.0211832i
$121$		−	7.26795i		−	0.660723i
$122$	1.46410			0.132554
$123$	12.2942	−	3.29423i	1.10853	−	0.297031i
$124$	−4.09808	−	4.09808i	−0.368018	−	0.368018i
$125$	2.66025			0.237940
$126$	0.294229	−	1.09808i	0.0262120	−	0.0978244i
$127$	9.00000	−	9.00000i	0.798621	−	0.798621i	−0.184257	−	0.982878i	$-0.558988\pi$
$127$	9.00000	−	9.00000i	0.798621	−	0.798621i	0.982878	+	0.184257i	$0.0589879\pi$
$128$	8.09808	−	8.09808i	0.715776	−	0.715776i
$129$	20.2583	−	5.42820i	1.78365	−	0.477927i
$130$	−0.222432	+	0.222432i	−0.0195086	+	0.0195086i
$131$	−9.39230	+	9.39230i	−0.820609	+	0.820609i	−0.986195	−	0.165586i	$-0.947048\pi$
$131$	−9.39230	+	9.39230i	−0.820609	+	0.820609i	0.165586	+	0.986195i	$0.447048\pi$
$132$	−5.59808	+	1.50000i	−0.487250	+	0.130558i
$133$	−1.26795	+	1.26795i	−0.109945	+	0.109945i
$134$	−1.80385	+	1.80385i	−0.155829	+	0.155829i
$135$		−	1.39230i		−	0.119831i
$136$	7.46410			0.640041
$137$	1.26795	+	1.26795i	0.108328	+	0.108328i	0.759193	−	0.650865i	$-0.225594\pi$
$137$	1.26795	+	1.26795i	0.108328	+	0.108328i	−0.650865	+	0.759193i	$0.725594\pi$
$138$	4.73205	−	1.26795i	0.402819	−	0.107935i
$139$	−4.53590			−0.384730			−0.192365	−	0.981323i	$-0.561616\pi$
$139$	−4.53590			−0.384730			−0.192365	+	0.981323i	$0.561616\pi$
$140$			0.339746i			0.0287138i
$141$	18.5263	−	4.96410i	1.56019	−	0.418053i
$142$	−4.85641	−	4.85641i	−0.407541	−	0.407541i
$143$	3.09808	−	3.09808i	0.259074	−	0.259074i
$144$	−3.69615	−	6.40192i	−0.308013	−	0.533494i
$145$	0.535898	+	1.33975i	0.0445039	+	0.111260i
$146$			2.92820i			0.242340i
$147$	−9.69615	−	5.59808i	−0.799725	−	0.461722i
$148$	6.00000	−	6.00000i	0.493197	−	0.493197i
$149$	−18.4641			−1.51264			−0.756319	−	0.654203i	$-0.773004\pi$
$149$	−18.4641			−1.51264			−0.756319	+	0.654203i	$0.773004\pi$
$150$	1.14359	+	4.26795i	0.0933740	+	0.348477i
$151$			11.6603i			0.948898i	0.880283	+	0.474449i	$0.157353\pi$
$151$			11.6603i			0.948898i	−0.880283	+	0.474449i	$0.842647\pi$
$152$		−	4.73205i		−	0.383820i
$153$	3.00000	−	11.1962i	0.242536	−	0.905155i
$154$			0.732051i			0.0589903i
$155$	−0.633975	+	0.633975i	−0.0509221	+	0.0509221i
$156$	5.89230	+	3.40192i	0.471762	+	0.272372i
$157$	12.4641	+	12.4641i	0.994744	+	0.994744i	0.999986	−	0.00524265i	$-0.00166880\pi$
$157$	12.4641	+	12.4641i	0.994744	+	0.994744i	−0.00524265	+	0.999986i	$0.501669\pi$
$158$	5.00000			0.397779
$159$	−8.59808	+	14.8923i	−0.681872	+	1.18104i
$160$	−0.973721	−	0.973721i	−0.0769794	−	0.0769794i
$161$			4.00000i			0.315244i
$162$	4.50000	−	1.20577i	0.353553	−	0.0947343i
$163$	3.90192	+	3.90192i	0.305622	+	0.305622i	0.843209	−	0.537586i	$-0.180664\pi$
$163$	3.90192	+	3.90192i	0.305622	+	0.305622i	−0.537586	+	0.843209i	$0.680664\pi$
$164$	−9.00000	−	9.00000i	−0.702782	−	0.702782i
$165$	0.232051	+	0.866025i	0.0180651	+	0.0674200i
$166$	−5.07180	+	5.07180i	−0.393648	+	0.393648i
$167$	6.73205			0.520942			0.260471	−	0.965482i	$-0.416122\pi$
$167$	6.73205			0.520942			0.260471	+	0.965482i	$0.416122\pi$
$168$	−2.36603	+	0.633975i	−0.182543	+	0.0489122i
$169$	7.85641			0.604339
$170$		−	0.535898i		−	0.0411015i
$171$	−7.09808	−	1.90192i	−0.542803	−	0.145444i
$172$	−14.8301	−	14.8301i	−1.13079	−	1.13079i
$173$	−6.53590			−0.496915			−0.248458	−	0.968643i	$-0.579924\pi$
$173$	−6.53590			−0.496915			−0.248458	+	0.968643i	$0.579924\pi$
$174$	−3.86603	+	2.89230i	−0.293083	+	0.219265i
$175$	−3.60770			−0.272716
$176$	3.36603	+	3.36603i	0.253724	+	0.253724i
$177$	−6.46410	+	11.1962i	−0.485872	+	0.841554i
$178$			3.66025i			0.274348i
$179$	14.5885			1.09039			0.545196	−	0.838308i	$-0.316455\pi$
$179$	14.5885			1.09039			0.545196	+	0.838308i	$0.316455\pi$
$180$	−1.20577	+	0.696152i	−0.0898729	+	0.0518881i
$181$	−18.3205			−1.36175			−0.680876	−	0.732398i	$-0.738401\pi$
$181$	−18.3205			−1.36175			−0.680876	+	0.732398i	$0.738401\pi$
$182$	0.607695	−	0.607695i	0.0450454	−	0.0450454i
$183$	−4.73205	+	1.26795i	−0.349803	+	0.0937295i
$184$	−7.46410	−	7.46410i	−0.550261	−	0.550261i
$185$	−0.928203	−	0.928203i	−0.0682429	−	0.0682429i
$186$	−2.59808	−	1.50000i	−0.190500	−	0.109985i
$187$			7.46410i			0.545829i
$188$	−13.5622	−	13.5622i	−0.989123	−	0.989123i
$189$			3.80385i			0.276689i
$190$	−0.339746			−0.0246478
$191$	−2.07180	−	2.07180i	−0.149910	−	0.149910i	0.628168	−	0.778078i	$-0.283805\pi$
$191$	−2.07180	−	2.07180i	−0.149910	−	0.149910i	−0.778078	+	0.628168i	$0.783805\pi$
$192$	−1.96410	+	3.40192i	−0.141747	+	0.245513i
$193$	3.92820	−	3.92820i	0.282758	−	0.282758i	−0.551450	−	0.834208i	$-0.685925\pi$
$193$	3.92820	−	3.92820i	0.282758	−	0.282758i	0.834208	+	0.551450i	$0.185925\pi$
$194$			3.12436i			0.224316i
$195$	0.526279	−	0.911543i	0.0376877	−	0.0652769i
$196$			11.1962i			0.799725i
$197$			11.0718i			0.788833i	0.918932	+	0.394416i	$0.129053\pi$
$197$			11.0718i			0.788833i	−0.918932	+	0.394416i	$0.870947\pi$
$198$	−2.59808	+	1.50000i	−0.184637	+	0.106600i
$199$	−0.732051			−0.0518937			−0.0259469	−	0.999663i	$-0.508260\pi$
$199$	−0.732051			−0.0518937			−0.0259469	+	0.999663i	$0.508260\pi$
$200$	6.73205	−	6.73205i	0.476028	−	0.476028i
$201$	4.26795	−	7.39230i	0.301038	−	0.521413i
$202$			4.53590i			0.319145i
$203$	−1.46410	−	3.66025i	−0.102760	−	0.256899i
$204$	−11.1962	+	3.00000i	−0.783887	+	0.210042i
$205$	−1.39230	+	1.39230i	−0.0972428	+	0.0972428i
$206$	−2.66025	−	2.66025i	−0.185349	−	0.185349i
$207$	−14.1962	+	8.19615i	−0.986701	+	0.569672i
$208$		−	5.58846i		−	0.387490i
$209$	4.73205			0.327323
$210$	0.0455173	+	0.169873i	0.00314099	+	0.0117223i
$211$	−5.02628	−	5.02628i	−0.346023	−	0.346023i	0.512603	−	0.858626i	$-0.328681\pi$
$211$	−5.02628	−	5.02628i	−0.346023	−	0.346023i	−0.858626	+	0.512603i	$0.828681\pi$
$212$	17.1962			1.18104
$213$	19.9019	+	11.4904i	1.36366	+	0.787308i
$214$	3.19615	−	3.19615i	0.218484	−	0.218484i
$215$	−2.29423	+	2.29423i	−0.156465	+	0.156465i
$216$	−7.09808	−	7.09808i	−0.482963	−	0.482963i
$217$	1.73205	−	1.73205i	0.117579	−	0.117579i
$218$	2.56218	−	2.56218i	0.173533	−	0.173533i
$219$	−2.53590	−	9.46410i	−0.171360	−	0.639525i
$220$	0.633975	−	0.633975i	0.0427426	−	0.0427426i
$221$	6.19615	−	6.19615i	0.416798	−	0.416798i
$222$	2.19615	−	3.80385i	0.147396	−	0.255298i
$223$	−2.73205			−0.182952			−0.0914758	−	0.995807i	$-0.529158\pi$
$223$	−2.73205			−0.182952			−0.0914758	+	0.995807i	$0.529158\pi$
$224$	2.66025	+	2.66025i	0.177746	+	0.177746i
$225$	−7.39230	−	12.8038i	−0.492820	−	0.853590i
$226$	5.80385			0.386066
$227$			15.1244i			1.00384i	0.864914	+	0.501919i	$0.167373\pi$
$227$			15.1244i			1.00384i	−0.864914	+	0.501919i	$0.832627\pi$
$228$	1.90192	+	7.09808i	0.125958	+	0.470082i
$229$	14.3205	+	14.3205i	0.946326	+	0.946326i	0.998631	−	0.0523053i	$-0.0166569\pi$
$229$	14.3205	+	14.3205i	0.946326	+	0.946326i	−0.0523053	+	0.998631i	$0.516657\pi$
$230$	−0.535898	+	0.535898i	−0.0353361	+	0.0353361i
$231$	−0.633975	−	2.36603i	−0.0417125	−	0.155673i
$232$	9.56218	+	4.09808i	0.627788	+	0.269052i
$233$		−	4.12436i		−	0.270196i	−0.990832	−	0.135098i	$-0.956865\pi$
$233$		−	4.12436i		−	0.270196i	0.990832	−	0.135098i	$-0.0431348\pi$
$234$	3.40192	+	0.911543i	0.222391	+	0.0595894i
$235$	−2.09808	+	2.09808i	−0.136863	+	0.136863i
$236$	12.9282			0.841554
$237$	−16.1603	+	4.33013i	−1.04972	+	0.281272i
$238$			1.46410i			0.0949036i
$239$			6.00000i			0.388108i	0.980991	+	0.194054i	$0.0621637\pi$
$239$			6.00000i			0.388108i	−0.980991	+	0.194054i	$0.937836\pi$
$240$	0.990381	+	0.571797i	0.0639288	+	0.0369093i
$241$		−	20.4641i		−	1.31821i	−0.752052	−	0.659104i	$-0.770936\pi$
$241$		−	20.4641i		−	1.31821i	0.752052	−	0.659104i	$-0.229064\pi$
$242$	−2.66025	+	2.66025i	−0.171008	+	0.171008i
$243$	−13.5000	+	7.79423i	−0.866025	+	0.500000i
$244$	3.46410	+	3.46410i	0.221766	+	0.221766i
$245$	1.73205			0.110657
$246$	−5.70577	−	3.29423i	−0.363787	−	0.210032i
$247$	−3.92820	−	3.92820i	−0.249946	−	0.249946i
$248$			6.46410i			0.410471i
$249$	12.0000	−	20.7846i	0.760469	−	1.31717i
$250$	−0.973721	−	0.973721i	−0.0615835	−	0.0615835i
$251$	12.3660	+	12.3660i	0.780537	+	0.780537i	0.979921	−	0.199385i	$-0.0638943\pi$
$251$	12.3660	+	12.3660i	0.780537	+	0.780537i	−0.199385	+	0.979921i	$0.563894\pi$
$252$	3.29423	−	1.90192i	0.207517	−	0.119810i
$253$	7.46410	−	7.46410i	0.469264	−	0.469264i
$254$	−6.58846			−0.413397
$255$	0.464102	+	1.73205i	0.0290632	+	0.108465i
$256$	−1.39230			−0.0870191
$257$			3.92820i			0.245035i	0.992466	+	0.122517i	$0.0390967\pi$
$257$			3.92820i			0.245035i	−0.992466	+	0.122517i	$0.960903\pi$
$258$	−9.40192	−	5.42820i	−0.585338	−	0.337945i
$259$	2.53590	+	2.53590i	0.157573	+	0.157573i
$260$	−1.05256			−0.0652769
$261$	9.99038	−	12.6962i	0.618389	−	0.785872i
$262$	6.87564			0.424779
$263$	−0.294229	−	0.294229i	−0.0181429	−	0.0181429i	0.697977	−	0.716120i	$-0.254084\pi$
$263$	−0.294229	−	0.294229i	−0.0181429	−	0.0181429i	−0.716120	+	0.697977i	$0.754084\pi$
$264$	5.59808	+	3.23205i	0.344538	+	0.198919i
$265$		−	2.66025i		−	0.163418i
$266$	0.928203			0.0569118
$267$	−3.16987	−	11.8301i	−0.193993	−	0.723992i
$268$	−8.53590			−0.521413
$269$	2.00000	−	2.00000i	0.121942	−	0.121942i	−0.643502	−	0.765444i	$-0.722519\pi$
$269$	2.00000	−	2.00000i	0.121942	−	0.121942i	0.765444	+	0.643502i	$0.222519\pi$
$270$	−0.509619	+	0.509619i	−0.0310144	+	0.0310144i
$271$	−15.8301	−	15.8301i	−0.961612	−	0.961612i	0.0376782	−	0.999290i	$-0.488004\pi$
$271$	−15.8301	−	15.8301i	−0.961612	−	0.961612i	−0.999290	+	0.0376782i	$0.988004\pi$
$272$	6.73205	+	6.73205i	0.408191	+	0.408191i
$273$	−1.43782	+	2.49038i	−0.0870210	+	0.150725i
$274$		−	0.928203i		−	0.0560748i
$275$	6.73205	+	6.73205i	0.405958	+	0.405958i
$276$	14.1962	+	8.19615i	0.854508	+	0.493350i
$277$	26.3923			1.58576			0.792880	−	0.609378i	$-0.208581\pi$
$277$	26.3923			1.58576			0.792880	+	0.609378i	$0.208581\pi$
$278$	1.66025	+	1.66025i	0.0995754	+	0.0995754i
$279$	9.69615	+	2.59808i	0.580493	+	0.155543i
$280$	0.267949	−	0.267949i	0.0160130	−	0.0160130i
$281$		−	1.73205i		−	0.103325i	−0.998665	−	0.0516627i	$-0.983548\pi$
$281$		−	1.73205i		−	0.103325i	0.998665	−	0.0516627i	$-0.0164521\pi$
$282$	−8.59808	−	4.96410i	−0.512008	−	0.295608i
$283$			6.00000i			0.356663i	0.983970	+	0.178331i	$0.0570699\pi$
$283$			6.00000i			0.356663i	−0.983970	+	0.178331i	$0.942930\pi$
$284$		−	22.9808i		−	1.36366i
$285$	1.09808	−	0.294229i	0.0650444	−	0.0174286i
$286$	−2.26795			−0.134107
$287$	3.80385	−	3.80385i	0.224534	−	0.224534i
$288$	−3.99038	+	14.8923i	−0.235135	+	0.877537i
$289$		−	2.07180i		−	0.121870i
$290$	0.294229	−	0.686533i	0.0172777	−	0.0403146i
$291$	−2.70577	−	10.0981i	−0.158615	−	0.591960i
$292$	−6.92820	+	6.92820i	−0.405442	+	0.405442i
$293$	8.12436	+	8.12436i	0.474630	+	0.474630i	0.903409	−	0.428779i	$-0.141056\pi$
$293$	8.12436	+	8.12436i	0.474630	+	0.474630i	−0.428779	+	0.903409i	$0.641056\pi$
$294$	1.50000	+	5.59808i	0.0874818	+	0.326486i
$295$		−	2.00000i		−	0.116445i
$296$	−9.46410			−0.550090
$297$	7.09808	−	7.09808i	0.411872	−	0.411872i
$298$	6.75833	+	6.75833i	0.391500	+	0.391500i
$299$	−12.3923			−0.716665
$300$	−7.39230	+	12.8038i	−0.426795	+	0.739230i
$301$	6.26795	−	6.26795i	0.361279	−	0.361279i
$302$	4.26795	−	4.26795i	0.245593	−	0.245593i
$303$	−3.92820	−	14.6603i	−0.225669	−	0.842210i
$304$	4.26795	−	4.26795i	0.244784	−	0.244784i
$305$	0.535898	−	0.535898i	0.0306855	−	0.0306855i
$306$	−5.19615	+	3.00000i	−0.297044	+	0.171499i
$307$	−23.4904	+	23.4904i	−1.34067	+	1.34067i	−0.445271	+	0.895396i	$0.646893\pi$
$307$	−23.4904	+	23.4904i	−1.34067	+	1.34067i	−0.895396	+	0.445271i	$0.853107\pi$
$308$	−1.73205	+	1.73205i	−0.0986928	+	0.0986928i
$309$	10.9019	+	6.29423i	0.620189	+	0.358066i
$310$	0.464102			0.0263592
$311$	−9.53590	−	9.53590i	−0.540731	−	0.540731i	0.383012	−	0.923743i	$-0.374887\pi$
$311$	−9.53590	−	9.53590i	−0.540731	−	0.540731i	−0.923743	+	0.383012i	$0.874887\pi$
$312$	−1.96410	−	7.33013i	−0.111195	−	0.414987i
$313$	−23.5885			−1.33330			−0.666649	−	0.745372i	$-0.732272\pi$
$313$	−23.5885			−1.33330			−0.666649	+	0.745372i	$0.732272\pi$
$314$		−	9.12436i		−	0.514917i
$315$	−0.294229	−	0.509619i	−0.0165779	−	0.0287138i
$316$	11.8301	+	11.8301i	0.665497	+	0.665497i
$317$	2.39230	−	2.39230i	0.134365	−	0.134365i	−0.636725	−	0.771091i	$-0.719712\pi$
$317$	2.39230	−	2.39230i	0.134365	−	0.134365i	0.771091	+	0.636725i	$0.219712\pi$
$318$	8.59808	−	2.30385i	0.482156	−	0.129193i
$319$	−4.09808	+	9.56218i	−0.229448	+	0.535379i
$320$		−	0.607695i		−	0.0339712i
$321$	−7.56218	+	13.0981i	−0.422080	+	0.731063i
$322$	1.46410	−	1.46410i	0.0815912	−	0.0815912i
$323$	9.46410			0.526597
$324$	13.5000	+	7.79423i	0.750000	+	0.433013i
$325$		−	11.1769i		−	0.619984i
$326$		−	2.85641i		−	0.158202i
$327$	−6.06218	+	10.5000i	−0.335239	+	0.580651i
$328$			14.1962i			0.783851i
$329$	5.73205	−	5.73205i	0.316018	−	0.316018i
$330$	0.232051	−	0.401924i	0.0127740	−	0.0221252i
$331$	−0.633975	−	0.633975i	−0.0348464	−	0.0348464i	0.689469	−	0.724315i	$-0.257844\pi$
$331$	−0.633975	−	0.633975i	−0.0348464	−	0.0348464i	−0.724315	+	0.689469i	$0.757844\pi$
$332$	−24.0000			−1.31717
$333$	−3.80385	+	14.1962i	−0.208450	+	0.777944i
$334$	−2.46410	−	2.46410i	−0.134830	−	0.134830i
$335$			1.32051i			0.0721471i
$336$	−2.70577	−	1.56218i	−0.147612	−	0.0852238i
$337$	−14.9282	−	14.9282i	−0.813191	−	0.813191i	0.171920	−	0.985111i	$-0.445003\pi$
$337$	−14.9282	−	14.9282i	−0.813191	−	0.813191i	−0.985111	+	0.171920i	$0.945003\pi$
$338$	−2.87564	−	2.87564i	−0.156414	−	0.156414i
$339$	−18.7583	+	5.02628i	−1.01881	+	0.272990i
$340$	1.26795	−	1.26795i	0.0687642	−	0.0687642i
$341$	−6.46410			−0.350051
$342$	1.90192	+	3.29423i	0.102844	+	0.178131i
$343$	−9.85641			−0.532196
$344$			23.3923i			1.26123i
$345$	1.26795	−	2.19615i	0.0682641	−	0.118237i
$346$	2.39230	+	2.39230i	0.128611	+	0.128611i
$347$	25.5167			1.36981			0.684903	−	0.728634i	$-0.259845\pi$
$347$	25.5167			1.36981			0.684903	+	0.728634i	$0.259845\pi$
$348$	−15.9904	−	2.30385i	−0.857174	−	0.123499i
$349$	9.33975			0.499945			0.249973	−	0.968253i	$-0.419578\pi$
$349$	9.33975			0.499945			0.249973	+	0.968253i	$0.419578\pi$
$350$	1.32051	+	1.32051i	0.0705841	+	0.0705841i
$351$	−11.7846			−0.629016
$352$		−	9.92820i		−	0.529175i
$353$	−32.7846			−1.74495			−0.872474	−	0.488660i	$-0.837486\pi$
$353$	−32.7846			−1.74495			−0.872474	+	0.488660i	$0.837486\pi$
$354$	6.46410	−	1.73205i	0.343563	−	0.0920575i
$355$	−3.55514			−0.188687
$356$	−8.66025	+	8.66025i	−0.458993	+	0.458993i
$357$	−1.26795	−	4.73205i	−0.0671070	−	0.250447i
$358$	−5.33975	−	5.33975i	−0.282214	−	0.282214i
$359$	−19.4904	−	19.4904i	−1.02866	−	1.02866i	−0.999577	−	0.0290861i	$-0.990740\pi$
$359$	−19.4904	−	19.4904i	−1.02866	−	1.02866i	−0.0290861	−	0.999577i	$-0.509260\pi$
$360$	1.50000	+	0.401924i	0.0790569	+	0.0211832i
$361$			13.0000i			0.684211i
$362$	6.70577	+	6.70577i	0.352448	+	0.352448i
$363$	6.29423	−	10.9019i	0.330361	−	0.572203i
$364$	2.87564			0.150725
$365$	1.07180	+	1.07180i	0.0561004	+	0.0561004i
$366$	2.19615	+	1.26795i	0.114795	+	0.0662768i
$367$	−14.4641	+	14.4641i	−0.755020	+	0.755020i	−0.975411	−	0.220392i	$-0.929266\pi$
$367$	−14.4641	+	14.4641i	−0.755020	+	0.755020i	0.220392	+	0.975411i	$0.429266\pi$
$368$		−	13.4641i		−	0.701865i
$369$	21.2942	+	5.70577i	1.10853	+	0.297031i
$370$			0.679492i			0.0353251i
$371$			7.26795i			0.377333i
$372$	−2.59808	−	9.69615i	−0.134704	−	0.502722i
$373$	−17.5359			−0.907974			−0.453987	−	0.891008i	$-0.649999\pi$
$373$	−17.5359			−0.907974			−0.453987	+	0.891008i	$0.649999\pi$
$374$	2.73205	−	2.73205i	0.141271	−	0.141271i
$375$	3.99038	+	2.30385i	0.206062	+	0.118970i
$376$			21.3923i			1.10322i
$377$	11.3397	−	4.53590i	0.584027	−	0.233611i
$378$	1.39230	−	1.39230i	0.0716124	−	0.0716124i
$379$	18.8564	−	18.8564i	0.968589	−	0.968589i	−0.0309329	−	0.999521i	$-0.509848\pi$
$379$	18.8564	−	18.8564i	0.968589	−	0.968589i	0.999521	+	0.0309329i	$0.00984783\pi$
$380$	−0.803848	−	0.803848i	−0.0412365	−	0.0412365i
$381$	21.2942	−	5.70577i	1.09094	−	0.292316i
$382$			1.51666i			0.0775991i
$383$	−12.7321			−0.650577			−0.325289	−	0.945615i	$-0.605461\pi$
$383$	−12.7321			−0.650577			−0.325289	+	0.945615i	$0.605461\pi$
$384$	19.1603	−	5.13397i	0.977768	−	0.261992i
$385$	0.267949	+	0.267949i	0.0136560	+	0.0136560i
$386$	−2.87564			−0.146366
$387$	35.0885	+	9.40192i	1.78365	+	0.477927i
$388$	−7.39230	+	7.39230i	−0.375287	+	0.375287i
$389$	−22.1962	+	22.1962i	−1.12539	+	1.12539i	−0.134472	+	0.990917i	$0.542934\pi$
$389$	−22.1962	+	22.1962i	−1.12539	+	1.12539i	−0.990917	+	0.134472i	$0.957066\pi$
$390$	−0.526279	+	0.141016i	−0.0266492	+	0.00714063i
$391$	14.9282	−	14.9282i	0.754952	−	0.754952i
$392$	8.83013	−	8.83013i	0.445989	−	0.445989i
$393$	−22.2224	+	5.95448i	−1.12097	+	0.300364i
$394$	4.05256	−	4.05256i	0.204165	−	0.204165i
$395$	1.83013	−	1.83013i	0.0920837	−	0.0920837i
$396$	−9.69615	−	2.59808i	−0.487250	−	0.130558i
$397$	26.3205			1.32099			0.660494	−	0.750831i	$-0.270347\pi$
$397$	26.3205			1.32099			0.660494	+	0.750831i	$0.270347\pi$
$398$	0.267949	+	0.267949i	0.0134311	+	0.0134311i
$399$	−3.00000	+	0.803848i	−0.150188	+	0.0402427i
$400$	12.1436			0.607180
$401$		−	29.7321i		−	1.48475i	−0.669986	−	0.742374i	$-0.733700\pi$
$401$		−	29.7321i		−	1.48475i	0.669986	−	0.742374i	$-0.266300\pi$
$402$	−4.26795	+	1.14359i	−0.212866	+	0.0570373i
$403$	5.36603	+	5.36603i	0.267301	+	0.267301i
$404$	−10.7321	+	10.7321i	−0.533939	+	0.533939i
$405$	1.20577	−	2.08846i	0.0599153	−	0.103776i
$406$	−0.803848	+	1.87564i	−0.0398943	+	0.0930867i
$407$		−	9.46410i		−	0.469118i
$408$	11.1962	+	6.46410i	0.554292	+	0.320021i
$409$	25.3923	−	25.3923i	1.25557	−	1.25557i	0.302382	−	0.953187i	$-0.402218\pi$
$409$	25.3923	−	25.3923i	1.25557	−	1.25557i	0.953187	−	0.302382i	$-0.0977817\pi$
$410$	1.01924			0.0503366
$411$	0.803848	+	3.00000i	0.0396509	+	0.147979i
$412$		−	12.5885i		−	0.620189i
$413$			5.46410i			0.268871i
$414$	8.19615	+	2.19615i	0.402819	+	0.107935i
$415$			3.71281i			0.182255i
$416$	−8.24167	+	8.24167i	−0.404081	+	0.404081i
$417$	−6.80385	−	3.92820i	−0.333186	−	0.192365i
$418$	−1.73205	−	1.73205i	−0.0847174	−	0.0847174i
$419$	−19.6603			−0.960466			−0.480233	−	0.877141i	$-0.659448\pi$
$419$	−19.6603			−0.960466			−0.480233	+	0.877141i	$0.659448\pi$
$420$	−0.294229	+	0.509619i	−0.0143569	+	0.0248669i
$421$	4.19615	+	4.19615i	0.204508	+	0.204508i	0.801928	−	0.597420i	$-0.203808\pi$
$421$	4.19615	+	4.19615i	0.204508	+	0.204508i	−0.597420	+	0.801928i	$0.703808\pi$
$422$			3.67949i			0.179115i
$423$	32.0885	+	8.59808i	1.56019	+	0.418053i
$424$	−13.5622	−	13.5622i	−0.658638	−	0.658638i
$425$	13.4641	+	13.4641i	0.653105	+	0.653105i
$426$	−3.07884	−	11.4904i	−0.149170	−	0.556711i
$427$	−1.46410	+	1.46410i	−0.0708528	+	0.0708528i
$428$	15.1244			0.731063
$429$	7.33013	−	1.96410i	0.353902	−	0.0948277i
$430$	1.67949			0.0809923
$431$		−	9.60770i		−	0.462786i	−0.972860	−	0.231393i	$-0.925672\pi$
$431$		−	9.60770i		−	0.462786i	0.972860	−	0.231393i	$-0.0743284\pi$
$432$		−	12.8038i		−	0.616025i
$433$	−1.46410	−	1.46410i	−0.0703602	−	0.0703602i	0.671051	−	0.741411i	$-0.265843\pi$
$433$	−1.46410	−	1.46410i	−0.0703602	−	0.0703602i	−0.741411	+	0.671051i	$0.765843\pi$
$434$	−1.26795			−0.0608635
$435$	−0.356406	+	2.47372i	−0.0170884	+	0.118606i
$436$	12.1244			0.580651
$437$	−9.46410	−	9.46410i	−0.452729	−	0.452729i
$438$	−2.53590	+	4.39230i	−0.121170	+	0.209872i
$439$		−	22.2487i		−	1.06187i	−0.847412	−	0.530937i	$-0.821840\pi$
$439$		−	22.2487i		−	1.06187i	0.847412	−	0.530937i	$-0.178160\pi$
$440$	−1.00000			−0.0476731
$441$	−9.69615	−	16.7942i	−0.461722	−	0.799725i
$442$	−4.53590			−0.215751
$443$	−4.07180	+	4.07180i	−0.193457	+	0.193457i	−0.797188	−	0.603731i	$-0.793680\pi$
$443$	−4.07180	+	4.07180i	−0.193457	+	0.193457i	0.603731	+	0.797188i	$0.293680\pi$
$444$	14.1962	−	3.80385i	0.673720	−	0.180523i
$445$	1.33975	+	1.33975i	0.0635100	+	0.0635100i
$446$	1.00000	+	1.00000i	0.0473514	+	0.0473514i
$447$	−27.6962	−	15.9904i	−1.30998	−	0.756319i
$448$			1.66025i			0.0784396i
$449$	26.8564	+	26.8564i	1.26743	+	1.26743i	0.947410	+	0.320022i	$0.103690\pi$
$449$	26.8564	+	26.8564i	1.26743	+	1.26743i	0.320022	+	0.947410i	$0.396310\pi$
$450$	−1.98076	+	7.39230i	−0.0933740	+	0.348477i
$451$	−14.1962			−0.668471
$452$	13.7321	+	13.7321i	0.645901	+	0.645901i
$453$	−10.0981	+	17.4904i	−0.474449	+	0.821770i
$454$	5.53590	−	5.53590i	0.259813	−	0.259813i
$455$		−	0.444864i		−	0.0208555i
$456$	4.09808	−	7.09808i	0.191910	−	0.332398i
$457$			20.2487i			0.947195i	0.880741	+	0.473597i	$0.157045\pi$
$457$			20.2487i			0.947195i	−0.880741	+	0.473597i	$0.842955\pi$
$458$		−	10.4833i		−	0.489854i
$459$	14.1962	−	14.1962i	0.662620	−	0.662620i
$460$	−2.53590			−0.118237
$461$	−10.8564	+	10.8564i	−0.505633	+	0.505633i	−0.913183	−	0.407550i	$-0.866383\pi$
$461$	−10.8564	+	10.8564i	−0.505633	+	0.505633i	0.407550	+	0.913183i	$0.366383\pi$
$462$	−0.633975	+	1.09808i	−0.0294952	+	0.0510871i
$463$			22.0000i			1.02243i	0.859454	+	0.511213i	$0.170804\pi$
$463$			22.0000i			1.02243i	−0.859454	+	0.511213i	$0.829196\pi$
$464$	4.92820	+	12.3205i	0.228786	+	0.571965i
$465$	−1.50000	+	0.401924i	−0.0695608	+	0.0186388i
$466$	−1.50962	+	1.50962i	−0.0699317	+	0.0699317i
$467$	−10.0981	−	10.0981i	−0.467283	−	0.467283i	0.433750	−	0.901033i	$-0.357190\pi$
$467$	−10.0981	−	10.0981i	−0.467283	−	0.467283i	−0.901033	+	0.433750i	$0.857190\pi$
$468$	5.89230	+	10.2058i	0.272372	+	0.471762i
$469$		−	3.60770i		−	0.166588i
$470$	1.53590			0.0708457
$471$	7.90192	+	29.4904i	0.364101	+	1.35885i
$472$	−10.1962	−	10.1962i	−0.469316	−	0.469316i
$473$	−23.3923			−1.07558
$474$	7.50000	+	4.33013i	0.344486	+	0.198889i
$475$	8.53590	−	8.53590i	0.391654	−	0.391654i
$476$	−3.46410	+	3.46410i	−0.158777	+	0.158777i
$477$	−25.7942	+	14.8923i	−1.18104	+	0.681872i
$478$	2.19615	−	2.19615i	0.100450	−	0.100450i
$479$	8.09808	−	8.09808i	0.370011	−	0.370011i	−0.497470	−	0.867481i	$-0.665738\pi$
$479$	8.09808	−	8.09808i	0.370011	−	0.370011i	0.867481	+	0.497470i	$0.165738\pi$
$480$	−0.617314	−	2.30385i	−0.0281764	−	0.105156i
$481$	−7.85641	+	7.85641i	−0.358221	+	0.358221i
$482$	−7.49038	+	7.49038i	−0.341178	+	0.341178i
$483$	−3.46410	+	6.00000i	−0.157622	+	0.273009i
$484$	−12.5885			−0.572203
$485$	1.14359	+	1.14359i	0.0519279	+	0.0519279i
$486$	7.79423	+	2.08846i	0.353553	+	0.0947343i
$487$	26.4449			1.19833			0.599166	−	0.800625i	$-0.295499\pi$
$487$	26.4449			1.19833			0.599166	+	0.800625i	$0.295499\pi$
$488$		−	5.46410i		−	0.247348i
$489$	2.47372	+	9.23205i	0.111866	+	0.417488i
$490$	−0.633975	−	0.633975i	−0.0286401	−	0.0286401i
$491$	16.4378	−	16.4378i	0.741829	−	0.741829i	−0.231101	−	0.972930i	$-0.574233\pi$
$491$	16.4378	−	16.4378i	0.741829	−	0.741829i	0.972930	+	0.231101i	$0.0742328\pi$
$492$	−5.70577	−	21.2942i	−0.257236	−	0.960018i
$493$	−8.19615	+	19.1244i	−0.369136	+	0.861318i
$494$			2.87564i			0.129381i
$495$	−0.401924	+	1.50000i	−0.0180651	+	0.0674200i
$496$	−5.83013	+	5.83013i	−0.261780	+	0.261780i
$497$	9.71281			0.435679
$498$	−12.0000	+	3.21539i	−0.537733	+	0.144085i
$499$			30.6410i			1.37168i	0.727752	+	0.685840i	$0.240565\pi$
$499$			30.6410i			1.37168i	−0.727752	+	0.685840i	$0.759435\pi$
$500$		−	4.60770i		−	0.206062i
$501$	10.0981	+	5.83013i	0.451149	+	0.260471i
$502$		−	9.05256i		−	0.404035i
$503$	22.8301	−	22.8301i	1.01795	−	1.01795i	0.0181090	−	0.999836i	$-0.494235\pi$
$503$	22.8301	−	22.8301i	1.01795	−	1.01795i	0.999836	−	0.0181090i	$-0.00576460\pi$
$504$	−4.09808	−	1.09808i	−0.182543	−	0.0489122i
$505$	1.66025	+	1.66025i	0.0738803	+	0.0738803i
$506$	−5.46410			−0.242909
$507$	11.7846	+	6.80385i	0.523373	+	0.302169i
$508$	−15.5885	−	15.5885i	−0.691626	−	0.691626i
$509$		−	41.6410i		−	1.84571i	−0.385153	−	0.922853i	$-0.625851\pi$
$509$		−	41.6410i		−	1.84571i	0.385153	−	0.922853i	$-0.374149\pi$
$510$	0.464102	−	0.803848i	0.0205508	−	0.0355950i
$511$	−2.92820	−	2.92820i	−0.129536	−	0.129536i
$512$	−15.6865	−	15.6865i	−0.693253	−	0.693253i
$513$	−9.00000	−	9.00000i	−0.397360	−	0.397360i
$514$	1.43782	−	1.43782i	0.0634196	−	0.0634196i
$515$	−1.94744			−0.0858145
$516$	−9.40192	−	35.0885i	−0.413897	−	1.54468i
$517$	−21.3923			−0.940832
$518$		−	1.85641i		−	0.0815658i
$519$	−9.80385	−	5.66025i	−0.430341	−	0.248458i
$520$	0.830127	+	0.830127i	0.0364035	+	0.0364035i
$521$	16.3205			0.715014			0.357507	−	0.933910i	$-0.383627\pi$
$521$	16.3205			0.715014			0.357507	+	0.933910i	$0.383627\pi$
$522$	−8.30385	+	0.990381i	−0.363450	+	0.0433478i
$523$	7.07180			0.309228			0.154614	−	0.987975i	$-0.450587\pi$
$523$	7.07180			0.309228			0.154614	+	0.987975i	$0.450587\pi$
$524$	16.2679	+	16.2679i	0.710669	+	0.710669i
$525$	−5.41154	−	3.12436i	−0.236179	−	0.136358i
$526$			0.215390i			0.00939146i
$527$	−12.9282			−0.563161
$528$	2.13397	+	7.96410i	0.0928693	+	0.346593i
$529$	−6.85641			−0.298105
$530$	−0.973721	+	0.973721i	−0.0422957	+	0.0422957i
$531$	−19.3923	+	11.1962i	−0.841554	+	0.485872i
$532$	2.19615	+	2.19615i	0.0952153	+	0.0952153i
$533$	11.7846	+	11.7846i	0.510448	+	0.510448i
$534$	−3.16987	+	5.49038i	−0.137174	+	0.237592i
$535$		−	2.33975i		−	0.101156i
$536$	6.73205	+	6.73205i	0.290780	+	0.290780i
$537$	21.8827	+	12.6340i	0.944308	+	0.545196i
$538$	−1.46410			−0.0631219
$539$	8.83013	+	8.83013i	0.380340	+	0.380340i
$540$	−2.41154			−0.103776
$541$	−18.7321	+	18.7321i	−0.805354	+	0.805354i	−0.983927	−	0.178573i	$-0.942852\pi$
$541$	−18.7321	+	18.7321i	−0.805354	+	0.805354i	0.178573	+	0.983927i	$0.442852\pi$
$542$			11.5885i			0.497767i
$543$	−27.4808	−	15.8660i	−1.17931	−	0.680876i
$544$		−	19.8564i		−	0.851336i
$545$		−	1.87564i		−	0.0803438i
$546$	1.43782	−	0.385263i	0.0615331	−	0.0164877i
$547$	−13.6603			−0.584070			−0.292035	−	0.956408i	$-0.594332\pi$
$547$	−13.6603			−0.584070			−0.292035	+	0.956408i	$0.594332\pi$
$548$	2.19615	−	2.19615i	0.0938150	−	0.0938150i
$549$	−8.19615	−	2.19615i	−0.349803	−	0.0937295i
$550$		−	4.92820i		−	0.210139i
$551$	12.1244	+	5.19615i	0.516515	+	0.221364i
$552$	−4.73205	−	17.6603i	−0.201409	−	0.751670i
$553$	−5.00000	+	5.00000i	−0.212622	+	0.212622i
$554$	−9.66025	−	9.66025i	−0.410425	−	0.410425i
$555$	−0.588457	−	2.19615i	−0.0249786	−	0.0932215i
$556$			7.85641i			0.333186i
$557$	36.9282			1.56470			0.782349	−	0.622840i	$-0.214021\pi$
$557$	36.9282			1.56470			0.782349	+	0.622840i	$0.214021\pi$
$558$	−2.59808	−	4.50000i	−0.109985	−	0.190500i
$559$	19.4186	+	19.4186i	0.821319	+	0.821319i
$560$	0.483340			0.0204248
$561$	−6.46410	+	11.1962i	−0.272915	+	0.472702i
$562$	−0.633975	+	0.633975i	−0.0267426	+	0.0267426i
$563$	−16.9545	+	16.9545i	−0.714546	+	0.714546i	−0.967483	−	0.252937i	$-0.918604\pi$
$563$	−16.9545	+	16.9545i	−0.714546	+	0.714546i	0.252937	+	0.967483i	$0.418604\pi$
$564$	−8.59808	−	32.0885i	−0.362044	−	1.35117i
$565$	2.12436	−	2.12436i	0.0893723	−	0.0893723i
$566$	2.19615	−	2.19615i	0.0923112	−	0.0923112i
$567$	−3.29423	+	5.70577i	−0.138345	+	0.239620i
$568$	−18.1244	+	18.1244i	−0.760481	+	0.760481i
$569$	−25.7846	+	25.7846i	−1.08095	+	1.08095i	−0.0845258	+	0.996421i	$0.526938\pi$
$569$	−25.7846	+	25.7846i	−1.08095	+	1.08095i	−0.996421	+	0.0845258i	$0.973062\pi$
$570$	−0.509619	−	0.294229i	−0.0213456	−	0.0123239i
$571$		0			0			−	1.00000i	$-0.5\pi$
$571$		0			0				1.00000i	$0.5\pi$
$572$	−5.36603	−	5.36603i	−0.224365	−	0.224365i
$573$	−1.31347	−	4.90192i	−0.0548709	−	0.204781i
$574$	−2.78461			−0.116227
$575$		−	26.9282i		−	1.12298i
$576$	−5.89230	+	3.40192i	−0.245513	+	0.141747i
$577$	−8.39230	−	8.39230i	−0.349376	−	0.349376i	0.510501	−	0.859877i	$-0.329460\pi$
$577$	−8.39230	−	8.39230i	−0.349376	−	0.349376i	−0.859877	+	0.510501i	$0.829460\pi$
$578$	−0.758330	+	0.758330i	−0.0315424	+	0.0315424i
$579$	9.29423	−	2.49038i	0.386255	−	0.103497i
$580$	2.32051	−	0.928203i	0.0963539	−	0.0385415i
$581$		−	10.1436i		−	0.420827i
$582$	−2.70577	+	4.68653i	−0.112158	+	0.194263i
$583$	13.5622	−	13.5622i	0.561688	−	0.561688i
$584$	10.9282			0.452212
$585$	1.57884	−	0.911543i	0.0652769	−	0.0376877i
$586$		−	5.94744i		−	0.245687i
$587$			42.3923i			1.74972i	0.484378	+	0.874859i	$0.339046\pi$
$587$			42.3923i			1.74972i	−0.484378	+	0.874859i	$0.660954\pi$
$588$	−9.69615	+	16.7942i	−0.399863	+	0.692582i
$589$			8.19615i			0.337717i
$590$	−0.732051	+	0.732051i	−0.0301381	+	0.0301381i
$591$	−9.58846	+	16.6077i	−0.394416	+	0.683149i
$592$	−8.53590	−	8.53590i	−0.350823	−	0.350823i
$593$	−0.607695			−0.0249550			−0.0124775	−	0.999922i	$-0.503972\pi$
$593$	−0.607695			−0.0249550			−0.0124775	+	0.999922i	$0.503972\pi$
$594$	−5.19615			−0.213201
$595$	0.535898	+	0.535898i	0.0219697	+	0.0219697i
$596$			31.9808i			1.30998i
$597$	−1.09808	−	0.633975i	−0.0449413	−	0.0259469i
$598$	4.53590	+	4.53590i	0.185487	+	0.185487i
$599$	12.5622	+	12.5622i	0.513277	+	0.513277i	0.915529	−	0.402252i	$-0.131773\pi$
$599$	12.5622	+	12.5622i	0.513277	+	0.513277i	−0.402252	+	0.915529i	$0.631773\pi$
$600$	15.9282	−	4.26795i	0.650266	−	0.174238i
$601$	9.58846	−	9.58846i	0.391121	−	0.391121i	−0.483966	−	0.875087i	$-0.660804\pi$
$601$	9.58846	−	9.58846i	0.391121	−	0.391121i	0.875087	+	0.483966i	$0.160804\pi$
$602$	−4.58846			−0.187012
$603$	12.8038	−	7.39230i	0.521413	−	0.301038i
$604$	20.1962			0.821770
$605$			1.94744i			0.0791747i
$606$	−3.92820	+	6.80385i	−0.159572	+	0.276387i
$607$	15.6340	+	15.6340i	0.634563	+	0.634563i	0.949209	−	0.314646i	$-0.101886\pi$
$607$	15.6340	+	15.6340i	0.634563	+	0.634563i	−0.314646	+	0.949209i	$0.601886\pi$
$608$	−12.5885			−0.510529
$609$	0.973721	−	6.75833i	0.0394571	−	0.273861i
$610$	−0.392305			−0.0158840
$611$	17.7583	+	17.7583i	0.718425	+	0.718425i
$612$	−19.3923	−	5.19615i	−0.783887	−	0.210042i
$613$			21.7846i			0.879872i	0.898029	+	0.439936i	$0.144999\pi$
$613$			21.7846i			0.879872i	−0.898029	+	0.439936i	$0.855001\pi$
$614$	17.1962			0.693980
$615$	−3.29423	+	0.882686i	−0.132836	+	0.0355933i
$616$	2.73205			0.110077
$617$	26.1962	−	26.1962i	1.05462	−	1.05462i	0.0561977	−	0.998420i	$-0.482102\pi$
$617$	26.1962	−	26.1962i	1.05462	−	1.05462i	0.998420	−	0.0561977i	$-0.0178977\pi$
$618$	−1.68653	−	6.29423i	−0.0678423	−	0.253191i
$619$	−18.6865	−	18.6865i	−0.751075	−	0.751075i	0.223605	−	0.974680i	$-0.428218\pi$
$619$	−18.6865	−	18.6865i	−0.751075	−	0.751075i	−0.974680	+	0.223605i	$0.928218\pi$
$620$	1.09808	+	1.09808i	0.0440998	+	0.0440998i
$621$	−28.3923			−1.13934
$622$			6.98076i			0.279903i
$623$	−3.66025	−	3.66025i	−0.146645	−	0.146645i
$624$	4.83975	−	8.38269i	0.193745	−	0.335576i
$625$	23.9282			0.957128
$626$	8.63397	+	8.63397i	0.345083	+	0.345083i
$627$	7.09808	+	4.09808i	0.283470	+	0.163661i
$628$	21.5885	−	21.5885i	0.861473	−	0.861473i
$629$		−	18.9282i		−	0.754717i
$630$	−0.0788383	+	0.294229i	−0.00314099	+	0.0117223i
$631$		−	8.58846i		−	0.341901i	−0.985280	−	0.170951i	$-0.945316\pi$
$631$		−	8.58846i		−	0.341901i	0.985280	−	0.170951i	$-0.0546838\pi$
$632$		−	18.6603i		−	0.742265i
$633$	−3.18653	−	11.8923i	−0.126653	−	0.472677i
$634$	−1.75129			−0.0695526
$635$	−2.41154	+	2.41154i	−0.0956992	+	0.0956992i
$636$	25.7942	+	14.8923i	1.02281	+	0.590518i
$637$		−	14.6603i		−	0.580860i
$638$	5.00000	−	2.00000i	0.197952	−	0.0791808i
$639$	19.9019	+	34.4711i	0.787308	+	1.36366i
$640$	−2.16987	+	2.16987i	−0.0857718	+	0.0857718i
$641$	−8.05256	−	8.05256i	−0.318057	−	0.318057i	0.529963	−	0.848020i	$-0.322206\pi$
$641$	−8.05256	−	8.05256i	−0.318057	−	0.318057i	−0.848020	+	0.529963i	$0.822206\pi$
$642$	7.56218	−	2.02628i	0.298455	−	0.0799709i
$643$		−	46.4449i		−	1.83161i	−0.401627	−	0.915803i	$-0.631555\pi$
$643$		−	46.4449i		−	1.83161i	0.401627	−	0.915803i	$-0.368445\pi$
$644$	6.92820			0.273009
$645$	−5.42820	+	1.45448i	−0.213735	+	0.0572702i
$646$	−3.46410	−	3.46410i	−0.136293	−	0.136293i
$647$	−17.8564			−0.702008			−0.351004	−	0.936374i	$-0.614160\pi$
$647$	−17.8564			−0.702008			−0.351004	+	0.936374i	$0.614160\pi$
$648$	−4.50000	−	16.7942i	−0.176777	−	0.659740i
$649$	10.1962	−	10.1962i	0.400234	−	0.400234i
$650$	−4.09103	+	4.09103i	−0.160464	+	0.160464i
$651$	4.09808	−	1.09808i	0.160616	−	0.0430370i
$652$	6.75833	−	6.75833i	0.264677	−	0.264677i
$653$	11.3923	−	11.3923i	0.445815	−	0.445815i	−0.448145	−	0.893961i	$-0.647915\pi$
$653$	11.3923	−	11.3923i	0.445815	−	0.445815i	0.893961	+	0.448145i	$0.147915\pi$
$654$	6.06218	−	1.62436i	0.237050	−	0.0635173i
$655$	2.51666	−	2.51666i	0.0983341	−	0.0983341i
$656$	−12.8038	+	12.8038i	−0.499906	+	0.499906i
$657$	4.39230	−	16.3923i	0.171360	−	0.639525i
$658$	−4.19615			−0.163583
$659$	−16.7583	−	16.7583i	−0.652812	−	0.652812i	0.300857	−	0.953669i	$-0.402727\pi$
$659$	−16.7583	−	16.7583i	−0.652812	−	0.652812i	−0.953669	+	0.300857i	$0.902727\pi$
$660$	1.50000	−	0.401924i	0.0583874	−	0.0156449i
$661$	−5.60770			−0.218114			−0.109057	−	0.994035i	$-0.534783\pi$
$661$	−5.60770			−0.218114			−0.109057	+	0.994035i	$0.534783\pi$
$662$			0.464102i			0.0180378i
$663$	14.6603	−	3.92820i	0.569357	−	0.152559i
$664$	18.9282	+	18.9282i	0.734557	+	0.734557i
$665$	0.339746	−	0.339746i	0.0131748	−	0.0131748i
$666$	6.58846	−	3.80385i	0.255298	−	0.147396i
$667$	27.3205	−	10.9282i	1.05785	−	0.423142i
$668$		−	11.6603i		−	0.451149i
$669$	−4.09808	−	2.36603i	−0.158441	−	0.0914758i
$670$	0.483340	−	0.483340i	0.0186730	−	0.0186730i
$671$	5.46410			0.210939
$672$	1.68653	+	6.29423i	0.0650594	+	0.242805i
$673$			24.3205i			0.937487i	0.883334	+	0.468743i	$0.155293\pi$
$673$			24.3205i			0.937487i	−0.883334	+	0.468743i	$0.844707\pi$
$674$			10.9282i			0.420939i
$675$		−	25.6077i		−	0.985641i
$676$		−	13.6077i		−	0.523373i
$677$	23.0526	−	23.0526i	0.885982	−	0.885982i	−0.108153	−	0.994134i	$-0.534493\pi$
$677$	23.0526	−	23.0526i	0.885982	−	0.885982i	0.994134	+	0.108153i	$0.0344935\pi$
$678$	8.70577	+	5.02628i	0.334343	+	0.193033i
$679$	−3.12436	−	3.12436i	−0.119902	−	0.119902i
$680$	−2.00000			−0.0766965
$681$	−13.0981	+	22.6865i	−0.501919	+	0.869350i
$682$	2.36603	+	2.36603i	0.0905998	+	0.0905998i
$683$		−	0.928203i		−	0.0355167i	−0.999842	−	0.0177584i	$-0.994347\pi$
$683$		−	0.928203i		−	0.0355167i	0.999842	−	0.0177584i	$-0.00565296\pi$
$684$	−3.29423	+	12.2942i	−0.125958	+	0.470082i
$685$	−0.339746	−	0.339746i	−0.0129810	−	0.0129810i
$686$	3.60770	+	3.60770i	0.137742	+	0.137742i
$687$	9.07884	+	33.8827i	0.346379	+	1.29271i
$688$	−21.0981	+	21.0981i	−0.804357	+	0.804357i
$689$	−22.5167			−0.857816
$690$	−1.26795	+	0.339746i	−0.0482700	+	0.0129339i
$691$	29.7128			1.13033			0.565164	−	0.824978i	$-0.308813\pi$
$691$	29.7128			1.13033			0.565164	+	0.824978i	$0.308813\pi$
$692$			11.3205i			0.430341i
$693$	1.09808	−	4.09808i	0.0417125	−	0.155673i
$694$	−9.33975	−	9.33975i	−0.354532	−	0.354532i
$695$	1.21539			0.0461024
$696$	10.7942	+	14.4282i	0.409154	+	0.546900i
$697$	−28.3923			−1.07544
$698$	−3.41858	−	3.41858i	−0.129395	−	0.129395i
$699$	3.57180	−	6.18653i	0.135098	−	0.233996i
$700$			6.24871i			0.236179i
$701$	−35.1051			−1.32590			−0.662951	−	0.748663i	$-0.730696\pi$
$701$	−35.1051			−1.32590			−0.662951	+	0.748663i	$0.730696\pi$
$702$	4.31347	+	4.31347i	0.162801	+	0.162801i
$703$	−12.0000			−0.452589
$704$	3.09808	−	3.09808i	0.116763	−	0.116763i
$705$	−4.96410	+	1.33013i	−0.186959	+	0.0500955i
$706$	12.0000	+	12.0000i	0.451626	+	0.451626i
$707$	−4.53590	−	4.53590i	−0.170590	−	0.170590i
$708$	19.3923	+	11.1962i	0.728807	+	0.420777i
$709$		−	21.5885i		−	0.810772i	−0.914146	−	0.405386i	$-0.867137\pi$
$709$		−	21.5885i		−	0.810772i	0.914146	−	0.405386i	$-0.132863\pi$
$710$	1.30127	+	1.30127i	0.0488358	+	0.0488358i
$711$	−27.9904	−	7.50000i	−1.04972	−	0.281272i
$712$	13.6603			0.511940
$713$	12.9282	+	12.9282i	0.484165	+	0.484165i
$714$	−1.26795	+	2.19615i	−0.0474518	+	0.0821889i
$715$	−0.830127	+	0.830127i	−0.0310450	+	0.0310450i
$716$		−	25.2679i		−	0.944308i
$717$	−5.19615	+	9.00000i	−0.194054	+	0.336111i
$718$			14.2679i			0.532475i
$719$		−	3.94744i		−	0.147215i	−0.997287	−	0.0736074i	$-0.976549\pi$
$719$		−	3.94744i		−	0.147215i	0.997287	−	0.0736074i	$-0.0234512\pi$
$720$	0.990381	+	1.71539i	0.0369093	+	0.0639288i
$721$	5.32051			0.198146
$722$	4.75833	−	4.75833i	0.177087	−	0.177087i
$723$	17.7224	−	30.6962i	0.659104	−	1.14160i
$724$			31.7321i			1.17931i
$725$	9.85641	+	24.6410i	0.366058	+	0.915144i
$726$	−6.29423	+	1.68653i	−0.233601	+	0.0625931i
$727$	−0.320508	+	0.320508i	−0.0118870	+	0.0118870i	−0.713025	−	0.701138i	$-0.752676\pi$
$727$	−0.320508	+	0.320508i	−0.0118870	+	0.0118870i	0.701138	+	0.713025i	$0.252676\pi$
$728$	−2.26795	−	2.26795i	−0.0840558	−	0.0840558i
$729$	−27.0000			−1.00000
$730$		−	0.784610i		−	0.0290397i
$731$	−46.7846			−1.73039
$732$	2.19615	+	8.19615i	0.0811721	+	0.302939i
$733$	−20.9808	−	20.9808i	−0.774942	−	0.774942i	0.204024	−	0.978966i	$-0.434598\pi$
$733$	−20.9808	−	20.9808i	−0.774942	−	0.774942i	−0.978966	+	0.204024i	$0.934598\pi$
$734$	10.5885			0.390827
$735$	2.59808	+	1.50000i	0.0958315	+	0.0553283i
$736$	−19.8564	+	19.8564i	−0.731917	+	0.731917i
$737$	−6.73205	+	6.73205i	−0.247978	+	0.247978i
$738$	−5.70577	−	9.88269i	−0.210032	−	0.363787i
$739$	−17.6147	+	17.6147i	−0.647969	+	0.647969i	−0.952502	−	0.304533i	$-0.901500\pi$
$739$	−17.6147	+	17.6147i	−0.647969	+	0.647969i	0.304533	+	0.952502i	$0.401500\pi$
$740$	−1.60770	+	1.60770i	−0.0591000	+	0.0591000i
$741$	−2.49038	−	9.29423i	−0.0914864	−	0.341432i
$742$	2.66025	−	2.66025i	0.0976610	−	0.0976610i
$743$	−3.19615	+	3.19615i	−0.117255	+	0.117255i	−0.763300	−	0.646044i	$-0.776422\pi$
$743$	−3.19615	+	3.19615i	−0.117255	+	0.117255i	0.646044	+	0.763300i	$0.276422\pi$
$744$	−5.59808	+	9.69615i	−0.205235	+	0.355478i
$745$	4.94744			0.181260
$746$	6.41858	+	6.41858i	0.235001	+	0.235001i
$747$	36.0000	−	20.7846i	1.31717	−	0.760469i
$748$	12.9282			0.472702
$749$			6.39230i			0.233570i
$750$	−0.617314	−	2.30385i	−0.0225411	−	0.0841246i
$751$	−24.7128	−	24.7128i	−0.901783	−	0.901783i	0.0938070	−	0.995590i	$-0.470096\pi$
$751$	−24.7128	−	24.7128i	−0.901783	−	0.901783i	−0.995590	+	0.0938070i	$0.970096\pi$
$752$	−19.2942	+	19.2942i	−0.703588	+	0.703588i
$753$	7.83975	+	29.2583i	0.285696	+	1.06623i
$754$	−5.81089	−	2.49038i	−0.211620	−	0.0906943i
$755$		−	3.12436i		−	0.113707i
$756$	6.58846			0.239620
$757$	−28.5885	+	28.5885i	−1.03907	+	1.03907i	−0.0398599	+	0.999205i	$0.512691\pi$
$757$	−28.5885	+	28.5885i	−1.03907	+	1.03907i	−0.999205	+	0.0398599i	$0.987309\pi$
$758$	−13.8038			−0.501378
$759$	17.6603	−	4.73205i	0.641027	−	0.171763i
$760$			1.26795i			0.0459934i
$761$		−	43.7128i		−	1.58459i	−0.610139	−	0.792294i	$-0.708887\pi$
$761$		−	43.7128i		−	1.58459i	0.610139	−	0.792294i	$-0.291113\pi$
$762$	−9.88269	−	5.70577i	−0.358012	−	0.206698i
$763$			5.12436i			0.185514i
$764$	−3.58846	+	3.58846i	−0.129826	+	0.129826i
$765$	−0.803848	+	3.00000i	−0.0290632	+	0.108465i
$766$	4.66025	+	4.66025i	0.168382	+	0.168382i
$767$	−16.9282			−0.611242
$768$	−2.08846	−	1.20577i	−0.0753607	−	0.0435095i
$769$	8.19615	+	8.19615i	0.295561	+	0.295561i	0.839272	−	0.543711i	$-0.182981\pi$
$769$	8.19615	+	8.19615i	0.295561	+	0.295561i	−0.543711	+	0.839272i	$0.682981\pi$
$770$		−	0.196152i		−	0.00706884i
$771$	−3.40192	+	5.89230i	−0.122517	+	0.212206i
$772$	−6.80385	−	6.80385i	−0.244876	−	0.244876i
$773$	−3.00000	−	3.00000i	−0.107903	−	0.107903i	0.651094	−	0.758997i	$-0.274310\pi$
$773$	−3.00000	−	3.00000i	−0.107903	−	0.107903i	−0.758997	+	0.651094i	$0.774310\pi$
$774$	−9.40192	−	16.2846i	−0.337945	−	0.585338i
$775$	−11.6603	+	11.6603i	−0.418849	+	0.418849i
$776$	11.6603			0.418579
$777$	1.60770	+	6.00000i	0.0576757	+	0.215249i
$778$	16.2487			0.582545
$779$			18.0000i			0.644917i
$780$	−1.57884	−	0.911543i	−0.0565315	−	0.0326385i
$781$	−18.1244	−	18.1244i	−0.648540	−	0.648540i
$782$	−10.9282			−0.390792
$783$	25.9808	−	10.3923i	0.928477	−	0.371391i
$784$	15.9282			0.568864
$785$	−3.33975	−	3.33975i	−0.119201	−	0.119201i
$786$	10.3135	+	5.95448i	0.367869	+	0.212389i
$787$			13.5167i			0.481817i	0.970548	+	0.240908i	$0.0774454\pi$
$787$			13.5167i			0.481817i	−0.970548	+	0.240908i	$0.922555\pi$
$788$	19.1769			0.683149
$789$	−0.186533	−	0.696152i	−0.00664077	−	0.0247837i
$790$	−1.33975			−0.0476660
$791$	−5.80385	+	5.80385i	−0.206361	+	0.206361i
$792$	5.59808	+	9.69615i	0.198919	+	0.344538i
$793$	−4.53590	−	4.53590i	−0.161074	−	0.161074i
$794$	−9.63397	−	9.63397i	−0.341897	−	0.341897i
$795$	2.30385	−	3.99038i	0.0817091	−	0.141524i
$796$			1.26795i			0.0449413i
$797$	−1.60770	−	1.60770i	−0.0569475	−	0.0569475i	0.678060	−	0.735007i	$-0.262821\pi$
$797$	−1.60770	−	1.60770i	−0.0569475	−	0.0569475i	−0.735007	+	0.678060i	$0.762821\pi$
$798$	1.39230	+	0.803848i	0.0492871	+	0.0284559i
$799$	−42.7846			−1.51361
$800$	−17.9090	−	17.9090i	−0.633178	−	0.633178i
$801$	5.49038	−	20.4904i	0.193993	−	0.723992i
$802$	−10.8827	+	10.8827i	−0.384281	+	0.384281i
$803$			10.9282i			0.385648i
$804$	−12.8038	−	7.39230i	−0.451557	−	0.260706i
$805$		−	1.07180i		−	0.0377759i
$806$		−	3.92820i		−	0.138365i
$807$	4.73205	−	1.26795i	0.166576	−	0.0446339i
$808$	16.9282			0.595532
$809$	6.78461	−	6.78461i	0.238534	−	0.238534i	−0.577709	−	0.816243i	$-0.696053\pi$
$809$	6.78461	−	6.78461i	0.238534	−	0.238534i	0.816243	+	0.577709i	$0.196053\pi$
$810$	−1.20577	+	0.323085i	−0.0423665	+	0.0113521i
$811$		−	41.5167i		−	1.45785i	−0.684595	−	0.728924i	$-0.740021\pi$
$811$		−	41.5167i		−	1.45785i	0.684595	−	0.728924i	$-0.259979\pi$
$812$	−6.33975	+	2.53590i	−0.222481	+	0.0889926i
$813$	−10.0359	−	37.4545i	−0.351974	−	1.31359i
$814$	−3.46410	+	3.46410i	−0.121417	+	0.121417i
$815$	−1.04552	−	1.04552i	−0.0366229	−	0.0366229i
$816$	4.26795	+	15.9282i	0.149408	+	0.557599i
$817$			29.6603i			1.03768i
$818$	−18.5885			−0.649930
$819$	−4.31347	+	2.49038i	−0.150725	+	0.0870210i
$820$	2.41154	+	2.41154i	0.0842147	+	0.0842147i
$821$	−3.00000			−0.104701			−0.0523504	−	0.998629i	$-0.516671\pi$
$821$	−3.00000			−0.104701			−0.0523504	+	0.998629i	$0.516671\pi$
$822$	0.803848	−	1.39230i	0.0280374	−	0.0485622i
$823$	32.4641	−	32.4641i	1.13163	−	1.13163i	0.141721	−	0.989907i	$-0.454736\pi$
$823$	32.4641	−	32.4641i	1.13163	−	1.13163i	0.989907	−	0.141721i	$-0.0452635\pi$
$824$	−9.92820	+	9.92820i	−0.345865	+	0.345865i
$825$	4.26795	+	15.9282i	0.148591	+	0.554549i
$826$	2.00000	−	2.00000i	0.0695889	−	0.0695889i
$827$	−3.63397	+	3.63397i	−0.126366	+	0.126366i	−0.767461	−	0.641095i	$-0.778480\pi$
$827$	−3.63397	+	3.63397i	−0.126366	+	0.126366i	0.641095	+	0.767461i	$0.278480\pi$
$828$	14.1962	+	24.5885i	0.493350	+	0.854508i
$829$	0.196152	−	0.196152i	0.00681266	−	0.00681266i	−0.703692	−	0.710505i	$-0.748467\pi$
$829$	0.196152	−	0.196152i	0.00681266	−	0.00681266i	0.710505	+	0.703692i	$0.248467\pi$
$830$	1.35898	−	1.35898i	0.0471710	−	0.0471710i
$831$	39.5885	+	22.8564i	1.37331	+	0.792880i
$832$	−5.14359			−0.178322
$833$	17.6603	+	17.6603i	0.611892	+	0.611892i
$834$	1.05256	+	3.92820i	0.0364471	+	0.136023i
$835$	−1.80385			−0.0624247
$836$		−	8.19615i		−	0.283470i
$837$	12.2942	+	12.2942i	0.424951	+	0.424951i
$838$	7.19615	+	7.19615i	0.248587	+	0.248587i
$839$	8.90192	−	8.90192i	0.307329	−	0.307329i	−0.536544	−	0.843872i	$-0.680270\pi$
$839$	8.90192	−	8.90192i	0.307329	−	0.307329i	0.843872	+	0.536544i	$0.180270\pi$
$840$	0.633975	−	0.169873i	0.0218742	−	0.00586117i
$841$	−21.0000	+	20.0000i	−0.724138	+	0.689655i
$842$		−	3.07180i		−	0.105861i
$843$	1.50000	−	2.59808i	0.0516627	−	0.0894825i
$844$	−8.70577	+	8.70577i	−0.299665	+	0.299665i
$845$	−2.10512			−0.0724183
$846$	−8.59808	−	14.8923i	−0.295608	−	0.512008i
$847$		−	5.32051i		−	0.182815i
$848$		−	24.4641i		−	0.840101i
$849$	−5.19615	+	9.00000i	−0.178331	+	0.308879i
$850$		−	9.85641i		−	0.338072i
$851$	−18.9282	+	18.9282i	−0.648850	+	0.648850i
$852$	19.9019	−	34.4711i	0.681829	−	1.18096i
$853$	2.85641	+	2.85641i	0.0978015	+	0.0978015i	0.754315	−	0.656513i	$-0.227969\pi$
$853$	2.85641	+	2.85641i	0.0978015	+	0.0978015i	−0.656513	+	0.754315i	$0.727969\pi$
$854$	1.07180			0.0366761
$855$	1.90192	+	0.509619i	0.0650444	+	0.0174286i
$856$	−11.9282	−	11.9282i	−0.407698	−	0.407698i
$857$			2.32051i			0.0792670i	0.999214	+	0.0396335i	$0.0126190\pi$
$857$			2.32051i			0.0792670i	−0.999214	+	0.0396335i	$0.987381\pi$
$858$	−3.40192	−	1.96410i	−0.116140	−	0.0670533i
$859$	35.5429	+	35.5429i	1.21271	+	1.21271i	0.970132	+	0.242577i	$0.0779928\pi$
$859$	35.5429	+	35.5429i	1.21271	+	1.21271i	0.242577	+	0.970132i	$0.422007\pi$
$860$	3.97372	+	3.97372i	0.135503	+	0.135503i
$861$	9.00000	−	2.41154i	0.306719	−	0.0821852i
$862$	−3.51666	+	3.51666i	−0.119778	+	0.119778i
$863$	6.58846			0.224274			0.112137	−	0.993693i	$-0.464230\pi$
$863$	6.58846			0.224274			0.112137	+	0.993693i	$0.464230\pi$
$864$	−18.8827	+	18.8827i	−0.642402	+	0.642402i
$865$	1.75129			0.0595456
$866$			1.07180i			0.0364211i
$867$	1.79423	−	3.10770i	0.0609352	−	0.105543i
$868$	−3.00000	−	3.00000i	−0.101827	−	0.101827i
$869$	18.6603			0.633006
$870$	1.03590	−	0.774991i	0.0351202	−	0.0262746i
$871$	11.1769			0.378715
$872$	−9.56218	−	9.56218i	−0.323816	−	0.323816i
$873$	4.68653	−	17.4904i	0.158615	−	0.591960i
$874$			6.92820i			0.234350i
$875$	1.94744			0.0658355
$876$	−16.3923	+	4.39230i	−0.553845	+	0.148402i
$877$	25.7321			0.868910			0.434455	−	0.900694i	$-0.356941\pi$
$877$	25.7321			0.868910			0.434455	+	0.900694i	$0.356941\pi$
$878$	−8.14359	+	8.14359i	−0.274833	+	0.274833i
$879$	5.15064	+	19.2224i	0.173727	+	0.648357i
$880$	−0.901924	−	0.901924i	−0.0304038	−	0.0304038i
$881$	18.2679	+	18.2679i	0.615463	+	0.615463i	0.944364	−	0.328901i	$-0.106678\pi$
$881$	18.2679	+	18.2679i	0.615463	+	0.615463i	−0.328901	+	0.944364i	$0.606678\pi$
$882$	−2.59808	+	9.69615i	−0.0874818	+	0.326486i
$883$		−	8.87564i		−	0.298689i	−0.988785	−	0.149345i	$-0.952284\pi$
$883$		−	8.87564i		−	0.298689i	0.988785	−	0.149345i	$-0.0477164\pi$
$884$	−10.7321	−	10.7321i	−0.360958	−	0.360958i
$885$	1.73205	−	3.00000i	0.0582223	−	0.100844i
$886$	2.98076			0.100141
$887$	−4.49038	−	4.49038i	−0.150772	−	0.150772i	0.627691	−	0.778463i	$-0.284000\pi$
$887$	−4.49038	−	4.49038i	−0.150772	−	0.150772i	−0.778463	+	0.627691i	$0.784000\pi$
$888$	−14.1962	−	8.19615i	−0.476392	−	0.275045i
$889$	6.58846	−	6.58846i	0.220970	−	0.220970i
$890$		−	0.980762i		−	0.0328752i
$891$	16.7942	−	4.50000i	0.562628	−	0.150756i
$892$			4.73205i			0.158441i
$893$			27.1244i			0.907682i
$894$	4.28461	+	15.9904i	0.143299	+	0.534798i
$895$	−3.90897			−0.130662
$896$	5.92820	−	5.92820i	0.198047	−	0.198047i
$897$	−18.5885	−	10.7321i	−0.620651	−	0.358333i
$898$		−	19.6603i		−	0.656071i
$899$	−16.5622	−	7.09808i	−0.552380	−	0.236734i
$900$	−22.1769	+	12.8038i	−0.739230	+	0.426795i
$901$	27.1244	−	27.1244i	0.903643	−	0.903643i
$902$	5.19615	+	5.19615i	0.173013	+	0.173013i
$903$	14.8301	−	3.97372i	0.493516	−	0.132237i
$904$		−	21.6603i		−	0.720409i
$905$	4.90897			0.163180
$906$	10.0981	−	2.70577i	0.335486	−	0.0898932i
$907$	−7.92820	−	7.92820i	−0.263252	−	0.263252i	0.563122	−	0.826374i	$-0.309600\pi$
$907$	−7.92820	−	7.92820i	−0.263252	−	0.263252i	−0.826374	+	0.563122i	$0.809600\pi$
$908$	26.1962			0.869350
$909$	6.80385	−	25.3923i	0.225669	−	0.842210i
$910$	−0.162831	+	0.162831i	−0.00539781	+	0.00539781i
$911$	35.0788	−	35.0788i	1.16221	−	1.16221i	0.178224	−	0.983990i	$-0.442965\pi$
$911$	35.0788	−	35.0788i	1.16221	−	1.16221i	0.983990	−	0.178224i	$-0.0570351\pi$
$912$	10.0981	−	2.70577i	0.334381	−	0.0895970i
$913$	−18.9282	+	18.9282i	−0.626432	+	0.626432i
$914$	7.41154	−	7.41154i	0.245152	−	0.245152i
$915$	1.26795	−	0.339746i	0.0419171	−	0.0112317i
$916$	24.8038	−	24.8038i	0.819542	−	0.819542i
$917$	−6.87564	+	6.87564i	−0.227054	+	0.227054i
$918$	−10.3923			−0.342997
$919$	16.4449			0.542466			0.271233	−	0.962514i	$-0.412569\pi$
$919$	16.4449			0.542466			0.271233	+	0.962514i	$0.412569\pi$
$920$	2.00000	+	2.00000i	0.0659380	+	0.0659380i
$921$	−55.5788	+	14.8923i	−1.83138	+	0.490718i
$922$	7.94744			0.261735
$923$			30.0910i			0.990458i
$924$	−4.09808	+	1.09808i	−0.134817	+	0.0361241i
$925$	−17.0718	−	17.0718i	−0.561317	−	0.561317i
$926$	8.05256	−	8.05256i	0.264624	−	0.264624i
$927$	10.9019	+	18.8827i	0.358066	+	0.620189i
$928$	10.9019	−	25.4378i	0.357873	−	0.835037i
$929$		−	14.2487i		−	0.467485i	−0.972299	−	0.233743i	$-0.924903\pi$
$929$		−	14.2487i		−	0.467485i	0.972299	−	0.233743i	$-0.0750973\pi$
$930$	0.696152	+	0.401924i	0.0228277	+	0.0131796i
$931$	11.1962	−	11.1962i	0.366939	−	0.366939i
$932$	−7.14359			−0.233996
$933$	−6.04552	−	22.5622i	−0.197921	−	0.738653i
$934$			7.39230i			0.241884i
$935$		−	2.00000i		−	0.0654070i
$936$	3.40192	−	12.6962i	0.111195	−	0.414987i
$937$		−	22.1051i		−	0.722143i	−0.932538	−	0.361071i	$-0.882411\pi$
$937$		−	22.1051i		−	0.722143i	0.932538	−	0.361071i	$-0.117589\pi$
$938$	−1.32051	+	1.32051i	−0.0431161	+	0.0431161i
$939$	−35.3827	−	20.4282i	−1.15467	−	0.666649i
$940$	3.63397	+	3.63397i	0.118527	+	0.118527i
$941$	37.1962			1.21256			0.606280	−	0.795251i	$-0.292661\pi$
$941$	37.1962			1.21256			0.606280	+	0.795251i	$0.292661\pi$
$942$	7.90192	−	13.6865i	0.257459	−	0.445931i
$943$	28.3923	+	28.3923i	0.924581	+	0.924581i
$944$		−	18.3923i		−	0.598619i
$945$		−	1.01924i		−	0.0331558i
$946$	8.56218	+	8.56218i	0.278380	+	0.278380i
$947$	−15.9019	−	15.9019i	−0.516743	−	0.516743i	0.399841	−	0.916584i	$-0.369065\pi$
$947$	−15.9019	−	15.9019i	−0.516743	−	0.516743i	−0.916584	+	0.399841i	$0.869065\pi$
$948$	7.50000	+	27.9904i	0.243589	+	0.909085i
$949$	9.07180	−	9.07180i	0.294483	−	0.294483i
$950$	−6.24871			−0.202735
$951$	5.66025	−	1.51666i	0.183546	−	0.0491811i
$952$	5.46410			0.177093
$953$			23.5885i			0.764105i	0.924141	+	0.382053i	$0.124783\pi$
$953$			23.5885i			0.764105i	−0.924141	+	0.382053i	$0.875217\pi$
$954$	14.8923	+	3.99038i	0.482156	+	0.129193i
$955$	0.555136	+	0.555136i	0.0179638	+	0.0179638i
$956$	10.3923			0.336111
$957$	−14.4282	+	10.7942i	−0.466398	+	0.348928i
$958$	−5.92820			−0.191532
$959$	0.928203	+	0.928203i	0.0299732	+	0.0299732i
$960$	0.526279	−	0.911543i	0.0169856	−	0.0294199i
$961$			19.8038i			0.638834i
$962$	5.75129			0.185429
$963$	−22.6865	+	13.0981i	−0.731063	+	0.422080i
$964$	−35.4449			−1.14160
$965$	−1.05256	+	1.05256i	−0.0338831	+	0.0338831i
$966$	3.46410	−	0.928203i	0.111456	−	0.0298644i
$967$	20.8301	+	20.8301i	0.669852	+	0.669852i	0.957682	−	0.287830i	$-0.0929338\pi$
$967$	20.8301	+	20.8301i	0.669852	+	0.669852i	−0.287830	+	0.957682i	$0.592934\pi$
$968$	9.92820	+	9.92820i	0.319105	+	0.319105i
$969$	14.1962	+	8.19615i	0.456046	+	0.263298i
$970$		−	0.837169i		−	0.0268799i
$971$	−15.7846	−	15.7846i	−0.506552	−	0.506552i	0.406914	−	0.913466i	$-0.366605\pi$
$971$	−15.7846	−	15.7846i	−0.506552	−	0.506552i	−0.913466	+	0.406914i	$0.866605\pi$
$972$	13.5000	+	23.3827i	0.433013	+	0.750000i
$973$	−3.32051			−0.106451
$974$	−9.67949	−	9.67949i	−0.310151	−	0.310151i
$975$	9.67949	−	16.7654i	0.309992	−	0.536922i
$976$	4.92820	−	4.92820i	0.157748	−	0.157748i
$977$			21.0000i			0.671850i	0.941889	+	0.335925i	$0.109049\pi$
$977$			21.0000i			0.671850i	−0.941889	+	0.335925i	$0.890951\pi$
$978$	2.47372	−	4.28461i	0.0791009	−	0.137007i
$979$			13.6603i			0.436584i
$980$		−	3.00000i		−	0.0958315i
$981$	−18.1865	+	10.5000i	−0.580651	+	0.335239i
$982$	−12.0333			−0.383999
$983$	−1.68653	+	1.68653i	−0.0537921	+	0.0537921i	−0.733491	−	0.679699i	$-0.762110\pi$
$983$	−1.68653	+	1.68653i	−0.0537921	+	0.0537921i	0.679699	+	0.733491i	$0.262110\pi$
$984$	−12.2942	+	21.2942i	−0.391926	+	0.678835i
$985$		−	2.96668i		−	0.0945263i
$986$	10.0000	−	4.00000i	0.318465	−	0.127386i
$987$	13.5622	−	3.63397i	0.431689	−	0.115671i
$988$	−6.80385	+	6.80385i	−0.216459	+	0.216459i
$989$	46.7846	+	46.7846i	1.48766	+	1.48766i
$990$	0.696152	−	0.401924i	0.0221252	−	0.0127740i
$991$			40.1962i			1.27687i	0.769675	+	0.638436i	$0.220418\pi$
$991$			40.1962i			1.27687i	−0.769675	+	0.638436i	$0.779582\pi$
$992$	17.1962			0.545978
$993$	−0.401924	−	1.50000i	−0.0127547	−	0.0476011i
$994$	−3.55514	−	3.55514i	−0.112762	−	0.112762i
$995$	0.196152			0.00621845
$996$	−36.0000	−	20.7846i	−1.14070	−	0.658586i
$997$	−5.07180	+	5.07180i	−0.160625	+	0.160625i	−0.782844	−	0.622218i	$-0.786232\pi$
$997$	−5.07180	+	5.07180i	−0.160625	+	0.160625i	0.622218	+	0.782844i	$0.286232\pi$
$998$	11.2154	−	11.2154i	0.355017	−	0.355017i
$999$	−18.0000	+	18.0000i	−0.569495	+	0.569495i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	87.2.f.b.17.1	yes	4
3.2	odd	2		87.2.f.a.17.2	✓	4
29.12	odd	4		87.2.f.a.41.2	yes	4
87.41	even	4	inner	87.2.f.b.41.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.f.a.17.2	✓	4	3.2	odd	2
87.2.f.a.41.2	yes	4	29.12	odd	4
87.2.f.b.17.1	yes	4	1.1	even	1	trivial
87.2.f.b.41.1	yes	4	87.41	even	4	inner

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	87.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.366025 - 0.366025i) q^{2} +(1.50000 + 0.866025i) q^{3} -1.73205i q^{4} -0.267949 q^{5} +(-0.232051 - 0.866025i) q^{6} +0.732051 q^{7} +(-1.36603 + 1.36603i) q^{8} +(1.50000 + 2.59808i) q^{9} +(0.0980762 + 0.0980762i) q^{10} +(-1.36603 - 1.36603i) q^{11} +(1.50000 - 2.59808i) q^{12} +2.26795i q^{13} +(-0.267949 - 0.267949i) q^{14} +(-0.401924 - 0.232051i) q^{15} -2.46410 q^{16} +(-2.73205 - 2.73205i) q^{17} +(0.401924 - 1.50000i) q^{18} +(-1.73205 + 1.73205i) q^{19} +0.464102i q^{20} +(1.09808 + 0.633975i) q^{21} +1.00000i q^{22} +5.46410i q^{23} +(-3.23205 + 0.866025i) q^{24} -4.92820 q^{25} +(0.830127 - 0.830127i) q^{26} +5.19615i q^{27} -1.26795i q^{28} +(-2.00000 - 5.00000i) q^{29} +(0.0621778 + 0.232051i) q^{30} +(2.36603 - 2.36603i) q^{31} +(3.63397 + 3.63397i) q^{32} +(-0.866025 - 3.23205i) q^{33} +2.00000i q^{34} -0.196152 q^{35} +(4.50000 - 2.59808i) q^{36} +(3.46410 + 3.46410i) q^{37} +1.26795 q^{38} +(-1.96410 + 3.40192i) q^{39} +(0.366025 - 0.366025i) q^{40} +(5.19615 - 5.19615i) q^{41} +(-0.169873 - 0.633975i) q^{42} +(8.56218 - 8.56218i) q^{43} +(-2.36603 + 2.36603i) q^{44} +(-0.401924 - 0.696152i) q^{45} +(2.00000 - 2.00000i) q^{46} +(7.83013 - 7.83013i) q^{47} +(-3.69615 - 2.13397i) q^{48} -6.46410 q^{49} +(1.80385 + 1.80385i) q^{50} +(-1.73205 - 6.46410i) q^{51} +3.92820 q^{52} +9.92820i q^{53} +(1.90192 - 1.90192i) q^{54} +(0.366025 + 0.366025i) q^{55} +(-1.00000 + 1.00000i) q^{56} +(-4.09808 + 1.09808i) q^{57} +(-1.09808 + 2.56218i) q^{58} +7.46410i q^{59} +(-0.401924 + 0.696152i) q^{60} +(-2.00000 + 2.00000i) q^{61} -1.73205 q^{62} +(1.09808 + 1.90192i) q^{63} +2.26795i q^{64} -0.607695i q^{65} +(-0.866025 + 1.50000i) q^{66} -4.92820i q^{67} +(-4.73205 + 4.73205i) q^{68} +(-4.73205 + 8.19615i) q^{69} +(0.0717968 + 0.0717968i) q^{70} +13.2679 q^{71} +(-5.59808 - 1.50000i) q^{72} +(-4.00000 - 4.00000i) q^{73} -2.53590i q^{74} +(-7.39230 - 4.26795i) q^{75} +(3.00000 + 3.00000i) q^{76} +(-1.00000 - 1.00000i) q^{77} +(1.96410 - 0.526279i) q^{78} +(-6.83013 + 6.83013i) q^{79} +0.660254 q^{80} +(-4.50000 + 7.79423i) q^{81} -3.80385 q^{82} -13.8564i q^{83} +(1.09808 - 1.90192i) q^{84} +(0.732051 + 0.732051i) q^{85} -6.26795 q^{86} +(1.33013 - 9.23205i) q^{87} +3.73205 q^{88} +(-5.00000 - 5.00000i) q^{89} +(-0.107695 + 0.401924i) q^{90} +1.66025i q^{91} +9.46410 q^{92} +(5.59808 - 1.50000i) q^{93} -5.73205 q^{94} +(0.464102 - 0.464102i) q^{95} +(2.30385 + 8.59808i) q^{96} +(-4.26795 - 4.26795i) q^{97} +(2.36603 + 2.36603i) q^{98} +(1.50000 - 5.59808i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{2} + 6 q^{3} - 8 q^{5} + 6 q^{6} - 4 q^{7} - 2 q^{8} + 6 q^{9} - 10 q^{10} - 2 q^{11} + 6 q^{12} - 8 q^{14} - 12 q^{15} + 4 q^{16} - 4 q^{17} + 12 q^{18} - 6 q^{21} - 6 q^{24} + 8 q^{25} - 14 q^{26}+ \cdots + 6 q^{99}+O(q^{100}) \) 4 * q + 2 * q^2 + 6 * q^3 - 8 * q^5 + 6 * q^6 - 4 * q^7 - 2 * q^8 + 6 * q^9 - 10 * q^10 - 2 * q^11 + 6 * q^12 - 8 * q^14 - 12 * q^15 + 4 * q^16 - 4 * q^17 + 12 * q^18 - 6 * q^21 - 6 * q^24 + 8 * q^25 - 14 * q^26 - 8 * q^29 - 24 * q^30 + 6 * q^31 + 18 * q^32 + 20 * q^35 + 18 * q^36 + 12 * q^38 + 6 * q^39 - 2 * q^40 - 18 * q^42 + 10 * q^43 - 6 * q^44 - 12 * q^45 + 8 * q^46 + 14 * q^47 + 6 * q^48 - 12 * q^49 + 28 * q^50 - 12 * q^52 + 18 * q^54 - 2 * q^55 - 4 * q^56 - 6 * q^57 + 6 * q^58 - 12 * q^60 - 8 * q^61 - 6 * q^63 - 12 * q^68 - 12 * q^69 + 28 * q^70 + 60 * q^71 - 12 * q^72 - 16 * q^73 + 12 * q^75 + 12 * q^76 - 4 * q^77 - 6 * q^78 - 10 * q^79 - 32 * q^80 - 18 * q^81 - 36 * q^82 - 6 * q^84 - 4 * q^85 - 32 * q^86 - 12 * q^87 + 8 * q^88 - 20 * q^89 - 42 * q^90 + 24 * q^92 + 12 * q^93 - 16 * q^94 - 12 * q^95 + 30 * q^96 - 24 * q^97 + 6 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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