LMFDB - Embedded newform 882.2.e.m.655.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,2,Mod(373,882)]

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, 2]))

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

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

chi := DirichletCharacter("882.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	882.e (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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			655.2
Root			$-1.22474 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	882.655
Dual form			882.2.e.m.373.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(0.724745 + 1.57313i) q^{3} +1.00000 q^{4} +(-1.72474 + 2.98735i) q^{5} +(0.724745 + 1.57313i) q^{6} +1.00000 q^{8} +(-1.94949 + 2.28024i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(0.724745 + 1.57313i) q^{3} +1.00000 q^{4} +(-1.72474 + 2.98735i) q^{5} +(0.724745 + 1.57313i) q^{6} +1.00000 q^{8} +(-1.94949 + 2.28024i) q^{9} +(-1.72474 + 2.98735i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(0.724745 + 1.57313i) q^{12} +(2.44949 + 4.24264i) q^{13} +(-5.94949 - 0.548188i) q^{15} +1.00000 q^{16} +(-1.00000 + 1.73205i) q^{17} +(-1.94949 + 2.28024i) q^{18} +(-3.72474 - 6.45145i) q^{19} +(-1.72474 + 2.98735i) q^{20} +(-1.00000 - 1.73205i) q^{22} +(0.500000 - 0.866025i) q^{23} +(0.724745 + 1.57313i) q^{24} +(-3.44949 - 5.97469i) q^{25} +(2.44949 + 4.24264i) q^{26} +(-5.00000 - 1.41421i) q^{27} +(-1.44949 + 2.51059i) q^{29} +(-5.94949 - 0.548188i) q^{30} +6.00000 q^{31} +1.00000 q^{32} +(2.00000 - 2.82843i) q^{33} +(-1.00000 + 1.73205i) q^{34} +(-1.94949 + 2.28024i) q^{36} +(3.89898 + 6.75323i) q^{37} +(-3.72474 - 6.45145i) q^{38} +(-4.89898 + 6.92820i) q^{39} +(-1.72474 + 2.98735i) q^{40} +(4.89898 + 8.48528i) q^{41} +(1.44949 - 2.51059i) q^{43} +(-1.00000 - 1.73205i) q^{44} +(-3.44949 - 9.75663i) q^{45} +(0.500000 - 0.866025i) q^{46} -9.79796 q^{47} +(0.724745 + 1.57313i) q^{48} +(-3.44949 - 5.97469i) q^{50} +(-3.44949 - 0.317837i) q^{51} +(2.44949 + 4.24264i) q^{52} +(0.550510 - 0.953512i) q^{53} +(-5.00000 - 1.41421i) q^{54} +6.89898 q^{55} +(7.44949 - 10.5352i) q^{57} +(-1.44949 + 2.51059i) q^{58} -2.00000 q^{59} +(-5.94949 - 0.548188i) q^{60} +11.4495 q^{61} +6.00000 q^{62} +1.00000 q^{64} -16.8990 q^{65} +(2.00000 - 2.82843i) q^{66} -3.10102 q^{67} +(-1.00000 + 1.73205i) q^{68} +(1.72474 + 0.158919i) q^{69} +9.89898 q^{71} +(-1.94949 + 2.28024i) q^{72} +(-1.44949 + 2.51059i) q^{73} +(3.89898 + 6.75323i) q^{74} +(6.89898 - 9.75663i) q^{75} +(-3.72474 - 6.45145i) q^{76} +(-4.89898 + 6.92820i) q^{78} +7.89898 q^{79} +(-1.72474 + 2.98735i) q^{80} +(-1.39898 - 8.89060i) q^{81} +(4.89898 + 8.48528i) q^{82} +(-1.00000 + 1.73205i) q^{83} +(-3.44949 - 5.97469i) q^{85} +(1.44949 - 2.51059i) q^{86} +(-5.00000 - 0.460702i) q^{87} +(-1.00000 - 1.73205i) q^{88} +(3.55051 + 6.14966i) q^{89} +(-3.44949 - 9.75663i) q^{90} +(0.500000 - 0.866025i) q^{92} +(4.34847 + 9.43879i) q^{93} -9.79796 q^{94} +25.6969 q^{95} +(0.724745 + 1.57313i) q^{96} +(3.44949 - 5.97469i) q^{97} +(5.89898 + 1.09638i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} + 4 q^{8} + 2 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 + 4 * q^8 + 2 * q^9	$ 4 q + 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} + 4 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{11} - 2 q^{12} - 14 q^{15} + 4 q^{16} - 4 q^{17} + 2 q^{18} - 10 q^{19} - 2 q^{20} - 4 q^{22} + 2 q^{23} - 2 q^{24} - 4 q^{25} - 20 q^{27} + 4 q^{29} - 14 q^{30} + 24 q^{31} + 4 q^{32} + 8 q^{33} - 4 q^{34} + 2 q^{36} - 4 q^{37} - 10 q^{38} - 2 q^{40} - 4 q^{43} - 4 q^{44} - 4 q^{45} + 2 q^{46} - 2 q^{48} - 4 q^{50} - 4 q^{51} + 12 q^{53} - 20 q^{54} + 8 q^{55} + 20 q^{57} + 4 q^{58} - 8 q^{59} - 14 q^{60} + 36 q^{61} + 24 q^{62} + 4 q^{64} - 48 q^{65} + 8 q^{66} - 32 q^{67} - 4 q^{68} + 2 q^{69} + 20 q^{71} + 2 q^{72} + 4 q^{73} - 4 q^{74} + 8 q^{75} - 10 q^{76} + 12 q^{79} - 2 q^{80} + 14 q^{81} - 4 q^{83} - 4 q^{85} - 4 q^{86} - 20 q^{87} - 4 q^{88} + 24 q^{89} - 4 q^{90} + 2 q^{92} - 12 q^{93} + 44 q^{95} - 2 q^{96} + 4 q^{97} + 4 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 + 4 * q^8 + 2 * q^9 - 2 * q^10 - 4 * q^11 - 2 * q^12 - 14 * q^15 + 4 * q^16 - 4 * q^17 + 2 * q^18 - 10 * q^19 - 2 * q^20 - 4 * q^22 + 2 * q^23 - 2 * q^24 - 4 * q^25 - 20 * q^27 + 4 * q^29 - 14 * q^30 + 24 * q^31 + 4 * q^32 + 8 * q^33 - 4 * q^34 + 2 * q^36 - 4 * q^37 - 10 * q^38 - 2 * q^40 - 4 * q^43 - 4 * q^44 - 4 * q^45 + 2 * q^46 - 2 * q^48 - 4 * q^50 - 4 * q^51 + 12 * q^53 - 20 * q^54 + 8 * q^55 + 20 * q^57 + 4 * q^58 - 8 * q^59 - 14 * q^60 + 36 * q^61 + 24 * q^62 + 4 * q^64 - 48 * q^65 + 8 * q^66 - 32 * q^67 - 4 * q^68 + 2 * q^69 + 20 * q^71 + 2 * q^72 + 4 * q^73 - 4 * q^74 + 8 * q^75 - 10 * q^76 + 12 * q^79 - 2 * q^80 + 14 * q^81 - 4 * q^83 - 4 * q^85 - 4 * q^86 - 20 * q^87 - 4 * q^88 + 24 * q^89 - 4 * q^90 + 2 * q^92 - 12 * q^93 + 44 * q^95 - 2 * q^96 + 4 * q^97 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	0.724745	+	1.57313i	0.418432	+	0.908248i
$3$	0.724745	+	1.57313i	0.418432	+	0.908248i
$4$	1.00000			0.500000
$5$	−1.72474	+	2.98735i	−0.771329	+	1.33598i	0.165505	+	0.986209i	$0.447075\pi$
$5$	−1.72474	+	2.98735i	−0.771329	+	1.33598i	−0.936835	+	0.349773i	$0.886259\pi$
$6$	0.724745	+	1.57313i	0.295876	+	0.642229i
$7$		0			0
$7$		0			0
$8$	1.00000			0.353553
$9$	−1.94949	+	2.28024i	−0.649830	+	0.760080i
$10$	−1.72474	+	2.98735i	−0.545412	+	0.944682i
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	0.674967	−	0.737848i	$-0.264158\pi$
$11$	−1.00000	−	1.73205i	−0.301511	−	0.522233i	−0.976478	+	0.215615i	$0.930824\pi$
$12$	0.724745	+	1.57313i	0.209216	+	0.454124i
$13$	2.44949	+	4.24264i	0.679366	+	1.17670i	0.975172	+	0.221449i	$0.0710785\pi$
$13$	2.44949	+	4.24264i	0.679366	+	1.17670i	−0.295806	+	0.955248i	$0.595588\pi$
$14$		0			0
$15$	−5.94949	−	0.548188i	−1.53615	−	0.141542i
$16$	1.00000			0.250000
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	−0.961436	−	0.275029i	$-0.911312\pi$
$17$	−1.00000	+	1.73205i	−0.242536	+	0.420084i	0.718900	+	0.695113i	$0.244646\pi$
$18$	−1.94949	+	2.28024i	−0.459499	+	0.537457i
$19$	−3.72474	−	6.45145i	−0.854515	−	1.48006i	−0.877094	−	0.480318i	$-0.840521\pi$
$19$	−3.72474	−	6.45145i	−0.854515	−	1.48006i	0.0225791	−	0.999745i	$-0.492812\pi$
$20$	−1.72474	+	2.98735i	−0.385665	+	0.667991i
$21$		0			0
$22$	−1.00000	−	1.73205i	−0.213201	−	0.369274i
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	−0.809177	−	0.587565i	$-0.800087\pi$
$23$	0.500000	−	0.866025i	0.104257	−	0.180579i	0.913434	+	0.406986i	$0.133420\pi$
$24$	0.724745	+	1.57313i	0.147938	+	0.321114i
$25$	−3.44949	−	5.97469i	−0.689898	−	1.19494i
$26$	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	$0.253414\pi$
$30$	−5.94949	−	0.548188i	−1.08622	−	0.100085i
$31$	6.00000			1.07763			0.538816	−	0.842424i	$-0.318872\pi$
$31$	6.00000			1.07763			0.538816	+	0.842424i	$0.318872\pi$
$32$	1.00000			0.176777
$33$	2.00000	−	2.82843i	0.348155	−	0.492366i
$34$	−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	0.985213	+	0.171337i	$0.0548086\pi$
$37$	3.89898	+	6.75323i	0.640988	+	1.11022i	−0.344224	+	0.938887i	$0.611858\pi$
$38$	−3.72474	−	6.45145i	−0.604233	−	1.04656i
$39$	−4.89898	+	6.92820i	−0.784465	+	1.10940i
$40$	−1.72474	+	2.98735i	−0.272706	+	0.472341i
$41$	4.89898	+	8.48528i	0.765092	+	1.32518i	0.940198	+	0.340629i	$0.110640\pi$
$41$	4.89898	+	8.48528i	0.765092	+	1.32518i	−0.175106	+	0.984550i	$0.556027\pi$
$42$		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
$45$	−3.44949	−	9.75663i	−0.514220	−	1.45443i
$46$	0.500000	−	0.866025i	0.0737210	−	0.127688i
$47$	−9.79796			−1.42918			−0.714590	−	0.699544i	$-0.753387\pi$
$47$	−9.79796			−1.42918			−0.714590	+	0.699544i	$0.753387\pi$
$48$	0.724745	+	1.57313i	0.104608	+	0.227062i
$49$		0			0
$50$	−3.44949	−	5.97469i	−0.487832	−	0.844949i
$51$	−3.44949	−	0.317837i	−0.483025	−	0.0445061i
$52$	2.44949	+	4.24264i	0.339683	+	0.588348i
$53$	0.550510	−	0.953512i	0.0756184	−	0.130975i	−0.825737	−	0.564056i	$-0.809240\pi$
$53$	0.550510	−	0.953512i	0.0756184	−	0.130975i	0.901355	+	0.433081i	$0.142574\pi$
$54$	−5.00000	−	1.41421i	−0.680414	−	0.192450i
$55$	6.89898			0.930258
$56$		0			0
$57$	7.44949	−	10.5352i	0.986709	−	1.39542i
$58$	−1.44949	+	2.51059i	−0.190327	+	0.329657i
$59$	−2.00000			−0.260378			−0.130189	−	0.991489i	$-0.541558\pi$
$59$	−2.00000			−0.260378			−0.130189	+	0.991489i	$0.541558\pi$
$60$	−5.94949	−	0.548188i	−0.768076	−	0.0707708i
$61$	11.4495			1.46596			0.732978	−	0.680252i	$-0.238130\pi$
$61$	11.4495			1.46596			0.732978	+	0.680252i	$0.238130\pi$
$62$	6.00000			0.762001
$63$		0			0
$64$	1.00000			0.125000
$65$	−16.8990			−2.09606
$66$	2.00000	−	2.82843i	0.246183	−	0.348155i
$67$	−3.10102			−0.378850			−0.189425	−	0.981895i	$-0.560662\pi$
$67$	−3.10102			−0.378850			−0.189425	+	0.981895i	$0.560662\pi$
$68$	−1.00000	+	1.73205i	−0.121268	+	0.210042i
$69$	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	$0.300153\pi$
$72$	−1.94949	+	2.28024i	−0.229750	+	0.268729i
$73$	−1.44949	+	2.51059i	−0.169650	+	0.293842i	−0.938297	−	0.345831i	$-0.887597\pi$
$73$	−1.44949	+	2.51059i	−0.169650	+	0.293842i	0.768647	+	0.639673i	$0.220930\pi$
$74$	3.89898	+	6.75323i	0.453247	+	0.785047i
$75$	6.89898	−	9.75663i	0.796626	−	1.12660i
$76$	−3.72474	−	6.45145i	−0.427258	−	0.740032i
$77$		0			0
$78$	−4.89898	+	6.92820i	−0.554700	+	0.784465i
$79$	7.89898			0.888705			0.444352	−	0.895852i	$-0.353434\pi$
$79$	7.89898			0.888705			0.444352	+	0.895852i	$0.353434\pi$
$80$	−1.72474	+	2.98735i	−0.192832	+	0.333995i
$81$	−1.39898	−	8.89060i	−0.155442	−	0.987845i
$82$	4.89898	+	8.48528i	0.541002	+	0.937043i
$83$	−1.00000	+	1.73205i	−0.109764	+	0.190117i	−0.915675	−	0.401920i	$-0.868343\pi$
$83$	−1.00000	+	1.73205i	−0.109764	+	0.190117i	0.805910	+	0.592037i	$0.201676\pi$
$84$		0			0
$85$	−3.44949	−	5.97469i	−0.374150	−	0.648046i
$86$	1.44949	−	2.51059i	0.156302	−	0.270724i
$87$	−5.00000	−	0.460702i	−0.536056	−	0.0493924i
$88$	−1.00000	−	1.73205i	−0.106600	−	0.184637i
$89$	3.55051	+	6.14966i	0.376353	+	0.651863i	0.990529	−	0.137307i	$-0.0438445\pi$
$89$	3.55051	+	6.14966i	0.376353	+	0.651863i	−0.614175	+	0.789170i	$0.710511\pi$
$90$	−3.44949	−	9.75663i	−0.363608	−	1.02844i
$91$		0			0
$92$	0.500000	−	0.866025i	0.0521286	−	0.0902894i
$93$	4.34847	+	9.43879i	0.450915	+	0.978757i
$94$	−9.79796			−1.01058
$95$	25.6969			2.63645
$96$	0.724745	+	1.57313i	0.0739690	+	0.160557i
$97$	3.44949	−	5.97469i	0.350243	−	0.606638i	−0.636049	−	0.771649i	$-0.719432\pi$
$97$	3.44949	−	5.97469i	0.350243	−	0.606638i	0.986292	+	0.165011i	$0.0527658\pi$
$98$		0			0
$99$	5.89898	+	1.09638i	0.592870	+	0.110190i
$100$	−3.44949	−	5.97469i	−0.344949	−	0.597469i
$101$	−3.62372	−	6.27647i	−0.360574	−	0.624533i	0.627481	−	0.778632i	$-0.284086\pi$
$101$	−3.62372	−	6.27647i	−0.360574	−	0.624533i	−0.988055	+	0.154099i	$0.950753\pi$
$102$	−3.44949	−	0.317837i	−0.341550	−	0.0314706i
$103$	−7.00000	+	12.1244i	−0.689730	+	1.19465i	0.282194	+	0.959357i	$0.408938\pi$
$103$	−7.00000	+	12.1244i	−0.689730	+	1.19465i	−0.971925	+	0.235291i	$0.924396\pi$
$104$	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	0.995474	+	0.0950377i	$0.0302972\pi$
$107$	6.00000	+	10.3923i	0.580042	+	1.00466i	−0.415432	+	0.909624i	$0.636370\pi$
$108$	−5.00000	−	1.41421i	−0.481125	−	0.136083i
$109$	8.34847	−	14.4600i	0.799638	−	1.38501i	−0.120213	−	0.992748i	$-0.538358\pi$
$109$	8.34847	−	14.4600i	0.799638	−	1.38501i	0.919852	−	0.392266i	$-0.128309\pi$
$110$	6.89898			0.657792
$111$	−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	$0.564431\pi$
$114$	7.44949	−	10.5352i	0.697709	−	0.986709i
$115$	1.72474	+	2.98735i	0.160833	+	0.278571i
$116$	−1.44949	+	2.51059i	−0.134582	+	0.233102i
$117$	−14.4495	−	2.68556i	−1.33586	−	0.248280i
$118$	−2.00000			−0.184115
$119$		0			0
$120$	−5.94949	−	0.548188i	−0.543112	−	0.0500425i
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	11.4495			1.03659
$123$	−9.79796	+	13.8564i	−0.883452	+	1.24939i
$124$	6.00000			0.538816
$125$	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	$0.542494\pi$
$128$	1.00000			0.0883883
$129$	5.00000	+	0.460702i	0.440225	+	0.0405625i
$130$	−16.8990			−1.48214
$131$	6.72474	−	11.6476i	0.587544	−	1.01766i	−0.407009	−	0.913424i	$-0.633428\pi$
$131$	6.72474	−	11.6476i	0.587544	−	1.01766i	0.994553	−	0.104232i	$-0.0332383\pi$
$132$	2.00000	−	2.82843i	0.174078	−	0.246183i
$133$		0			0
$134$	−3.10102			−0.267887
$135$	12.8485	−	12.4976i	1.10582	−	1.07562i
$136$	−1.00000	+	1.73205i	−0.0857493	+	0.148522i
$137$	5.89898	+	10.2173i	0.503984	+	0.872926i	0.999989	+	0.00460626i	$0.00146622\pi$
$137$	5.89898	+	10.2173i	0.503984	+	0.872926i	−0.496006	+	0.868319i	$0.665200\pi$
$138$	1.72474	+	0.158919i	0.146820	+	0.0135281i
$139$	−4.72474	−	8.18350i	−0.400748	−	0.694115i	0.593069	−	0.805152i	$-0.297916\pi$
$139$	−4.72474	−	8.18350i	−0.400748	−	0.694115i	−0.993816	+	0.111037i	$0.964583\pi$
$140$		0			0
$141$	−7.10102	−	15.4135i	−0.598014	−	1.29805i
$142$	9.89898			0.830704
$143$	4.89898	−	8.48528i	0.409673	−	0.709575i
$144$	−1.94949	+	2.28024i	−0.162457	+	0.190020i
$145$	−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
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$	6.89898	−	9.75663i	0.563299	−	0.796626i
$151$	2.50000	+	4.33013i	0.203447	+	0.352381i	0.949637	−	0.313353i	$-0.101452\pi$
$151$	2.50000	+	4.33013i	0.203447	+	0.352381i	−0.746190	+	0.665733i	$0.768119\pi$
$152$	−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
$156$	−4.89898	+	6.92820i	−0.392232	+	0.554700i
$157$	6.34847			0.506663			0.253332	−	0.967380i	$-0.418474\pi$
$157$	6.34847			0.506663			0.253332	+	0.967380i	$0.418474\pi$
$158$	7.89898			0.628409
$159$	1.89898	+	0.174973i	0.150599	+	0.0138762i
$160$	−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	0.869955	−	0.493132i	$-0.164148\pi$
$163$	0.101021	+	0.174973i	0.00791254	+	0.0137049i	−0.862042	+	0.506837i	$0.830815\pi$
$164$	4.89898	+	8.48528i	0.382546	+	0.662589i
$165$	5.00000	+	10.8530i	0.389249	+	0.844905i
$166$	−1.00000	+	1.73205i	−0.0776151	+	0.134433i
$167$	−9.34847	−	16.1920i	−0.723406	−	1.25298i	−0.959627	−	0.281277i	$-0.909242\pi$
$167$	−9.34847	−	16.1920i	−0.723406	−	1.25298i	0.236220	−	0.971700i	$-0.424091\pi$
$168$		0			0
$169$	−5.50000	+	9.52628i	−0.423077	+	0.732791i
$170$	−3.44949	−	5.97469i	−0.264564	−	0.458238i
$171$	21.9722	+	4.08372i	1.68026	+	0.312290i
$172$	1.44949	−	2.51059i	0.110523	−	0.191431i
$173$	−12.8990			−0.980691			−0.490346	−	0.871528i	$-0.663129\pi$
$173$	−12.8990			−0.980691			−0.490346	+	0.871528i	$0.663129\pi$
$174$	−5.00000	−	0.460702i	−0.379049	−	0.0349257i
$175$		0			0
$176$	−1.00000	−	1.73205i	−0.0753778	−	0.130558i
$177$	−1.44949	−	3.14626i	−0.108950	−	0.236488i
$178$	3.55051	+	6.14966i	0.266122	+	0.460937i
$179$	4.34847	−	7.53177i	0.325020	−	0.562951i	−0.656497	−	0.754329i	$-0.727962\pi$
$179$	4.34847	−	7.53177i	0.325020	−	0.562951i	0.981516	+	0.191378i	$0.0612957\pi$
$180$	−3.44949	−	9.75663i	−0.257110	−	0.727216i
$181$	4.34847			0.323219			0.161610	−	0.986855i	$-0.448331\pi$
$181$	4.34847			0.323219			0.161610	+	0.986855i	$0.448331\pi$
$182$		0			0
$183$	8.29796	+	18.0116i	0.613403	+	1.33145i
$184$	0.500000	−	0.866025i	0.0368605	−	0.0638442i
$185$	−26.8990			−1.97765
$186$	4.34847	+	9.43879i	0.318845	+	0.692086i
$187$	4.00000			0.292509
$188$	−9.79796			−0.714590
$189$		0			0
$190$	25.6969			1.86425
$191$	13.8990			1.00569			0.502847	−	0.864375i	$-0.332286\pi$
$191$	13.8990			1.00569			0.502847	+	0.864375i	$0.332286\pi$
$192$	0.724745	+	1.57313i	0.0523040	+	0.113531i
$193$	−8.10102			−0.583124			−0.291562	−	0.956552i	$-0.594175\pi$
$193$	−8.10102			−0.583124			−0.291562	+	0.956552i	$0.594175\pi$
$194$	3.44949	−	5.97469i	0.247659	−	0.428958i
$195$	−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	$0.649400\pi$
$198$	5.89898	+	1.09638i	0.419222	+	0.0779161i
$199$	−3.44949	+	5.97469i	−0.244528	+	0.423535i	−0.961999	−	0.273054i	$-0.911966\pi$
$199$	−3.44949	+	5.97469i	−0.244528	+	0.423535i	0.717471	+	0.696588i	$0.245300\pi$
$200$	−3.44949	−	5.97469i	−0.243916	−	0.422474i
$201$	−2.24745	−	4.87832i	−0.158523	−	0.344090i
$202$	−3.62372	−	6.27647i	−0.254964	−	0.441611i
$203$		0			0
$204$	−3.44949	−	0.317837i	−0.241513	−	0.0222531i
$205$	−33.7980			−2.36055
$206$	−7.00000	+	12.1244i	−0.487713	+	0.844744i
$207$	1.00000	+	2.82843i	0.0695048	+	0.196589i
$208$	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	$0.867375\pi$
$212$	0.550510	−	0.953512i	0.0378092	−	0.0654875i
$213$	7.17423	+	15.5724i	0.491570	+	1.06700i
$214$	6.00000	+	10.3923i	0.410152	+	0.710403i
$215$	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
$219$	−5.00000	−	0.460702i	−0.337869	−	0.0311313i
$220$	6.89898			0.465129
$221$	−9.79796			−0.659082
$222$	−7.79796	+	11.0280i	−0.523365	+	0.740150i
$223$	10.4495	−	18.0990i	0.699750	−	1.21200i	−0.268804	−	0.963195i	$-0.586628\pi$
$223$	10.4495	−	18.0990i	0.699750	−	1.21200i	0.968553	−	0.248807i	$-0.0800384\pi$
$224$		0			0
$225$	20.3485	+	3.78194i	1.35656	+	0.252129i
$226$	7.94949	+	13.7689i	0.528792	+	0.915895i
$227$	0.275255	+	0.476756i	0.0182693	+	0.0316434i	0.875016	−	0.484095i	$-0.160851\pi$
$227$	0.275255	+	0.476756i	0.0182693	+	0.0316434i	−0.856746	+	0.515738i	$0.827518\pi$
$228$	7.44949	−	10.5352i	0.493355	−	0.697709i
$229$	11.6237	−	20.1329i	0.768117	−	1.33042i	−0.170465	−	0.985364i	$-0.554527\pi$
$229$	11.6237	−	20.1329i	0.768117	−	1.33042i	0.938583	−	0.345055i	$-0.112140\pi$
$230$	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	0.957599	−	0.288106i	$-0.0930254\pi$
$233$	3.50000	+	6.06218i	0.229293	+	0.397146i	−0.728306	+	0.685252i	$0.759692\pi$
$234$	−14.4495	−	2.68556i	−0.944593	−	0.175561i
$235$	16.8990	−	29.2699i	1.10237	−	1.90936i
$236$	−2.00000			−0.130189
$237$	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	$0.697494\pi$
$240$	−5.94949	−	0.548188i	−0.384038	−	0.0353854i
$241$	4.44949	+	7.70674i	0.286617	+	0.496435i	0.973000	−	0.230805i	$-0.0741360\pi$
$241$	4.44949	+	7.70674i	0.286617	+	0.496435i	−0.686383	+	0.727240i	$0.740803\pi$
$242$	3.50000	−	6.06218i	0.224989	−	0.389692i
$243$	12.9722	−	8.64420i	0.832167	−	0.554526i
$244$	11.4495			0.732978
$245$		0			0
$246$	−9.79796	+	13.8564i	−0.624695	+	0.883452i
$247$	18.2474	−	31.6055i	1.16106	−	2.01101i
$248$	6.00000			0.381000
$249$	−3.44949	−	0.317837i	−0.218603	−	0.0201421i
$250$	6.55051			0.414291
$251$	12.5505			0.792181			0.396091	−	0.918211i	$-0.370367\pi$
$251$	12.5505			0.792181			0.396091	+	0.918211i	$0.370367\pi$
$252$		0			0
$253$	−2.00000			−0.125739
$254$	−3.00000			−0.188237
$255$	6.89898	−	9.75663i	0.432031	−	0.610984i
$256$	1.00000			0.0625000
$257$	−13.8990	+	24.0737i	−0.866995	+	1.50168i	−0.00194150	+	0.999998i	$0.500618\pi$
$257$	−13.8990	+	24.0737i	−0.866995	+	1.50168i	−0.865053	+	0.501680i	$0.832715\pi$
$258$	5.00000	+	0.460702i	0.311286	+	0.0286820i
$259$		0			0
$260$	−16.8990			−1.04803
$261$	−2.89898	−	8.19955i	−0.179442	−	0.507540i
$262$	6.72474	−	11.6476i	0.415456	−	0.719591i
$263$	−8.05051	−	13.9439i	−0.496416	−	0.859817i	0.503576	−	0.863951i	$-0.332017\pi$
$263$	−8.05051	−	13.9439i	−0.496416	−	0.859817i	−0.999991	+	0.00413383i	$0.998684\pi$
$264$	2.00000	−	2.82843i	0.123091	−	0.174078i
$265$	1.89898	+	3.28913i	0.116653	+	0.202050i
$266$		0			0
$267$	−7.10102	+	10.0424i	−0.434575	+	0.614582i
$268$	−3.10102			−0.189425
$269$	1.82577	−	3.16232i	0.111319	−	0.192810i	−0.804983	−	0.593297i	$-0.797826\pi$
$269$	1.82577	−	3.16232i	0.111319	−	0.192810i	0.916302	+	0.400487i	$0.131159\pi$
$270$	12.8485	−	12.4976i	0.781933	−	0.760578i
$271$	−8.44949	−	14.6349i	−0.513270	−	0.889010i	−0.999882	−	0.0153912i	$-0.995101\pi$
$271$	−8.44949	−	14.6349i	−0.513270	−	0.889010i	0.486612	−	0.873618i	$-0.338233\pi$
$272$	−1.00000	+	1.73205i	−0.0606339	+	0.105021i
$273$		0			0
$274$	5.89898	+	10.2173i	0.356370	+	0.617252i
$275$	−6.89898	+	11.9494i	−0.416024	+	0.720575i
$276$	1.72474	+	0.158919i	0.103817	+	0.00956578i
$277$	−5.34847	−	9.26382i	−0.321358	−	0.556609i	0.659410	−	0.751783i	$-0.270806\pi$
$277$	−5.34847	−	9.26382i	−0.321358	−	0.556609i	−0.980769	+	0.195174i	$0.937473\pi$
$278$	−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	$-0.0251222\pi$
$282$	−7.10102	−	15.4135i	−0.422860	−	0.917860i
$283$	−20.5505			−1.22160			−0.610801	−	0.791785i	$-0.709152\pi$
$283$	−20.5505			−1.22160			−0.610801	+	0.791785i	$0.709152\pi$
$284$	9.89898			0.587396
$285$	18.6237	+	40.4247i	1.10317	+	2.39455i
$286$	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
$290$	−5.00000	−	8.66025i	−0.293610	−	0.508548i
$291$	11.8990	+	1.09638i	0.697531	+	0.0642707i
$292$	−1.44949	+	2.51059i	−0.0848250	+	0.146921i
$293$	−13.6237	−	23.5970i	−0.795906	−	1.37855i	−0.922262	−	0.386565i	$-0.873661\pi$
$293$	−13.6237	−	23.5970i	−0.795906	−	1.37855i	0.126356	−	0.991985i	$-0.459672\pi$
$294$		0			0
$295$	3.44949	−	5.97469i	0.200837	−	0.347860i
$296$	3.89898	+	6.75323i	0.226624	+	0.392524i
$297$	2.55051	+	10.0745i	0.147996	+	0.584580i
$298$	3.00000	−	5.19615i	0.173785	−	0.301005i
$299$	4.89898			0.283315
$300$	6.89898	−	9.75663i	0.398313	−	0.563299i
$301$		0			0
$302$	2.50000	+	4.33013i	0.143859	+	0.249171i
$303$	7.24745	−	10.2494i	0.416355	−	0.588815i
$304$	−3.72474	−	6.45145i	−0.213629	−	0.370016i
$305$	−19.7474	+	34.2036i	−1.13074	+	1.95849i
$306$	−2.00000	−	5.65685i	−0.114332	−	0.323381i
$307$	0.752551			0.0429504			0.0214752	−	0.999769i	$-0.493164\pi$
$307$	0.752551			0.0429504			0.0214752	+	0.999769i	$0.493164\pi$
$308$		0			0
$309$	−24.1464	−	2.22486i	−1.37364	−	0.126568i
$310$	−10.3485	+	17.9241i	−0.587754	+	1.01802i
$311$	1.30306			0.0738898			0.0369449	−	0.999317i	$-0.488237\pi$
$311$	1.30306			0.0738898			0.0369449	+	0.999317i	$0.488237\pi$
$312$	−4.89898	+	6.92820i	−0.277350	+	0.392232i
$313$	24.6969			1.39595			0.697977	−	0.716120i	$-0.254084\pi$
$313$	24.6969			1.39595			0.697977	+	0.716120i	$0.254084\pi$
$314$	6.34847			0.358265
$315$		0			0
$316$	7.89898			0.444352
$317$	−8.69694			−0.488469			−0.244234	−	0.969716i	$-0.578537\pi$
$317$	−8.69694			−0.488469			−0.244234	+	0.969716i	$0.578537\pi$
$318$	1.89898	+	0.174973i	0.106489	+	0.00981198i
$319$	5.79796			0.324623
$320$	−1.72474	+	2.98735i	−0.0964162	+	0.166998i
$321$	−12.0000	+	16.9706i	−0.669775	+	0.947204i
$322$		0			0
$323$	14.8990			0.829001
$324$	−1.39898	−	8.89060i	−0.0777211	−	0.493922i
$325$	16.8990	−	29.2699i	0.937387	−	1.62360i
$326$	0.101021	+	0.174973i	0.00559501	+	0.00969084i
$327$	28.7980	+	2.65345i	1.59253	+	0.146736i
$328$	4.89898	+	8.48528i	0.270501	+	0.468521i
$329$		0			0
$330$	5.00000	+	10.8530i	0.275241	+	0.597438i
$331$	−24.6969			−1.35747			−0.678733	−	0.734385i	$-0.737471\pi$
$331$	−24.6969			−1.35747			−0.678733	+	0.734385i	$0.737471\pi$
$332$	−1.00000	+	1.73205i	−0.0548821	+	0.0950586i
$333$	−23.0000	−	4.27475i	−1.26039	−	0.234255i
$334$	−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	$-0.581013\pi$
$338$	−5.50000	+	9.52628i	−0.299161	+	0.518161i
$339$	−15.8990	+	22.4846i	−0.863514	+	1.22119i
$340$	−3.44949	−	5.97469i	−0.187075	−	0.324023i
$341$	−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
$345$	−3.44949	+	4.87832i	−0.185714	+	0.262640i
$346$	−12.8990			−0.693453
$347$	−19.5959			−1.05196			−0.525982	−	0.850496i	$-0.676302\pi$
$347$	−19.5959			−1.05196			−0.525982	+	0.850496i	$0.676302\pi$
$348$	−5.00000	−	0.460702i	−0.268028	−	0.0246962i
$349$	−10.4495	+	18.0990i	−0.559348	+	0.968820i	0.438203	+	0.898876i	$0.355615\pi$
$349$	−10.4495	+	18.0990i	−0.559348	+	0.968820i	−0.997551	+	0.0699435i	$0.977718\pi$
$350$		0			0
$351$	−6.24745	−	24.6773i	−0.333464	−	1.31718i
$352$	−1.00000	−	1.73205i	−0.0533002	−	0.0923186i
$353$	3.00000	+	5.19615i	0.159674	+	0.276563i	0.934751	−	0.355303i	$-0.115622\pi$
$353$	3.00000	+	5.19615i	0.159674	+	0.276563i	−0.775077	+	0.631867i	$0.782289\pi$
$354$	−1.44949	−	3.14626i	−0.0770395	−	0.167222i
$355$	−17.0732	+	29.5717i	−0.906152	+	1.56950i
$356$	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	0.687649	−	0.726043i	$-0.258643\pi$
$359$	−5.39898	−	9.35131i	−0.284947	−	0.493543i	−0.972596	+	0.232500i	$0.925309\pi$
$360$	−3.44949	−	9.75663i	−0.181804	−	0.514220i
$361$	−18.2474	+	31.6055i	−0.960392	+	1.66345i
$362$	4.34847			0.228550
$363$	12.0732	+	1.11243i	0.633679	+	0.0583875i
$364$		0			0
$365$	−5.00000	−	8.66025i	−0.261712	−	0.453298i
$366$	8.29796	+	18.0116i	0.433741	+	0.941479i
$367$	−2.89898	−	5.02118i	−0.151325	−	0.262103i	0.780389	−	0.625294i	$-0.215021\pi$
$367$	−2.89898	−	5.02118i	−0.151325	−	0.262103i	−0.931715	+	0.363190i	$0.881687\pi$
$368$	0.500000	−	0.866025i	0.0260643	−	0.0451447i
$369$	−28.8990	−	5.37113i	−1.50442	−	0.279610i
$370$	−26.8990			−1.39841
$371$		0			0
$372$	4.34847	+	9.43879i	0.225458	+	0.489379i
$373$	−1.44949	+	2.51059i	−0.0750517	+	0.129993i	−0.901109	−	0.433593i	$-0.857246\pi$
$373$	−1.44949	+	2.51059i	−0.0750517	+	0.129993i	0.826057	+	0.563587i	$0.190579\pi$
$374$	4.00000			0.206835
$375$	4.74745	+	10.3048i	0.245157	+	0.532139i
$376$	−9.79796			−0.505291
$377$	−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	$0.738227\pi$
$380$	25.6969			1.31823
$381$	−2.17423	−	4.71940i	−0.111389	−	0.241782i
$382$	13.8990			0.711134
$383$	−3.44949	+	5.97469i	−0.176261	+	0.305292i	−0.940597	−	0.339526i	$-0.889734\pi$
$383$	−3.44949	+	5.97469i	−0.176261	+	0.305292i	0.764336	+	0.644818i	$0.223067\pi$
$384$	0.724745	+	1.57313i	0.0369845	+	0.0802786i
$385$		0			0
$386$	−8.10102			−0.412331
$387$	2.89898	+	8.19955i	0.147363	+	0.416807i
$388$	3.44949	−	5.97469i	0.175121	−	0.303319i
$389$	7.55051	+	13.0779i	0.382826	+	0.663074i	0.991465	−	0.130373i	$-0.0416175\pi$
$389$	7.55051	+	13.0779i	0.382826	+	0.663074i	−0.608639	+	0.793447i	$0.708284\pi$
$390$	−12.2474	−	26.5843i	−0.620174	−	1.34615i
$391$	1.00000	+	1.73205i	0.0505722	+	0.0875936i
$392$		0			0
$393$	23.1969	+	2.13737i	1.17013	+	0.107816i
$394$	−12.6969			−0.639663
$395$	−13.6237	+	23.5970i	−0.685484	+	1.18729i
$396$	5.89898	+	1.09638i	0.296435	+	0.0550950i
$397$	−4.65153	−	8.05669i	−0.233454	−	0.404354i	0.725369	−	0.688361i	$-0.241669\pi$
$397$	−4.65153	−	8.05669i	−0.233454	−	0.404354i	−0.958822	+	0.284007i	$0.908336\pi$
$398$	−3.44949	+	5.97469i	−0.172907	+	0.299484i
$399$		0			0
$400$	−3.44949	−	5.97469i	−0.172474	−	0.298735i
$401$	5.05051	−	8.74774i	0.252210	−	0.436841i	−0.711924	−	0.702257i	$-0.752176\pi$
$401$	5.05051	−	8.74774i	0.252210	−	0.436841i	0.964134	+	0.265416i	$0.0855091\pi$
$402$	−2.24745	−	4.87832i	−0.112093	−	0.243308i
$403$	14.6969	+	25.4558i	0.732107	+	1.26805i
$404$	−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
$408$	−3.44949	−	0.317837i	−0.170775	−	0.0157353i
$409$	5.79796			0.286691			0.143345	−	0.989673i	$-0.454214\pi$
$409$	5.79796			0.286691			0.143345	+	0.989673i	$0.454214\pi$
$410$	−33.7980			−1.66916
$411$	−11.7980	+	16.6848i	−0.581950	+	0.823002i
$412$	−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
$416$	2.44949	+	4.24264i	0.120096	+	0.208013i
$417$	9.44949	−	13.3636i	0.462744	−	0.654418i
$418$	−7.44949	+	12.9029i	−0.364366	+	0.631101i
$419$	−12.2753	−	21.2614i	−0.599685	−	1.03869i	−0.992867	−	0.119225i	$-0.961959\pi$
$419$	−12.2753	−	21.2614i	−0.599685	−	1.03869i	0.393182	−	0.919461i	$-0.371374\pi$
$420$		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
$423$	19.1010	−	22.3417i	0.928723	−	1.08629i
$424$	0.550510	−	0.953512i	0.0267351	−	0.0463066i
$425$	13.7980			0.669299
$426$	7.17423	+	15.5724i	0.347593	+	0.754485i
$427$		0			0
$428$	6.00000	+	10.3923i	0.290021	+	0.502331i
$429$	16.8990	+	1.55708i	0.815890	+	0.0751764i
$430$	5.00000	+	8.66025i	0.241121	+	0.417635i
$431$	3.79796	−	6.57826i	0.182941	−	0.316864i	−0.759940	−	0.649994i	$-0.774772\pi$
$431$	3.79796	−	6.57826i	0.182941	−	0.316864i	0.942881	+	0.333130i	$0.108105\pi$
$432$	−5.00000	−	1.41421i	−0.240563	−	0.0680414i
$433$	11.7980			0.566974			0.283487	−	0.958976i	$-0.408509\pi$
$433$	11.7980			0.566974			0.283487	+	0.958976i	$0.408509\pi$
$434$		0			0
$435$	10.0000	−	14.1421i	0.479463	−	0.678064i
$436$	8.34847	−	14.4600i	0.399819	−	0.692507i
$437$	−7.44949			−0.356357
$438$	−5.00000	−	0.460702i	−0.238909	−	0.0220132i
$439$	21.7980			1.04036			0.520180	−	0.854057i	$-0.325865\pi$
$439$	21.7980			1.04036			0.520180	+	0.854057i	$0.325865\pi$
$440$	6.89898			0.328896
$441$		0			0
$442$	−9.79796			−0.466041
$443$	−5.10102			−0.242357			−0.121178	−	0.992631i	$-0.538667\pi$
$443$	−5.10102			−0.242357			−0.121178	+	0.992631i	$0.538667\pi$
$444$	−7.79796	+	11.0280i	−0.370075	+	0.523365i
$445$	−24.4949			−1.16117
$446$	10.4495	−	18.0990i	0.494798	−	0.857015i
$447$	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	$0.644596\pi$
$450$	20.3485	+	3.78194i	0.959236	+	0.178282i
$451$	9.79796	−	16.9706i	0.461368	−	0.799113i
$452$	7.94949	+	13.7689i	0.373913	+	0.647636i
$453$	−5.00000	+	7.07107i	−0.234920	+	0.332228i
$454$	0.275255	+	0.476756i	0.0129184	+	0.0223753i
$455$		0			0
$456$	7.44949	−	10.5352i	0.348854	−	0.493355i
$457$	31.4949			1.47327			0.736635	−	0.676291i	$-0.236414\pi$
$457$	31.4949			1.47327			0.736635	+	0.676291i	$0.236414\pi$
$458$	11.6237	−	20.1329i	0.543141	−	0.940748i
$459$	7.44949	−	7.24604i	0.347712	−	0.338216i
$460$	1.72474	+	2.98735i	0.0804166	+	0.139286i
$461$	−10.1742	+	17.6223i	−0.473861	+	0.820752i	−0.999552	−	0.0299238i	$-0.990474\pi$
$461$	−10.1742	+	17.6223i	−0.473861	+	0.820752i	0.525691	+	0.850676i	$0.323807\pi$
$462$		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	$0.629645\pi$
$464$	−1.44949	+	2.51059i	−0.0672909	+	0.116551i
$465$	−35.6969	−	3.28913i	−1.65541	−	0.152530i
$466$	3.50000	+	6.06218i	0.162134	+	0.280825i
$467$	−5.00000	−	8.66025i	−0.231372	−	0.400749i	0.726840	−	0.686807i	$-0.240988\pi$
$467$	−5.00000	−	8.66025i	−0.231372	−	0.400749i	−0.958212	+	0.286058i	$0.907655\pi$
$468$	−14.4495	−	2.68556i	−0.667928	−	0.124140i
$469$		0			0
$470$	16.8990	−	29.2699i	0.779492	−	1.35012i
$471$	4.60102	+	9.98698i	0.212004	+	0.460176i
$472$	−2.00000			−0.0920575
$473$	−5.79796			−0.266590
$474$	5.72474	+	12.4261i	0.262946	+	0.570751i
$475$	−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
$479$	14.7980	+	25.6308i	0.676136	+	1.17110i	0.976135	+	0.217163i	$0.0696802\pi$
$479$	14.7980	+	25.6308i	0.676136	+	1.17110i	−0.299999	+	0.953939i	$0.596987\pi$
$480$	−5.94949	−	0.548188i	−0.271556	−	0.0250213i
$481$	−19.1010	+	33.0839i	−0.870932	+	1.50850i
$482$	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
$486$	12.9722	−	8.64420i	0.588431	−	0.392109i
$487$	−11.1969	+	19.3937i	−0.507382	+	0.878811i	0.492582	+	0.870266i	$0.336053\pi$
$487$	−11.1969	+	19.3937i	−0.507382	+	0.878811i	−0.999963	+	0.00854475i	$0.997280\pi$
$488$	11.4495			0.518294
$489$	−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	$0.806021\pi$
$492$	−9.79796	+	13.8564i	−0.441726	+	0.624695i
$493$	−2.89898	−	5.02118i	−0.130563	−	0.226143i
$494$	18.2474	−	31.6055i	0.820992	−	1.42200i
$495$	−13.4495	+	15.7313i	−0.604510	+	0.707070i
$496$	6.00000			0.269408
$497$		0			0
$498$	−3.44949	−	0.317837i	−0.154575	−	0.0142426i
$499$	−16.6969	+	28.9199i	−0.747458	+	1.29463i	0.201580	+	0.979472i	$0.435392\pi$
$499$	−16.6969	+	28.9199i	−0.747458	+	1.29463i	−0.949038	+	0.315163i	$0.897941\pi$
$500$	6.55051			0.292948
$501$	18.6969	−	26.4415i	0.835318	−	1.18132i
$502$	12.5505			0.560157
$503$	24.4949			1.09217			0.546087	−	0.837729i	$-0.316117\pi$
$503$	24.4949			1.09217			0.546087	+	0.837729i	$0.316117\pi$
$504$		0			0
$505$	25.0000			1.11249
$506$	−2.00000			−0.0889108
$507$	−18.9722	−	1.74810i	−0.842585	−	0.0776361i
$508$	−3.00000			−0.133103
$509$	8.44949	−	14.6349i	0.374517	−	0.648683i	−0.615738	−	0.787951i	$-0.711142\pi$
$509$	8.44949	−	14.6349i	0.374517	−	0.648683i	0.990255	+	0.139269i	$0.0444752\pi$
$510$	6.89898	−	9.75663i	0.305492	−	0.432031i
$511$		0			0
$512$	1.00000			0.0441942
$513$	9.50000	+	37.5248i	0.419435	+	1.65676i
$514$	−13.8990	+	24.0737i	−0.613058	+	1.06185i
$515$	−24.1464	−	41.8228i	−1.06402	−	1.84293i
$516$	5.00000	+	0.460702i	0.220113	+	0.0202813i
$517$	9.79796	+	16.9706i	0.430914	+	0.746364i
$518$		0			0
$519$	−9.34847	−	20.2918i	−0.410352	−	0.890711i
$520$	−16.8990			−0.741069
$521$	19.3485	−	33.5125i	0.847672	−	1.46821i	−0.0356087	−	0.999366i	$-0.511337\pi$
$521$	19.3485	−	33.5125i	0.847672	−	1.46821i	0.883281	−	0.468845i	$-0.155330\pi$
$522$	−2.89898	−	8.19955i	−0.126885	−	0.358885i
$523$	−0.174235	−	0.301783i	−0.00761875	−	0.0131961i	0.862191	−	0.506584i	$-0.169092\pi$
$523$	−0.174235	−	0.301783i	−0.00761875	−	0.0131961i	−0.869810	+	0.493387i	$0.835758\pi$
$524$	6.72474	−	11.6476i	0.293772	−	0.508828i
$525$		0			0
$526$	−8.05051	−	13.9439i	−0.351019	−	0.607983i
$527$	−6.00000	+	10.3923i	−0.261364	+	0.452696i
$528$	2.00000	−	2.82843i	0.0870388	−	0.123091i
$529$	11.0000	+	19.0526i	0.478261	+	0.828372i
$530$	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
$534$	−7.10102	+	10.0424i	−0.307291	+	0.434575i
$535$	−41.3939			−1.78961
$536$	−3.10102			−0.133944
$537$	15.0000	+	1.38211i	0.647298	+	0.0596423i
$538$	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	−0.981758	−	0.190133i	$-0.939108\pi$
$541$	−15.2474	−	26.4094i	−0.655539	−	1.13543i	0.326219	−	0.945294i	$-0.394225\pi$
$542$	−8.44949	−	14.6349i	−0.362937	−	0.628625i
$543$	3.15153	+	6.84072i	0.135245	+	0.293563i
$544$	−1.00000	+	1.73205i	−0.0428746	+	0.0742611i
$545$	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
$549$	−22.3207	+	26.1076i	−0.952623	+	1.11424i
$550$	−6.89898	+	11.9494i	−0.294173	+	0.509523i
$551$	21.5959			0.920017
$552$	1.72474	+	0.158919i	0.0734100	+	0.00676403i
$553$		0			0
$554$	−5.34847	−	9.26382i	−0.227235	−	0.393582i
$555$	−19.4949	−	42.3157i	−0.827512	−	1.79620i
$556$	−4.72474	−	8.18350i	−0.200374	−	0.347058i
$557$	1.55051	−	2.68556i	0.0656972	−	0.113791i	−0.831306	−	0.555815i	$-0.812406\pi$
$557$	1.55051	−	2.68556i	0.0656972	−	0.113791i	0.897003	+	0.442024i	$0.145740\pi$
$558$	−11.6969	+	13.6814i	−0.495171	+	0.579181i
$559$	14.2020			0.600682
$560$		0			0
$561$	2.89898	+	6.29253i	0.122395	+	0.265671i
$562$	9.50000	−	16.4545i	0.400733	−	0.694090i
$563$	13.9444			0.587686			0.293843	−	0.955854i	$-0.405066\pi$
$563$	13.9444			0.587686			0.293843	+	0.955854i	$0.405066\pi$
$564$	−7.10102	−	15.4135i	−0.299007	−	0.649025i
$565$	−54.8434			−2.30728
$566$	−20.5505			−0.863802
$567$		0			0
$568$	9.89898			0.415352
$569$	−30.0000			−1.25767			−0.628833	−	0.777541i	$-0.716467\pi$
$569$	−30.0000			−1.25767			−0.628833	+	0.777541i	$0.716467\pi$
$570$	18.6237	+	40.4247i	0.780062	+	1.69320i
$571$	14.2020			0.594337			0.297168	−	0.954825i	$-0.403958\pi$
$571$	14.2020			0.594337			0.297168	+	0.954825i	$0.403958\pi$
$572$	4.89898	−	8.48528i	0.204837	−	0.354787i
$573$	10.0732	+	21.8649i	0.420815	+	0.913421i
$574$		0			0
$575$	−6.89898			−0.287707
$576$	−1.94949	+	2.28024i	−0.0812287	+	0.0950100i
$577$	−11.7980	+	20.4347i	−0.491155	+	0.850706i	−0.999948	−	0.0101829i	$-0.996759\pi$
$577$	−11.7980	+	20.4347i	−0.491155	+	0.850706i	0.508793	+	0.860889i	$0.330092\pi$
$578$	6.50000	+	11.2583i	0.270364	+	0.468285i
$579$	−5.87117	−	12.7440i	−0.243998	−	0.529622i
$580$	−5.00000	−	8.66025i	−0.207614	−	0.359597i
$581$		0			0
$582$	11.8990	+	1.09638i	0.493229	+	0.0454463i
$583$	−2.20204			−0.0911992
$584$	−1.44949	+	2.51059i	−0.0599803	+	0.103889i
$585$	32.9444	−	38.5337i	1.36208	−	1.59317i
$586$	−13.6237	−	23.5970i	−0.562791	−	0.974782i
$587$	9.07321	−	15.7153i	0.374492	−	0.648639i	−0.615759	−	0.787934i	$-0.711151\pi$
$587$	9.07321	−	15.7153i	0.374492	−	0.648639i	0.990251	+	0.139296i	$0.0444839\pi$
$588$		0			0
$589$	−22.3485	−	38.7087i	−0.920853	−	1.59496i
$590$	3.44949	−	5.97469i	0.142013	−	0.245974i
$591$	−9.20204	−	19.9740i	−0.378521	−	0.821619i
$592$	3.89898	+	6.75323i	0.160247	+	0.277556i
$593$	7.34847	+	12.7279i	0.301765	+	0.522673i	0.976536	−	0.215355i	$-0.0690907\pi$
$593$	7.34847	+	12.7279i	0.301765	+	0.522673i	−0.674770	+	0.738028i	$0.735757\pi$
$594$	2.55051	+	10.0745i	0.104649	+	0.413360i
$595$		0			0
$596$	3.00000	−	5.19615i	0.122885	−	0.212843i
$597$	−11.8990	−	1.09638i	−0.486993	−	0.0448717i
$598$	4.89898			0.200334
$599$	−14.2020			−0.580280			−0.290140	−	0.956984i	$-0.593702\pi$
$599$	−14.2020			−0.580280			−0.290140	+	0.956984i	$0.593702\pi$
$600$	6.89898	−	9.75663i	0.281650	−	0.398313i
$601$	6.34847	−	10.9959i	0.258959	−	0.448531i	−0.707004	−	0.707210i	$-0.749954\pi$
$601$	6.34847	−	10.9959i	0.258959	−	0.448531i	0.965963	+	0.258679i	$0.0832871\pi$
$602$		0			0
$603$	6.04541	−	7.07107i	0.246188	−	0.287956i
$604$	2.50000	+	4.33013i	0.101724	+	0.176190i
$605$	12.0732	+	20.9114i	0.490846	+	0.850170i
$606$	7.24745	−	10.2494i	0.294407	−	0.416355i
$607$	4.34847	−	7.53177i	0.176499	−	0.305705i	−0.764180	−	0.645003i	$-0.776856\pi$
$607$	4.34847	−	7.53177i	0.176499	−	0.305705i	0.940679	+	0.339298i	$0.110189\pi$
$608$	−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
$612$	−2.00000	−	5.65685i	−0.0808452	−	0.228665i
$613$	−7.34847	+	12.7279i	−0.296802	+	0.514076i	−0.975402	−	0.220432i	$-0.929253\pi$
$613$	−7.34847	+	12.7279i	−0.296802	+	0.514076i	0.678601	+	0.734508i	$0.262587\pi$
$614$	0.752551			0.0303705
$615$	−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	$-0.504813\pi$
$618$	−24.1464	−	2.22486i	−0.971312	−	0.0894970i
$619$	2.07321	+	3.59091i	0.0833295	+	0.144331i	0.904678	−	0.426096i	$-0.140111\pi$
$619$	2.07321	+	3.59091i	0.0833295	+	0.144331i	−0.821349	+	0.570426i	$0.806778\pi$
$620$	−10.3485	+	17.9241i	−0.415605	+	0.719848i
$621$	−3.72474	+	3.62302i	−0.149469	+	0.145387i
$622$	1.30306			0.0522480
$623$		0			0
$624$	−4.89898	+	6.92820i	−0.196116	+	0.277350i
$625$	5.94949	−	10.3048i	0.237980	−	0.412193i
$626$	24.6969			0.987088
$627$	−25.6969	−	2.36773i	−1.02624	−	0.0945578i
$628$	6.34847			0.253332
$629$	−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	$0.382676\pi$
$632$	7.89898			0.314205
$633$	3.10102	−	4.38551i	0.123255	−	0.174308i
$634$	−8.69694			−0.345400
$635$	5.17423	−	8.96204i	0.205333	−	0.355648i
$636$	1.89898	+	0.174973i	0.0752994	+	0.00693812i
$637$		0			0
$638$	5.79796			0.229543
$639$	−19.2980	+	22.5720i	−0.763415	+	0.892936i
$640$	−1.72474	+	2.98735i	−0.0681765	+	0.118085i
$641$	−20.7474	−	35.9356i	−0.819475	−	1.41937i	−0.906070	−	0.423129i	$-0.860932\pi$
$641$	−20.7474	−	35.9356i	−0.819475	−	1.41937i	0.0865947	−	0.996244i	$-0.472401\pi$
$642$	−12.0000	+	16.9706i	−0.473602	+	0.669775i
$643$	−9.69694	−	16.7956i	−0.382410	−	0.662353i	0.608996	−	0.793173i	$-0.291572\pi$
$643$	−9.69694	−	16.7956i	−0.382410	−	0.662353i	−0.991406	+	0.130820i	$0.958239\pi$
$644$		0			0
$645$	−10.0000	+	14.1421i	−0.393750	+	0.556846i
$646$	14.8990			0.586193
$647$	10.6515	−	18.4490i	0.418755	−	0.725305i	−0.577060	−	0.816702i	$-0.695800\pi$
$647$	10.6515	−	18.4490i	0.418755	−	0.725305i	0.995815	+	0.0913973i	$0.0291333\pi$
$648$	−1.39898	−	8.89060i	−0.0549571	−	0.349256i
$649$	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
$653$	4.89898	−	8.48528i	0.191712	−	0.332055i	−0.754106	−	0.656753i	$-0.771929\pi$
$653$	4.89898	−	8.48528i	0.191712	−	0.332055i	0.945818	+	0.324698i	$0.105263\pi$
$654$	28.7980	+	2.65345i	1.12609	+	0.103758i
$655$	23.1969	+	40.1783i	0.906379	+	1.56990i
$656$	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	$0.195828\pi$
$660$	5.00000	+	10.8530i	0.194625	+	0.422453i
$661$	9.44949			0.367543			0.183771	−	0.982969i	$-0.441169\pi$
$661$	9.44949			0.367543			0.183771	+	0.982969i	$0.441169\pi$
$662$	−24.6969			−0.959874
$663$	−7.10102	−	15.4135i	−0.275781	−	0.598610i
$664$	−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
$668$	−9.34847	−	16.1920i	−0.361703	−	0.626488i
$669$	36.0454	+	3.32124i	1.39360	+	0.128406i
$670$	5.34847	−	9.26382i	0.206629	−	0.357893i
$671$	−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
$675$	8.79796	+	34.7518i	0.338634	+	1.33760i
$676$	−5.50000	+	9.52628i	−0.211538	+	0.366395i
$677$	−14.6969			−0.564849			−0.282425	−	0.959289i	$-0.591139\pi$
$677$	−14.6969			−0.564849			−0.282425	+	0.959289i	$0.591139\pi$
$678$	−15.8990	+	22.4846i	−0.610597	+	0.863514i
$679$		0			0
$680$	−3.44949	−	5.97469i	−0.132282	−	0.229119i
$681$	−0.550510	+	0.778539i	−0.0210956	+	0.0298337i
$682$	−6.00000	−	10.3923i	−0.229752	−	0.397942i
$683$	−16.1010	+	27.8878i	−0.616088	+	1.06710i	0.374104	+	0.927387i	$0.377950\pi$
$683$	−16.1010	+	27.8878i	−0.616088	+	1.06710i	−0.990193	+	0.139710i	$0.955383\pi$
$684$	21.9722	+	4.08372i	0.840128	+	0.156145i
$685$	−40.6969			−1.55495
$686$		0			0
$687$	40.0959	+	3.69445i	1.52975	+	0.140952i
$688$	1.44949	−	2.51059i	0.0552613	−	0.0957153i
$689$	5.39388			0.205490
$690$	−3.44949	+	4.87832i	−0.131320	+	0.185714i
$691$	6.95459			0.264565			0.132283	−	0.991212i	$-0.457769\pi$
$691$	6.95459			0.264565			0.132283	+	0.991212i	$0.457769\pi$
$692$	−12.8990			−0.490346
$693$		0			0
$694$	−19.5959			−0.743851
$695$	32.5959			1.23643
$696$	−5.00000	−	0.460702i	−0.189525	−	0.0174629i
$697$	−19.5959			−0.742248
$698$	−10.4495	+	18.0990i	−0.395519	+	0.685059i
$699$	−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	$0.0774293\pi$
$702$	−6.24745	−	24.6773i	−0.235795	−	0.931385i
$703$	29.0454	−	50.3081i	1.09547	−	1.89741i
$704$	−1.00000	−	1.73205i	−0.0376889	−	0.0652791i
$705$	58.2929	+	5.37113i	2.19544	+	0.202288i
$706$	3.00000	+	5.19615i	0.112906	+	0.195560i
$707$		0			0
$708$	−1.44949	−	3.14626i	−0.0544752	−	0.118244i
$709$	−11.5959			−0.435494			−0.217747	−	0.976005i	$-0.569871\pi$
$709$	−11.5959			−0.435494			−0.217747	+	0.976005i	$0.569871\pi$
$710$	−17.0732	+	29.5717i	−0.640746	+	1.10981i
$711$	−15.3990	+	18.0116i	−0.577507	+	0.675486i
$712$	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
$716$	4.34847	−	7.53177i	0.162510	−	0.281475i
$717$	−12.7980	+	18.0990i	−0.477949	+	0.675921i
$718$	−5.39898	−	9.35131i	−0.201488	−	0.348988i
$719$	4.89898	+	8.48528i	0.182701	+	0.316448i	0.942799	−	0.333360i	$-0.108183\pi$
$719$	4.89898	+	8.48528i	0.182701	+	0.316448i	−0.760098	+	0.649808i	$0.774849\pi$
$720$	−3.44949	−	9.75663i	−0.128555	−	0.363608i
$721$		0			0
$722$	−18.2474	+	31.6055i	−0.679100	+	1.17624i
$723$	−8.89898	+	12.5851i	−0.330957	+	0.468043i
$724$	4.34847			0.161610
$725$	20.0000			0.742781
$726$	12.0732	+	1.11243i	0.448079	+	0.0412862i
$727$	−20.2474	+	35.0696i	−0.750936	+	1.30066i	0.196433	+	0.980517i	$0.437064\pi$
$727$	−20.2474	+	35.0696i	−0.750936	+	1.30066i	−0.947369	+	0.320143i	$0.896269\pi$
$728$		0			0
$729$	23.0000	+	14.1421i	0.851852	+	0.523783i
$730$	−5.00000	−	8.66025i	−0.185058	−	0.320530i
$731$	2.89898	+	5.02118i	0.107223	+	0.185715i
$732$	8.29796	+	18.0116i	0.306701	+	0.665726i
$733$	6.27526	−	10.8691i	0.231782	−	0.401458i	−0.726551	−	0.687113i	$-0.758878\pi$
$733$	6.27526	−	10.8691i	0.231782	−	0.401458i	0.958333	+	0.285655i	$0.0922111\pi$
$734$	−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
$738$	−28.8990	−	5.37113i	−1.06379	−	0.197714i
$739$	12.7980	−	22.1667i	0.470781	−	0.815416i	−0.528661	−	0.848833i	$-0.677306\pi$
$739$	12.7980	−	22.1667i	0.470781	−	0.815416i	0.999441	+	0.0334173i	$0.0106390\pi$
$740$	−26.8990			−0.988826
$741$	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	$-0.396261\pi$
$744$	4.34847	+	9.43879i	0.159423	+	0.346043i
$745$	10.3485	+	17.9241i	0.379139	+	0.656687i
$746$	−1.44949	+	2.51059i	−0.0530696	+	0.0919192i
$747$	−2.00000	−	5.65685i	−0.0731762	−	0.206973i
$748$	4.00000			0.146254
$749$		0			0
$750$	4.74745	+	10.3048i	0.173352	+	0.376279i
$751$	−20.2980	+	35.1571i	−0.740683	+	1.28290i	0.211502	+	0.977378i	$0.432165\pi$
$751$	−20.2980	+	35.1571i	−0.740683	+	1.28290i	−0.952185	+	0.305523i	$0.901169\pi$
$752$	−9.79796			−0.357295
$753$	9.09592	+	19.7436i	0.331474	+	0.719497i
$754$	−14.2020			−0.517208
$755$	−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	$0.360228\pi$
$758$	−26.4949			−0.962338
$759$	−1.44949	−	3.14626i	−0.0526131	−	0.114202i
$760$	25.6969			0.932126
$761$	−1.00000	+	1.73205i	−0.0362500	+	0.0627868i	−0.883581	−	0.468278i	$-0.844875\pi$
$761$	−1.00000	+	1.73205i	−0.0362500	+	0.0627868i	0.847331	+	0.531065i	$0.178208\pi$
$762$	−2.17423	−	4.71940i	−0.0787642	−	0.170966i
$763$		0			0
$764$	13.8990			0.502847
$765$	20.3485	+	3.78194i	0.735700	+	0.136736i
$766$	−3.44949	+	5.97469i	−0.124635	+	0.215874i
$767$	−4.89898	−	8.48528i	−0.176892	−	0.306386i
$768$	0.724745	+	1.57313i	0.0261520	+	0.0567655i
$769$	−27.0454	−	46.8440i	−0.975282	−	1.68924i	−0.679000	−	0.734138i	$-0.737586\pi$
$769$	−27.0454	−	46.8440i	−0.975282	−	1.68924i	−0.296282	−	0.955100i	$-0.595747\pi$
$770$		0			0
$771$	−47.9444	−	4.41761i	−1.72667	−	0.159096i
$772$	−8.10102			−0.291562
$773$	9.97219	−	17.2723i	0.358675	−	0.621243i	−0.629065	−	0.777353i	$-0.716562\pi$
$773$	9.97219	−	17.2723i	0.358675	−	0.621243i	0.987740	+	0.156110i	$0.0498953\pi$
$774$	2.89898	+	8.19955i	0.104202	+	0.294727i
$775$	−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
$779$	36.4949	−	63.2110i	1.30757	−	2.26477i
$780$	−12.2474	−	26.5843i	−0.438529	−	0.951872i
$781$	−9.89898	−	17.1455i	−0.354213	−	0.613515i
$782$	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
$786$	23.1969	+	2.13737i	0.827407	+	0.0762376i
$787$	47.3939			1.68941			0.844705	−	0.535233i	$-0.179776\pi$
$787$	47.3939			1.68941			0.844705	+	0.535233i	$0.179776\pi$
$788$	−12.6969			−0.452310
$789$	16.1010	−	22.7703i	0.573212	−	0.810643i
$790$	−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
$794$	−4.65153	−	8.05669i	−0.165077	−	0.285921i
$795$	−3.79796	+	5.37113i	−0.134700	+	0.190494i
$796$	−3.44949	+	5.97469i	−0.122264	+	0.211767i
$797$	−17.9722	−	31.1288i	−0.636608	−	1.10264i	−0.986172	−	0.165725i	$-0.947004\pi$
$797$	−17.9722	−	31.1288i	−0.636608	−	1.10264i	0.349564	−	0.936912i	$-0.386330\pi$
$798$		0			0
$799$	9.79796	−	16.9706i	0.346627	−	0.600375i
$800$	−3.44949	−	5.97469i	−0.121958	−	0.211237i
$801$	−20.9444	−	3.89270i	−0.740034	−	0.137542i
$802$	5.05051	−	8.74774i	0.178340	−	0.308893i
$803$	5.79796			0.204606
$804$	−2.24745	−	4.87832i	−0.0792614	−	0.172045i
$805$		0			0
$806$	14.6969	+	25.4558i	0.517678	+	0.896644i
$807$	6.29796	+	0.580296i	0.221699	+	0.0204274i
$808$	−3.62372	−	6.27647i	−0.127482	−	0.220806i
$809$	17.8990	−	31.0019i	0.629295	−	1.08997i	−0.358399	−	0.933569i	$-0.616677\pi$
$809$	17.8990	−	31.0019i	0.629295	−	1.08997i	0.987694	−	0.156402i	$-0.0499894\pi$
$810$	28.9722	+	11.1548i	1.01798	+	0.391939i
$811$	−2.00000			−0.0702295			−0.0351147	−	0.999383i	$-0.511180\pi$
$811$	−2.00000			−0.0702295			−0.0351147	+	0.999383i	$0.511180\pi$
$812$		0			0
$813$	16.8990	−	23.8988i	0.592673	−	0.838166i
$814$	7.79796	−	13.5065i	0.273318	−	0.473401i
$815$	−0.696938			−0.0244127
$816$	−3.44949	−	0.317837i	−0.120756	−	0.0111265i
$817$	−21.5959			−0.755546
$818$	5.79796			0.202721
$819$		0			0
$820$	−33.7980			−1.18028
$821$	39.5959			1.38191			0.690954	−	0.722899i	$-0.257191\pi$
$821$	39.5959			1.38191			0.690954	+	0.722899i	$0.257191\pi$
$822$	−11.7980	+	16.6848i	−0.411501	+	0.581950i
$823$	45.3939			1.58233			0.791166	−	0.611602i	$-0.209475\pi$
$823$	45.3939			1.58233			0.791166	+	0.611602i	$0.209475\pi$
$824$	−7.00000	+	12.1244i	−0.243857	+	0.422372i
$825$	−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	$0.430293\pi$
$828$	1.00000	+	2.82843i	0.0347524	+	0.0982946i
$829$	−15.3485	+	26.5843i	−0.533074	+	0.923312i	0.466180	+	0.884690i	$0.345630\pi$
$829$	−15.3485	+	26.5843i	−0.533074	+	0.923312i	−0.999254	+	0.0386218i	$0.987703\pi$
$830$	−3.44949	−	5.97469i	−0.119734	−	0.207385i
$831$	10.6969	−	15.1278i	0.371073	−	0.524776i
$832$	2.44949	+	4.24264i	0.0849208	+	0.147087i
$833$		0			0
$834$	9.44949	−	13.3636i	0.327209	−	0.462744i
$835$	64.4949			2.23194
$836$	−7.44949	+	12.9029i	−0.257646	+	0.446256i
$837$	−30.0000	−	8.48528i	−1.03695	−	0.293294i
$838$	−12.2753	−	21.2614i	−0.424042	−	0.734462i
$839$	22.4495	−	38.8837i	0.775042	−	1.34241i	−0.159728	−	0.987161i	$-0.551062\pi$
$839$	22.4495	−	38.8837i	0.775042	−	1.34241i	0.934771	−	0.355252i	$-0.115605\pi$
$840$		0			0
$841$	10.2980	+	17.8366i	0.355102	+	0.615055i
$842$	−6.55051	+	11.3458i	−0.225745	+	0.391003i
$843$	32.7702	+	3.01945i	1.12866	+	0.103996i
$844$	−1.55051	−	2.68556i	−0.0533708	−	0.0924409i
$845$	−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
$849$	−14.8939	−	32.3287i	−0.511157	−	1.10952i
$850$	13.7980			0.473266
$851$	7.79796			0.267311
$852$	7.17423	+	15.5724i	0.245785	+	0.533502i
$853$	19.4217	−	33.6393i	0.664986	−	1.15179i	−0.314303	−	0.949323i	$-0.601771\pi$
$853$	19.4217	−	33.6393i	0.664986	−	1.15179i	0.979289	−	0.202467i	$-0.0648957\pi$
$854$		0			0
$855$	−50.0959	+	58.5952i	−1.71324	+	2.00391i
$856$	6.00000	+	10.3923i	0.205076	+	0.355202i
$857$	12.5505	+	21.7381i	0.428717	+	0.742560i	0.996760	−	0.0804393i	$-0.0256323\pi$
$857$	12.5505	+	21.7381i	0.428717	+	0.742560i	−0.568042	+	0.822999i	$0.692299\pi$
$858$	16.8990	+	1.55708i	0.576922	+	0.0531578i
$859$	5.00000	−	8.66025i	0.170598	−	0.295484i	−0.768031	−	0.640412i	$-0.778763\pi$
$859$	5.00000	−	8.66025i	0.170598	−	0.295484i	0.938629	+	0.344928i	$0.112097\pi$
$860$	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	0.847592	−	0.530649i	$-0.178052\pi$
$863$	−1.05051	−	1.81954i	−0.0357598	−	0.0619378i	−0.883351	+	0.468711i	$0.844718\pi$
$864$	−5.00000	−	1.41421i	−0.170103	−	0.0481125i
$865$	22.2474	−	38.5337i	0.756436	−	1.31019i
$866$	11.7980			0.400911
$867$	−13.0000	+	18.3848i	−0.441503	+	0.624380i
$868$		0			0
$869$	−7.89898	−	13.6814i	−0.267955	−	0.464111i
$870$	10.0000	−	14.1421i	0.339032	−	0.479463i
$871$	−7.59592	−	13.1565i	−0.257378	−	0.445792i
$872$	8.34847	−	14.4600i	0.282715	−	0.489676i
$873$	6.89898	+	19.5133i	0.233495	+	0.660424i
$874$	−7.44949			−0.251983
$875$		0			0
$876$	−5.00000	−	0.460702i	−0.168934	−	0.0155657i
$877$	13.2474	−	22.9453i	0.447335	−	0.774806i	−0.550877	−	0.834586i	$-0.685707\pi$
$877$	13.2474	−	22.9453i	0.447335	−	0.774806i	0.998212	+	0.0597803i	$0.0190400\pi$
$878$	21.7980			0.735645
$879$	27.2474	−	38.5337i	0.919034	−	1.29971i
$880$	6.89898			0.232565
$881$	−19.5959			−0.660203			−0.330102	−	0.943945i	$-0.607083\pi$
$881$	−19.5959			−0.660203			−0.330102	+	0.943945i	$0.607083\pi$
$882$		0			0
$883$	−0.202041			−0.00679922			−0.00339961	−	0.999994i	$-0.501082\pi$
$883$	−0.202041			−0.00679922			−0.00339961	+	0.999994i	$0.501082\pi$
$884$	−9.79796			−0.329541
$885$	11.8990	+	1.09638i	0.399980	+	0.0368543i
$886$	−5.10102			−0.171372
$887$	16.8990	−	29.2699i	0.567412	−	0.982787i	−0.429409	−	0.903110i	$-0.641278\pi$
$887$	16.8990	−	29.2699i	0.567412	−	0.982787i	0.996821	−	0.0796764i	$-0.0253887\pi$
$888$	−7.79796	+	11.0280i	−0.261682	+	0.370075i
$889$		0			0
$890$	−24.4949			−0.821071
$891$	−14.0000	+	11.3137i	−0.469018	+	0.379023i
$892$	10.4495	−	18.0990i	0.349875	−	0.606001i
$893$	36.4949	+	63.2110i	1.22126	+	2.11528i
$894$	10.3485	+	0.953512i	0.346105	+	0.0318902i
$895$	15.0000	+	25.9808i	0.501395	+	0.868441i
$896$		0			0
$897$	3.55051	+	7.70674i	0.118548	+	0.257321i
$898$	−18.5959			−0.620554
$899$	−8.69694	+	15.0635i	−0.290059	+	0.502397i
$900$	20.3485	+	3.78194i	0.678282	+	0.126065i
$901$	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
$905$	−7.50000	+	12.9904i	−0.249308	+	0.431815i
$906$	−5.00000	+	7.07107i	−0.166114	+	0.234920i
$907$	13.3485	+	23.1202i	0.443229	+	0.767695i	0.997927	−	0.0643570i	$-0.0204996\pi$
$907$	13.3485	+	23.1202i	0.443229	+	0.767695i	−0.554698	+	0.832052i	$0.687166\pi$
$908$	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	$-0.109044\pi$
$912$	7.44949	−	10.5352i	0.246677	−	0.348854i
$913$	4.00000			0.132381
$914$	31.4949			1.04176
$915$	−68.1186	−	6.27647i	−2.25193	−	0.207494i
$916$	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	0.833926	−	0.551876i	$-0.186088\pi$
$919$	−1.84847	−	3.20164i	−0.0609754	−	0.105612i	−0.894902	+	0.446263i	$0.852754\pi$
$920$	1.72474	+	2.98735i	0.0568632	+	0.0984899i
$921$	0.545408	+	1.18386i	0.0179718	+	0.0390096i
$922$	−10.1742	+	17.6223i	−0.335071	+	0.580359i
$923$	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
$927$	−14.0000	−	39.5980i	−0.459820	−	1.30057i
$928$	−1.44949	+	2.51059i	−0.0475818	+	0.0824142i
$929$	−34.2929			−1.12511			−0.562556	−	0.826759i	$-0.690182\pi$
$929$	−34.2929			−1.12511			−0.562556	+	0.826759i	$0.690182\pi$
$930$	−35.6969	−	3.28913i	−1.17055	−	0.107855i
$931$		0			0
$932$	3.50000	+	6.06218i	0.114646	+	0.198573i
$933$	0.944387	+	2.04989i	0.0309178	+	0.0671103i
$934$	−5.00000	−	8.66025i	−0.163605	−	0.283372i
$935$	−6.89898	+	11.9494i	−0.225621	+	0.390787i
$936$	−14.4495	−	2.68556i	−0.472296	−	0.0877804i
$937$	6.40408			0.209212			0.104606	−	0.994514i	$-0.466642\pi$
$937$	6.40408			0.209212			0.104606	+	0.994514i	$0.466642\pi$
$938$		0			0
$939$	17.8990	+	38.8515i	0.584111	+	1.26787i
$940$	16.8990	−	29.2699i	0.551184	−	0.954679i
$941$	3.44949			0.112450			0.0562251	−	0.998418i	$-0.482094\pi$
$941$	3.44949			0.112450			0.0562251	+	0.998418i	$0.482094\pi$
$942$	4.60102	+	9.98698i	0.149909	+	0.325393i
$943$	9.79796			0.319065
$944$	−2.00000			−0.0650945
$945$		0			0
$946$	−5.79796			−0.188508
$947$	3.50510			0.113901			0.0569503	−	0.998377i	$-0.481862\pi$
$947$	3.50510			0.113901			0.0569503	+	0.998377i	$0.481862\pi$
$948$	5.72474	+	12.4261i	0.185931	+	0.403582i
$949$	−14.2020			−0.461018
$950$	−25.6969	+	44.5084i	−0.833719	+	1.44404i
$951$	−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	$0.145604\pi$
$954$	1.10102	+	3.11416i	0.0356469	+	0.100825i
$955$	−23.9722	+	41.5211i	−0.775722	+	1.34359i
$956$	6.39898	+	11.0834i	0.206958	+	0.358461i
$957$	4.20204	+	9.12096i	0.135833	+	0.294839i
$958$	14.7980	+	25.6308i	0.478100	+	0.828094i
$959$		0			0
$960$	−5.94949	−	0.548188i	−0.192019	−	0.0176927i
$961$	5.00000			0.161290
$962$	−19.1010	+	33.0839i	−0.615842	+	1.06667i
$963$	−35.3939	−	6.57826i	−1.14055	−	0.211981i
$964$	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	$0.757927\pi$
$968$	3.50000	−	6.06218i	0.112494	−	0.194846i
$969$	10.7980	+	23.4381i	0.346880	+	0.752939i
$970$	11.8990	+	20.6096i	0.382053	+	0.661736i
$971$	26.9722	+	46.7172i	0.865579	+	1.49923i	0.866471	+	0.499227i	$0.166383\pi$
$971$	26.9722	+	46.7172i	0.865579	+	1.49923i	−0.000892350		1.00000i	$0.500284\pi$
$972$	12.9722	−	8.64420i	0.416083	−	0.277263i
$973$		0			0
$974$	−11.1969	+	19.3937i	−0.358773	+	0.621413i
$975$	58.2929	+	5.37113i	1.86687	+	0.172014i
$976$	11.4495			0.366489
$977$	1.59592			0.0510579			0.0255290	−	0.999674i	$-0.491873\pi$
$977$	1.59592			0.0510579			0.0255290	+	0.999674i	$0.491873\pi$
$978$	−0.202041	+	0.285729i	−0.00646056	+	0.00913661i
$979$	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
$983$	−22.5959	−	39.1373i	−0.720698	−	1.24829i	−0.960720	−	0.277518i	$-0.910488\pi$
$983$	−22.5959	−	39.1373i	−0.720698	−	1.24829i	0.240023	−	0.970767i	$-0.422845\pi$
$984$	−9.79796	+	13.8564i	−0.312348	+	0.441726i
$985$	21.8990	−	37.9301i	0.697760	−	1.20855i
$986$	−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
$990$	−13.4495	+	15.7313i	−0.427453	+	0.499974i
$991$	−8.89898	+	15.4135i	−0.282685	+	0.489625i	−0.972045	−	0.234794i	$-0.924559\pi$
$991$	−8.89898	+	15.4135i	−0.282685	+	0.489625i	0.689360	+	0.724419i	$0.257892\pi$
$992$	6.00000			0.190500
$993$	−17.8990	−	38.8515i	−0.568007	−	1.23292i
$994$		0			0
$995$	−11.8990	−	20.6096i	−0.377223	−	0.653369i
$996$	−3.44949	−	0.317837i	−0.109301	−	0.0100711i
$997$	−8.92679	−	15.4616i	−0.282714	−	0.489675i	0.689338	−	0.724440i	$-0.257901\pi$
$997$	−8.92679	−	15.4616i	−0.282714	−	0.489675i	−0.972052	+	0.234764i	$0.924568\pi$
$998$	−16.6969	+	28.9199i	−0.528532	+	0.915445i
$999$	−9.94439	−	39.2801i	−0.314626	−	1.24277i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.2.e.m.655.2		4
3.2	odd	2		2646.2.e.l.2125.2		4
7.2	even	3		882.2.h.k.79.1		4
7.3	odd	6		882.2.f.j.295.2		4
7.4	even	3		126.2.f.c.43.1	✓	4
7.5	odd	6		882.2.h.l.79.2		4
7.6	odd	2		882.2.e.n.655.1		4
9.4	even	3		882.2.h.k.67.1		4
9.5	odd	6		2646.2.h.m.361.1		4
21.2	odd	6		2646.2.h.m.667.1		4
21.5	even	6		2646.2.h.n.667.2		4
21.11	odd	6		378.2.f.d.127.2		4
21.17	even	6		2646.2.f.k.883.1		4
21.20	even	2		2646.2.e.k.2125.1		4
28.11	odd	6		1008.2.r.e.673.2		4
63.4	even	3		126.2.f.c.85.2	yes	4
63.5	even	6		2646.2.e.k.1549.1		4
63.11	odd	6		1134.2.a.i.1.1		2
63.13	odd	6		882.2.h.l.67.2		4
63.23	odd	6		2646.2.e.l.1549.2		4
63.25	even	3		1134.2.a.p.1.2		2
63.31	odd	6		882.2.f.j.589.1		4
63.32	odd	6		378.2.f.d.253.2		4
63.38	even	6		7938.2.a.bm.1.2		2
63.40	odd	6		882.2.e.n.373.1		4
63.41	even	6		2646.2.h.n.361.2		4
63.52	odd	6		7938.2.a.bn.1.1		2
63.58	even	3	inner	882.2.e.m.373.2		4
63.59	even	6		2646.2.f.k.1765.1		4
84.11	even	6		3024.2.r.e.2017.2		4
252.11	even	6		9072.2.a.bd.1.1		2
252.67	odd	6		1008.2.r.e.337.1		4
252.95	even	6		3024.2.r.e.1009.2		4
252.151	odd	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	7.4	even	3
126.2.f.c.85.2	yes	4	63.4	even	3
378.2.f.d.127.2		4	21.11	odd	6
378.2.f.d.253.2		4	63.32	odd	6
882.2.e.m.373.2		4	63.58	even	3	inner
882.2.e.m.655.2		4	1.1	even	1	trivial
882.2.e.n.373.1		4	63.40	odd	6
882.2.e.n.655.1		4	7.6	odd	2
882.2.f.j.295.2		4	7.3	odd	6
882.2.f.j.589.1		4	63.31	odd	6
882.2.h.k.67.1		4	9.4	even	3
882.2.h.k.79.1		4	7.2	even	3
882.2.h.l.67.2		4	63.13	odd	6
882.2.h.l.79.2		4	7.5	odd	6
1008.2.r.e.337.1		4	252.67	odd	6
1008.2.r.e.673.2		4	28.11	odd	6
1134.2.a.i.1.1		2	63.11	odd	6
1134.2.a.p.1.2		2	63.25	even	3
2646.2.e.k.1549.1		4	63.5	even	6
2646.2.e.k.2125.1		4	21.20	even	2
2646.2.e.l.1549.2		4	63.23	odd	6
2646.2.e.l.2125.2		4	3.2	odd	2
2646.2.f.k.883.1		4	21.17	even	6
2646.2.f.k.1765.1		4	63.59	even	6
2646.2.h.m.361.1		4	9.5	odd	6
2646.2.h.m.667.1		4	21.2	odd	6
2646.2.h.n.361.2		4	63.41	even	6
2646.2.h.n.667.2		4	21.5	even	6
3024.2.r.e.1009.2		4	252.95	even	6
3024.2.r.e.2017.2		4	84.11	even	6
7938.2.a.bm.1.2		2	63.38	even	6
7938.2.a.bn.1.1		2	63.52	odd	6
9072.2.a.bd.1.1		2	252.11	even	6
9072.2.a.bk.1.2		2	252.151	odd	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.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.724745 + 1.57313i) q^{3} +1.00000 q^{4} +(-1.72474 + 2.98735i) q^{5} +(0.724745 + 1.57313i) q^{6} +1.00000 q^{8} +(-1.94949 + 2.28024i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(0.724745 + 1.57313i) q^{3} +1.00000 q^{4} +(-1.72474 + 2.98735i) q^{5} +(0.724745 + 1.57313i) q^{6} +1.00000 q^{8} +(-1.94949 + 2.28024i) q^{9} +(-1.72474 + 2.98735i) q^{10} +(-1.00000 - 1.73205i) q^{11} +(0.724745 + 1.57313i) q^{12} +(2.44949 + 4.24264i) q^{13} +(-5.94949 - 0.548188i) q^{15} +1.00000 q^{16} +(-1.00000 + 1.73205i) q^{17} +(-1.94949 + 2.28024i) q^{18} +(-3.72474 - 6.45145i) q^{19} +(-1.72474 + 2.98735i) q^{20} +(-1.00000 - 1.73205i) q^{22} +(0.500000 - 0.866025i) q^{23} +(0.724745 + 1.57313i) q^{24} +(-3.44949 - 5.97469i) q^{25} +(2.44949 + 4.24264i) q^{26} +(-5.00000 - 1.41421i) q^{27} +(-1.44949 + 2.51059i) q^{29} +(-5.94949 - 0.548188i) q^{30} +6.00000 q^{31} +1.00000 q^{32} +(2.00000 - 2.82843i) q^{33} +(-1.00000 + 1.73205i) q^{34} +(-1.94949 + 2.28024i) q^{36} +(3.89898 + 6.75323i) q^{37} +(-3.72474 - 6.45145i) q^{38} +(-4.89898 + 6.92820i) q^{39} +(-1.72474 + 2.98735i) q^{40} +(4.89898 + 8.48528i) q^{41} +(1.44949 - 2.51059i) q^{43} +(-1.00000 - 1.73205i) q^{44} +(-3.44949 - 9.75663i) q^{45} +(0.500000 - 0.866025i) q^{46} -9.79796 q^{47} +(0.724745 + 1.57313i) q^{48} +(-3.44949 - 5.97469i) q^{50} +(-3.44949 - 0.317837i) q^{51} +(2.44949 + 4.24264i) q^{52} +(0.550510 - 0.953512i) q^{53} +(-5.00000 - 1.41421i) q^{54} +6.89898 q^{55} +(7.44949 - 10.5352i) q^{57} +(-1.44949 + 2.51059i) q^{58} -2.00000 q^{59} +(-5.94949 - 0.548188i) q^{60} +11.4495 q^{61} +6.00000 q^{62} +1.00000 q^{64} -16.8990 q^{65} +(2.00000 - 2.82843i) q^{66} -3.10102 q^{67} +(-1.00000 + 1.73205i) q^{68} +(1.72474 + 0.158919i) q^{69} +9.89898 q^{71} +(-1.94949 + 2.28024i) q^{72} +(-1.44949 + 2.51059i) q^{73} +(3.89898 + 6.75323i) q^{74} +(6.89898 - 9.75663i) q^{75} +(-3.72474 - 6.45145i) q^{76} +(-4.89898 + 6.92820i) q^{78} +7.89898 q^{79} +(-1.72474 + 2.98735i) q^{80} +(-1.39898 - 8.89060i) q^{81} +(4.89898 + 8.48528i) q^{82} +(-1.00000 + 1.73205i) q^{83} +(-3.44949 - 5.97469i) q^{85} +(1.44949 - 2.51059i) q^{86} +(-5.00000 - 0.460702i) q^{87} +(-1.00000 - 1.73205i) q^{88} +(3.55051 + 6.14966i) q^{89} +(-3.44949 - 9.75663i) q^{90} +(0.500000 - 0.866025i) q^{92} +(4.34847 + 9.43879i) q^{93} -9.79796 q^{94} +25.6969 q^{95} +(0.724745 + 1.57313i) q^{96} +(3.44949 - 5.97469i) q^{97} +(5.89898 + 1.09638i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} + 4 q^{8} + 2 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 + 4 * q^8 + 2 * q^9	\( 4 q + 4 q^{2} - 2 q^{3} + 4 q^{4} - 2 q^{5} - 2 q^{6} + 4 q^{8} + 2 q^{9} - 2 q^{10} - 4 q^{11} - 2 q^{12} - 14 q^{15} + 4 q^{16} - 4 q^{17} + 2 q^{18} - 10 q^{19} - 2 q^{20} - 4 q^{22} + 2 q^{23} - 2 q^{24} - 4 q^{25} - 20 q^{27} + 4 q^{29} - 14 q^{30} + 24 q^{31} + 4 q^{32} + 8 q^{33} - 4 q^{34} + 2 q^{36} - 4 q^{37} - 10 q^{38} - 2 q^{40} - 4 q^{43} - 4 q^{44} - 4 q^{45} + 2 q^{46} - 2 q^{48} - 4 q^{50} - 4 q^{51} + 12 q^{53} - 20 q^{54} + 8 q^{55} + 20 q^{57} + 4 q^{58} - 8 q^{59} - 14 q^{60} + 36 q^{61} + 24 q^{62} + 4 q^{64} - 48 q^{65} + 8 q^{66} - 32 q^{67} - 4 q^{68} + 2 q^{69} + 20 q^{71} + 2 q^{72} + 4 q^{73} - 4 q^{74} + 8 q^{75} - 10 q^{76} + 12 q^{79} - 2 q^{80} + 14 q^{81} - 4 q^{83} - 4 q^{85} - 4 q^{86} - 20 q^{87} - 4 q^{88} + 24 q^{89} - 4 q^{90} + 2 q^{92} - 12 q^{93} + 44 q^{95} - 2 q^{96} + 4 q^{97} + 4 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 2 * q^3 + 4 * q^4 - 2 * q^5 - 2 * q^6 + 4 * q^8 + 2 * q^9 - 2 * q^10 - 4 * q^11 - 2 * q^12 - 14 * q^15 + 4 * q^16 - 4 * q^17 + 2 * q^18 - 10 * q^19 - 2 * q^20 - 4 * q^22 + 2 * q^23 - 2 * q^24 - 4 * q^25 - 20 * q^27 + 4 * q^29 - 14 * q^30 + 24 * q^31 + 4 * q^32 + 8 * q^33 - 4 * q^34 + 2 * q^36 - 4 * q^37 - 10 * q^38 - 2 * q^40 - 4 * q^43 - 4 * q^44 - 4 * q^45 + 2 * q^46 - 2 * q^48 - 4 * q^50 - 4 * q^51 + 12 * q^53 - 20 * q^54 + 8 * q^55 + 20 * q^57 + 4 * q^58 - 8 * q^59 - 14 * q^60 + 36 * q^61 + 24 * q^62 + 4 * q^64 - 48 * q^65 + 8 * q^66 - 32 * q^67 - 4 * q^68 + 2 * q^69 + 20 * q^71 + 2 * q^72 + 4 * q^73 - 4 * q^74 + 8 * q^75 - 10 * q^76 + 12 * q^79 - 2 * q^80 + 14 * q^81 - 4 * q^83 - 4 * q^85 - 4 * q^86 - 20 * q^87 - 4 * q^88 + 24 * q^89 - 4 * q^90 + 2 * q^92 - 12 * q^93 + 44 * q^95 - 2 * q^96 + 4 * q^97 + 4 * q^99

Introduction

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