LMFDB - Embedded newform 882.2.h.l.79.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(67,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 4]))

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

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

chi := DirichletCharacter("882.67");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.h (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$7.04280545828$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{2} + 4 $ x^4 - 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			79.2
Root			$1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	882.79
Dual form			882.2.h.l.67.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(1.72474 + 0.158919i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.44949 q^{5} +(-0.724745 - 1.57313i) q^{6} +1.00000 q^{8} +(2.94949 + 0.548188i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(1.72474 + 0.158919i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.44949 q^{5} +(-0.724745 - 1.57313i) q^{6} +1.00000 q^{8} +(2.94949 + 0.548188i) q^{9} +(1.72474 + 2.98735i) q^{10} +2.00000 q^{11} +(-1.00000 + 1.41421i) q^{12} +(-2.44949 - 4.24264i) q^{13} +(-5.94949 - 0.548188i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(-1.00000 - 2.82843i) q^{18} +(3.72474 - 6.45145i) q^{19} +(1.72474 - 2.98735i) q^{20} +(-1.00000 - 1.73205i) q^{22} -1.00000 q^{23} +(1.72474 + 0.158919i) q^{24} +6.89898 q^{25} +(-2.44949 + 4.24264i) q^{26} +(5.00000 + 1.41421i) q^{27} +(-1.44949 + 2.51059i) q^{29} +(2.50000 + 5.42650i) q^{30} +(3.00000 - 5.19615i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.44949 + 0.317837i) q^{33} +(1.00000 - 1.73205i) q^{34} +(-1.94949 + 2.28024i) q^{36} +(3.89898 - 6.75323i) q^{37} -7.44949 q^{38} +(-3.55051 - 7.70674i) q^{39} -3.44949 q^{40} +(-4.89898 - 8.48528i) q^{41} +(1.44949 - 2.51059i) q^{43} +(-1.00000 + 1.73205i) q^{44} +(-10.1742 - 1.89097i) q^{45} +(0.500000 + 0.866025i) q^{46} +(-4.89898 - 8.48528i) q^{47} +(-0.724745 - 1.57313i) q^{48} +(-3.44949 - 5.97469i) q^{50} +(1.44949 + 3.14626i) q^{51} +4.89898 q^{52} +(0.550510 + 0.953512i) q^{53} +(-1.27526 - 5.03723i) q^{54} -6.89898 q^{55} +(7.44949 - 10.5352i) q^{57} +2.89898 q^{58} +(-1.00000 + 1.73205i) q^{59} +(3.44949 - 4.87832i) q^{60} +(5.72474 + 9.91555i) q^{61} -6.00000 q^{62} +1.00000 q^{64} +(8.44949 + 14.6349i) q^{65} +(-1.44949 - 3.14626i) q^{66} +(1.55051 - 2.68556i) q^{67} -2.00000 q^{68} +(-1.72474 - 0.158919i) q^{69} +9.89898 q^{71} +(2.94949 + 0.548188i) q^{72} +(1.44949 + 2.51059i) q^{73} -7.79796 q^{74} +(11.8990 + 1.09638i) q^{75} +(3.72474 + 6.45145i) q^{76} +(-4.89898 + 6.92820i) q^{78} +(-3.94949 - 6.84072i) q^{79} +(1.72474 + 2.98735i) q^{80} +(8.39898 + 3.23375i) q^{81} +(-4.89898 + 8.48528i) q^{82} +(1.00000 - 1.73205i) q^{83} +(-3.44949 - 5.97469i) q^{85} -2.89898 q^{86} +(-2.89898 + 4.09978i) q^{87} +2.00000 q^{88} +(-3.55051 + 6.14966i) q^{89} +(3.44949 + 9.75663i) q^{90} +(0.500000 - 0.866025i) q^{92} +(6.00000 - 8.48528i) q^{93} +(-4.89898 + 8.48528i) q^{94} +(-12.8485 + 22.2542i) q^{95} +(-1.00000 + 1.41421i) q^{96} +(-3.44949 + 5.97469i) q^{97} +(5.89898 + 1.09638i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 4 q^{5} + 2 q^{6} + 4 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 4 * q^5 + 2 * q^6 + 4 * q^8 + 2 * q^9	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 4 q^{5} + 2 q^{6} + 4 q^{8} + 2 q^{9} + 2 q^{10} + 8 q^{11} - 4 q^{12} - 14 q^{15} - 2 q^{16} + 4 q^{17} - 4 q^{18} + 10 q^{19} + 2 q^{20} - 4 q^{22} - 4 q^{23} + 2 q^{24} + 8 q^{25} + 20 q^{27} + 4 q^{29} + 10 q^{30} + 12 q^{31} - 2 q^{32} + 4 q^{33} + 4 q^{34} + 2 q^{36} - 4 q^{37} - 20 q^{38} - 24 q^{39} - 4 q^{40} - 4 q^{43} - 4 q^{44} - 26 q^{45} + 2 q^{46} + 2 q^{48} - 4 q^{50} - 4 q^{51} + 12 q^{53} - 10 q^{54} - 8 q^{55} + 20 q^{57} - 8 q^{58} - 4 q^{59} + 4 q^{60} + 18 q^{61} - 24 q^{62} + 4 q^{64} + 24 q^{65} + 4 q^{66} + 16 q^{67} - 8 q^{68} - 2 q^{69} + 20 q^{71} + 2 q^{72} - 4 q^{73} + 8 q^{74} + 28 q^{75} + 10 q^{76} - 6 q^{79} + 2 q^{80} + 14 q^{81} + 4 q^{83} - 4 q^{85} + 8 q^{86} + 8 q^{87} + 8 q^{88} - 24 q^{89} + 4 q^{90} + 2 q^{92} + 24 q^{93} - 22 q^{95} - 4 q^{96} - 4 q^{97} + 4 q^{99}+O(q^{100}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 4 * q^5 + 2 * q^6 + 4 * q^8 + 2 * q^9 + 2 * q^10 + 8 * q^11 - 4 * q^12 - 14 * q^15 - 2 * q^16 + 4 * q^17 - 4 * q^18 + 10 * q^19 + 2 * q^20 - 4 * q^22 - 4 * q^23 + 2 * q^24 + 8 * q^25 + 20 * q^27 + 4 * q^29 + 10 * q^30 + 12 * q^31 - 2 * q^32 + 4 * q^33 + 4 * q^34 + 2 * q^36 - 4 * q^37 - 20 * q^38 - 24 * q^39 - 4 * q^40 - 4 * q^43 - 4 * q^44 - 26 * q^45 + 2 * q^46 + 2 * q^48 - 4 * q^50 - 4 * q^51 + 12 * q^53 - 10 * q^54 - 8 * q^55 + 20 * q^57 - 8 * q^58 - 4 * q^59 + 4 * q^60 + 18 * q^61 - 24 * q^62 + 4 * q^64 + 24 * q^65 + 4 * q^66 + 16 * q^67 - 8 * q^68 - 2 * q^69 + 20 * q^71 + 2 * q^72 - 4 * q^73 + 8 * q^74 + 28 * q^75 + 10 * q^76 - 6 * q^79 + 2 * q^80 + 14 * q^81 + 4 * q^83 - 4 * q^85 + 8 * q^86 + 8 * q^87 + 8 * q^88 - 24 * q^89 + 4 * q^90 + 2 * q^92 + 24 * q^93 - 22 * q^95 - 4 * q^96 - 4 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	1.72474	+	0.158919i	0.995782	+	0.0917517i
$3$	1.72474	+	0.158919i	0.995782	+	0.0917517i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−3.44949			−1.54266			−0.771329	−	0.636436i	$-0.780408\pi$
$5$	−3.44949			−1.54266			−0.771329	+	0.636436i	$0.780408\pi$
$6$	−0.724745	−	1.57313i	−0.295876	−	0.642229i
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	2.94949	+	0.548188i	0.983163	+	0.182729i
$10$	1.72474	+	2.98735i	0.545412	+	0.944682i
$11$	2.00000			0.603023			0.301511	−	0.953463i	$-0.402509\pi$
$11$	2.00000			0.603023			0.301511	+	0.953463i	$0.402509\pi$
$12$	−1.00000	+	1.41421i	−0.288675	+	0.408248i
$13$	−2.44949	−	4.24264i	−0.679366	−	1.17670i	−0.975172	−	0.221449i	$-0.928921\pi$
$13$	−2.44949	−	4.24264i	−0.679366	−	1.17670i	0.295806	−	0.955248i	$-0.404412\pi$
$14$		0			0
$15$	−5.94949	−	0.548188i	−1.53615	−	0.141542i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	0.961436	−	0.275029i	$-0.0886875\pi$
$17$	1.00000	+	1.73205i	0.242536	+	0.420084i	−0.718900	+	0.695113i	$0.755354\pi$
$18$	−1.00000	−	2.82843i	−0.235702	−	0.666667i
$19$	3.72474	−	6.45145i	0.854515	−	1.48006i	−0.0225791	−	0.999745i	$-0.507188\pi$
$19$	3.72474	−	6.45145i	0.854515	−	1.48006i	0.877094	−	0.480318i	$-0.159479\pi$
$20$	1.72474	−	2.98735i	0.385665	−	0.667991i
$21$		0			0
$22$	−1.00000	−	1.73205i	−0.213201	−	0.369274i
$23$	−1.00000			−0.208514			−0.104257	−	0.994550i	$-0.533247\pi$
$23$	−1.00000			−0.208514			−0.104257	+	0.994550i	$0.533247\pi$
$24$	1.72474	+	0.158919i	0.352062	+	0.0324391i
$25$	6.89898			1.37980
$26$	−2.44949	+	4.24264i	−0.480384	+	0.832050i
$27$	5.00000	+	1.41421i	0.962250	+	0.272166i
$28$		0			0
$29$	−1.44949	+	2.51059i	−0.269163	+	0.466205i	−0.968646	−	0.248445i	$-0.920081\pi$
$29$	−1.44949	+	2.51059i	−0.269163	+	0.466205i	0.699483	+	0.714650i	$0.253414\pi$
$30$	2.50000	+	5.42650i	0.456435	+	0.990739i
$31$	3.00000	−	5.19615i	0.538816	−	0.933257i	−0.460152	−	0.887840i	$-0.652205\pi$
$31$	3.00000	−	5.19615i	0.538816	−	0.933257i	0.998968	−	0.0454165i	$-0.0144615\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	3.44949	+	0.317837i	0.600479	+	0.0553284i
$34$	1.00000	−	1.73205i	0.171499	−	0.297044i
$35$		0			0
$36$	−1.94949	+	2.28024i	−0.324915	+	0.380040i
$37$	3.89898	−	6.75323i	0.640988	−	1.11022i	−0.344224	−	0.938887i	$-0.611858\pi$
$37$	3.89898	−	6.75323i	0.640988	−	1.11022i	0.985213	−	0.171337i	$-0.0548086\pi$
$38$	−7.44949			−1.20847
$39$	−3.55051	−	7.70674i	−0.568537	−	1.23407i
$40$	−3.44949			−0.545412
$41$	−4.89898	−	8.48528i	−0.765092	−	1.32518i	−0.940198	−	0.340629i	$-0.889360\pi$
$41$	−4.89898	−	8.48528i	−0.765092	−	1.32518i	0.175106	−	0.984550i	$-0.443973\pi$
$42$		0			0
$43$	1.44949	−	2.51059i	0.221045	−	0.382861i	−0.734080	−	0.679062i	$-0.762387\pi$
$43$	1.44949	−	2.51059i	0.221045	−	0.382861i	0.955126	+	0.296201i	$0.0957199\pi$
$44$	−1.00000	+	1.73205i	−0.150756	+	0.261116i
$45$	−10.1742	−	1.89097i	−1.51669	−	0.281889i
$46$	0.500000	+	0.866025i	0.0737210	+	0.127688i
$47$	−4.89898	−	8.48528i	−0.714590	−	1.23771i	−0.963118	−	0.269081i	$-0.913280\pi$
$47$	−4.89898	−	8.48528i	−0.714590	−	1.23771i	0.248528	−	0.968625i	$-0.420053\pi$
$48$	−0.724745	−	1.57313i	−0.104608	−	0.227062i
$49$		0			0
$50$	−3.44949	−	5.97469i	−0.487832	−	0.844949i
$51$	1.44949	+	3.14626i	0.202969	+	0.440565i
$52$	4.89898			0.679366
$53$	0.550510	+	0.953512i	0.0756184	+	0.130975i	0.901355	−	0.433081i	$-0.142574\pi$
$53$	0.550510	+	0.953512i	0.0756184	+	0.130975i	−0.825737	+	0.564056i	$0.809240\pi$
$54$	−1.27526	−	5.03723i	−0.173540	−	0.685481i
$55$	−6.89898			−0.930258
$56$		0			0
$57$	7.44949	−	10.5352i	0.986709	−	1.39542i
$58$	2.89898			0.380655
$59$	−1.00000	+	1.73205i	−0.130189	+	0.225494i	−0.923749	−	0.382998i	$-0.874892\pi$
$59$	−1.00000	+	1.73205i	−0.130189	+	0.225494i	0.793560	+	0.608492i	$0.208225\pi$
$60$	3.44949	−	4.87832i	0.445327	−	0.629788i
$61$	5.72474	+	9.91555i	0.732978	+	1.26956i	0.955605	+	0.294652i	$0.0952037\pi$
$61$	5.72474	+	9.91555i	0.732978	+	1.26956i	−0.222626	+	0.974904i	$0.571463\pi$
$62$	−6.00000			−0.762001
$63$		0			0
$64$	1.00000			0.125000
$65$	8.44949	+	14.6349i	1.04803	+	1.81524i
$66$	−1.44949	−	3.14626i	−0.178420	−	0.387278i
$67$	1.55051	−	2.68556i	0.189425	−	0.328094i	−0.755634	−	0.654994i	$-0.772671\pi$
$67$	1.55051	−	2.68556i	0.189425	−	0.328094i	0.945059	+	0.326901i	$0.106004\pi$
$68$	−2.00000			−0.242536
$69$	−1.72474	−	0.158919i	−0.207635	−	0.0191316i
$70$		0			0
$71$	9.89898			1.17479			0.587396	−	0.809299i	$-0.300153\pi$
$71$	9.89898			1.17479			0.587396	+	0.809299i	$0.300153\pi$
$72$	2.94949	+	0.548188i	0.347601	+	0.0646046i
$73$	1.44949	+	2.51059i	0.169650	+	0.293842i	0.938297	−	0.345831i	$-0.112403\pi$
$73$	1.44949	+	2.51059i	0.169650	+	0.293842i	−0.768647	+	0.639673i	$0.779070\pi$
$74$	−7.79796			−0.906494
$75$	11.8990	+	1.09638i	1.37398	+	0.126599i
$76$	3.72474	+	6.45145i	0.427258	+	0.740032i
$77$		0			0
$78$	−4.89898	+	6.92820i	−0.554700	+	0.784465i
$79$	−3.94949	−	6.84072i	−0.444352	−	0.769641i	0.553655	−	0.832746i	$-0.313233\pi$
$79$	−3.94949	−	6.84072i	−0.444352	−	0.769641i	−0.998007	+	0.0631057i	$0.979899\pi$
$80$	1.72474	+	2.98735i	0.192832	+	0.333995i
$81$	8.39898	+	3.23375i	0.933220	+	0.359306i
$82$	−4.89898	+	8.48528i	−0.541002	+	0.937043i
$83$	1.00000	−	1.73205i	0.109764	−	0.190117i	−0.805910	−	0.592037i	$-0.798324\pi$
$83$	1.00000	−	1.73205i	0.109764	−	0.190117i	0.915675	+	0.401920i	$0.131657\pi$
$84$		0			0
$85$	−3.44949	−	5.97469i	−0.374150	−	0.648046i
$86$	−2.89898			−0.312605
$87$	−2.89898	+	4.09978i	−0.310803	+	0.439542i
$88$	2.00000			0.213201
$89$	−3.55051	+	6.14966i	−0.376353	+	0.651863i	−0.990529	−	0.137307i	$-0.956155\pi$
$89$	−3.55051	+	6.14966i	−0.376353	+	0.651863i	0.614175	+	0.789170i	$0.289489\pi$
$90$	3.44949	+	9.75663i	0.363608	+	1.02844i
$91$		0			0
$92$	0.500000	−	0.866025i	0.0521286	−	0.0902894i
$93$	6.00000	−	8.48528i	0.622171	−	0.879883i
$94$	−4.89898	+	8.48528i	−0.505291	+	0.875190i
$95$	−12.8485	+	22.2542i	−1.31823	+	2.28323i
$96$	−1.00000	+	1.41421i	−0.102062	+	0.144338i
$97$	−3.44949	+	5.97469i	−0.350243	+	0.606638i	−0.986292	−	0.165011i	$-0.947234\pi$
$97$	−3.44949	+	5.97469i	−0.350243	+	0.606638i	0.636049	+	0.771649i	$0.280568\pi$
$98$		0			0
$99$	5.89898	+	1.09638i	0.592870	+	0.110190i
$100$	−3.44949	+	5.97469i	−0.344949	+	0.597469i
$101$	−7.24745			−0.721148			−0.360574	−	0.932731i	$-0.617419\pi$
$101$	−7.24745			−0.721148			−0.360574	+	0.932731i	$0.617419\pi$
$102$	2.00000	−	2.82843i	0.198030	−	0.280056i
$103$	−14.0000			−1.37946			−0.689730	−	0.724066i	$-0.742271\pi$
$103$	−14.0000			−1.37946			−0.689730	+	0.724066i	$0.742271\pi$
$104$	−2.44949	−	4.24264i	−0.240192	−	0.416025i
$105$		0			0
$106$	0.550510	−	0.953512i	0.0534703	−	0.0926132i
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	−0.415432	−	0.909624i	$-0.636370\pi$
$107$	6.00000	−	10.3923i	0.580042	−	1.00466i	0.995474	−	0.0950377i	$-0.0302972\pi$
$108$	−3.72474	+	3.62302i	−0.358414	+	0.348625i
$109$	8.34847	+	14.4600i	0.799638	+	1.38501i	0.919852	+	0.392266i	$0.128309\pi$
$109$	8.34847	+	14.4600i	0.799638	+	1.38501i	−0.120213	+	0.992748i	$0.538358\pi$
$110$	3.44949	+	5.97469i	0.328896	+	0.569664i
$111$	7.79796	−	11.0280i	0.740150	−	1.04673i
$112$		0			0
$113$	7.94949	+	13.7689i	0.747825	+	1.29527i	0.948863	+	0.315688i	$0.102235\pi$
$113$	7.94949	+	13.7689i	0.747825	+	1.29527i	−0.201038	+	0.979583i	$0.564431\pi$
$114$	−12.8485	−	1.18386i	−1.20337	−	0.110879i
$115$	3.44949			0.321667
$116$	−1.44949	−	2.51059i	−0.134582	−	0.233102i
$117$	−4.89898	−	13.8564i	−0.452911	−	1.28103i
$118$	2.00000			0.184115
$119$		0			0
$120$	−5.94949	−	0.548188i	−0.543112	−	0.0500425i
$121$	−7.00000			−0.636364
$122$	5.72474	−	9.91555i	0.518294	−	0.897712i
$123$	−7.10102	−	15.4135i	−0.640277	−	1.38979i
$124$	3.00000	+	5.19615i	0.269408	+	0.466628i
$125$	−6.55051			−0.585895
$126$		0			0
$127$	−3.00000			−0.266207			−0.133103	−	0.991102i	$-0.542494\pi$
$127$	−3.00000			−0.266207			−0.133103	+	0.991102i	$0.542494\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	2.89898	−	4.09978i	0.255241	−	0.360965i
$130$	8.44949	−	14.6349i	0.741069	−	1.28357i
$131$	13.4495			1.17509			0.587544	−	0.809192i	$-0.300095\pi$
$131$	13.4495			1.17509			0.587544	+	0.809192i	$0.300095\pi$
$132$	−2.00000	+	2.82843i	−0.174078	+	0.246183i
$133$		0			0
$134$	−3.10102			−0.267887
$135$	−17.2474	−	4.87832i	−1.48442	−	0.419859i
$136$	1.00000	+	1.73205i	0.0857493	+	0.148522i
$137$	−11.7980			−1.00797			−0.503984	−	0.863713i	$-0.668133\pi$
$137$	−11.7980			−1.00797			−0.503984	+	0.863713i	$0.668133\pi$
$138$	0.724745	+	1.57313i	0.0616944	+	0.133914i
$139$	4.72474	+	8.18350i	0.400748	+	0.694115i	0.993816	−	0.111037i	$-0.0354171\pi$
$139$	4.72474	+	8.18350i	0.400748	+	0.694115i	−0.593069	+	0.805152i	$0.702084\pi$
$140$		0			0
$141$	−7.10102	−	15.4135i	−0.598014	−	1.29805i
$142$	−4.94949	−	8.57277i	−0.415352	−	0.719411i
$143$	−4.89898	−	8.48528i	−0.409673	−	0.709575i
$144$	−1.00000	−	2.82843i	−0.0833333	−	0.235702i
$145$	5.00000	−	8.66025i	0.415227	−	0.719195i
$146$	1.44949	−	2.51059i	0.119961	−	0.207778i
$147$		0			0
$148$	3.89898	+	6.75323i	0.320494	+	0.555112i
$149$	−6.00000			−0.491539			−0.245770	−	0.969328i	$-0.579041\pi$
$149$	−6.00000			−0.491539			−0.245770	+	0.969328i	$0.579041\pi$
$150$	−5.00000	−	10.8530i	−0.408248	−	0.886144i
$151$	−5.00000			−0.406894			−0.203447	−	0.979086i	$-0.565214\pi$
$151$	−5.00000			−0.406894			−0.203447	+	0.979086i	$0.565214\pi$
$152$	3.72474	−	6.45145i	0.302117	−	0.523281i
$153$	2.00000	+	5.65685i	0.161690	+	0.457330i
$154$		0			0
$155$	−10.3485	+	17.9241i	−0.831209	+	1.43970i
$156$	8.44949	+	0.778539i	0.676501	+	0.0623330i
$157$	3.17423	−	5.49794i	0.253332	−	0.438783i	−0.711109	−	0.703081i	$-0.751807\pi$
$157$	3.17423	−	5.49794i	0.253332	−	0.438783i	0.964441	+	0.264298i	$0.0851403\pi$
$158$	−3.94949	+	6.84072i	−0.314205	+	0.544218i
$159$	0.797959	+	1.73205i	0.0632823	+	0.137361i
$160$	1.72474	−	2.98735i	0.136353	−	0.236170i
$161$		0			0
$162$	−1.39898	−	8.89060i	−0.109914	−	0.698512i
$163$	0.101021	−	0.174973i	0.00791254	−	0.0137049i	−0.862042	−	0.506837i	$-0.830815\pi$
$163$	0.101021	−	0.174973i	0.00791254	−	0.0137049i	0.869955	+	0.493132i	$0.164148\pi$
$164$	9.79796			0.765092
$165$	−11.8990	−	1.09638i	−0.926334	−	0.0853528i
$166$	−2.00000			−0.155230
$167$	9.34847	+	16.1920i	0.723406	+	1.25298i	0.959627	+	0.281277i	$0.0907579\pi$
$167$	9.34847	+	16.1920i	0.723406	+	1.25298i	−0.236220	+	0.971700i	$0.575909\pi$
$168$		0			0
$169$	−5.50000	+	9.52628i	−0.423077	+	0.732791i
$170$	−3.44949	+	5.97469i	−0.264564	+	0.458238i
$171$	14.5227	−	16.9866i	1.11058	−	1.29900i
$172$	1.44949	+	2.51059i	0.110523	+	0.191431i
$173$	−6.44949	−	11.1708i	−0.490346	−	0.849304i	0.509593	−	0.860416i	$-0.329796\pi$
$173$	−6.44949	−	11.1708i	−0.490346	−	0.849304i	−0.999938	+	0.0111123i	$0.996463\pi$
$174$	5.00000	+	0.460702i	0.379049	+	0.0349257i
$175$		0			0
$176$	−1.00000	−	1.73205i	−0.0753778	−	0.130558i
$177$	−2.00000	+	2.82843i	−0.150329	+	0.212598i
$178$	7.10102			0.532244
$179$	4.34847	+	7.53177i	0.325020	+	0.562951i	0.981516	−	0.191378i	$-0.0612957\pi$
$179$	4.34847	+	7.53177i	0.325020	+	0.562951i	−0.656497	+	0.754329i	$0.727962\pi$
$180$	6.72474	−	7.86566i	0.501233	−	0.586272i
$181$	−4.34847			−0.323219			−0.161610	−	0.986855i	$-0.551669\pi$
$181$	−4.34847			−0.323219			−0.161610	+	0.986855i	$0.551669\pi$
$182$		0			0
$183$	8.29796	+	18.0116i	0.613403	+	1.33145i
$184$	−1.00000			−0.0737210
$185$	−13.4495	+	23.2952i	−0.988826	+	1.71270i
$186$	−10.3485	−	0.953512i	−0.758787	−	0.0699149i
$187$	2.00000	+	3.46410i	0.146254	+	0.253320i
$188$	9.79796			0.714590
$189$		0			0
$190$	25.6969			1.86425
$191$	−6.94949	−	12.0369i	−0.502847	−	0.870957i	−0.999995	−	0.00329106i	$-0.998952\pi$
$191$	−6.94949	−	12.0369i	−0.502847	−	0.870957i	0.497147	−	0.867666i	$-0.334381\pi$
$192$	1.72474	+	0.158919i	0.124473	+	0.0114690i
$193$	4.05051	−	7.01569i	0.291562	−	0.505000i	−0.682617	−	0.730776i	$-0.739158\pi$
$193$	4.05051	−	7.01569i	0.291562	−	0.505000i	0.974179	+	0.225776i	$0.0724917\pi$
$194$	6.89898			0.495318
$195$	12.2474	+	26.5843i	0.877058	+	1.90374i
$196$		0			0
$197$	−12.6969			−0.904619			−0.452310	−	0.891861i	$-0.649400\pi$
$197$	−12.6969			−0.904619			−0.452310	+	0.891861i	$0.649400\pi$
$198$	−2.00000	−	5.65685i	−0.142134	−	0.402015i
$199$	3.44949	+	5.97469i	0.244528	+	0.423535i	0.961999	−	0.273054i	$-0.0880337\pi$
$199$	3.44949	+	5.97469i	0.244528	+	0.423535i	−0.717471	+	0.696588i	$0.754700\pi$
$200$	6.89898			0.487832
$201$	3.10102	−	4.38551i	0.218729	−	0.309330i
$202$	3.62372	+	6.27647i	0.254964	+	0.441611i
$203$		0			0
$204$	−3.44949	−	0.317837i	−0.241513	−	0.0222531i
$205$	16.8990	+	29.2699i	1.18028	+	2.04430i
$206$	7.00000	+	12.1244i	0.487713	+	0.844744i
$207$	−2.94949	−	0.548188i	−0.205004	−	0.0381017i
$208$	−2.44949	+	4.24264i	−0.169842	+	0.294174i
$209$	7.44949	−	12.9029i	0.515292	−	0.892512i
$210$		0			0
$211$	−1.55051	−	2.68556i	−0.106742	−	0.184882i	0.807707	−	0.589584i	$-0.200708\pi$
$211$	−1.55051	−	2.68556i	−0.106742	−	0.184882i	−0.914448	+	0.404703i	$0.867375\pi$
$212$	−1.10102			−0.0756184
$213$	17.0732	+	1.57313i	1.16984	+	0.107789i
$214$	−12.0000			−0.820303
$215$	−5.00000	+	8.66025i	−0.340997	+	0.590624i
$216$	5.00000	+	1.41421i	0.340207	+	0.0962250i
$217$		0			0
$218$	8.34847	−	14.4600i	0.565430	−	0.979353i
$219$	2.10102	+	4.56048i	0.141974	+	0.308169i
$220$	3.44949	−	5.97469i	0.232565	−	0.402814i
$221$	4.89898	−	8.48528i	0.329541	−	0.570782i
$222$	−13.4495	−	1.23924i	−0.902671	−	0.0831724i
$223$	−10.4495	+	18.0990i	−0.699750	+	1.21200i	0.268804	+	0.963195i	$0.413372\pi$
$223$	−10.4495	+	18.0990i	−0.699750	+	1.21200i	−0.968553	+	0.248807i	$0.919962\pi$
$224$		0			0
$225$	20.3485	+	3.78194i	1.35656	+	0.252129i
$226$	7.94949	−	13.7689i	0.528792	−	0.915895i
$227$	0.550510			0.0365386			0.0182693	−	0.999833i	$-0.494184\pi$
$227$	0.550510			0.0365386			0.0182693	+	0.999833i	$0.494184\pi$
$228$	5.39898	+	11.7190i	0.357556	+	0.776112i
$229$	23.2474			1.53623			0.768117	−	0.640309i	$-0.221194\pi$
$229$	23.2474			1.53623			0.768117	+	0.640309i	$0.221194\pi$
$230$	−1.72474	−	2.98735i	−0.113726	−	0.196980i
$231$		0			0
$232$	−1.44949	+	2.51059i	−0.0951637	+	0.164828i
$233$	3.50000	−	6.06218i	0.229293	−	0.397146i	−0.728306	−	0.685252i	$-0.759692\pi$
$233$	3.50000	−	6.06218i	0.229293	−	0.397146i	0.957599	+	0.288106i	$0.0930254\pi$
$234$	−9.55051	+	11.1708i	−0.624336	+	0.730261i
$235$	16.8990	+	29.2699i	1.10237	+	1.90936i
$236$	−1.00000	−	1.73205i	−0.0650945	−	0.112747i
$237$	−5.72474	−	12.4261i	−0.371862	−	0.807164i
$238$		0			0
$239$	6.39898	+	11.0834i	0.413916	+	0.716923i	0.995314	−	0.0966962i	$-0.0308275\pi$
$239$	6.39898	+	11.0834i	0.413916	+	0.716923i	−0.581398	+	0.813619i	$0.697494\pi$
$240$	2.50000	+	5.42650i	0.161374	+	0.350279i
$241$	8.89898			0.573234			0.286617	−	0.958045i	$-0.407469\pi$
$241$	8.89898			0.573234			0.286617	+	0.958045i	$0.407469\pi$
$242$	3.50000	+	6.06218i	0.224989	+	0.389692i
$243$	13.9722	+	6.91215i	0.896317	+	0.443415i
$244$	−11.4495			−0.732978
$245$		0			0
$246$	−9.79796	+	13.8564i	−0.624695	+	0.883452i
$247$	−36.4949			−2.32211
$248$	3.00000	−	5.19615i	0.190500	−	0.329956i
$249$	2.00000	−	2.82843i	0.126745	−	0.179244i
$250$	3.27526	+	5.67291i	0.207145	+	0.358786i
$251$	−12.5505			−0.792181			−0.396091	−	0.918211i	$-0.629633\pi$
$251$	−12.5505			−0.792181			−0.396091	+	0.918211i	$0.629633\pi$
$252$		0			0
$253$	−2.00000			−0.125739
$254$	1.50000	+	2.59808i	0.0941184	+	0.163018i
$255$	−5.00000	−	10.8530i	−0.313112	−	0.679642i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−27.7980			−1.73399			−0.866995	−	0.498318i	$-0.833951\pi$
$257$	−27.7980			−1.73399			−0.866995	+	0.498318i	$0.833951\pi$
$258$	−5.00000	−	0.460702i	−0.311286	−	0.0286820i
$259$		0			0
$260$	−16.8990			−1.04803
$261$	−5.65153	+	6.61037i	−0.349821	+	0.409171i
$262$	−6.72474	−	11.6476i	−0.415456	−	0.719591i
$263$	16.1010			0.992831			0.496416	−	0.868085i	$-0.334649\pi$
$263$	16.1010			0.992831			0.496416	+	0.868085i	$0.334649\pi$
$264$	3.44949	+	0.317837i	0.212301	+	0.0195615i
$265$	−1.89898	−	3.28913i	−0.116653	−	0.202050i
$266$		0			0
$267$	−7.10102	+	10.0424i	−0.434575	+	0.614582i
$268$	1.55051	+	2.68556i	0.0947125	+	0.164047i
$269$	−1.82577	−	3.16232i	−0.111319	−	0.192810i	0.804983	−	0.593297i	$-0.202174\pi$
$269$	−1.82577	−	3.16232i	−0.111319	−	0.192810i	−0.916302	+	0.400487i	$0.868841\pi$
$270$	4.39898	+	17.3759i	0.267713	+	1.05746i
$271$	8.44949	−	14.6349i	0.513270	−	0.889010i	−0.486612	−	0.873618i	$-0.661767\pi$
$271$	8.44949	−	14.6349i	0.513270	−	0.889010i	0.999882	−	0.0153912i	$-0.00489937\pi$
$272$	1.00000	−	1.73205i	0.0606339	−	0.105021i
$273$		0			0
$274$	5.89898	+	10.2173i	0.356370	+	0.617252i
$275$	13.7980			0.832048
$276$	1.00000	−	1.41421i	0.0601929	−	0.0851257i
$277$	10.6969			0.642717			0.321358	−	0.946958i	$-0.395861\pi$
$277$	10.6969			0.642717			0.321358	+	0.946958i	$0.395861\pi$
$278$	4.72474	−	8.18350i	0.283371	−	0.490814i
$279$	11.6969	−	13.6814i	0.700277	−	0.819086i
$280$		0			0
$281$	9.50000	−	16.4545i	0.566722	−	0.981592i	−0.430165	−	0.902750i	$-0.641545\pi$
$281$	9.50000	−	16.4545i	0.566722	−	0.981592i	0.996887	−	0.0788417i	$-0.0251222\pi$
$282$	−9.79796	+	13.8564i	−0.583460	+	0.825137i
$283$	−10.2753	+	17.7973i	−0.610801	+	1.05794i	0.380305	+	0.924861i	$0.375819\pi$
$283$	−10.2753	+	17.7973i	−0.610801	+	1.05794i	−0.991106	+	0.133077i	$0.957514\pi$
$284$	−4.94949	+	8.57277i	−0.293698	+	0.508700i
$285$	−25.6969	+	36.3410i	−1.52216	+	2.15265i
$286$	−4.89898	+	8.48528i	−0.289683	+	0.501745i
$287$		0			0
$288$	−1.94949	+	2.28024i	−0.114875	+	0.134364i
$289$	6.50000	−	11.2583i	0.382353	−	0.662255i
$290$	−10.0000			−0.587220
$291$	−6.89898	+	9.75663i	−0.404425	+	0.571944i
$292$	−2.89898			−0.169650
$293$	13.6237	+	23.5970i	0.795906	+	1.37855i	0.922262	+	0.386565i	$0.126339\pi$
$293$	13.6237	+	23.5970i	0.795906	+	1.37855i	−0.126356	+	0.991985i	$0.540328\pi$
$294$		0			0
$295$	3.44949	−	5.97469i	0.200837	−	0.347860i
$296$	3.89898	−	6.75323i	0.226624	−	0.392524i
$297$	10.0000	+	2.82843i	0.580259	+	0.164122i
$298$	3.00000	+	5.19615i	0.173785	+	0.301005i
$299$	2.44949	+	4.24264i	0.141658	+	0.245358i
$300$	−6.89898	+	9.75663i	−0.398313	+	0.563299i
$301$		0			0
$302$	2.50000	+	4.33013i	0.143859	+	0.249171i
$303$	−12.5000	−	1.15175i	−0.718106	−	0.0661666i
$304$	−7.44949			−0.427258
$305$	−19.7474	−	34.2036i	−1.13074	−	1.95849i
$306$	3.89898	−	4.56048i	0.222890	−	0.260705i
$307$	−0.752551			−0.0429504			−0.0214752	−	0.999769i	$-0.506836\pi$
$307$	−0.752551			−0.0429504			−0.0214752	+	0.999769i	$0.506836\pi$
$308$		0			0
$309$	−24.1464	−	2.22486i	−1.37364	−	0.126568i
$310$	20.6969			1.17551
$311$	0.651531	−	1.12848i	0.0369449	−	0.0639905i	−0.846962	−	0.531654i	$-0.821571\pi$
$311$	0.651531	−	1.12848i	0.0369449	−	0.0639905i	0.883907	+	0.467663i	$0.154904\pi$
$312$	−3.55051	−	7.70674i	−0.201008	−	0.436308i
$313$	12.3485	+	21.3882i	0.697977	+	1.20893i	0.969167	+	0.246405i	$0.0792495\pi$
$313$	12.3485	+	21.3882i	0.697977	+	1.20893i	−0.271190	+	0.962526i	$0.587417\pi$
$314$	−6.34847			−0.358265
$315$		0			0
$316$	7.89898			0.444352
$317$	4.34847	+	7.53177i	0.244234	+	0.423026i	0.961916	−	0.273345i	$-0.0881300\pi$
$317$	4.34847	+	7.53177i	0.244234	+	0.423026i	−0.717682	+	0.696371i	$0.754797\pi$
$318$	1.10102	−	1.55708i	0.0617422	−	0.0873166i
$319$	−2.89898	+	5.02118i	−0.162312	+	0.281132i
$320$	−3.44949			−0.192832
$321$	12.0000	−	16.9706i	0.669775	−	0.947204i
$322$		0			0
$323$	14.8990			0.829001
$324$	−7.00000	+	5.65685i	−0.388889	+	0.314270i
$325$	−16.8990	−	29.2699i	−0.937387	−	1.62360i
$326$	−0.202041			−0.0111900
$327$	12.1010	+	26.2665i	0.669188	+	1.45254i
$328$	−4.89898	−	8.48528i	−0.270501	−	0.468521i
$329$		0			0
$330$	5.00000	+	10.8530i	0.275241	+	0.597438i
$331$	12.3485	+	21.3882i	0.678733	+	1.17560i	0.975363	+	0.220608i	$0.0708041\pi$
$331$	12.3485	+	21.3882i	0.678733	+	1.17560i	−0.296629	+	0.954993i	$0.595863\pi$
$332$	1.00000	+	1.73205i	0.0548821	+	0.0950586i
$333$	15.2020	−	17.7812i	0.833067	−	0.974404i
$334$	9.34847	−	16.1920i	0.511525	−	0.885988i
$335$	−5.34847	+	9.26382i	−0.292218	+	0.506137i
$336$		0			0
$337$	−17.6969	−	30.6520i	−0.964014	−	1.66972i	−0.712242	−	0.701934i	$-0.752320\pi$
$337$	−17.6969	−	30.6520i	−0.964014	−	1.66972i	−0.251772	−	0.967787i	$-0.581013\pi$
$338$	11.0000			0.598321
$339$	11.5227	+	25.0112i	0.625827	+	1.35842i
$340$	6.89898			0.374150
$341$	6.00000	−	10.3923i	0.324918	−	0.562775i
$342$	−21.9722	−	4.08372i	−1.18812	−	0.220822i
$343$		0			0
$344$	1.44949	−	2.51059i	0.0781512	−	0.135362i
$345$	5.94949	+	0.548188i	0.320310	+	0.0295135i
$346$	−6.44949	+	11.1708i	−0.346727	+	0.600548i
$347$	9.79796	−	16.9706i	0.525982	−	0.911028i	−0.473560	−	0.880762i	$-0.657031\pi$
$347$	9.79796	−	16.9706i	0.525982	−	0.911028i	0.999542	−	0.0302659i	$-0.00963541\pi$
$348$	−2.10102	−	4.56048i	−0.112627	−	0.244467i
$349$	10.4495	−	18.0990i	0.559348	−	0.968820i	−0.438203	−	0.898876i	$-0.644385\pi$
$349$	10.4495	−	18.0990i	0.559348	−	0.968820i	0.997551	−	0.0699435i	$-0.0222819\pi$
$350$		0			0
$351$	−6.24745	−	24.6773i	−0.333464	−	1.31718i
$352$	−1.00000	+	1.73205i	−0.0533002	+	0.0923186i
$353$	6.00000			0.319348			0.159674	−	0.987170i	$-0.448956\pi$
$353$	6.00000			0.319348			0.159674	+	0.987170i	$0.448956\pi$
$354$	3.44949	+	0.317837i	0.183338	+	0.0168929i
$355$	−34.1464			−1.81230
$356$	−3.55051	−	6.14966i	−0.188177	−	0.325932i
$357$		0			0
$358$	4.34847	−	7.53177i	0.229824	−	0.398066i
$359$	−5.39898	+	9.35131i	−0.284947	+	0.493543i	−0.972596	−	0.232500i	$-0.925309\pi$
$359$	−5.39898	+	9.35131i	−0.284947	+	0.493543i	0.687649	+	0.726043i	$0.258643\pi$
$360$	−10.1742	−	1.89097i	−0.536229	−	0.0996628i
$361$	−18.2474	−	31.6055i	−0.960392	−	1.66345i
$362$	2.17423	+	3.76588i	0.114275	+	0.197931i
$363$	−12.0732	−	1.11243i	−0.633679	−	0.0583875i
$364$		0			0
$365$	−5.00000	−	8.66025i	−0.261712	−	0.453298i
$366$	11.4495	−	16.1920i	0.598474	−	0.846371i
$367$	−5.79796			−0.302651			−0.151325	−	0.988484i	$-0.548354\pi$
$367$	−5.79796			−0.302651			−0.151325	+	0.988484i	$0.548354\pi$
$368$	0.500000	+	0.866025i	0.0260643	+	0.0451447i
$369$	−9.79796	−	27.7128i	−0.510061	−	1.44267i
$370$	26.8990			1.39841
$371$		0			0
$372$	4.34847	+	9.43879i	0.225458	+	0.489379i
$373$	2.89898			0.150103			0.0750517	−	0.997180i	$-0.476088\pi$
$373$	2.89898			0.150103			0.0750517	+	0.997180i	$0.476088\pi$
$374$	2.00000	−	3.46410i	0.103418	−	0.179124i
$375$	−11.2980	−	1.04100i	−0.583424	−	0.0537569i
$376$	−4.89898	−	8.48528i	−0.252646	−	0.437595i
$377$	14.2020			0.731442
$378$		0			0
$379$	−26.4949			−1.36095			−0.680476	−	0.732771i	$-0.738227\pi$
$379$	−26.4949			−1.36095			−0.680476	+	0.732771i	$0.738227\pi$
$380$	−12.8485	−	22.2542i	−0.659113	−	1.14162i
$381$	−5.17423	−	0.476756i	−0.265084	−	0.0244249i
$382$	−6.94949	+	12.0369i	−0.355567	+	0.615860i
$383$	−6.89898			−0.352521			−0.176261	−	0.984344i	$-0.556400\pi$
$383$	−6.89898			−0.352521			−0.176261	+	0.984344i	$0.556400\pi$
$384$	−0.724745	−	1.57313i	−0.0369845	−	0.0802786i
$385$		0			0
$386$	−8.10102			−0.412331
$387$	5.65153	−	6.61037i	0.287283	−	0.336024i
$388$	−3.44949	−	5.97469i	−0.175121	−	0.303319i
$389$	−15.1010			−0.765652			−0.382826	−	0.923820i	$-0.625049\pi$
$389$	−15.1010			−0.765652			−0.382826	+	0.923820i	$0.625049\pi$
$390$	16.8990	−	23.8988i	0.855713	−	1.21016i
$391$	−1.00000	−	1.73205i	−0.0505722	−	0.0875936i
$392$		0			0
$393$	23.1969	+	2.13737i	1.17013	+	0.107816i
$394$	6.34847	+	10.9959i	0.319831	+	0.553964i
$395$	13.6237	+	23.5970i	0.685484	+	1.18729i
$396$	−3.89898	+	4.56048i	−0.195931	+	0.229173i
$397$	4.65153	−	8.05669i	0.233454	−	0.404354i	−0.725369	−	0.688361i	$-0.758331\pi$
$397$	4.65153	−	8.05669i	0.233454	−	0.404354i	0.958822	+	0.284007i	$0.0916640\pi$
$398$	3.44949	−	5.97469i	0.172907	−	0.299484i
$399$		0			0
$400$	−3.44949	−	5.97469i	−0.172474	−	0.298735i
$401$	−10.1010			−0.504421			−0.252210	−	0.967672i	$-0.581158\pi$
$401$	−10.1010			−0.504421			−0.252210	+	0.967672i	$0.581158\pi$
$402$	−5.34847	−	0.492810i	−0.266757	−	0.0245791i
$403$	−29.3939			−1.46421
$404$	3.62372	−	6.27647i	0.180287	−	0.312266i
$405$	−28.9722	−	11.1548i	−1.43964	−	0.554286i
$406$		0			0
$407$	7.79796	−	13.5065i	0.386530	−	0.669490i
$408$	1.44949	+	3.14626i	0.0717604	+	0.155763i
$409$	2.89898	−	5.02118i	0.143345	−	0.248281i	−0.785409	−	0.618977i	$-0.787547\pi$
$409$	2.89898	−	5.02118i	0.143345	−	0.248281i	0.928754	+	0.370696i	$0.120881\pi$
$410$	16.8990	−	29.2699i	0.834581	−	1.44554i
$411$	−20.3485	−	1.87492i	−1.00372	−	0.0924828i
$412$	7.00000	−	12.1244i	0.344865	−	0.597324i
$413$		0			0
$414$	1.00000	+	2.82843i	0.0491473	+	0.139010i
$415$	−3.44949	+	5.97469i	−0.169329	+	0.293286i
$416$	4.89898			0.240192
$417$	6.84847	+	14.8653i	0.335371	+	0.727957i
$418$	−14.8990			−0.728733
$419$	12.2753	+	21.2614i	0.599685	+	1.03869i	0.992867	+	0.119225i	$0.0380410\pi$
$419$	12.2753	+	21.2614i	0.599685	+	1.03869i	−0.393182	+	0.919461i	$0.628626\pi$
$420$		0			0
$421$	−6.55051	+	11.3458i	−0.319252	+	0.552961i	−0.980332	−	0.197354i	$-0.936765\pi$
$421$	−6.55051	+	11.3458i	−0.319252	+	0.552961i	0.661080	+	0.750316i	$0.270098\pi$
$422$	−1.55051	+	2.68556i	−0.0754777	+	0.130731i
$423$	−9.79796	−	27.7128i	−0.476393	−	1.34744i
$424$	0.550510	+	0.953512i	0.0267351	+	0.0463066i
$425$	6.89898	+	11.9494i	0.334650	+	0.579630i
$426$	−7.17423	−	15.5724i	−0.347593	−	0.754485i
$427$		0			0
$428$	6.00000	+	10.3923i	0.290021	+	0.502331i
$429$	−7.10102	−	15.4135i	−0.342841	−	0.744170i
$430$	10.0000			0.482243
$431$	3.79796	+	6.57826i	0.182941	+	0.316864i	0.942881	−	0.333130i	$-0.108105\pi$
$431$	3.79796	+	6.57826i	0.182941	+	0.316864i	−0.759940	+	0.649994i	$0.774772\pi$
$432$	−1.27526	−	5.03723i	−0.0613557	−	0.242354i
$433$	−11.7980			−0.566974			−0.283487	−	0.958976i	$-0.591491\pi$
$433$	−11.7980			−0.566974			−0.283487	+	0.958976i	$0.591491\pi$
$434$		0			0
$435$	10.0000	−	14.1421i	0.479463	−	0.678064i
$436$	−16.6969			−0.799638
$437$	−3.72474	+	6.45145i	−0.178179	+	0.308615i
$438$	2.89898	−	4.09978i	0.138519	−	0.195895i
$439$	10.8990	+	18.8776i	0.520180	+	0.900978i	0.999725	+	0.0234607i	$0.00746845\pi$
$439$	10.8990	+	18.8776i	0.520180	+	0.900978i	−0.479545	+	0.877517i	$0.659198\pi$
$440$	−6.89898			−0.328896
$441$		0			0
$442$	−9.79796			−0.466041
$443$	2.55051	+	4.41761i	0.121178	+	0.209887i	0.920233	−	0.391372i	$-0.127999\pi$
$443$	2.55051	+	4.41761i	0.121178	+	0.209887i	−0.799054	+	0.601259i	$0.794666\pi$
$444$	5.65153	+	12.2672i	0.268210	+	0.582177i
$445$	12.2474	−	21.2132i	0.580585	−	1.00560i
$446$	20.8990			0.989595
$447$	−10.3485	−	0.953512i	−0.489466	−	0.0450996i
$448$		0			0
$449$	−18.5959			−0.877596			−0.438798	−	0.898586i	$-0.644596\pi$
$449$	−18.5959			−0.877596			−0.438798	+	0.898586i	$0.644596\pi$
$450$	−6.89898	−	19.5133i	−0.325221	−	0.919864i
$451$	−9.79796	−	16.9706i	−0.461368	−	0.799113i
$452$	−15.8990			−0.747825
$453$	−8.62372	−	0.794593i	−0.405178	−	0.0373332i
$454$	−0.275255	−	0.476756i	−0.0129184	−	0.0223753i
$455$		0			0
$456$	7.44949	−	10.5352i	0.348854	−	0.493355i
$457$	−15.7474	−	27.2754i	−0.736635	−	1.27589i	−0.954002	−	0.299799i	$-0.903080\pi$
$457$	−15.7474	−	27.2754i	−0.736635	−	1.27589i	0.217368	−	0.976090i	$-0.430253\pi$
$458$	−11.6237	−	20.1329i	−0.543141	−	0.940748i
$459$	2.55051	+	10.0745i	0.119048	+	0.470236i
$460$	−1.72474	+	2.98735i	−0.0804166	+	0.139286i
$461$	10.1742	−	17.6223i	0.473861	−	0.820752i	−0.525691	−	0.850676i	$-0.676193\pi$
$461$	10.1742	−	17.6223i	0.473861	−	0.820752i	0.999552	+	0.0299238i	$0.00952645\pi$
$462$		0			0
$463$	12.8485	+	22.2542i	0.597119	+	1.03424i	0.993244	+	0.116044i	$0.0370213\pi$
$463$	12.8485	+	22.2542i	0.597119	+	1.03424i	−0.396125	+	0.918197i	$0.629645\pi$
$464$	2.89898			0.134582
$465$	−20.6969	+	29.2699i	−0.959798	+	1.35736i
$466$	−7.00000			−0.324269
$467$	5.00000	−	8.66025i	0.231372	−	0.400749i	−0.726840	−	0.686807i	$-0.759012\pi$
$467$	5.00000	−	8.66025i	0.231372	−	0.400749i	0.958212	+	0.286058i	$0.0923451\pi$
$468$	14.4495	+	2.68556i	0.667928	+	0.124140i
$469$		0			0
$470$	16.8990	−	29.2699i	0.779492	−	1.35012i
$471$	6.34847	−	8.97809i	0.292522	−	0.413689i
$472$	−1.00000	+	1.73205i	−0.0460287	+	0.0797241i
$473$	2.89898	−	5.02118i	0.133295	−	0.230874i
$474$	−7.89898	+	11.1708i	−0.362812	+	0.513094i
$475$	25.6969	−	44.5084i	1.17906	−	2.04219i
$476$		0			0
$477$	1.10102	+	3.11416i	0.0504123	+	0.142587i
$478$	6.39898	−	11.0834i	0.292683	−	0.506941i
$479$	29.5959			1.35227			0.676136	−	0.736777i	$-0.263653\pi$
$479$	29.5959			1.35227			0.676136	+	0.736777i	$0.263653\pi$
$480$	3.44949	−	4.87832i	0.157447	−	0.222664i
$481$	−38.2020			−1.74186
$482$	−4.44949	−	7.70674i	−0.202669	−	0.351032i
$483$		0			0
$484$	3.50000	−	6.06218i	0.159091	−	0.275554i
$485$	11.8990	−	20.6096i	0.540305	−	0.935835i
$486$	−1.00000	−	15.5563i	−0.0453609	−	0.705650i
$487$	−11.1969	−	19.3937i	−0.507382	−	0.878811i	−0.999963	−	0.00854475i	$-0.997280\pi$
$487$	−11.1969	−	19.3937i	−0.507382	−	0.878811i	0.492582	−	0.870266i	$-0.336053\pi$
$488$	5.72474	+	9.91555i	0.259147	+	0.448856i
$489$	0.202041	−	0.285729i	0.00913661	−	0.0129211i
$490$		0			0
$491$	1.89898	+	3.28913i	0.0856997	+	0.148436i	0.905689	−	0.423942i	$-0.139354\pi$
$491$	1.89898	+	3.28913i	0.0856997	+	0.148436i	−0.819989	+	0.572379i	$0.806021\pi$
$492$	16.8990	+	1.55708i	0.761865	+	0.0701985i
$493$	−5.79796			−0.261127
$494$	18.2474	+	31.6055i	0.820992	+	1.42200i
$495$	−20.3485	−	3.78194i	−0.914596	−	0.169986i
$496$	−6.00000			−0.269408
$497$		0			0
$498$	−3.44949	−	0.317837i	−0.154575	−	0.0142426i
$499$	33.3939			1.49492			0.747458	−	0.664309i	$-0.231274\pi$
$499$	33.3939			1.49492			0.747458	+	0.664309i	$0.231274\pi$
$500$	3.27526	−	5.67291i	0.146474	−	0.253700i
$501$	13.5505	+	29.4128i	0.605392	+	1.31407i
$502$	6.27526	+	10.8691i	0.280078	+	0.485110i
$503$	−24.4949			−1.09217			−0.546087	−	0.837729i	$-0.683883\pi$
$503$	−24.4949			−1.09217			−0.546087	+	0.837729i	$0.683883\pi$
$504$		0			0
$505$	25.0000			1.11249
$506$	1.00000	+	1.73205i	0.0444554	+	0.0769991i
$507$	−11.0000	+	15.5563i	−0.488527	+	0.690882i
$508$	1.50000	−	2.59808i	0.0665517	−	0.115271i
$509$	16.8990			0.749034			0.374517	−	0.927220i	$-0.377809\pi$
$509$	16.8990			0.749034			0.374517	+	0.927220i	$0.377809\pi$
$510$	−6.89898	+	9.75663i	−0.305492	+	0.432031i
$511$		0			0
$512$	1.00000			0.0441942
$513$	27.7474	−	26.9897i	1.22508	−	1.19162i
$514$	13.8990	+	24.0737i	0.613058	+	1.06185i
$515$	48.2929			2.12804
$516$	2.10102	+	4.56048i	0.0924923	+	0.200764i
$517$	−9.79796	−	16.9706i	−0.430914	−	0.746364i
$518$		0			0
$519$	−9.34847	−	20.2918i	−0.410352	−	0.890711i
$520$	8.44949	+	14.6349i	0.370535	+	0.641785i
$521$	−19.3485	−	33.5125i	−0.847672	−	1.46821i	−0.883281	−	0.468845i	$-0.844670\pi$
$521$	−19.3485	−	33.5125i	−0.847672	−	1.46821i	0.0356087	−	0.999366i	$-0.488663\pi$
$522$	8.55051	+	1.58919i	0.374246	+	0.0695568i
$523$	0.174235	−	0.301783i	0.00761875	−	0.0131961i	−0.862191	−	0.506584i	$-0.830908\pi$
$523$	0.174235	−	0.301783i	0.00761875	−	0.0131961i	0.869810	+	0.493387i	$0.164242\pi$
$524$	−6.72474	+	11.6476i	−0.293772	+	0.508828i
$525$		0			0
$526$	−8.05051	−	13.9439i	−0.351019	−	0.607983i
$527$	12.0000			0.522728
$528$	−1.44949	−	3.14626i	−0.0630809	−	0.136924i
$529$	−22.0000			−0.956522
$530$	−1.89898	+	3.28913i	−0.0824864	+	0.142871i
$531$	−3.89898	+	4.56048i	−0.169201	+	0.197908i
$532$		0			0
$533$	−24.0000	+	41.5692i	−1.03956	+	1.80056i
$534$	12.2474	+	1.12848i	0.529999	+	0.0488343i
$535$	−20.6969	+	35.8481i	−0.894807	+	1.54985i
$536$	1.55051	−	2.68556i	0.0669718	−	0.115999i
$537$	6.30306	+	13.6814i	0.271997	+	0.590397i
$538$	−1.82577	+	3.16232i	−0.0787143	+	0.136337i
$539$		0			0
$540$	12.8485	−	12.4976i	0.552910	−	0.537810i
$541$	−15.2474	+	26.4094i	−0.655539	+	1.13543i	0.326219	+	0.945294i	$0.394225\pi$
$541$	−15.2474	+	26.4094i	−0.655539	+	1.13543i	−0.981758	+	0.190133i	$0.939108\pi$
$542$	−16.8990			−0.725873
$543$	−7.50000	−	0.691053i	−0.321856	−	0.0296559i
$544$	−2.00000			−0.0857493
$545$	−28.7980	−	49.8795i	−1.23357	−	2.13660i
$546$		0			0
$547$	−15.7980	+	27.3629i	−0.675472	+	1.16995i	0.300859	+	0.953669i	$0.402727\pi$
$547$	−15.7980	+	27.3629i	−0.675472	+	1.16995i	−0.976331	+	0.216283i	$0.930607\pi$
$548$	5.89898	−	10.2173i	0.251992	−	0.436463i
$549$	11.4495	+	32.3840i	0.488652	+	1.38212i
$550$	−6.89898	−	11.9494i	−0.294173	−	0.509523i
$551$	10.7980	+	18.7026i	0.460009	+	0.796758i
$552$	−1.72474	−	0.158919i	−0.0734100	−	0.00676403i
$553$		0			0
$554$	−5.34847	−	9.26382i	−0.227235	−	0.393582i
$555$	−26.8990	+	38.0409i	−1.14180	+	1.61475i
$556$	−9.44949			−0.400748
$557$	1.55051	+	2.68556i	0.0656972	+	0.113791i	0.897003	−	0.442024i	$-0.145740\pi$
$557$	1.55051	+	2.68556i	0.0656972	+	0.113791i	−0.831306	+	0.555815i	$0.812406\pi$
$558$	−17.6969	−	3.28913i	−0.749171	−	0.139240i
$559$	−14.2020			−0.600682
$560$		0			0
$561$	2.89898	+	6.29253i	0.122395	+	0.265671i
$562$	−19.0000			−0.801467
$563$	6.97219	−	12.0762i	0.293843	−	0.508951i	−0.680872	−	0.732402i	$-0.738399\pi$
$563$	6.97219	−	12.0762i	0.293843	−	0.508951i	0.974715	+	0.223451i	$0.0717324\pi$
$564$	16.8990	+	1.55708i	0.711575	+	0.0655648i
$565$	−27.4217	−	47.4957i	−1.15364	−	1.99816i
$566$	20.5505			0.863802
$567$		0			0
$568$	9.89898			0.415352
$569$	15.0000	+	25.9808i	0.628833	+	1.08917i	0.987786	+	0.155815i	$0.0498003\pi$
$569$	15.0000	+	25.9808i	0.628833	+	1.08917i	−0.358954	+	0.933355i	$0.616866\pi$
$570$	44.3207	+	4.08372i	1.85639	+	0.171048i
$571$	−7.10102	+	12.2993i	−0.297168	+	0.514711i	−0.975487	−	0.220057i	$-0.929376\pi$
$571$	−7.10102	+	12.2993i	−0.297168	+	0.514711i	0.678319	+	0.734768i	$0.262709\pi$
$572$	9.79796			0.409673
$573$	−10.0732	−	21.8649i	−0.420815	−	0.913421i
$574$		0			0
$575$	−6.89898			−0.287707
$576$	2.94949	+	0.548188i	0.122895	+	0.0228412i
$577$	11.7980	+	20.4347i	0.491155	+	0.850706i	0.999948	−	0.0101829i	$-0.00324136\pi$
$577$	11.7980	+	20.4347i	0.491155	+	0.850706i	−0.508793	+	0.860889i	$0.669908\pi$
$578$	−13.0000			−0.540729
$579$	8.10102	−	11.4566i	0.336667	−	0.476119i
$580$	5.00000	+	8.66025i	0.207614	+	0.359597i
$581$		0			0
$582$	11.8990	+	1.09638i	0.493229	+	0.0454463i
$583$	1.10102	+	1.90702i	0.0455996	+	0.0789808i
$584$	1.44949	+	2.51059i	0.0599803	+	0.103889i
$585$	16.8990	+	47.7975i	0.698687	+	1.97618i
$586$	13.6237	−	23.5970i	0.562791	−	0.974782i
$587$	−9.07321	+	15.7153i	−0.374492	+	0.648639i	−0.990251	−	0.139296i	$-0.955516\pi$
$587$	−9.07321	+	15.7153i	−0.374492	+	0.648639i	0.615759	+	0.787934i	$0.288849\pi$
$588$		0			0
$589$	−22.3485	−	38.7087i	−0.920853	−	1.59496i
$590$	−6.89898			−0.284026
$591$	−21.8990	−	2.01778i	−0.900804	−	0.0830004i
$592$	−7.79796			−0.320494
$593$	−7.34847	+	12.7279i	−0.301765	+	0.522673i	−0.976536	−	0.215355i	$-0.930909\pi$
$593$	−7.34847	+	12.7279i	−0.301765	+	0.522673i	0.674770	+	0.738028i	$0.264243\pi$
$594$	−2.55051	−	10.0745i	−0.104649	−	0.413360i
$595$		0			0
$596$	3.00000	−	5.19615i	0.122885	−	0.212843i
$597$	5.00000	+	10.8530i	0.204636	+	0.444184i
$598$	2.44949	−	4.24264i	0.100167	−	0.173494i
$599$	7.10102	−	12.2993i	0.290140	−	0.502537i	−0.683703	−	0.729761i	$-0.739632\pi$
$599$	7.10102	−	12.2993i	0.290140	−	0.502537i	0.973843	+	0.227224i	$0.0729648\pi$
$600$	11.8990	+	1.09638i	0.485774	+	0.0447594i
$601$	−6.34847	+	10.9959i	−0.258959	+	0.448531i	−0.965963	−	0.258679i	$-0.916713\pi$
$601$	−6.34847	+	10.9959i	−0.258959	+	0.448531i	0.707004	+	0.707210i	$0.250046\pi$
$602$		0			0
$603$	6.04541	−	7.07107i	0.246188	−	0.287956i
$604$	2.50000	−	4.33013i	0.101724	−	0.176190i
$605$	24.1464			0.981692
$606$	5.25255	+	11.4012i	0.213370	+	0.463142i
$607$	8.69694			0.352998			0.176499	−	0.984301i	$-0.443523\pi$
$607$	8.69694			0.352998			0.176499	+	0.984301i	$0.443523\pi$
$608$	3.72474	+	6.45145i	0.151058	+	0.261641i
$609$		0			0
$610$	−19.7474	+	34.2036i	−0.799551	+	1.38486i
$611$	−24.0000	+	41.5692i	−0.970936	+	1.68171i
$612$	−5.89898	−	1.09638i	−0.238452	−	0.0443184i
$613$	−7.34847	−	12.7279i	−0.296802	−	0.514076i	0.678601	−	0.734508i	$-0.262587\pi$
$613$	−7.34847	−	12.7279i	−0.296802	−	0.514076i	−0.975402	+	0.220432i	$0.929253\pi$
$614$	0.376276	+	0.651729i	0.0151852	+	0.0263016i
$615$	24.4949	+	53.1687i	0.987730	+	2.14397i
$616$		0			0
$617$	−21.6969	−	37.5802i	−0.873486	−	1.51292i	−0.858367	−	0.513036i	$-0.828521\pi$
$617$	−21.6969	−	37.5802i	−0.873486	−	1.51292i	−0.0151189	−	0.999886i	$-0.504813\pi$
$618$	10.1464	+	22.0239i	0.408149	+	0.885929i
$619$	4.14643			0.166659			0.0833295	−	0.996522i	$-0.473445\pi$
$619$	4.14643			0.166659			0.0833295	+	0.996522i	$0.473445\pi$
$620$	−10.3485	−	17.9241i	−0.415605	−	0.719848i
$621$	−5.00000	−	1.41421i	−0.200643	−	0.0567504i
$622$	−1.30306			−0.0522480
$623$		0			0
$624$	−4.89898	+	6.92820i	−0.196116	+	0.277350i
$625$	−11.8990			−0.475959
$626$	12.3485	−	21.3882i	0.493544	−	0.854843i
$627$	14.8990	−	21.0703i	0.595008	−	0.841468i
$628$	3.17423	+	5.49794i	0.126666	+	0.219392i
$629$	15.5959			0.621850
$630$		0			0
$631$	18.1010			0.720590			0.360295	−	0.932838i	$-0.382676\pi$
$631$	18.1010			0.720590			0.360295	+	0.932838i	$0.382676\pi$
$632$	−3.94949	−	6.84072i	−0.157102	−	0.272109i
$633$	−2.24745	−	4.87832i	−0.0893281	−	0.193896i
$634$	4.34847	−	7.53177i	0.172700	−	0.299125i
$635$	10.3485			0.410666
$636$	−1.89898	−	0.174973i	−0.0752994	−	0.00693812i
$637$		0			0
$638$	5.79796			0.229543
$639$	29.1969	+	5.42650i	1.15501	+	0.214669i
$640$	1.72474	+	2.98735i	0.0681765	+	0.118085i
$641$	41.4949			1.63895			0.819475	−	0.573115i	$-0.194265\pi$
$641$	41.4949			1.63895			0.819475	+	0.573115i	$0.194265\pi$
$642$	−20.6969	−	1.90702i	−0.816843	−	0.0752642i
$643$	9.69694	+	16.7956i	0.382410	+	0.662353i	0.991406	−	0.130820i	$-0.0417609\pi$
$643$	9.69694	+	16.7956i	0.382410	+	0.662353i	−0.608996	+	0.793173i	$0.708428\pi$
$644$		0			0
$645$	−10.0000	+	14.1421i	−0.393750	+	0.556846i
$646$	−7.44949	−	12.9029i	−0.293096	−	0.507658i
$647$	−10.6515	−	18.4490i	−0.418755	−	0.725305i	0.577060	−	0.816702i	$-0.304200\pi$
$647$	−10.6515	−	18.4490i	−0.418755	−	0.725305i	−0.995815	+	0.0913973i	$0.970867\pi$
$648$	8.39898	+	3.23375i	0.329943	+	0.127034i
$649$	−2.00000	+	3.46410i	−0.0785069	+	0.135978i
$650$	−16.8990	+	29.2699i	−0.662833	+	1.14806i
$651$		0			0
$652$	0.101021	+	0.174973i	0.00395627	+	0.00685246i
$653$	−9.79796			−0.383424			−0.191712	−	0.981451i	$-0.561404\pi$
$653$	−9.79796			−0.383424			−0.191712	+	0.981451i	$0.561404\pi$
$654$	16.6969	−	23.6130i	0.652902	−	0.923343i
$655$	−46.3939			−1.81276
$656$	−4.89898	+	8.48528i	−0.191273	+	0.331295i
$657$	2.89898	+	8.19955i	0.113100	+	0.319895i
$658$		0			0
$659$	−2.34847	+	4.06767i	−0.0914834	+	0.158454i	−0.908136	−	0.418676i	$-0.862494\pi$
$659$	−2.34847	+	4.06767i	−0.0914834	+	0.158454i	0.816652	+	0.577130i	$0.195828\pi$
$660$	6.89898	−	9.75663i	0.268542	−	0.379776i
$661$	4.72474	−	8.18350i	0.183771	−	0.318301i	−0.759391	−	0.650635i	$-0.774503\pi$
$661$	4.72474	−	8.18350i	0.183771	−	0.318301i	0.943162	+	0.332334i	$0.107836\pi$
$662$	12.3485	−	21.3882i	0.479937	−	0.831275i
$663$	9.79796	−	13.8564i	0.380521	−	0.538138i
$664$	1.00000	−	1.73205i	0.0388075	−	0.0672166i
$665$		0			0
$666$	−23.0000	−	4.27475i	−0.891232	−	0.165643i
$667$	1.44949	−	2.51059i	0.0561245	−	0.0972104i
$668$	−18.6969			−0.723406
$669$	−20.8990	+	29.5556i	−0.808001	+	1.14269i
$670$	10.6969			0.413259
$671$	11.4495	+	19.8311i	0.442003	+	0.765571i
$672$		0			0
$673$	−15.2980	+	26.4968i	−0.589693	+	1.02138i	0.404579	+	0.914503i	$0.367418\pi$
$673$	−15.2980	+	26.4968i	−0.589693	+	1.02138i	−0.994272	+	0.106875i	$0.965915\pi$
$674$	−17.6969	+	30.6520i	−0.681661	+	1.18067i
$675$	34.4949	+	9.75663i	1.32771	+	0.375533i
$676$	−5.50000	−	9.52628i	−0.211538	−	0.366395i
$677$	−7.34847	−	12.7279i	−0.282425	−	0.489174i	0.689557	−	0.724232i	$-0.257805\pi$
$677$	−7.34847	−	12.7279i	−0.282425	−	0.489174i	−0.971981	+	0.235058i	$0.924472\pi$
$678$	15.8990	−	22.4846i	0.610597	−	0.863514i
$679$		0			0
$680$	−3.44949	−	5.97469i	−0.132282	−	0.229119i
$681$	0.949490	+	0.0874863i	0.0363845	+	0.00335248i
$682$	−12.0000			−0.459504
$683$	−16.1010	−	27.8878i	−0.616088	−	1.06710i	−0.990193	−	0.139710i	$-0.955383\pi$
$683$	−16.1010	−	27.8878i	−0.616088	−	1.06710i	0.374104	−	0.927387i	$-0.377950\pi$
$684$	7.44949	+	21.0703i	0.284838	+	0.805645i
$685$	40.6969			1.55495
$686$		0			0
$687$	40.0959	+	3.69445i	1.52975	+	0.140952i
$688$	−2.89898			−0.110523
$689$	2.69694	−	4.67123i	0.102745	−	0.177960i
$690$	−2.50000	−	5.42650i	−0.0951734	−	0.206583i
$691$	3.47730	+	6.02285i	0.132283	+	0.229120i	0.924556	−	0.381046i	$-0.124436\pi$
$691$	3.47730	+	6.02285i	0.132283	+	0.229120i	−0.792274	+	0.610166i	$0.791103\pi$
$692$	12.8990			0.490346
$693$		0			0
$694$	−19.5959			−0.743851
$695$	−16.2980	−	28.2289i	−0.618217	−	1.07078i
$696$	−2.89898	+	4.09978i	−0.109886	+	0.155402i
$697$	9.79796	−	16.9706i	0.371124	−	0.642806i
$698$	−20.8990			−0.791038
$699$	7.00000	−	9.89949i	0.264764	−	0.374433i
$700$		0			0
$701$	51.3939			1.94112			0.970560	−	0.240860i	$-0.0774293\pi$
$701$	51.3939			1.94112			0.970560	+	0.240860i	$0.0774293\pi$
$702$	−18.2474	+	17.7491i	−0.688706	+	0.669897i
$703$	−29.0454	−	50.3081i	−1.09547	−	1.89741i
$704$	2.00000			0.0753778
$705$	24.4949	+	53.1687i	0.922531	+	2.00245i
$706$	−3.00000	−	5.19615i	−0.112906	−	0.195560i
$707$		0			0
$708$	−1.44949	−	3.14626i	−0.0544752	−	0.118244i
$709$	5.79796	+	10.0424i	0.217747	+	0.377149i	0.954119	−	0.299428i	$-0.0967959\pi$
$709$	5.79796	+	10.0424i	0.217747	+	0.377149i	−0.736372	+	0.676577i	$0.763463\pi$
$710$	17.0732	+	29.5717i	0.640746	+	1.10981i
$711$	−7.89898	−	22.3417i	−0.296235	−	0.837879i
$712$	−3.55051	+	6.14966i	−0.133061	+	0.230468i
$713$	−3.00000	+	5.19615i	−0.112351	+	0.194597i
$714$		0			0
$715$	16.8990	+	29.2699i	0.631986	+	1.09463i
$716$	−8.69694			−0.325020
$717$	9.27526	+	20.1329i	0.346391	+	0.751876i
$718$	10.7980			0.402976
$719$	−4.89898	+	8.48528i	−0.182701	+	0.316448i	−0.942799	−	0.333360i	$-0.891817\pi$
$719$	−4.89898	+	8.48528i	−0.182701	+	0.316448i	0.760098	+	0.649808i	$0.225151\pi$
$720$	3.44949	+	9.75663i	0.128555	+	0.363608i
$721$		0			0
$722$	−18.2474	+	31.6055i	−0.679100	+	1.17624i
$723$	15.3485	+	1.41421i	0.570816	+	0.0525952i
$724$	2.17423	−	3.76588i	0.0808048	−	0.139958i
$725$	−10.0000	+	17.3205i	−0.371391	+	0.643268i
$726$	5.07321	+	11.0119i	0.188285	+	0.408691i
$727$	20.2474	−	35.0696i	0.750936	−	1.30066i	−0.196433	−	0.980517i	$-0.562936\pi$
$727$	20.2474	−	35.0696i	0.750936	−	1.30066i	0.947369	−	0.320143i	$-0.103731\pi$
$728$		0			0
$729$	23.0000	+	14.1421i	0.851852	+	0.523783i
$730$	−5.00000	+	8.66025i	−0.185058	+	0.320530i
$731$	5.79796			0.214445
$732$	−19.7474	−	1.81954i	−0.729887	−	0.0672520i
$733$	12.5505			0.463564			0.231782	−	0.972768i	$-0.425544\pi$
$733$	12.5505			0.463564			0.231782	+	0.972768i	$0.425544\pi$
$734$	2.89898	+	5.02118i	0.107003	+	0.185335i
$735$		0			0
$736$	0.500000	−	0.866025i	0.0184302	−	0.0319221i
$737$	3.10102	−	5.37113i	0.114228	−	0.197848i
$738$	−19.1010	+	22.3417i	−0.703118	+	0.822409i
$739$	12.7980	+	22.1667i	0.470781	+	0.815416i	0.999441	−	0.0334173i	$-0.0106390\pi$
$739$	12.7980	+	22.1667i	0.470781	+	0.815416i	−0.528661	+	0.848833i	$0.677306\pi$
$740$	−13.4495	−	23.2952i	−0.494413	−	0.856349i
$741$	−62.9444	−	5.79972i	−2.31232	−	0.213058i
$742$		0			0
$743$	−18.0000	−	31.1769i	−0.660356	−	1.14377i	−0.980522	−	0.196409i	$-0.937072\pi$
$743$	−18.0000	−	31.1769i	−0.660356	−	1.14377i	0.320166	−	0.947361i	$-0.396261\pi$
$744$	6.00000	−	8.48528i	0.219971	−	0.311086i
$745$	20.6969			0.758277
$746$	−1.44949	−	2.51059i	−0.0530696	−	0.0919192i
$747$	3.89898	−	4.56048i	0.142656	−	0.166859i
$748$	−4.00000			−0.146254
$749$		0			0
$750$	4.74745	+	10.3048i	0.173352	+	0.376279i
$751$	40.5959			1.48137			0.740683	−	0.671855i	$-0.234502\pi$
$751$	40.5959			1.48137			0.740683	+	0.671855i	$0.234502\pi$
$752$	−4.89898	+	8.48528i	−0.178647	+	0.309426i
$753$	−21.6464	−	1.99451i	−0.788840	−	0.0726840i
$754$	−7.10102	−	12.2993i	−0.258604	−	0.447915i
$755$	17.2474			0.627699
$756$		0			0
$757$	23.3939			0.850265			0.425132	−	0.905131i	$-0.360228\pi$
$757$	23.3939			0.850265			0.425132	+	0.905131i	$0.360228\pi$
$758$	13.2474	+	22.9453i	0.481169	+	0.833409i
$759$	−3.44949	−	0.317837i	−0.125209	−	0.0115368i
$760$	−12.8485	+	22.2542i	−0.466063	+	0.807245i
$761$	−2.00000			−0.0724999			−0.0362500	−	0.999343i	$-0.511541\pi$
$761$	−2.00000			−0.0724999			−0.0362500	+	0.999343i	$0.511541\pi$
$762$	2.17423	+	4.71940i	0.0787642	+	0.170966i
$763$		0			0
$764$	13.8990			0.502847
$765$	−6.89898	−	19.5133i	−0.249433	−	0.705503i
$766$	3.44949	+	5.97469i	0.124635	+	0.215874i
$767$	9.79796			0.353784
$768$	−1.00000	+	1.41421i	−0.0360844	+	0.0510310i
$769$	27.0454	+	46.8440i	0.975282	+	1.68924i	0.679000	+	0.734138i	$0.262414\pi$
$769$	27.0454	+	46.8440i	0.975282	+	1.68924i	0.296282	+	0.955100i	$0.404253\pi$
$770$		0			0
$771$	−47.9444	−	4.41761i	−1.72667	−	0.159096i
$772$	4.05051	+	7.01569i	0.145781	+	0.252500i
$773$	−9.97219	−	17.2723i	−0.358675	−	0.621243i	0.629065	−	0.777353i	$-0.283438\pi$
$773$	−9.97219	−	17.2723i	−0.358675	−	0.621243i	−0.987740	+	0.156110i	$0.950105\pi$
$774$	−8.55051	−	1.58919i	−0.307342	−	0.0571221i
$775$	20.6969	−	35.8481i	0.743456	−	1.28770i
$776$	−3.44949	+	5.97469i	−0.123829	+	0.214479i
$777$		0			0
$778$	7.55051	+	13.0779i	0.270699	+	0.468864i
$779$	−72.9898			−2.61513
$780$	−29.1464	−	2.68556i	−1.04361	−	0.0961586i
$781$	19.7980			0.708427
$782$	−1.00000	+	1.73205i	−0.0357599	+	0.0619380i
$783$	−10.7980	+	10.5031i	−0.385888	+	0.375349i
$784$		0			0
$785$	−10.9495	+	18.9651i	−0.390804	+	0.676892i
$786$	−9.74745	−	21.1578i	−0.347680	−	0.754675i
$787$	23.6969	−	41.0443i	0.844705	−	1.46307i	−0.0411728	−	0.999152i	$-0.513109\pi$
$787$	23.6969	−	41.0443i	0.844705	−	1.46307i	0.885877	−	0.463919i	$-0.153557\pi$
$788$	6.34847	−	10.9959i	0.226155	−	0.391712i
$789$	27.7702	+	2.55875i	0.988644	+	0.0910940i
$790$	13.6237	−	23.5970i	0.484710	−	0.839543i
$791$		0			0
$792$	5.89898	+	1.09638i	0.209611	+	0.0389580i
$793$	28.0454	−	48.5761i	0.995922	−	1.72499i
$794$	−9.30306			−0.330153
$795$	−2.75255	−	5.97469i	−0.0976229	−	0.211900i
$796$	−6.89898			−0.244528
$797$	17.9722	+	31.1288i	0.636608	+	1.10264i	0.986172	+	0.165725i	$0.0529963\pi$
$797$	17.9722	+	31.1288i	0.636608	+	1.10264i	−0.349564	+	0.936912i	$0.613670\pi$
$798$		0			0
$799$	9.79796	−	16.9706i	0.346627	−	0.600375i
$800$	−3.44949	+	5.97469i	−0.121958	+	0.211237i
$801$	−13.8434	+	16.1920i	−0.489131	+	0.572117i
$802$	5.05051	+	8.74774i	0.178340	+	0.308893i
$803$	2.89898	+	5.02118i	0.102303	+	0.177194i
$804$	2.24745	+	4.87832i	0.0792614	+	0.172045i
$805$		0			0
$806$	14.6969	+	25.4558i	0.517678	+	0.896644i
$807$	−2.64643	−	5.74434i	−0.0931587	−	0.202210i
$808$	−7.24745			−0.254964
$809$	17.8990	+	31.0019i	0.629295	+	1.08997i	0.987694	+	0.156402i	$0.0499894\pi$
$809$	17.8990	+	31.0019i	0.629295	+	1.08997i	−0.358399	+	0.933569i	$0.616677\pi$
$810$	4.82577	+	30.6681i	0.169560	+	1.07757i
$811$	2.00000			0.0702295			0.0351147	−	0.999383i	$-0.488820\pi$
$811$	2.00000			0.0702295			0.0351147	+	0.999383i	$0.488820\pi$
$812$		0			0
$813$	16.8990	−	23.8988i	0.592673	−	0.838166i
$814$	−15.5959			−0.546637
$815$	−0.348469	+	0.603566i	−0.0122063	+	0.0211420i
$816$	2.00000	−	2.82843i	0.0700140	−	0.0990148i
$817$	−10.7980	−	18.7026i	−0.377773	−	0.654322i
$818$	−5.79796			−0.202721
$819$		0			0
$820$	−33.7980			−1.18028
$821$	−19.7980	−	34.2911i	−0.690954	−	1.19677i	−0.971526	−	0.236934i	$-0.923858\pi$
$821$	−19.7980	−	34.2911i	−0.690954	−	1.19677i	0.280572	−	0.959833i	$-0.409476\pi$
$822$	8.55051	+	18.5597i	0.298233	+	0.647346i
$823$	−22.6969	+	39.3123i	−0.791166	+	1.37034i	0.134080	+	0.990970i	$0.457192\pi$
$823$	−22.6969	+	39.3123i	−0.791166	+	1.37034i	−0.925246	+	0.379368i	$0.876141\pi$
$824$	−14.0000			−0.487713
$825$	23.7980	+	2.19275i	0.828539	+	0.0763418i
$826$		0			0
$827$	12.4949			0.434490			0.217245	−	0.976117i	$-0.430293\pi$
$827$	12.4949			0.434490			0.217245	+	0.976117i	$0.430293\pi$
$828$	1.94949	−	2.28024i	0.0677495	−	0.0792438i
$829$	15.3485	+	26.5843i	0.533074	+	0.923312i	0.999254	+	0.0386218i	$0.0122967\pi$
$829$	15.3485	+	26.5843i	0.533074	+	0.923312i	−0.466180	+	0.884690i	$0.654370\pi$
$830$	6.89898			0.239467
$831$	18.4495	+	1.69994i	0.640006	+	0.0589704i
$832$	−2.44949	−	4.24264i	−0.0849208	−	0.147087i
$833$		0			0
$834$	9.44949	−	13.3636i	0.327209	−	0.462744i
$835$	−32.2474	−	55.8542i	−1.11597	−	1.93291i
$836$	7.44949	+	12.9029i	0.257646	+	0.446256i
$837$	22.3485	−	21.7381i	0.772476	−	0.751379i
$838$	12.2753	−	21.2614i	0.424042	−	0.734462i
$839$	−22.4495	+	38.8837i	−0.775042	+	1.34241i	0.159728	+	0.987161i	$0.448938\pi$
$839$	−22.4495	+	38.8837i	−0.775042	+	1.34241i	−0.934771	+	0.355252i	$0.884395\pi$
$840$		0			0
$841$	10.2980	+	17.8366i	0.355102	+	0.615055i
$842$	13.1010			0.451491
$843$	19.0000	−	26.8701i	0.654395	−	0.925454i
$844$	3.10102			0.106742
$845$	18.9722	−	32.8608i	0.652663	−	1.13045i
$846$	−19.1010	+	22.3417i	−0.656707	+	0.768123i
$847$		0			0
$848$	0.550510	−	0.953512i	0.0189046	−	0.0327437i
$849$	−20.5505	+	29.0628i	−0.705292	+	0.997433i
$850$	6.89898	−	11.9494i	0.236633	−	0.409860i
$851$	−3.89898	+	6.75323i	−0.133655	+	0.231498i
$852$	−9.89898	+	13.9993i	−0.339133	+	0.479607i
$853$	−19.4217	+	33.6393i	−0.664986	+	1.15179i	0.314303	+	0.949323i	$0.398229\pi$
$853$	−19.4217	+	33.6393i	−0.664986	+	1.15179i	−0.979289	+	0.202467i	$0.935104\pi$
$854$		0			0
$855$	−50.0959	+	58.5952i	−1.71324	+	2.00391i
$856$	6.00000	−	10.3923i	0.205076	−	0.355202i
$857$	25.1010			0.857435			0.428717	−	0.903439i	$-0.358966\pi$
$857$	25.1010			0.857435			0.428717	+	0.903439i	$0.358966\pi$
$858$	−9.79796	+	13.8564i	−0.334497	+	0.473050i
$859$	10.0000			0.341196			0.170598	−	0.985341i	$-0.445430\pi$
$859$	10.0000			0.341196			0.170598	+	0.985341i	$0.445430\pi$
$860$	−5.00000	−	8.66025i	−0.170499	−	0.295312i
$861$		0			0
$862$	3.79796	−	6.57826i	0.129359	−	0.224056i
$863$	−1.05051	+	1.81954i	−0.0357598	+	0.0619378i	−0.883351	−	0.468711i	$-0.844718\pi$
$863$	−1.05051	+	1.81954i	−0.0357598	+	0.0619378i	0.847592	+	0.530649i	$0.178052\pi$
$864$	−3.72474	+	3.62302i	−0.126718	+	0.123258i
$865$	22.2474	+	38.5337i	0.756436	+	1.31019i
$866$	5.89898	+	10.2173i	0.200455	+	0.347199i
$867$	13.0000	−	18.3848i	0.441503	−	0.624380i
$868$		0			0
$869$	−7.89898	−	13.6814i	−0.267955	−	0.464111i
$870$	−17.2474	−	1.58919i	−0.584743	−	0.0538785i
$871$	−15.1918			−0.514756
$872$	8.34847	+	14.4600i	0.282715	+	0.489676i
$873$	−13.4495	+	15.7313i	−0.455196	+	0.532425i
$874$	7.44949			0.251983
$875$		0			0
$876$	−5.00000	−	0.460702i	−0.168934	−	0.0155657i
$877$	−26.4949			−0.894669			−0.447335	−	0.894367i	$-0.647627\pi$
$877$	−26.4949			−0.894669			−0.447335	+	0.894367i	$0.647627\pi$
$878$	10.8990	−	18.8776i	0.367823	−	0.637088i
$879$	19.7474	+	42.8638i	0.666065	+	1.44576i
$880$	3.44949	+	5.97469i	0.116282	+	0.201407i
$881$	19.5959			0.660203			0.330102	−	0.943945i	$-0.392917\pi$
$881$	19.5959			0.660203			0.330102	+	0.943945i	$0.392917\pi$
$882$		0			0
$883$	−0.202041			−0.00679922			−0.00339961	−	0.999994i	$-0.501082\pi$
$883$	−0.202041			−0.00679922			−0.00339961	+	0.999994i	$0.501082\pi$
$884$	4.89898	+	8.48528i	0.164771	+	0.285391i
$885$	6.89898	−	9.75663i	0.231907	−	0.327966i
$886$	2.55051	−	4.41761i	0.0856861	−	0.148413i
$887$	33.7980			1.13482			0.567412	−	0.823434i	$-0.307945\pi$
$887$	33.7980			1.13482			0.567412	+	0.823434i	$0.307945\pi$
$888$	7.79796	−	11.0280i	0.261682	−	0.370075i
$889$		0			0
$890$	−24.4949			−0.821071
$891$	16.7980	+	6.46750i	0.562753	+	0.216669i
$892$	−10.4495	−	18.0990i	−0.349875	−	0.606001i
$893$	−72.9898			−2.44251
$894$	4.34847	+	9.43879i	0.145435	+	0.315680i
$895$	−15.0000	−	25.9808i	−0.501395	−	0.868441i
$896$		0			0
$897$	3.55051	+	7.70674i	0.118548	+	0.257321i
$898$	9.29796	+	16.1045i	0.310277	+	0.537415i
$899$	8.69694	+	15.0635i	0.290059	+	0.502397i
$900$	−13.4495	+	15.7313i	−0.448316	+	0.524377i
$901$	−1.10102	+	1.90702i	−0.0366803	+	0.0635322i
$902$	−9.79796	+	16.9706i	−0.326236	+	0.565058i
$903$		0			0
$904$	7.94949	+	13.7689i	0.264396	+	0.457947i
$905$	15.0000			0.498617
$906$	3.62372	+	7.86566i	0.120390	+	0.261319i
$907$	−26.6969			−0.886457			−0.443229	−	0.896409i	$-0.646167\pi$
$907$	−26.6969			−0.886457			−0.443229	+	0.896409i	$0.646167\pi$
$908$	−0.275255	+	0.476756i	−0.00913466	+	0.0158217i
$909$	−21.3763	−	3.97297i	−0.709006	−	0.131775i
$910$		0			0
$911$	22.9949	−	39.8283i	0.761855	−	1.31957i	−0.180038	−	0.983660i	$-0.557622\pi$
$911$	22.9949	−	39.8283i	0.761855	−	1.31957i	0.941893	−	0.335912i	$-0.109044\pi$
$912$	−12.8485	−	1.18386i	−0.425455	−	0.0392016i
$913$	2.00000	−	3.46410i	0.0661903	−	0.114645i
$914$	−15.7474	+	27.2754i	−0.520879	+	0.902189i
$915$	−28.6237	−	62.1307i	−0.946271	−	2.05398i
$916$	−11.6237	+	20.1329i	−0.384059	+	0.665209i
$917$		0			0
$918$	7.44949	−	7.24604i	0.245870	−	0.239155i
$919$	−1.84847	+	3.20164i	−0.0609754	+	0.105612i	−0.894902	−	0.446263i	$-0.852754\pi$
$919$	−1.84847	+	3.20164i	−0.0609754	+	0.105612i	0.833926	+	0.551876i	$0.186088\pi$
$920$	3.44949			0.113726
$921$	−1.29796	−	0.119594i	−0.0427692	−	0.00394077i
$922$	−20.3485			−0.670141
$923$	−24.2474	−	41.9978i	−0.798114	−	1.38237i
$924$		0			0
$925$	26.8990	−	46.5904i	0.884433	−	1.53188i
$926$	12.8485	−	22.2542i	0.422227	−	0.731318i
$927$	−41.2929	−	7.67463i	−1.35624	−	0.252068i
$928$	−1.44949	−	2.51059i	−0.0475818	−	0.0824142i
$929$	−17.1464	−	29.6985i	−0.562556	−	0.974376i	−0.997272	−	0.0738083i	$-0.976485\pi$
$929$	−17.1464	−	29.6985i	−0.562556	−	0.974376i	0.434716	−	0.900567i	$-0.356849\pi$
$930$	35.6969	+	3.28913i	1.17055	+	0.107855i
$931$		0			0
$932$	3.50000	+	6.06218i	0.114646	+	0.198573i
$933$	1.30306	−	1.84281i	0.0426603	−	0.0603308i
$934$	−10.0000			−0.327210
$935$	−6.89898	−	11.9494i	−0.225621	−	0.390787i
$936$	−4.89898	−	13.8564i	−0.160128	−	0.452911i
$937$	−6.40408			−0.209212			−0.104606	−	0.994514i	$-0.533358\pi$
$937$	−6.40408			−0.209212			−0.104606	+	0.994514i	$0.533358\pi$
$938$		0			0
$939$	17.8990	+	38.8515i	0.584111	+	1.26787i
$940$	−33.7980			−1.10237
$941$	1.72474	−	2.98735i	0.0562251	−	0.0973847i	−0.836543	−	0.547901i	$-0.815427\pi$
$941$	1.72474	−	2.98735i	0.0562251	−	0.0973847i	0.892768	+	0.450517i	$0.148760\pi$
$942$	−10.9495	−	1.00889i	−0.356754	−	0.0328714i
$943$	4.89898	+	8.48528i	0.159533	+	0.276319i
$944$	2.00000			0.0650945
$945$		0			0
$946$	−5.79796			−0.188508
$947$	−1.75255	−	3.03551i	−0.0569503	−	0.0986408i	0.836145	−	0.548509i	$-0.184804\pi$
$947$	−1.75255	−	3.03551i	−0.0569503	−	0.0986408i	−0.893095	+	0.449868i	$0.851471\pi$
$948$	13.6237	+	1.25529i	0.442478	+	0.0407701i
$949$	7.10102	−	12.2993i	0.230509	−	0.399253i
$950$	−51.3939			−1.66744
$951$	6.30306	+	13.6814i	0.204391	+	0.443651i
$952$		0			0
$953$	55.3939			1.79438			0.897192	−	0.441641i	$-0.145604\pi$
$953$	55.3939			1.79438			0.897192	+	0.441641i	$0.145604\pi$
$954$	2.14643	−	2.51059i	0.0694932	−	0.0812833i
$955$	23.9722	+	41.5211i	0.775722	+	1.34359i
$956$	−12.7980			−0.413916
$957$	−5.79796	+	8.19955i	−0.187421	+	0.265054i
$958$	−14.7980	−	25.6308i	−0.478100	−	0.828094i
$959$		0			0
$960$	−5.94949	−	0.548188i	−0.192019	−	0.0176927i
$961$	−2.50000	−	4.33013i	−0.0806452	−	0.139682i
$962$	19.1010	+	33.0839i	0.615842	+	1.06667i
$963$	23.3939	−	27.3629i	0.753857	−	0.881756i
$964$	−4.44949	+	7.70674i	−0.143308	+	0.248217i
$965$	−13.9722	+	24.2005i	−0.449781	+	0.779043i
$966$		0			0
$967$	7.29796	+	12.6404i	0.234687	+	0.406489i	0.959182	−	0.282791i	$-0.0912603\pi$
$967$	7.29796	+	12.6404i	0.234687	+	0.406489i	−0.724495	+	0.689280i	$0.757927\pi$
$968$	−7.00000			−0.224989
$969$	25.6969	+	2.36773i	0.825505	+	0.0760623i
$970$	−23.7980			−0.764106
$971$	−26.9722	+	46.7172i	−0.865579	+	1.49923i	0.000892350		1.00000i	$0.499716\pi$
$971$	−26.9722	+	46.7172i	−0.865579	+	1.49923i	−0.866471	+	0.499227i	$0.833617\pi$
$972$	−12.9722	+	8.64420i	−0.416083	+	0.277263i
$973$		0			0
$974$	−11.1969	+	19.3937i	−0.358773	+	0.621413i
$975$	−24.4949	−	53.1687i	−0.784465	−	1.70276i
$976$	5.72474	−	9.91555i	0.183245	−	0.317389i
$977$	−0.797959	+	1.38211i	−0.0255290	+	0.0442175i	−0.878508	−	0.477728i	$-0.841460\pi$
$977$	−0.797959	+	1.38211i	−0.0255290	+	0.0442175i	0.852979	+	0.521946i	$0.174794\pi$
$978$	−0.348469	−	0.0321081i	−0.0111428	−	0.00102670i
$979$	−7.10102	+	12.2993i	−0.226950	+	0.393088i
$980$		0			0
$981$	16.6969	+	47.2261i	0.533092	+	1.50781i
$982$	1.89898	−	3.28913i	0.0605989	−	0.104960i
$983$	−45.1918			−1.44140			−0.720698	−	0.693249i	$-0.756178\pi$
$983$	−45.1918			−1.44140			−0.720698	+	0.693249i	$0.756178\pi$
$984$	−7.10102	−	15.4135i	−0.226372	−	0.491364i
$985$	43.7980			1.39552
$986$	2.89898	+	5.02118i	0.0923223	+	0.159907i
$987$		0			0
$988$	18.2474	−	31.6055i	0.580529	−	1.00551i
$989$	−1.44949	+	2.51059i	−0.0460911	+	0.0798321i
$990$	6.89898	+	19.5133i	0.219264	+	0.620172i
$991$	−8.89898	−	15.4135i	−0.282685	−	0.489625i	0.689360	−	0.724419i	$-0.257892\pi$
$991$	−8.89898	−	15.4135i	−0.282685	−	0.489625i	−0.972045	+	0.234794i	$0.924559\pi$
$992$	3.00000	+	5.19615i	0.0952501	+	0.164978i
$993$	17.8990	+	38.8515i	0.568007	+	1.23292i
$994$		0			0
$995$	−11.8990	−	20.6096i	−0.377223	−	0.653369i
$996$	1.44949	+	3.14626i	0.0459288	+	0.0996932i
$997$	−17.8536			−0.565428			−0.282714	−	0.959204i	$-0.591235\pi$
$997$	−17.8536			−0.565428			−0.282714	+	0.959204i	$0.591235\pi$
$998$	−16.6969	−	28.9199i	−0.528532	−	0.915445i
$999$	29.0454	−	28.2522i	0.918956	−	0.893859i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.h.l.79.2		4
3.2	odd	2		2646.2.h.n.667.2		4
7.2	even	3		882.2.f.j.295.2		4
7.3	odd	6		882.2.e.m.655.2		4
7.4	even	3		882.2.e.n.655.1		4
7.5	odd	6		126.2.f.c.43.1	✓	4
7.6	odd	2		882.2.h.k.79.1		4
9.4	even	3		882.2.e.n.373.1		4
9.5	odd	6		2646.2.e.k.1549.1		4
21.2	odd	6		2646.2.f.k.883.1		4
21.5	even	6		378.2.f.d.127.2		4
21.11	odd	6		2646.2.e.k.2125.1		4
21.17	even	6		2646.2.e.l.2125.2		4
21.20	even	2		2646.2.h.m.667.1		4
28.19	even	6		1008.2.r.e.673.2		4
63.2	odd	6		7938.2.a.bm.1.2		2
63.4	even	3	inner	882.2.h.l.67.2		4
63.5	even	6		378.2.f.d.253.2		4
63.13	odd	6		882.2.e.m.373.2		4
63.16	even	3		7938.2.a.bn.1.1		2
63.23	odd	6		2646.2.f.k.1765.1		4
63.31	odd	6		882.2.h.k.67.1		4
63.32	odd	6		2646.2.h.n.361.2		4
63.40	odd	6		126.2.f.c.85.2	yes	4
63.41	even	6		2646.2.e.l.1549.2		4
63.47	even	6		1134.2.a.i.1.1		2
63.58	even	3		882.2.f.j.589.1		4
63.59	even	6		2646.2.h.m.361.1		4
63.61	odd	6		1134.2.a.p.1.2		2
84.47	odd	6		3024.2.r.e.2017.2		4
252.47	odd	6		9072.2.a.bd.1.1		2
252.103	even	6		1008.2.r.e.337.1		4
252.131	odd	6		3024.2.r.e.1009.2		4
252.187	even	6		9072.2.a.bk.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.2.f.c.43.1	✓	4	7.5	odd	6
126.2.f.c.85.2	yes	4	63.40	odd	6
378.2.f.d.127.2		4	21.5	even	6
378.2.f.d.253.2		4	63.5	even	6
882.2.e.m.373.2		4	63.13	odd	6
882.2.e.m.655.2		4	7.3	odd	6
882.2.e.n.373.1		4	9.4	even	3
882.2.e.n.655.1		4	7.4	even	3
882.2.f.j.295.2		4	7.2	even	3
882.2.f.j.589.1		4	63.58	even	3
882.2.h.k.67.1		4	63.31	odd	6
882.2.h.k.79.1		4	7.6	odd	2
882.2.h.l.67.2		4	63.4	even	3	inner
882.2.h.l.79.2		4	1.1	even	1	trivial
1008.2.r.e.337.1		4	252.103	even	6
1008.2.r.e.673.2		4	28.19	even	6
1134.2.a.i.1.1		2	63.47	even	6
1134.2.a.p.1.2		2	63.61	odd	6
2646.2.e.k.1549.1		4	9.5	odd	6
2646.2.e.k.2125.1		4	21.11	odd	6
2646.2.e.l.1549.2		4	63.41	even	6
2646.2.e.l.2125.2		4	21.17	even	6
2646.2.f.k.883.1		4	21.2	odd	6
2646.2.f.k.1765.1		4	63.23	odd	6
2646.2.h.m.361.1		4	63.59	even	6
2646.2.h.m.667.1		4	21.20	even	2
2646.2.h.n.361.2		4	63.32	odd	6
2646.2.h.n.667.2		4	3.2	odd	2
3024.2.r.e.1009.2		4	252.131	odd	6
3024.2.r.e.2017.2		4	84.47	odd	6
7938.2.a.bm.1.2		2	63.2	odd	6
7938.2.a.bn.1.1		2	63.16	even	3
9072.2.a.bd.1.1		2	252.47	odd	6
9072.2.a.bk.1.2		2	252.187	even	6

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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	882.h (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.72474 + 0.158919i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.44949 q^{5} +(-0.724745 - 1.57313i) q^{6} +1.00000 q^{8} +(2.94949 + 0.548188i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(1.72474 + 0.158919i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.44949 q^{5} +(-0.724745 - 1.57313i) q^{6} +1.00000 q^{8} +(2.94949 + 0.548188i) q^{9} +(1.72474 + 2.98735i) q^{10} +2.00000 q^{11} +(-1.00000 + 1.41421i) q^{12} +(-2.44949 - 4.24264i) q^{13} +(-5.94949 - 0.548188i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(1.00000 + 1.73205i) q^{17} +(-1.00000 - 2.82843i) q^{18} +(3.72474 - 6.45145i) q^{19} +(1.72474 - 2.98735i) q^{20} +(-1.00000 - 1.73205i) q^{22} -1.00000 q^{23} +(1.72474 + 0.158919i) q^{24} +6.89898 q^{25} +(-2.44949 + 4.24264i) q^{26} +(5.00000 + 1.41421i) q^{27} +(-1.44949 + 2.51059i) q^{29} +(2.50000 + 5.42650i) q^{30} +(3.00000 - 5.19615i) q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.44949 + 0.317837i) q^{33} +(1.00000 - 1.73205i) q^{34} +(-1.94949 + 2.28024i) q^{36} +(3.89898 - 6.75323i) q^{37} -7.44949 q^{38} +(-3.55051 - 7.70674i) q^{39} -3.44949 q^{40} +(-4.89898 - 8.48528i) q^{41} +(1.44949 - 2.51059i) q^{43} +(-1.00000 + 1.73205i) q^{44} +(-10.1742 - 1.89097i) q^{45} +(0.500000 + 0.866025i) q^{46} +(-4.89898 - 8.48528i) q^{47} +(-0.724745 - 1.57313i) q^{48} +(-3.44949 - 5.97469i) q^{50} +(1.44949 + 3.14626i) q^{51} +4.89898 q^{52} +(0.550510 + 0.953512i) q^{53} +(-1.27526 - 5.03723i) q^{54} -6.89898 q^{55} +(7.44949 - 10.5352i) q^{57} +2.89898 q^{58} +(-1.00000 + 1.73205i) q^{59} +(3.44949 - 4.87832i) q^{60} +(5.72474 + 9.91555i) q^{61} -6.00000 q^{62} +1.00000 q^{64} +(8.44949 + 14.6349i) q^{65} +(-1.44949 - 3.14626i) q^{66} +(1.55051 - 2.68556i) q^{67} -2.00000 q^{68} +(-1.72474 - 0.158919i) q^{69} +9.89898 q^{71} +(2.94949 + 0.548188i) q^{72} +(1.44949 + 2.51059i) q^{73} -7.79796 q^{74} +(11.8990 + 1.09638i) q^{75} +(3.72474 + 6.45145i) q^{76} +(-4.89898 + 6.92820i) q^{78} +(-3.94949 - 6.84072i) q^{79} +(1.72474 + 2.98735i) q^{80} +(8.39898 + 3.23375i) q^{81} +(-4.89898 + 8.48528i) q^{82} +(1.00000 - 1.73205i) q^{83} +(-3.44949 - 5.97469i) q^{85} -2.89898 q^{86} +(-2.89898 + 4.09978i) q^{87} +2.00000 q^{88} +(-3.55051 + 6.14966i) q^{89} +(3.44949 + 9.75663i) q^{90} +(0.500000 - 0.866025i) q^{92} +(6.00000 - 8.48528i) q^{93} +(-4.89898 + 8.48528i) q^{94} +(-12.8485 + 22.2542i) q^{95} +(-1.00000 + 1.41421i) q^{96} +(-3.44949 + 5.97469i) q^{97} +(5.89898 + 1.09638i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 4 q^{5} + 2 q^{6} + 4 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 4 * q^5 + 2 * q^6 + 4 * q^8 + 2 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 4 q^{5} + 2 q^{6} + 4 q^{8} + 2 q^{9} + 2 q^{10} + 8 q^{11} - 4 q^{12} - 14 q^{15} - 2 q^{16} + 4 q^{17} - 4 q^{18} + 10 q^{19} + 2 q^{20} - 4 q^{22} - 4 q^{23} + 2 q^{24} + 8 q^{25} + 20 q^{27} + 4 q^{29} + 10 q^{30} + 12 q^{31} - 2 q^{32} + 4 q^{33} + 4 q^{34} + 2 q^{36} - 4 q^{37} - 20 q^{38} - 24 q^{39} - 4 q^{40} - 4 q^{43} - 4 q^{44} - 26 q^{45} + 2 q^{46} + 2 q^{48} - 4 q^{50} - 4 q^{51} + 12 q^{53} - 10 q^{54} - 8 q^{55} + 20 q^{57} - 8 q^{58} - 4 q^{59} + 4 q^{60} + 18 q^{61} - 24 q^{62} + 4 q^{64} + 24 q^{65} + 4 q^{66} + 16 q^{67} - 8 q^{68} - 2 q^{69} + 20 q^{71} + 2 q^{72} - 4 q^{73} + 8 q^{74} + 28 q^{75} + 10 q^{76} - 6 q^{79} + 2 q^{80} + 14 q^{81} + 4 q^{83} - 4 q^{85} + 8 q^{86} + 8 q^{87} + 8 q^{88} - 24 q^{89} + 4 q^{90} + 2 q^{92} + 24 q^{93} - 22 q^{95} - 4 q^{96} - 4 q^{97} + 4 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 4 * q^5 + 2 * q^6 + 4 * q^8 + 2 * q^9 + 2 * q^10 + 8 * q^11 - 4 * q^12 - 14 * q^15 - 2 * q^16 + 4 * q^17 - 4 * q^18 + 10 * q^19 + 2 * q^20 - 4 * q^22 - 4 * q^23 + 2 * q^24 + 8 * q^25 + 20 * q^27 + 4 * q^29 + 10 * q^30 + 12 * q^31 - 2 * q^32 + 4 * q^33 + 4 * q^34 + 2 * q^36 - 4 * q^37 - 20 * q^38 - 24 * q^39 - 4 * q^40 - 4 * q^43 - 4 * q^44 - 26 * q^45 + 2 * q^46 + 2 * q^48 - 4 * q^50 - 4 * q^51 + 12 * q^53 - 10 * q^54 - 8 * q^55 + 20 * q^57 - 8 * q^58 - 4 * q^59 + 4 * q^60 + 18 * q^61 - 24 * q^62 + 4 * q^64 + 24 * q^65 + 4 * q^66 + 16 * q^67 - 8 * q^68 - 2 * q^69 + 20 * q^71 + 2 * q^72 - 4 * q^73 + 8 * q^74 + 28 * q^75 + 10 * q^76 - 6 * q^79 + 2 * q^80 + 14 * q^81 + 4 * q^83 - 4 * q^85 + 8 * q^86 + 8 * q^87 + 8 * q^88 - 24 * q^89 + 4 * q^90 + 2 * q^92 + 24 * q^93 - 22 * q^95 - 4 * q^96 - 4 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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