LMFDB - Embedded newform 570.2.i.b.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [570,2,Mod(121,570)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(570, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

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

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

chi := DirichletCharacter("570.121");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 570 = 2 \cdot 3 \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	570.i (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.55147291521$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	570.121
Dual form			570.2.i.b.391.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} -1.00000 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} -1.00000 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +2.00000 q^{11} +1.00000 q^{12} +(1.50000 - 2.59808i) q^{13} +(0.500000 + 0.866025i) q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +1.00000 q^{18} +(4.00000 + 1.73205i) q^{19} -1.00000 q^{20} +(0.500000 + 0.866025i) q^{21} +(-1.00000 - 1.73205i) q^{22} +(3.00000 - 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} -3.00000 q^{26} +1.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +(5.00000 - 8.66025i) q^{29} -1.00000 q^{30} +1.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.00000 - 1.73205i) q^{33} +(-2.00000 + 3.46410i) q^{34} +(-0.500000 - 0.866025i) q^{35} +(-0.500000 - 0.866025i) q^{36} -5.00000 q^{37} +(-0.500000 - 4.33013i) q^{38} -3.00000 q^{39} +(0.500000 + 0.866025i) q^{40} +(-1.00000 - 1.73205i) q^{41} +(0.500000 - 0.866025i) q^{42} +(2.50000 + 4.33013i) q^{43} +(-1.00000 + 1.73205i) q^{44} -1.00000 q^{45} -6.00000 q^{46} +(-0.500000 + 0.866025i) q^{48} -6.00000 q^{49} +1.00000 q^{50} +(-2.00000 + 3.46410i) q^{51} +(1.50000 + 2.59808i) q^{52} +(6.00000 - 10.3923i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(1.00000 + 1.73205i) q^{55} -1.00000 q^{56} +(-0.500000 - 4.33013i) q^{57} -10.0000 q^{58} +(1.00000 + 1.73205i) q^{59} +(0.500000 + 0.866025i) q^{60} +(-2.50000 + 4.33013i) q^{61} +(-0.500000 - 0.866025i) q^{62} +(0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +3.00000 q^{65} +(-1.00000 + 1.73205i) q^{66} +(2.50000 - 4.33013i) q^{67} +4.00000 q^{68} -6.00000 q^{69} +(-0.500000 + 0.866025i) q^{70} +(-0.500000 + 0.866025i) q^{72} +(-5.50000 - 9.52628i) q^{73} +(2.50000 + 4.33013i) q^{74} +1.00000 q^{75} +(-3.50000 + 2.59808i) q^{76} -2.00000 q^{77} +(1.50000 + 2.59808i) q^{78} +(5.50000 + 9.52628i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.00000 + 1.73205i) q^{82} +2.00000 q^{83} -1.00000 q^{84} +(2.00000 - 3.46410i) q^{85} +(2.50000 - 4.33013i) q^{86} -10.0000 q^{87} +2.00000 q^{88} +(0.500000 + 0.866025i) q^{90} +(-1.50000 + 2.59808i) q^{91} +(3.00000 + 5.19615i) q^{92} +(-0.500000 - 0.866025i) q^{93} +(0.500000 + 4.33013i) q^{95} +1.00000 q^{96} +(1.00000 + 1.73205i) q^{97} +(3.00000 + 5.19615i) q^{98} +(-1.00000 + 1.73205i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - 2 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 - q^3 - q^4 + q^5 - q^6 - 2 * q^7 + 2 * q^8 - q^9	$ 2 q - q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - 2 q^{7} + 2 q^{8} - q^{9} + q^{10} + 4 q^{11} + 2 q^{12} + 3 q^{13} + q^{14} + q^{15} - q^{16} - 4 q^{17} + 2 q^{18} + 8 q^{19} - 2 q^{20} + q^{21} - 2 q^{22} + 6 q^{23} - q^{24} - q^{25} - 6 q^{26} + 2 q^{27} + q^{28} + 10 q^{29} - 2 q^{30} + 2 q^{31} - q^{32} - 2 q^{33} - 4 q^{34} - q^{35} - q^{36} - 10 q^{37} - q^{38} - 6 q^{39} + q^{40} - 2 q^{41} + q^{42} + 5 q^{43} - 2 q^{44} - 2 q^{45} - 12 q^{46} - q^{48} - 12 q^{49} + 2 q^{50} - 4 q^{51} + 3 q^{52} + 12 q^{53} - q^{54} + 2 q^{55} - 2 q^{56} - q^{57} - 20 q^{58} + 2 q^{59} + q^{60} - 5 q^{61} - q^{62} + q^{63} + 2 q^{64} + 6 q^{65} - 2 q^{66} + 5 q^{67} + 8 q^{68} - 12 q^{69} - q^{70} - q^{72} - 11 q^{73} + 5 q^{74} + 2 q^{75} - 7 q^{76} - 4 q^{77} + 3 q^{78} + 11 q^{79} + q^{80} - q^{81} - 2 q^{82} + 4 q^{83} - 2 q^{84} + 4 q^{85} + 5 q^{86} - 20 q^{87} + 4 q^{88} + q^{90} - 3 q^{91} + 6 q^{92} - q^{93} + q^{95} + 2 q^{96} + 2 q^{97} + 6 q^{98} - 2 q^{99}+O(q^{100}) $ 2 * q - q^2 - q^3 - q^4 + q^5 - q^6 - 2 * q^7 + 2 * q^8 - q^9 + q^10 + 4 * q^11 + 2 * q^12 + 3 * q^13 + q^14 + q^15 - q^16 - 4 * q^17 + 2 * q^18 + 8 * q^19 - 2 * q^20 + q^21 - 2 * q^22 + 6 * q^23 - q^24 - q^25 - 6 * q^26 + 2 * q^27 + q^28 + 10 * q^29 - 2 * q^30 + 2 * q^31 - q^32 - 2 * q^33 - 4 * q^34 - q^35 - q^36 - 10 * q^37 - q^38 - 6 * q^39 + q^40 - 2 * q^41 + q^42 + 5 * q^43 - 2 * q^44 - 2 * q^45 - 12 * q^46 - q^48 - 12 * q^49 + 2 * q^50 - 4 * q^51 + 3 * q^52 + 12 * q^53 - q^54 + 2 * q^55 - 2 * q^56 - q^57 - 20 * q^58 + 2 * q^59 + q^60 - 5 * q^61 - q^62 + q^63 + 2 * q^64 + 6 * q^65 - 2 * q^66 + 5 * q^67 + 8 * q^68 - 12 * q^69 - q^70 - q^72 - 11 * q^73 + 5 * q^74 + 2 * q^75 - 7 * q^76 - 4 * q^77 + 3 * q^78 + 11 * q^79 + q^80 - q^81 - 2 * q^82 + 4 * q^83 - 2 * q^84 + 4 * q^85 + 5 * q^86 - 20 * q^87 + 4 * q^88 + q^90 - 3 * q^91 + 6 * q^92 - q^93 + q^95 + 2 * q^96 + 2 * q^97 + 6 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/570\mathbb{Z}\right)^\times$.

$n$	$191$	$211$	$457$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$5$	0.500000	+	0.866025i	0.223607	+	0.387298i
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	−1.00000			−0.377964			−0.188982	−	0.981981i	$-0.560519\pi$
$7$	−1.00000			−0.377964			−0.188982	+	0.981981i	$0.560519\pi$
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	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			0.288675
$13$	1.50000	−	2.59808i	0.416025	−	0.720577i	−0.579510	−	0.814965i	$-0.696756\pi$
$13$	1.50000	−	2.59808i	0.416025	−	0.720577i	0.995535	+	0.0943882i	$0.0300895\pi$
$14$	0.500000	+	0.866025i	0.133631	+	0.231455i
$15$	0.500000	−	0.866025i	0.129099	−	0.223607i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	0.514782	−	0.857321i	$-0.327873\pi$
$17$	−2.00000	−	3.46410i	−0.485071	−	0.840168i	−0.999853	+	0.0171533i	$0.994540\pi$
$18$	1.00000			0.235702
$19$	4.00000	+	1.73205i	0.917663	+	0.397360i
$19$	4.00000	+	1.73205i	0.917663	+	0.397360i
$20$	−1.00000			−0.223607
$21$	0.500000	+	0.866025i	0.109109	+	0.188982i
$22$	−1.00000	−	1.73205i	−0.213201	−	0.369274i
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	−0.362892	−	0.931831i	$-0.618211\pi$
$23$	3.00000	−	5.19615i	0.625543	−	1.08347i	0.988436	−	0.151642i	$-0.0484560\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−3.00000			−0.588348
$27$	1.00000			0.192450
$28$	0.500000	−	0.866025i	0.0944911	−	0.163663i
$29$	5.00000	−	8.66025i	0.928477	−	1.60817i	0.142605	−	0.989780i	$-0.454452\pi$
$29$	5.00000	−	8.66025i	0.928477	−	1.60817i	0.785872	−	0.618389i	$-0.212214\pi$
$30$	−1.00000			−0.182574
$31$	1.00000			0.179605			0.0898027	−	0.995960i	$-0.471376\pi$
$31$	1.00000			0.179605			0.0898027	+	0.995960i	$0.471376\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−1.00000	−	1.73205i	−0.174078	−	0.301511i
$34$	−2.00000	+	3.46410i	−0.342997	+	0.594089i
$35$	−0.500000	−	0.866025i	−0.0845154	−	0.146385i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−5.00000			−0.821995			−0.410997	−	0.911636i	$-0.634819\pi$
$37$	−5.00000			−0.821995			−0.410997	+	0.911636i	$0.634819\pi$
$38$	−0.500000	−	4.33013i	−0.0811107	−	0.702439i
$39$	−3.00000			−0.480384
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	−1.00000	−	1.73205i	−0.156174	−	0.270501i	0.777312	−	0.629115i	$-0.216583\pi$
$41$	−1.00000	−	1.73205i	−0.156174	−	0.270501i	−0.933486	+	0.358614i	$0.883249\pi$
$42$	0.500000	−	0.866025i	0.0771517	−	0.133631i
$43$	2.50000	+	4.33013i	0.381246	+	0.660338i	0.991241	−	0.132068i	$-0.0421616\pi$
$43$	2.50000	+	4.33013i	0.381246	+	0.660338i	−0.609994	+	0.792406i	$0.708828\pi$
$44$	−1.00000	+	1.73205i	−0.150756	+	0.261116i
$45$	−1.00000			−0.149071
$46$	−6.00000			−0.884652
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−6.00000			−0.857143
$50$	1.00000			0.141421
$51$	−2.00000	+	3.46410i	−0.280056	+	0.485071i
$52$	1.50000	+	2.59808i	0.208013	+	0.360288i
$53$	6.00000	−	10.3923i	0.824163	−	1.42749i	−0.0783936	−	0.996922i	$-0.524979\pi$
$53$	6.00000	−	10.3923i	0.824163	−	1.42749i	0.902557	−	0.430570i	$-0.141688\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	1.00000	+	1.73205i	0.134840	+	0.233550i
$56$	−1.00000			−0.133631
$57$	−0.500000	−	4.33013i	−0.0662266	−	0.573539i
$58$	−10.0000			−1.31306
$59$	1.00000	+	1.73205i	0.130189	+	0.225494i	0.923749	−	0.382998i	$-0.125108\pi$
$59$	1.00000	+	1.73205i	0.130189	+	0.225494i	−0.793560	+	0.608492i	$0.791775\pi$
$60$	0.500000	+	0.866025i	0.0645497	+	0.111803i
$61$	−2.50000	+	4.33013i	−0.320092	+	0.554416i	−0.980507	−	0.196485i	$-0.937047\pi$
$61$	−2.50000	+	4.33013i	−0.320092	+	0.554416i	0.660415	+	0.750901i	$0.270381\pi$
$62$	−0.500000	−	0.866025i	−0.0635001	−	0.109985i
$63$	0.500000	−	0.866025i	0.0629941	−	0.109109i
$64$	1.00000			0.125000
$65$	3.00000			0.372104
$66$	−1.00000	+	1.73205i	−0.123091	+	0.213201i
$67$	2.50000	−	4.33013i	0.305424	−	0.529009i	−0.671932	−	0.740613i	$-0.734535\pi$
$67$	2.50000	−	4.33013i	0.305424	−	0.529009i	0.977356	+	0.211604i	$0.0678686\pi$
$68$	4.00000			0.485071
$69$	−6.00000			−0.722315
$70$	−0.500000	+	0.866025i	−0.0597614	+	0.103510i
$71$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$71$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−5.50000	−	9.52628i	−0.643726	−	1.11497i	−0.984594	−	0.174855i	$-0.944054\pi$
$73$	−5.50000	−	9.52628i	−0.643726	−	1.11497i	0.340868	−	0.940111i	$-0.389279\pi$
$74$	2.50000	+	4.33013i	0.290619	+	0.503367i
$75$	1.00000			0.115470
$76$	−3.50000	+	2.59808i	−0.401478	+	0.298020i
$77$	−2.00000			−0.227921
$78$	1.50000	+	2.59808i	0.169842	+	0.294174i
$79$	5.50000	+	9.52628i	0.618798	+	1.07179i	0.989705	+	0.143120i	$0.0457135\pi$
$79$	5.50000	+	9.52628i	0.618798	+	1.07179i	−0.370907	+	0.928670i	$0.620953\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−1.00000	+	1.73205i	−0.110432	+	0.191273i
$83$	2.00000			0.219529			0.109764	−	0.993958i	$-0.464990\pi$
$83$	2.00000			0.219529			0.109764	+	0.993958i	$0.464990\pi$
$84$	−1.00000			−0.109109
$85$	2.00000	−	3.46410i	0.216930	−	0.375735i
$86$	2.50000	−	4.33013i	0.269582	−	0.466930i
$87$	−10.0000			−1.07211
$88$	2.00000			0.213201
$89$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$89$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$90$	0.500000	+	0.866025i	0.0527046	+	0.0912871i
$91$	−1.50000	+	2.59808i	−0.157243	+	0.272352i
$92$	3.00000	+	5.19615i	0.312772	+	0.541736i
$93$	−0.500000	−	0.866025i	−0.0518476	−	0.0898027i
$94$		0			0
$95$	0.500000	+	4.33013i	0.0512989	+	0.444262i
$96$	1.00000			0.102062
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	0.912317	−	0.409484i	$-0.134291\pi$
$97$	1.00000	+	1.73205i	0.101535	+	0.175863i	−0.810782	+	0.585348i	$0.800958\pi$
$98$	3.00000	+	5.19615i	0.303046	+	0.524891i
$99$	−1.00000	+	1.73205i	−0.100504	+	0.174078i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	−0.975796	−	0.218685i	$-0.929823\pi$
$101$	−3.00000	+	5.19615i	−0.298511	+	0.517036i	0.677284	+	0.735721i	$0.263157\pi$
$102$	4.00000			0.396059
$103$	19.0000			1.87213			0.936063	−	0.351833i	$-0.114441\pi$
$103$	19.0000			1.87213			0.936063	+	0.351833i	$0.114441\pi$
$104$	1.50000	−	2.59808i	0.147087	−	0.254762i
$105$	−0.500000	+	0.866025i	−0.0487950	+	0.0845154i
$106$	−12.0000			−1.16554
$107$	−4.00000			−0.386695			−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000			−0.386695			−0.193347	+	0.981130i	$0.561934\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	9.00000	+	15.5885i	0.862044	+	1.49310i	0.869953	+	0.493135i	$0.164149\pi$
$109$	9.00000	+	15.5885i	0.862044	+	1.49310i	−0.00790932	+	0.999969i	$0.502518\pi$
$110$	1.00000	−	1.73205i	0.0953463	−	0.165145i
$111$	2.50000	+	4.33013i	0.237289	+	0.410997i
$112$	0.500000	+	0.866025i	0.0472456	+	0.0818317i
$113$	14.0000			1.31701			0.658505	−	0.752577i	$-0.271189\pi$
$113$	14.0000			1.31701			0.658505	+	0.752577i	$0.271189\pi$
$114$	−3.50000	+	2.59808i	−0.327805	+	0.243332i
$115$	6.00000			0.559503
$116$	5.00000	+	8.66025i	0.464238	+	0.804084i
$117$	1.50000	+	2.59808i	0.138675	+	0.240192i
$118$	1.00000	−	1.73205i	0.0920575	−	0.159448i
$119$	2.00000	+	3.46410i	0.183340	+	0.317554i
$120$	0.500000	−	0.866025i	0.0456435	−	0.0790569i
$121$	−7.00000			−0.636364
$122$	5.00000			0.452679
$123$	−1.00000	+	1.73205i	−0.0901670	+	0.156174i
$124$	−0.500000	+	0.866025i	−0.0449013	+	0.0777714i
$125$	−1.00000			−0.0894427
$126$	−1.00000			−0.0890871
$127$	−8.00000	+	13.8564i	−0.709885	+	1.22956i	0.255014	+	0.966937i	$0.417920\pi$
$127$	−8.00000	+	13.8564i	−0.709885	+	1.22956i	−0.964899	+	0.262620i	$0.915413\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	2.50000	−	4.33013i	0.220113	−	0.381246i
$130$	−1.50000	−	2.59808i	−0.131559	−	0.227866i
$131$	3.00000	+	5.19615i	0.262111	+	0.453990i	0.966803	−	0.255524i	$-0.0822479\pi$
$131$	3.00000	+	5.19615i	0.262111	+	0.453990i	−0.704692	+	0.709514i	$0.748915\pi$
$132$	2.00000			0.174078
$133$	−4.00000	−	1.73205i	−0.346844	−	0.150188i
$134$	−5.00000			−0.431934
$135$	0.500000	+	0.866025i	0.0430331	+	0.0745356i
$136$	−2.00000	−	3.46410i	−0.171499	−	0.297044i
$137$	1.00000	−	1.73205i	0.0854358	−	0.147979i	−0.820141	−	0.572161i	$-0.806105\pi$
$137$	1.00000	−	1.73205i	0.0854358	−	0.147979i	0.905577	+	0.424182i	$0.139438\pi$
$138$	3.00000	+	5.19615i	0.255377	+	0.442326i
$139$	4.50000	−	7.79423i	0.381685	−	0.661098i	−0.609618	−	0.792695i	$-0.708677\pi$
$139$	4.50000	−	7.79423i	0.381685	−	0.661098i	0.991303	+	0.131597i	$0.0420106\pi$
$140$	1.00000			0.0845154
$141$		0			0
$142$		0			0
$143$	3.00000	−	5.19615i	0.250873	−	0.434524i
$144$	1.00000			0.0833333
$145$	10.0000			0.830455
$146$	−5.50000	+	9.52628i	−0.455183	+	0.788400i
$147$	3.00000	+	5.19615i	0.247436	+	0.428571i
$148$	2.50000	−	4.33013i	0.205499	−	0.355934i
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	−0.953703	−	0.300750i	$-0.902763\pi$
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	0.216394	−	0.976306i	$-0.430570\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$		0			0			−	1.00000i	$-0.5\pi$
$151$		0			0				1.00000i	$0.5\pi$
$152$	4.00000	+	1.73205i	0.324443	+	0.140488i
$153$	4.00000			0.323381
$154$	1.00000	+	1.73205i	0.0805823	+	0.139573i
$155$	0.500000	+	0.866025i	0.0401610	+	0.0695608i
$156$	1.50000	−	2.59808i	0.120096	−	0.208013i
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	0.999762	+	0.0217953i	$0.00693820\pi$
$157$	6.50000	+	11.2583i	0.518756	+	0.898513i	−0.481006	+	0.876717i	$0.659728\pi$
$158$	5.50000	−	9.52628i	0.437557	−	0.757870i
$159$	−12.0000			−0.951662
$160$	−1.00000			−0.0790569
$161$	−3.00000	+	5.19615i	−0.236433	+	0.409514i
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	−17.0000			−1.33154			−0.665771	−	0.746156i	$-0.731897\pi$
$163$	−17.0000			−1.33154			−0.665771	+	0.746156i	$0.731897\pi$
$164$	2.00000			0.156174
$165$	1.00000	−	1.73205i	0.0778499	−	0.134840i
$166$	−1.00000	−	1.73205i	−0.0776151	−	0.134433i
$167$	−7.00000	+	12.1244i	−0.541676	+	0.938211i	0.457132	+	0.889399i	$0.348877\pi$
$167$	−7.00000	+	12.1244i	−0.541676	+	0.938211i	−0.998808	+	0.0488118i	$0.984457\pi$
$168$	0.500000	+	0.866025i	0.0385758	+	0.0668153i
$169$	2.00000	+	3.46410i	0.153846	+	0.266469i
$170$	−4.00000			−0.306786
$171$	−3.50000	+	2.59808i	−0.267652	+	0.198680i
$172$	−5.00000			−0.381246
$173$	13.0000	+	22.5167i	0.988372	+	1.71191i	0.625871	+	0.779926i	$0.284744\pi$
$173$	13.0000	+	22.5167i	0.988372	+	1.71191i	0.362500	+	0.931984i	$0.381923\pi$
$174$	5.00000	+	8.66025i	0.379049	+	0.656532i
$175$	0.500000	−	0.866025i	0.0377964	−	0.0654654i
$176$	−1.00000	−	1.73205i	−0.0753778	−	0.130558i
$177$	1.00000	−	1.73205i	0.0751646	−	0.130189i
$178$		0			0
$179$	−10.0000			−0.747435			−0.373718	−	0.927543i	$-0.621917\pi$
$179$	−10.0000			−0.747435			−0.373718	+	0.927543i	$0.621917\pi$
$180$	0.500000	−	0.866025i	0.0372678	−	0.0645497i
$181$	3.00000	−	5.19615i	0.222988	−	0.386227i	−0.732726	−	0.680524i	$-0.761752\pi$
$181$	3.00000	−	5.19615i	0.222988	−	0.386227i	0.955714	+	0.294297i	$0.0950855\pi$
$182$	3.00000			0.222375
$183$	5.00000			0.369611
$184$	3.00000	−	5.19615i	0.221163	−	0.383065i
$185$	−2.50000	−	4.33013i	−0.183804	−	0.318357i
$186$	−0.500000	+	0.866025i	−0.0366618	+	0.0635001i
$187$	−4.00000	−	6.92820i	−0.292509	−	0.506640i
$188$		0			0
$189$	−1.00000			−0.0727393
$190$	3.50000	−	2.59808i	0.253917	−	0.188484i
$191$	16.0000			1.15772			0.578860	−	0.815427i	$-0.303498\pi$
$191$	16.0000			1.15772			0.578860	+	0.815427i	$0.303498\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−12.5000	−	21.6506i	−0.899770	−	1.55845i	−0.827788	−	0.561041i	$-0.810401\pi$
$193$	−12.5000	−	21.6506i	−0.899770	−	1.55845i	−0.0719816	−	0.997406i	$-0.522932\pi$
$194$	1.00000	−	1.73205i	0.0717958	−	0.124354i
$195$	−1.50000	−	2.59808i	−0.107417	−	0.186052i
$196$	3.00000	−	5.19615i	0.214286	−	0.371154i
$197$	−18.0000			−1.28245			−0.641223	−	0.767354i	$-0.721573\pi$
$197$	−18.0000			−1.28245			−0.641223	+	0.767354i	$0.721573\pi$
$198$	2.00000			0.142134
$199$	−2.50000	+	4.33013i	−0.177220	+	0.306955i	−0.940927	−	0.338608i	$-0.890044\pi$
$199$	−2.50000	+	4.33013i	−0.177220	+	0.306955i	0.763707	+	0.645563i	$0.223377\pi$
$200$	−0.500000	+	0.866025i	−0.0353553	+	0.0612372i
$201$	−5.00000			−0.352673
$202$	6.00000			0.422159
$203$	−5.00000	+	8.66025i	−0.350931	+	0.607831i
$204$	−2.00000	−	3.46410i	−0.140028	−	0.242536i
$205$	1.00000	−	1.73205i	0.0698430	−	0.120972i
$206$	−9.50000	−	16.4545i	−0.661896	−	1.14644i
$207$	3.00000	+	5.19615i	0.208514	+	0.361158i
$208$	−3.00000			−0.208013
$209$	8.00000	+	3.46410i	0.553372	+	0.239617i
$210$	1.00000			0.0690066
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	0.939156	−	0.343490i	$-0.111609\pi$
$211$	2.50000	+	4.33013i	0.172107	+	0.298098i	−0.767049	+	0.641588i	$0.778276\pi$
$212$	6.00000	+	10.3923i	0.412082	+	0.713746i
$213$		0			0
$214$	2.00000	+	3.46410i	0.136717	+	0.236801i
$215$	−2.50000	+	4.33013i	−0.170499	+	0.295312i
$216$	1.00000			0.0680414
$217$	−1.00000			−0.0678844
$218$	9.00000	−	15.5885i	0.609557	−	1.05578i
$219$	−5.50000	+	9.52628i	−0.371656	+	0.643726i
$220$	−2.00000			−0.134840
$221$	−12.0000			−0.807207
$222$	2.50000	−	4.33013i	0.167789	−	0.290619i
$223$	0.500000	+	0.866025i	0.0334825	+	0.0579934i	0.882281	−	0.470723i	$-0.156007\pi$
$223$	0.500000	+	0.866025i	0.0334825	+	0.0579934i	−0.848799	+	0.528716i	$0.822674\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$	−0.500000	−	0.866025i	−0.0333333	−	0.0577350i
$226$	−7.00000	−	12.1244i	−0.465633	−	0.806500i
$227$	−18.0000			−1.19470			−0.597351	−	0.801980i	$-0.703780\pi$
$227$	−18.0000			−1.19470			−0.597351	+	0.801980i	$0.703780\pi$
$228$	4.00000	+	1.73205i	0.264906	+	0.114708i
$229$	−5.00000			−0.330409			−0.165205	−	0.986259i	$-0.552828\pi$
$229$	−5.00000			−0.330409			−0.165205	+	0.986259i	$0.552828\pi$
$230$	−3.00000	−	5.19615i	−0.197814	−	0.342624i
$231$	1.00000	+	1.73205i	0.0657952	+	0.113961i
$232$	5.00000	−	8.66025i	0.328266	−	0.568574i
$233$	2.00000	+	3.46410i	0.131024	+	0.226941i	0.924072	−	0.382219i	$-0.124840\pi$
$233$	2.00000	+	3.46410i	0.131024	+	0.226941i	−0.793047	+	0.609160i	$0.791507\pi$
$234$	1.50000	−	2.59808i	0.0980581	−	0.169842i
$235$		0			0
$236$	−2.00000			−0.130189
$237$	5.50000	−	9.52628i	0.357263	−	0.618798i
$238$	2.00000	−	3.46410i	0.129641	−	0.224544i
$239$	−18.0000			−1.16432			−0.582162	−	0.813073i	$-0.697793\pi$
$239$	−18.0000			−1.16432			−0.582162	+	0.813073i	$0.697793\pi$
$240$	−1.00000			−0.0645497
$241$	−2.50000	+	4.33013i	−0.161039	+	0.278928i	−0.935242	−	0.354010i	$-0.884818\pi$
$241$	−2.50000	+	4.33013i	−0.161039	+	0.278928i	0.774202	+	0.632938i	$0.218151\pi$
$242$	3.50000	+	6.06218i	0.224989	+	0.389692i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−2.50000	−	4.33013i	−0.160046	−	0.277208i
$245$	−3.00000	−	5.19615i	−0.191663	−	0.331970i
$246$	2.00000			0.127515
$247$	10.5000	−	7.79423i	0.668099	−	0.495935i
$248$	1.00000			0.0635001
$249$	−1.00000	−	1.73205i	−0.0633724	−	0.109764i
$250$	0.500000	+	0.866025i	0.0316228	+	0.0547723i
$251$	1.00000	−	1.73205i	0.0631194	−	0.109326i	−0.832739	−	0.553666i	$-0.813228\pi$
$251$	1.00000	−	1.73205i	0.0631194	−	0.109326i	0.895858	+	0.444340i	$0.146562\pi$
$252$	0.500000	+	0.866025i	0.0314970	+	0.0545545i
$253$	6.00000	−	10.3923i	0.377217	−	0.653359i
$254$	16.0000			1.00393
$255$	−4.00000			−0.250490
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	−0.757159	−	0.653231i	$-0.773413\pi$
$257$	3.00000	−	5.19615i	0.187135	−	0.324127i	0.944294	+	0.329104i	$0.106747\pi$
$258$	−5.00000			−0.311286
$259$	5.00000			0.310685
$260$	−1.50000	+	2.59808i	−0.0930261	+	0.161126i
$261$	5.00000	+	8.66025i	0.309492	+	0.536056i
$262$	3.00000	−	5.19615i	0.185341	−	0.321019i
$263$	5.00000	+	8.66025i	0.308313	+	0.534014i	0.977993	−	0.208635i	$-0.0669022\pi$
$263$	5.00000	+	8.66025i	0.308313	+	0.534014i	−0.669680	+	0.742650i	$0.733569\pi$
$264$	−1.00000	−	1.73205i	−0.0615457	−	0.106600i
$265$	12.0000			0.737154
$266$	0.500000	+	4.33013i	0.0306570	+	0.265497i
$267$		0			0
$268$	2.50000	+	4.33013i	0.152712	+	0.264505i
$269$	−5.00000	−	8.66025i	−0.304855	−	0.528025i	0.672374	−	0.740212i	$-0.265275\pi$
$269$	−5.00000	−	8.66025i	−0.304855	−	0.528025i	−0.977229	+	0.212187i	$0.931941\pi$
$270$	0.500000	−	0.866025i	0.0304290	−	0.0527046i
$271$	4.00000	+	6.92820i	0.242983	+	0.420858i	0.961563	−	0.274586i	$-0.0885408\pi$
$271$	4.00000	+	6.92820i	0.242983	+	0.420858i	−0.718580	+	0.695444i	$0.755208\pi$
$272$	−2.00000	+	3.46410i	−0.121268	+	0.210042i
$273$	3.00000			0.181568
$274$	−2.00000			−0.120824
$275$	−1.00000	+	1.73205i	−0.0603023	+	0.104447i
$276$	3.00000	−	5.19615i	0.180579	−	0.312772i
$277$	−10.0000			−0.600842			−0.300421	−	0.953807i	$-0.597127\pi$
$277$	−10.0000			−0.600842			−0.300421	+	0.953807i	$0.597127\pi$
$278$	−9.00000			−0.539784
$279$	−0.500000	+	0.866025i	−0.0299342	+	0.0518476i
$280$	−0.500000	−	0.866025i	−0.0298807	−	0.0517549i
$281$	15.0000	−	25.9808i	0.894825	−	1.54988i	0.0608039	−	0.998150i	$-0.480634\pi$
$281$	15.0000	−	25.9808i	0.894825	−	1.54988i	0.834021	−	0.551733i	$-0.186033\pi$
$282$		0			0
$283$	−4.00000	−	6.92820i	−0.237775	−	0.411839i	0.722300	−	0.691580i	$-0.243085\pi$
$283$	−4.00000	−	6.92820i	−0.237775	−	0.411839i	−0.960076	+	0.279741i	$0.909752\pi$
$284$		0			0
$285$	3.50000	−	2.59808i	0.207322	−	0.153897i
$286$	−6.00000			−0.354787
$287$	1.00000	+	1.73205i	0.0590281	+	0.102240i
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$	−5.00000	−	8.66025i	−0.293610	−	0.508548i
$291$	1.00000	−	1.73205i	0.0586210	−	0.101535i
$292$	11.0000			0.643726
$293$	−26.0000			−1.51894			−0.759468	−	0.650545i	$-0.774541\pi$
$293$	−26.0000			−1.51894			−0.759468	+	0.650545i	$0.774541\pi$
$294$	3.00000	−	5.19615i	0.174964	−	0.303046i
$295$	−1.00000	+	1.73205i	−0.0582223	+	0.100844i
$296$	−5.00000			−0.290619
$297$	2.00000			0.116052
$298$	−9.00000	+	15.5885i	−0.521356	+	0.903015i
$299$	−9.00000	−	15.5885i	−0.520483	−	0.901504i
$300$	−0.500000	+	0.866025i	−0.0288675	+	0.0500000i
$301$	−2.50000	−	4.33013i	−0.144098	−	0.249584i
$302$		0			0
$303$	6.00000			0.344691
$304$	−0.500000	−	4.33013i	−0.0286770	−	0.248350i
$305$	−5.00000			−0.286299
$306$	−2.00000	−	3.46410i	−0.114332	−	0.198030i
$307$	−2.00000	−	3.46410i	−0.114146	−	0.197707i	0.803292	−	0.595585i	$-0.203080\pi$
$307$	−2.00000	−	3.46410i	−0.114146	−	0.197707i	−0.917438	+	0.397879i	$0.869747\pi$
$308$	1.00000	−	1.73205i	0.0569803	−	0.0986928i
$309$	−9.50000	−	16.4545i	−0.540436	−	0.936063i
$310$	0.500000	−	0.866025i	0.0283981	−	0.0491869i
$311$	−10.0000			−0.567048			−0.283524	−	0.958965i	$-0.591504\pi$
$311$	−10.0000			−0.567048			−0.283524	+	0.958965i	$0.591504\pi$
$312$	−3.00000			−0.169842
$313$	−9.00000	+	15.5885i	−0.508710	+	0.881112i	0.491239	+	0.871025i	$0.336544\pi$
$313$	−9.00000	+	15.5885i	−0.508710	+	0.881112i	−0.999949	+	0.0100869i	$0.996789\pi$
$314$	6.50000	−	11.2583i	0.366816	−	0.635344i
$315$	1.00000			0.0563436
$316$	−11.0000			−0.618798
$317$	−15.0000	+	25.9808i	−0.842484	+	1.45922i	0.0453045	+	0.998973i	$0.485574\pi$
$317$	−15.0000	+	25.9808i	−0.842484	+	1.45922i	−0.887788	+	0.460252i	$0.847759\pi$
$318$	6.00000	+	10.3923i	0.336463	+	0.582772i
$319$	10.0000	−	17.3205i	0.559893	−	0.969762i
$320$	0.500000	+	0.866025i	0.0279508	+	0.0484123i
$321$	2.00000	+	3.46410i	0.111629	+	0.193347i
$322$	6.00000			0.334367
$323$	−2.00000	−	17.3205i	−0.111283	−	0.963739i
$324$	1.00000			0.0555556
$325$	1.50000	+	2.59808i	0.0832050	+	0.144115i
$326$	8.50000	+	14.7224i	0.470771	+	0.815400i
$327$	9.00000	−	15.5885i	0.497701	−	0.862044i
$328$	−1.00000	−	1.73205i	−0.0552158	−	0.0956365i
$329$		0			0
$330$	−2.00000			−0.110096
$331$	5.00000			0.274825			0.137412	−	0.990514i	$-0.456121\pi$
$331$	5.00000			0.274825			0.137412	+	0.990514i	$0.456121\pi$
$332$	−1.00000	+	1.73205i	−0.0548821	+	0.0950586i
$333$	2.50000	−	4.33013i	0.136999	−	0.237289i
$334$	14.0000			0.766046
$335$	5.00000			0.273179
$336$	0.500000	−	0.866025i	0.0272772	−	0.0472456i
$337$	−11.5000	−	19.9186i	−0.626445	−	1.08503i	−0.988260	−	0.152784i	$-0.951176\pi$
$337$	−11.5000	−	19.9186i	−0.626445	−	1.08503i	0.361815	−	0.932250i	$-0.382157\pi$
$338$	2.00000	−	3.46410i	0.108786	−	0.188422i
$339$	−7.00000	−	12.1244i	−0.380188	−	0.658505i
$340$	2.00000	+	3.46410i	0.108465	+	0.187867i
$341$	2.00000			0.108306
$342$	4.00000	+	1.73205i	0.216295	+	0.0936586i
$343$	13.0000			0.701934
$344$	2.50000	+	4.33013i	0.134791	+	0.233465i
$345$	−3.00000	−	5.19615i	−0.161515	−	0.279751i
$346$	13.0000	−	22.5167i	0.698884	−	1.21050i
$347$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$347$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$348$	5.00000	−	8.66025i	0.268028	−	0.464238i
$349$	17.0000			0.909989			0.454995	−	0.890494i	$-0.349641\pi$
$349$	17.0000			0.909989			0.454995	+	0.890494i	$0.349641\pi$
$350$	−1.00000			−0.0534522
$351$	1.50000	−	2.59808i	0.0800641	−	0.138675i
$352$	−1.00000	+	1.73205i	−0.0533002	+	0.0923186i
$353$	−6.00000			−0.319348			−0.159674	−	0.987170i	$-0.551044\pi$
$353$	−6.00000			−0.319348			−0.159674	+	0.987170i	$0.551044\pi$
$354$	−2.00000			−0.106299
$355$		0			0
$356$		0			0
$357$	2.00000	−	3.46410i	0.105851	−	0.183340i
$358$	5.00000	+	8.66025i	0.264258	+	0.457709i
$359$	1.00000	+	1.73205i	0.0527780	+	0.0914141i	0.891207	−	0.453596i	$-0.149859\pi$
$359$	1.00000	+	1.73205i	0.0527780	+	0.0914141i	−0.838429	+	0.545010i	$0.816526\pi$
$360$	−1.00000			−0.0527046
$361$	13.0000	+	13.8564i	0.684211	+	0.729285i
$362$	−6.00000			−0.315353
$363$	3.50000	+	6.06218i	0.183702	+	0.318182i
$364$	−1.50000	−	2.59808i	−0.0786214	−	0.136176i
$365$	5.50000	−	9.52628i	0.287883	−	0.498628i
$366$	−2.50000	−	4.33013i	−0.130677	−	0.226339i
$367$	3.50000	−	6.06218i	0.182699	−	0.316443i	−0.760100	−	0.649806i	$-0.774850\pi$
$367$	3.50000	−	6.06218i	0.182699	−	0.316443i	0.942799	+	0.333363i	$0.108183\pi$
$368$	−6.00000			−0.312772
$369$	2.00000			0.104116
$370$	−2.50000	+	4.33013i	−0.129969	+	0.225113i
$371$	−6.00000	+	10.3923i	−0.311504	+	0.539542i
$372$	1.00000			0.0518476
$373$	−22.0000			−1.13912			−0.569558	−	0.821951i	$-0.692886\pi$
$373$	−22.0000			−1.13912			−0.569558	+	0.821951i	$0.692886\pi$
$374$	−4.00000	+	6.92820i	−0.206835	+	0.358249i
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$		0			0
$377$	−15.0000	−	25.9808i	−0.772539	−	1.33808i
$378$	0.500000	+	0.866025i	0.0257172	+	0.0445435i
$379$	−11.0000			−0.565032			−0.282516	−	0.959263i	$-0.591169\pi$
$379$	−11.0000			−0.565032			−0.282516	+	0.959263i	$0.591169\pi$
$380$	−4.00000	−	1.73205i	−0.205196	−	0.0888523i
$381$	16.0000			0.819705
$382$	−8.00000	−	13.8564i	−0.409316	−	0.708955i
$383$	18.0000	+	31.1769i	0.919757	+	1.59307i	0.799783	+	0.600289i	$0.204948\pi$
$383$	18.0000	+	31.1769i	0.919757	+	1.59307i	0.119974	+	0.992777i	$0.461719\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	−1.00000	−	1.73205i	−0.0509647	−	0.0882735i
$386$	−12.5000	+	21.6506i	−0.636233	+	1.10199i
$387$	−5.00000			−0.254164
$388$	−2.00000			−0.101535
$389$	5.00000	−	8.66025i	0.253510	−	0.439092i	−0.710980	−	0.703213i	$-0.751748\pi$
$389$	5.00000	−	8.66025i	0.253510	−	0.439092i	0.964490	+	0.264120i	$0.0850816\pi$
$390$	−1.50000	+	2.59808i	−0.0759555	+	0.131559i
$391$	−24.0000			−1.21373
$392$	−6.00000			−0.303046
$393$	3.00000	−	5.19615i	0.151330	−	0.262111i
$394$	9.00000	+	15.5885i	0.453413	+	0.785335i
$395$	−5.50000	+	9.52628i	−0.276735	+	0.479319i
$396$	−1.00000	−	1.73205i	−0.0502519	−	0.0870388i
$397$	0.500000	+	0.866025i	0.0250943	+	0.0434646i	0.878300	−	0.478110i	$-0.158678\pi$
$397$	0.500000	+	0.866025i	0.0250943	+	0.0434646i	−0.853206	+	0.521575i	$0.825345\pi$
$398$	5.00000			0.250627
$399$	0.500000	+	4.33013i	0.0250313	+	0.216777i
$400$	1.00000			0.0500000
$401$	19.0000	+	32.9090i	0.948815	+	1.64340i	0.747927	+	0.663781i	$0.231049\pi$
$401$	19.0000	+	32.9090i	0.948815	+	1.64340i	0.200888	+	0.979614i	$0.435617\pi$
$402$	2.50000	+	4.33013i	0.124689	+	0.215967i
$403$	1.50000	−	2.59808i	0.0747203	−	0.129419i
$404$	−3.00000	−	5.19615i	−0.149256	−	0.258518i
$405$	0.500000	−	0.866025i	0.0248452	−	0.0430331i
$406$	10.0000			0.496292
$407$	−10.0000			−0.495682
$408$	−2.00000	+	3.46410i	−0.0990148	+	0.171499i
$409$	15.0000	−	25.9808i	0.741702	−	1.28467i	−0.210017	−	0.977698i	$-0.567352\pi$
$409$	15.0000	−	25.9808i	0.741702	−	1.28467i	0.951720	−	0.306968i	$-0.0993146\pi$
$410$	−2.00000			−0.0987730
$411$	−2.00000			−0.0986527
$412$	−9.50000	+	16.4545i	−0.468031	+	0.810654i
$413$	−1.00000	−	1.73205i	−0.0492068	−	0.0852286i
$414$	3.00000	−	5.19615i	0.147442	−	0.255377i
$415$	1.00000	+	1.73205i	0.0490881	+	0.0850230i
$416$	1.50000	+	2.59808i	0.0735436	+	0.127381i
$417$	−9.00000			−0.440732
$418$	−1.00000	−	8.66025i	−0.0489116	−	0.423587i
$419$	−24.0000			−1.17248			−0.586238	−	0.810139i	$-0.699392\pi$
$419$	−24.0000			−1.17248			−0.586238	+	0.810139i	$0.699392\pi$
$420$	−0.500000	−	0.866025i	−0.0243975	−	0.0422577i
$421$	7.00000	+	12.1244i	0.341159	+	0.590905i	0.984648	−	0.174550i	$-0.0558472\pi$
$421$	7.00000	+	12.1244i	0.341159	+	0.590905i	−0.643489	+	0.765455i	$0.722514\pi$
$422$	2.50000	−	4.33013i	0.121698	−	0.210787i
$423$		0			0
$424$	6.00000	−	10.3923i	0.291386	−	0.504695i
$425$	4.00000			0.194029
$426$		0			0
$427$	2.50000	−	4.33013i	0.120983	−	0.209550i
$428$	2.00000	−	3.46410i	0.0966736	−	0.167444i
$429$	−6.00000			−0.289683
$430$	5.00000			0.241121
$431$	10.0000	−	17.3205i	0.481683	−	0.834300i	−0.518096	−	0.855323i	$-0.673359\pi$
$431$	10.0000	−	17.3205i	0.481683	−	0.834300i	0.999779	+	0.0210230i	$0.00669232\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	−14.5000	+	25.1147i	−0.696826	+	1.20694i	0.272736	+	0.962089i	$0.412071\pi$
$433$	−14.5000	+	25.1147i	−0.696826	+	1.20694i	−0.969561	+	0.244848i	$0.921262\pi$
$434$	0.500000	+	0.866025i	0.0240008	+	0.0415705i
$435$	−5.00000	−	8.66025i	−0.239732	−	0.415227i
$436$	−18.0000			−0.862044
$437$	21.0000	−	15.5885i	1.00457	−	0.745697i
$438$	11.0000			0.525600
$439$	20.5000	+	35.5070i	0.978412	+	1.69466i	0.668184	+	0.743996i	$0.267072\pi$
$439$	20.5000	+	35.5070i	0.978412	+	1.69466i	0.310228	+	0.950662i	$0.399595\pi$
$440$	1.00000	+	1.73205i	0.0476731	+	0.0825723i
$441$	3.00000	−	5.19615i	0.142857	−	0.247436i
$442$	6.00000	+	10.3923i	0.285391	+	0.494312i
$443$	−6.00000	+	10.3923i	−0.285069	+	0.493753i	−0.972626	−	0.232377i	$-0.925350\pi$
$443$	−6.00000	+	10.3923i	−0.285069	+	0.493753i	0.687557	+	0.726130i	$0.258683\pi$
$444$	−5.00000			−0.237289
$445$		0			0
$446$	0.500000	−	0.866025i	0.0236757	−	0.0410075i
$447$	−9.00000	+	15.5885i	−0.425685	+	0.737309i
$448$	−1.00000			−0.0472456
$449$	28.0000			1.32140			0.660701	−	0.750649i	$-0.270259\pi$
$449$	28.0000			1.32140			0.660701	+	0.750649i	$0.270259\pi$
$450$	−0.500000	+	0.866025i	−0.0235702	+	0.0408248i
$451$	−2.00000	−	3.46410i	−0.0941763	−	0.163118i
$452$	−7.00000	+	12.1244i	−0.329252	+	0.570282i
$453$		0			0
$454$	9.00000	+	15.5885i	0.422391	+	0.731603i
$455$	−3.00000			−0.140642
$456$	−0.500000	−	4.33013i	−0.0234146	−	0.202777i
$457$	23.0000			1.07589			0.537947	−	0.842978i	$-0.319200\pi$
$457$	23.0000			1.07589			0.537947	+	0.842978i	$0.319200\pi$
$458$	2.50000	+	4.33013i	0.116817	+	0.202334i
$459$	−2.00000	−	3.46410i	−0.0933520	−	0.161690i
$460$	−3.00000	+	5.19615i	−0.139876	+	0.242272i
$461$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$461$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$462$	1.00000	−	1.73205i	0.0465242	−	0.0805823i
$463$	1.00000			0.0464739			0.0232370	−	0.999730i	$-0.492603\pi$
$463$	1.00000			0.0464739			0.0232370	+	0.999730i	$0.492603\pi$
$464$	−10.0000			−0.464238
$465$	0.500000	−	0.866025i	0.0231869	−	0.0401610i
$466$	2.00000	−	3.46410i	0.0926482	−	0.160471i
$467$	30.0000			1.38823			0.694117	−	0.719862i	$-0.255795\pi$
$467$	30.0000			1.38823			0.694117	+	0.719862i	$0.255795\pi$
$468$	−3.00000			−0.138675
$469$	−2.50000	+	4.33013i	−0.115439	+	0.199947i
$470$		0			0
$471$	6.50000	−	11.2583i	0.299504	−	0.518756i
$472$	1.00000	+	1.73205i	0.0460287	+	0.0797241i
$473$	5.00000	+	8.66025i	0.229900	+	0.398199i
$474$	−11.0000			−0.505247
$475$	−3.50000	+	2.59808i	−0.160591	+	0.119208i
$476$	−4.00000			−0.183340
$477$	6.00000	+	10.3923i	0.274721	+	0.475831i
$478$	9.00000	+	15.5885i	0.411650	+	0.712999i
$479$	−21.0000	+	36.3731i	−0.959514	+	1.66193i	−0.235833	+	0.971794i	$0.575782\pi$
$479$	−21.0000	+	36.3731i	−0.959514	+	1.66193i	−0.723681	+	0.690134i	$0.757551\pi$
$480$	0.500000	+	0.866025i	0.0228218	+	0.0395285i
$481$	−7.50000	+	12.9904i	−0.341971	+	0.592310i
$482$	5.00000			0.227744
$483$	6.00000			0.273009
$484$	3.50000	−	6.06218i	0.159091	−	0.275554i
$485$	−1.00000	+	1.73205i	−0.0454077	+	0.0786484i
$486$	1.00000			0.0453609
$487$	16.0000			0.725029			0.362515	−	0.931978i	$-0.381918\pi$
$487$	16.0000			0.725029			0.362515	+	0.931978i	$0.381918\pi$
$488$	−2.50000	+	4.33013i	−0.113170	+	0.196016i
$489$	8.50000	+	14.7224i	0.384383	+	0.665771i
$490$	−3.00000	+	5.19615i	−0.135526	+	0.234738i
$491$	−14.0000	−	24.2487i	−0.631811	−	1.09433i	−0.987181	−	0.159603i	$-0.948978\pi$
$491$	−14.0000	−	24.2487i	−0.631811	−	1.09433i	0.355370	−	0.934726i	$-0.384355\pi$
$492$	−1.00000	−	1.73205i	−0.0450835	−	0.0780869i
$493$	−40.0000			−1.80151
$494$	−12.0000	−	5.19615i	−0.539906	−	0.233786i
$495$	−2.00000			−0.0898933
$496$	−0.500000	−	0.866025i	−0.0224507	−	0.0388857i
$497$		0			0
$498$	−1.00000	+	1.73205i	−0.0448111	+	0.0776151i
$499$	12.5000	+	21.6506i	0.559577	+	0.969216i	0.997532	+	0.0702185i	$0.0223697\pi$
$499$	12.5000	+	21.6506i	0.559577	+	0.969216i	−0.437955	+	0.898997i	$0.644297\pi$
$500$	0.500000	−	0.866025i	0.0223607	−	0.0387298i
$501$	14.0000			0.625474
$502$	−2.00000			−0.0892644
$503$	−22.0000	+	38.1051i	−0.980932	+	1.69902i	−0.322151	+	0.946688i	$0.604406\pi$
$503$	−22.0000	+	38.1051i	−0.980932	+	1.69902i	−0.658781	+	0.752335i	$0.728928\pi$
$504$	0.500000	−	0.866025i	0.0222718	−	0.0385758i
$505$	−6.00000			−0.266996
$506$	−12.0000			−0.533465
$507$	2.00000	−	3.46410i	0.0888231	−	0.153846i
$508$	−8.00000	−	13.8564i	−0.354943	−	0.614779i
$509$	4.00000	−	6.92820i	0.177297	−	0.307087i	−0.763657	−	0.645622i	$-0.776598\pi$
$509$	4.00000	−	6.92820i	0.177297	−	0.307087i	0.940954	+	0.338535i	$0.109931\pi$
$510$	2.00000	+	3.46410i	0.0885615	+	0.153393i
$511$	5.50000	+	9.52628i	0.243306	+	0.421418i
$512$	1.00000			0.0441942
$513$	4.00000	+	1.73205i	0.176604	+	0.0764719i
$514$	−6.00000			−0.264649
$515$	9.50000	+	16.4545i	0.418620	+	0.725071i
$516$	2.50000	+	4.33013i	0.110056	+	0.190623i
$517$		0			0
$518$	−2.50000	−	4.33013i	−0.109844	−	0.190255i
$519$	13.0000	−	22.5167i	0.570637	−	0.988372i
$520$	3.00000			0.131559
$521$	8.00000			0.350486			0.175243	−	0.984525i	$-0.443929\pi$
$521$	8.00000			0.350486			0.175243	+	0.984525i	$0.443929\pi$
$522$	5.00000	−	8.66025i	0.218844	−	0.379049i
$523$	5.50000	−	9.52628i	0.240498	−	0.416555i	−0.720358	−	0.693602i	$-0.756023\pi$
$523$	5.50000	−	9.52628i	0.240498	−	0.416555i	0.960856	+	0.277047i	$0.0893559\pi$
$524$	−6.00000			−0.262111
$525$	−1.00000			−0.0436436
$526$	5.00000	−	8.66025i	0.218010	−	0.377605i
$527$	−2.00000	−	3.46410i	−0.0871214	−	0.150899i
$528$	−1.00000	+	1.73205i	−0.0435194	+	0.0753778i
$529$	−6.50000	−	11.2583i	−0.282609	−	0.489493i
$530$	−6.00000	−	10.3923i	−0.260623	−	0.451413i
$531$	−2.00000			−0.0867926
$532$	3.50000	−	2.59808i	0.151744	−	0.112641i
$533$	−6.00000			−0.259889
$534$		0			0
$535$	−2.00000	−	3.46410i	−0.0864675	−	0.149766i
$536$	2.50000	−	4.33013i	0.107984	−	0.187033i
$537$	5.00000	+	8.66025i	0.215766	+	0.373718i
$538$	−5.00000	+	8.66025i	−0.215565	+	0.373370i
$539$	−12.0000			−0.516877
$540$	−1.00000			−0.0430331
$541$	4.50000	−	7.79423i	0.193470	−	0.335100i	−0.752928	−	0.658103i	$-0.771359\pi$
$541$	4.50000	−	7.79423i	0.193470	−	0.335100i	0.946398	+	0.323003i	$0.104692\pi$
$542$	4.00000	−	6.92820i	0.171815	−	0.297592i
$543$	−6.00000			−0.257485
$544$	4.00000			0.171499
$545$	−9.00000	+	15.5885i	−0.385518	+	0.667736i
$546$	−1.50000	−	2.59808i	−0.0641941	−	0.111187i
$547$	4.50000	−	7.79423i	0.192406	−	0.333257i	−0.753641	−	0.657286i	$-0.771704\pi$
$547$	4.50000	−	7.79423i	0.192406	−	0.333257i	0.946047	+	0.324029i	$0.105038\pi$
$548$	1.00000	+	1.73205i	0.0427179	+	0.0739895i
$549$	−2.50000	−	4.33013i	−0.106697	−	0.184805i
$550$	2.00000			0.0852803
$551$	35.0000	−	25.9808i	1.49105	−	1.10682i
$552$	−6.00000			−0.255377
$553$	−5.50000	−	9.52628i	−0.233884	−	0.405099i
$554$	5.00000	+	8.66025i	0.212430	+	0.367939i
$555$	−2.50000	+	4.33013i	−0.106119	+	0.183804i
$556$	4.50000	+	7.79423i	0.190843	+	0.330549i
$557$	6.00000	−	10.3923i	0.254228	−	0.440336i	−0.710457	−	0.703740i	$-0.751512\pi$
$557$	6.00000	−	10.3923i	0.254228	−	0.440336i	0.964686	+	0.263404i	$0.0848453\pi$
$558$	1.00000			0.0423334
$559$	15.0000			0.634432
$560$	−0.500000	+	0.866025i	−0.0211289	+	0.0365963i
$561$	−4.00000	+	6.92820i	−0.168880	+	0.292509i
$562$	−30.0000			−1.26547
$563$	22.0000			0.927189			0.463595	−	0.886047i	$-0.346559\pi$
$563$	22.0000			0.927189			0.463595	+	0.886047i	$0.346559\pi$
$564$		0			0
$565$	7.00000	+	12.1244i	0.294492	+	0.510075i
$566$	−4.00000	+	6.92820i	−0.168133	+	0.291214i
$567$	0.500000	+	0.866025i	0.0209980	+	0.0363696i
$568$		0			0
$569$		0			0			−	1.00000i	$-0.5\pi$
$569$		0			0				1.00000i	$0.5\pi$
$570$	−4.00000	−	1.73205i	−0.167542	−	0.0725476i
$571$	39.0000			1.63210			0.816050	−	0.577982i	$-0.196160\pi$
$571$	39.0000			1.63210			0.816050	+	0.577982i	$0.196160\pi$
$572$	3.00000	+	5.19615i	0.125436	+	0.217262i
$573$	−8.00000	−	13.8564i	−0.334205	−	0.578860i
$574$	1.00000	−	1.73205i	0.0417392	−	0.0722944i
$575$	3.00000	+	5.19615i	0.125109	+	0.216695i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−18.0000			−0.749350			−0.374675	−	0.927156i	$-0.622246\pi$
$577$	−18.0000			−0.749350			−0.374675	+	0.927156i	$0.622246\pi$
$578$	−1.00000			−0.0415945
$579$	−12.5000	+	21.6506i	−0.519482	+	0.899770i
$580$	−5.00000	+	8.66025i	−0.207614	+	0.359597i
$581$	−2.00000			−0.0829740
$582$	−2.00000			−0.0829027
$583$	12.0000	−	20.7846i	0.496989	−	0.860811i
$584$	−5.50000	−	9.52628i	−0.227592	−	0.394200i
$585$	−1.50000	+	2.59808i	−0.0620174	+	0.107417i
$586$	13.0000	+	22.5167i	0.537025	+	0.930155i
$587$	−9.00000	−	15.5885i	−0.371470	−	0.643404i	0.618322	−	0.785925i	$-0.287813\pi$
$587$	−9.00000	−	15.5885i	−0.371470	−	0.643404i	−0.989792	+	0.142520i	$0.954479\pi$
$588$	−6.00000			−0.247436
$589$	4.00000	+	1.73205i	0.164817	+	0.0713679i
$590$	2.00000			0.0823387
$591$	9.00000	+	15.5885i	0.370211	+	0.641223i
$592$	2.50000	+	4.33013i	0.102749	+	0.177967i
$593$	−14.0000	+	24.2487i	−0.574911	+	0.995775i	0.421140	+	0.906996i	$0.361630\pi$
$593$	−14.0000	+	24.2487i	−0.574911	+	0.995775i	−0.996051	+	0.0887797i	$0.971703\pi$
$594$	−1.00000	−	1.73205i	−0.0410305	−	0.0710669i
$595$	−2.00000	+	3.46410i	−0.0819920	+	0.142014i
$596$	18.0000			0.737309
$597$	5.00000			0.204636
$598$	−9.00000	+	15.5885i	−0.368037	+	0.637459i
$599$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$599$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$600$	1.00000			0.0408248
$601$	7.00000			0.285536			0.142768	−	0.989756i	$-0.454400\pi$
$601$	7.00000			0.285536			0.142768	+	0.989756i	$0.454400\pi$
$602$	−2.50000	+	4.33013i	−0.101892	+	0.176483i
$603$	2.50000	+	4.33013i	0.101808	+	0.176336i
$604$		0			0
$605$	−3.50000	−	6.06218i	−0.142295	−	0.246463i
$606$	−3.00000	−	5.19615i	−0.121867	−	0.211079i
$607$	−9.00000			−0.365299			−0.182649	−	0.983178i	$-0.558467\pi$
$607$	−9.00000			−0.365299			−0.182649	+	0.983178i	$0.558467\pi$
$608$	−3.50000	+	2.59808i	−0.141944	+	0.105366i
$609$	10.0000			0.405220
$610$	2.50000	+	4.33013i	0.101222	+	0.175322i
$611$		0			0
$612$	−2.00000	+	3.46410i	−0.0808452	+	0.140028i
$613$	11.0000	+	19.0526i	0.444286	+	0.769526i	0.998002	−	0.0631797i	$-0.0201241\pi$
$613$	11.0000	+	19.0526i	0.444286	+	0.769526i	−0.553716	+	0.832705i	$0.686791\pi$
$614$	−2.00000	+	3.46410i	−0.0807134	+	0.139800i
$615$	−2.00000			−0.0806478
$616$	−2.00000			−0.0805823
$617$	−12.0000	+	20.7846i	−0.483102	+	0.836757i	−0.999812	−	0.0194037i	$-0.993823\pi$
$617$	−12.0000	+	20.7846i	−0.483102	+	0.836757i	0.516710	+	0.856161i	$0.327157\pi$
$618$	−9.50000	+	16.4545i	−0.382146	+	0.661896i
$619$	−29.0000			−1.16561			−0.582804	−	0.812613i	$-0.698045\pi$
$619$	−29.0000			−1.16561			−0.582804	+	0.812613i	$0.698045\pi$
$620$	−1.00000			−0.0401610
$621$	3.00000	−	5.19615i	0.120386	−	0.208514i
$622$	5.00000	+	8.66025i	0.200482	+	0.347245i
$623$		0			0
$624$	1.50000	+	2.59808i	0.0600481	+	0.104006i
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	18.0000			0.719425
$627$	−1.00000	−	8.66025i	−0.0399362	−	0.345857i
$628$	−13.0000			−0.518756
$629$	10.0000	+	17.3205i	0.398726	+	0.690614i
$630$	−0.500000	−	0.866025i	−0.0199205	−	0.0345033i
$631$	21.5000	−	37.2391i	0.855901	−	1.48246i	−0.0199047	−	0.999802i	$-0.506336\pi$
$631$	21.5000	−	37.2391i	0.855901	−	1.48246i	0.875806	−	0.482663i	$-0.160330\pi$
$632$	5.50000	+	9.52628i	0.218778	+	0.378935i
$633$	2.50000	−	4.33013i	0.0993661	−	0.172107i
$634$	30.0000			1.19145
$635$	−16.0000			−0.634941
$636$	6.00000	−	10.3923i	0.237915	−	0.412082i
$637$	−9.00000	+	15.5885i	−0.356593	+	0.617637i
$638$	−20.0000			−0.791808
$639$		0			0
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	−12.0000	−	20.7846i	−0.473972	−	0.820943i	0.525584	−	0.850741i	$-0.323847\pi$
$641$	−12.0000	−	20.7846i	−0.473972	−	0.820943i	−0.999556	+	0.0297987i	$0.990513\pi$
$642$	2.00000	−	3.46410i	0.0789337	−	0.136717i
$643$	−20.5000	−	35.5070i	−0.808441	−	1.40026i	−0.913943	−	0.405842i	$-0.866978\pi$
$643$	−20.5000	−	35.5070i	−0.808441	−	1.40026i	0.105502	−	0.994419i	$-0.466355\pi$
$644$	−3.00000	−	5.19615i	−0.118217	−	0.204757i
$645$	5.00000			0.196875
$646$	−14.0000	+	10.3923i	−0.550823	+	0.408880i
$647$	46.0000			1.80845			0.904223	−	0.427060i	$-0.140451\pi$
$647$	46.0000			1.80845			0.904223	+	0.427060i	$0.140451\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	2.00000	+	3.46410i	0.0785069	+	0.135978i
$650$	1.50000	−	2.59808i	0.0588348	−	0.101905i
$651$	0.500000	+	0.866025i	0.0195965	+	0.0339422i
$652$	8.50000	−	14.7224i	0.332886	−	0.576575i
$653$		0			0			−	1.00000i	$-0.5\pi$
$653$		0			0				1.00000i	$0.5\pi$
$654$	−18.0000			−0.703856
$655$	−3.00000	+	5.19615i	−0.117220	+	0.203030i
$656$	−1.00000	+	1.73205i	−0.0390434	+	0.0676252i
$657$	11.0000			0.429151
$658$		0			0
$659$	−9.00000	+	15.5885i	−0.350590	+	0.607240i	−0.986353	−	0.164644i	$-0.947352\pi$
$659$	−9.00000	+	15.5885i	−0.350590	+	0.607240i	0.635763	+	0.771885i	$0.280686\pi$
$660$	1.00000	+	1.73205i	0.0389249	+	0.0674200i
$661$	−23.0000	+	39.8372i	−0.894596	+	1.54949i	−0.0602929	+	0.998181i	$0.519203\pi$
$661$	−23.0000	+	39.8372i	−0.894596	+	1.54949i	−0.834303	+	0.551306i	$0.814130\pi$
$662$	−2.50000	−	4.33013i	−0.0971653	−	0.168295i
$663$	6.00000	+	10.3923i	0.233021	+	0.403604i
$664$	2.00000			0.0776151
$665$	−0.500000	−	4.33013i	−0.0193892	−	0.167915i
$666$	−5.00000			−0.193746
$667$	−30.0000	−	51.9615i	−1.16160	−	2.01196i
$668$	−7.00000	−	12.1244i	−0.270838	−	0.469105i
$669$	0.500000	−	0.866025i	0.0193311	−	0.0334825i
$670$	−2.50000	−	4.33013i	−0.0965834	−	0.167287i
$671$	−5.00000	+	8.66025i	−0.193023	+	0.334325i
$672$	−1.00000			−0.0385758
$673$	−23.0000			−0.886585			−0.443292	−	0.896377i	$-0.646190\pi$
$673$	−23.0000			−0.886585			−0.443292	+	0.896377i	$0.646190\pi$
$674$	−11.5000	+	19.9186i	−0.442963	+	0.767235i
$675$	−0.500000	+	0.866025i	−0.0192450	+	0.0333333i
$676$	−4.00000			−0.153846
$677$	48.0000			1.84479			0.922395	−	0.386248i	$-0.126229\pi$
$677$	48.0000			1.84479			0.922395	+	0.386248i	$0.126229\pi$
$678$	−7.00000	+	12.1244i	−0.268833	+	0.465633i
$679$	−1.00000	−	1.73205i	−0.0383765	−	0.0664700i
$680$	2.00000	−	3.46410i	0.0766965	−	0.132842i
$681$	9.00000	+	15.5885i	0.344881	+	0.597351i
$682$	−1.00000	−	1.73205i	−0.0382920	−	0.0663237i
$683$		0			0			−	1.00000i	$-0.5\pi$
$683$		0			0				1.00000i	$0.5\pi$
$684$	−0.500000	−	4.33013i	−0.0191180	−	0.165567i
$685$	2.00000			0.0764161
$686$	−6.50000	−	11.2583i	−0.248171	−	0.429845i
$687$	2.50000	+	4.33013i	0.0953809	+	0.165205i
$688$	2.50000	−	4.33013i	0.0953116	−	0.165085i
$689$	−18.0000	−	31.1769i	−0.685745	−	1.18775i
$690$	−3.00000	+	5.19615i	−0.114208	+	0.197814i
$691$	4.00000			0.152167			0.0760836	−	0.997101i	$-0.475758\pi$
$691$	4.00000			0.152167			0.0760836	+	0.997101i	$0.475758\pi$
$692$	−26.0000			−0.988372
$693$	1.00000	−	1.73205i	0.0379869	−	0.0657952i
$694$		0			0
$695$	9.00000			0.341389
$696$	−10.0000			−0.379049
$697$	−4.00000	+	6.92820i	−0.151511	+	0.262424i
$698$	−8.50000	−	14.7224i	−0.321730	−	0.557252i
$699$	2.00000	−	3.46410i	0.0756469	−	0.131024i
$700$	0.500000	+	0.866025i	0.0188982	+	0.0327327i
$701$	−14.0000	−	24.2487i	−0.528773	−	0.915861i	−0.999437	−	0.0335489i	$-0.989319\pi$
$701$	−14.0000	−	24.2487i	−0.528773	−	0.915861i	0.470664	−	0.882312i	$-0.344014\pi$
$702$	−3.00000			−0.113228
$703$	−20.0000	−	8.66025i	−0.754314	−	0.326628i
$704$	2.00000			0.0753778
$705$		0			0
$706$	3.00000	+	5.19615i	0.112906	+	0.195560i
$707$	3.00000	−	5.19615i	0.112827	−	0.195421i
$708$	1.00000	+	1.73205i	0.0375823	+	0.0650945i
$709$	−9.50000	+	16.4545i	−0.356780	+	0.617961i	−0.987421	−	0.158114i	$-0.949459\pi$
$709$	−9.50000	+	16.4545i	−0.356780	+	0.617961i	0.630641	+	0.776075i	$0.282792\pi$
$710$		0			0
$711$	−11.0000			−0.412532
$712$		0			0
$713$	3.00000	−	5.19615i	0.112351	−	0.194597i
$714$	−4.00000			−0.149696
$715$	6.00000			0.224387
$716$	5.00000	−	8.66025i	0.186859	−	0.323649i
$717$	9.00000	+	15.5885i	0.336111	+	0.582162i
$718$	1.00000	−	1.73205i	0.0373197	−	0.0646396i
$719$	−13.0000	−	22.5167i	−0.484818	−	0.839730i	0.515030	−	0.857172i	$-0.327781\pi$
$719$	−13.0000	−	22.5167i	−0.484818	−	0.839730i	−0.999848	+	0.0174426i	$0.994448\pi$
$720$	0.500000	+	0.866025i	0.0186339	+	0.0322749i
$721$	−19.0000			−0.707597
$722$	5.50000	−	18.1865i	0.204689	−	0.676833i
$723$	5.00000			0.185952
$724$	3.00000	+	5.19615i	0.111494	+	0.193113i
$725$	5.00000	+	8.66025i	0.185695	+	0.321634i
$726$	3.50000	−	6.06218i	0.129897	−	0.224989i
$727$	22.5000	+	38.9711i	0.834479	+	1.44536i	0.894454	+	0.447160i	$0.147564\pi$
$727$	22.5000	+	38.9711i	0.834479	+	1.44536i	−0.0599753	+	0.998200i	$0.519102\pi$
$728$	−1.50000	+	2.59808i	−0.0555937	+	0.0962911i
$729$	1.00000			0.0370370
$730$	−11.0000			−0.407128
$731$	10.0000	−	17.3205i	0.369863	−	0.640622i
$732$	−2.50000	+	4.33013i	−0.0924027	+	0.160046i
$733$	−34.0000			−1.25582			−0.627909	−	0.778287i	$-0.716089\pi$
$733$	−34.0000			−1.25582			−0.627909	+	0.778287i	$0.716089\pi$
$734$	−7.00000			−0.258375
$735$	−3.00000	+	5.19615i	−0.110657	+	0.191663i
$736$	3.00000	+	5.19615i	0.110581	+	0.191533i
$737$	5.00000	−	8.66025i	0.184177	−	0.319005i
$738$	−1.00000	−	1.73205i	−0.0368105	−	0.0637577i
$739$	−0.500000	−	0.866025i	−0.0183928	−	0.0318573i	0.856683	−	0.515844i	$-0.172522\pi$
$739$	−0.500000	−	0.866025i	−0.0183928	−	0.0318573i	−0.875075	+	0.483987i	$0.839188\pi$
$740$	5.00000			0.183804
$741$	−12.0000	−	5.19615i	−0.440831	−	0.190885i
$742$	12.0000			0.440534
$743$	−3.00000	−	5.19615i	−0.110059	−	0.190628i	0.805735	−	0.592277i	$-0.201771\pi$
$743$	−3.00000	−	5.19615i	−0.110059	−	0.190628i	−0.915794	+	0.401648i	$0.868437\pi$
$744$	−0.500000	−	0.866025i	−0.0183309	−	0.0317500i
$745$	9.00000	−	15.5885i	0.329734	−	0.571117i
$746$	11.0000	+	19.0526i	0.402739	+	0.697564i
$747$	−1.00000	+	1.73205i	−0.0365881	+	0.0633724i
$748$	8.00000			0.292509
$749$	4.00000			0.146157
$750$	0.500000	−	0.866025i	0.0182574	−	0.0316228i
$751$	23.5000	−	40.7032i	0.857527	−	1.48528i	−0.0167534	−	0.999860i	$-0.505333\pi$
$751$	23.5000	−	40.7032i	0.857527	−	1.48528i	0.874281	−	0.485421i	$-0.161334\pi$
$752$		0			0
$753$	−2.00000			−0.0728841
$754$	−15.0000	+	25.9808i	−0.546268	+	0.946164i
$755$		0			0
$756$	0.500000	−	0.866025i	0.0181848	−	0.0314970i
$757$	3.50000	+	6.06218i	0.127210	+	0.220334i	0.922595	−	0.385771i	$-0.126065\pi$
$757$	3.50000	+	6.06218i	0.127210	+	0.220334i	−0.795385	+	0.606105i	$0.792731\pi$
$758$	5.50000	+	9.52628i	0.199769	+	0.346010i
$759$	−12.0000			−0.435572
$760$	0.500000	+	4.33013i	0.0181369	+	0.157070i
$761$	10.0000			0.362500			0.181250	−	0.983437i	$-0.441986\pi$
$761$	10.0000			0.362500			0.181250	+	0.983437i	$0.441986\pi$
$762$	−8.00000	−	13.8564i	−0.289809	−	0.501965i
$763$	−9.00000	−	15.5885i	−0.325822	−	0.564340i
$764$	−8.00000	+	13.8564i	−0.289430	+	0.501307i
$765$	2.00000	+	3.46410i	0.0723102	+	0.125245i
$766$	18.0000	−	31.1769i	0.650366	−	1.12647i
$767$	6.00000			0.216647
$768$	1.00000			0.0360844
$769$	16.5000	−	28.5788i	0.595005	−	1.03058i	−0.398541	−	0.917151i	$-0.630483\pi$
$769$	16.5000	−	28.5788i	0.595005	−	1.03058i	0.993546	−	0.113429i	$-0.0361834\pi$
$770$	−1.00000	+	1.73205i	−0.0360375	+	0.0624188i
$771$	−6.00000			−0.216085
$772$	25.0000			0.899770
$773$	3.00000	−	5.19615i	0.107903	−	0.186893i	−0.807018	−	0.590527i	$-0.798920\pi$
$773$	3.00000	−	5.19615i	0.107903	−	0.186893i	0.914920	+	0.403634i	$0.132253\pi$
$774$	2.50000	+	4.33013i	0.0898606	+	0.155643i
$775$	−0.500000	+	0.866025i	−0.0179605	+	0.0311086i
$776$	1.00000	+	1.73205i	0.0358979	+	0.0621770i
$777$	−2.50000	−	4.33013i	−0.0896870	−	0.155342i
$778$	−10.0000			−0.358517
$779$	−1.00000	−	8.66025i	−0.0358287	−	0.310286i
$780$	3.00000			0.107417
$781$		0			0
$782$	12.0000	+	20.7846i	0.429119	+	0.743256i
$783$	5.00000	−	8.66025i	0.178685	−	0.309492i
$784$	3.00000	+	5.19615i	0.107143	+	0.185577i
$785$	−6.50000	+	11.2583i	−0.231995	+	0.401827i
$786$	−6.00000			−0.214013
$787$	−23.0000			−0.819861			−0.409931	−	0.912117i	$-0.634447\pi$
$787$	−23.0000			−0.819861			−0.409931	+	0.912117i	$0.634447\pi$
$788$	9.00000	−	15.5885i	0.320612	−	0.555316i
$789$	5.00000	−	8.66025i	0.178005	−	0.308313i
$790$	11.0000			0.391362
$791$	−14.0000			−0.497783
$792$	−1.00000	+	1.73205i	−0.0355335	+	0.0615457i
$793$	7.50000	+	12.9904i	0.266333	+	0.461302i
$794$	0.500000	−	0.866025i	0.0177443	−	0.0307341i
$795$	−6.00000	−	10.3923i	−0.212798	−	0.368577i
$796$	−2.50000	−	4.33013i	−0.0886102	−	0.153477i
$797$	2.00000			0.0708436			0.0354218	−	0.999372i	$-0.488723\pi$
$797$	2.00000			0.0708436			0.0354218	+	0.999372i	$0.488723\pi$
$798$	3.50000	−	2.59808i	0.123899	−	0.0919709i
$799$		0			0
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$		0			0
$802$	19.0000	−	32.9090i	0.670913	−	1.16206i
$803$	−11.0000	−	19.0526i	−0.388182	−	0.672350i
$804$	2.50000	−	4.33013i	0.0881682	−	0.152712i
$805$	−6.00000			−0.211472
$806$	−3.00000			−0.105670
$807$	−5.00000	+	8.66025i	−0.176008	+	0.304855i
$808$	−3.00000	+	5.19615i	−0.105540	+	0.182800i
$809$	50.0000			1.75791			0.878953	−	0.476908i	$-0.158243\pi$
$809$	50.0000			1.75791			0.878953	+	0.476908i	$0.158243\pi$
$810$	−1.00000			−0.0351364
$811$	14.0000	−	24.2487i	0.491606	−	0.851487i	−0.508347	−	0.861152i	$-0.669743\pi$
$811$	14.0000	−	24.2487i	0.491606	−	0.851487i	0.999953	+	0.00966502i	$0.00307652\pi$
$812$	−5.00000	−	8.66025i	−0.175466	−	0.303915i
$813$	4.00000	−	6.92820i	0.140286	−	0.242983i
$814$	5.00000	+	8.66025i	0.175250	+	0.303542i
$815$	−8.50000	−	14.7224i	−0.297742	−	0.515704i
$816$	4.00000			0.140028
$817$	2.50000	+	21.6506i	0.0874639	+	0.757460i
$818$	−30.0000			−1.04893
$819$	−1.50000	−	2.59808i	−0.0524142	−	0.0907841i
$820$	1.00000	+	1.73205i	0.0349215	+	0.0604858i
$821$	5.00000	−	8.66025i	0.174501	−	0.302245i	−0.765487	−	0.643451i	$-0.777502\pi$
$821$	5.00000	−	8.66025i	0.174501	−	0.302245i	0.939989	+	0.341206i	$0.110835\pi$
$822$	1.00000	+	1.73205i	0.0348790	+	0.0604122i
$823$	22.0000	−	38.1051i	0.766872	−	1.32826i	−0.172379	−	0.985031i	$-0.555146\pi$
$823$	22.0000	−	38.1051i	0.766872	−	1.32826i	0.939251	−	0.343230i	$-0.111521\pi$
$824$	19.0000			0.661896
$825$	2.00000			0.0696311
$826$	−1.00000	+	1.73205i	−0.0347945	+	0.0602658i
$827$	11.0000	−	19.0526i	0.382507	−	0.662522i	−0.608913	−	0.793237i	$-0.708394\pi$
$827$	11.0000	−	19.0526i	0.382507	−	0.662522i	0.991420	+	0.130715i	$0.0417273\pi$
$828$	−6.00000			−0.208514
$829$	23.0000			0.798823			0.399412	−	0.916772i	$-0.369214\pi$
$829$	23.0000			0.798823			0.399412	+	0.916772i	$0.369214\pi$
$830$	1.00000	−	1.73205i	0.0347105	−	0.0601204i
$831$	5.00000	+	8.66025i	0.173448	+	0.300421i
$832$	1.50000	−	2.59808i	0.0520031	−	0.0900721i
$833$	12.0000	+	20.7846i	0.415775	+	0.720144i
$834$	4.50000	+	7.79423i	0.155822	+	0.269892i
$835$	−14.0000			−0.484490
$836$	−7.00000	+	5.19615i	−0.242100	+	0.179713i
$837$	1.00000			0.0345651
$838$	12.0000	+	20.7846i	0.414533	+	0.717992i
$839$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$839$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$840$	−0.500000	+	0.866025i	−0.0172516	+	0.0298807i
$841$	−35.5000	−	61.4878i	−1.22414	−	2.12027i
$842$	7.00000	−	12.1244i	0.241236	−	0.417833i
$843$	−30.0000			−1.03325
$844$	−5.00000			−0.172107
$845$	−2.00000	+	3.46410i	−0.0688021	+	0.119169i
$846$		0			0
$847$	7.00000			0.240523
$848$	−12.0000			−0.412082
$849$	−4.00000	+	6.92820i	−0.137280	+	0.237775i
$850$	−2.00000	−	3.46410i	−0.0685994	−	0.118818i
$851$	−15.0000	+	25.9808i	−0.514193	+	0.890609i
$852$		0			0
$853$	8.50000	+	14.7224i	0.291034	+	0.504086i	0.974055	−	0.226313i	$-0.0726672\pi$
$853$	8.50000	+	14.7224i	0.291034	+	0.504086i	−0.683020	+	0.730400i	$0.739334\pi$
$854$	−5.00000			−0.171096
$855$	−4.00000	−	1.73205i	−0.136797	−	0.0592349i
$856$	−4.00000			−0.136717
$857$	−12.0000	−	20.7846i	−0.409912	−	0.709989i	0.584967	−	0.811057i	$-0.301107\pi$
$857$	−12.0000	−	20.7846i	−0.409912	−	0.709989i	−0.994880	+	0.101068i	$0.967774\pi$
$858$	3.00000	+	5.19615i	0.102418	+	0.177394i
$859$	−18.5000	+	32.0429i	−0.631212	+	1.09329i	0.356092	+	0.934451i	$0.384109\pi$
$859$	−18.5000	+	32.0429i	−0.631212	+	1.09329i	−0.987304	+	0.158840i	$0.949225\pi$
$860$	−2.50000	−	4.33013i	−0.0852493	−	0.147656i
$861$	1.00000	−	1.73205i	0.0340799	−	0.0590281i
$862$	−20.0000			−0.681203
$863$	46.0000			1.56586			0.782929	−	0.622111i	$-0.213725\pi$
$863$	46.0000			1.56586			0.782929	+	0.622111i	$0.213725\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	−13.0000	+	22.5167i	−0.442013	+	0.765589i
$866$	29.0000			0.985460
$867$	−1.00000			−0.0339618
$868$	0.500000	−	0.866025i	0.0169711	−	0.0293948i
$869$	11.0000	+	19.0526i	0.373149	+	0.646314i
$870$	−5.00000	+	8.66025i	−0.169516	+	0.293610i
$871$	−7.50000	−	12.9904i	−0.254128	−	0.440162i
$872$	9.00000	+	15.5885i	0.304778	+	0.527892i
$873$	−2.00000			−0.0676897
$874$	−24.0000	−	10.3923i	−0.811812	−	0.351525i
$875$	1.00000			0.0338062
$876$	−5.50000	−	9.52628i	−0.185828	−	0.321863i
$877$	−7.50000	−	12.9904i	−0.253257	−	0.438654i	0.711164	−	0.703027i	$-0.248168\pi$
$877$	−7.50000	−	12.9904i	−0.253257	−	0.438654i	−0.964421	+	0.264373i	$0.914835\pi$
$878$	20.5000	−	35.5070i	0.691841	−	1.19830i
$879$	13.0000	+	22.5167i	0.438479	+	0.759468i
$880$	1.00000	−	1.73205i	0.0337100	−	0.0583874i
$881$	34.0000			1.14549			0.572745	−	0.819734i	$-0.305879\pi$
$881$	34.0000			1.14549			0.572745	+	0.819734i	$0.305879\pi$
$882$	−6.00000			−0.202031
$883$	−15.5000	+	26.8468i	−0.521617	+	0.903466i	0.478067	+	0.878323i	$0.341337\pi$
$883$	−15.5000	+	26.8468i	−0.521617	+	0.903466i	−0.999684	+	0.0251431i	$0.991996\pi$
$884$	6.00000	−	10.3923i	0.201802	−	0.349531i
$885$	2.00000			0.0672293
$886$	12.0000			0.403148
$887$	12.0000	−	20.7846i	0.402921	−	0.697879i	−0.591156	−	0.806557i	$-0.701328\pi$
$887$	12.0000	−	20.7846i	0.402921	−	0.697879i	0.994077	+	0.108678i	$0.0346618\pi$
$888$	2.50000	+	4.33013i	0.0838945	+	0.145310i
$889$	8.00000	−	13.8564i	0.268311	−	0.464729i
$890$		0			0
$891$	−1.00000	−	1.73205i	−0.0335013	−	0.0580259i
$892$	−1.00000			−0.0334825
$893$		0			0
$894$	18.0000			0.602010
$895$	−5.00000	−	8.66025i	−0.167132	−	0.289480i
$896$	0.500000	+	0.866025i	0.0167038	+	0.0289319i
$897$	−9.00000	+	15.5885i	−0.300501	+	0.520483i
$898$	−14.0000	−	24.2487i	−0.467186	−	0.809190i
$899$	5.00000	−	8.66025i	0.166759	−	0.288836i
$900$	1.00000			0.0333333
$901$	−48.0000			−1.59911
$902$	−2.00000	+	3.46410i	−0.0665927	+	0.115342i
$903$	−2.50000	+	4.33013i	−0.0831948	+	0.144098i
$904$	14.0000			0.465633
$905$	6.00000			0.199447
$906$		0			0
$907$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$907$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$908$	9.00000	−	15.5885i	0.298675	−	0.517321i
$909$	−3.00000	−	5.19615i	−0.0995037	−	0.172345i
$910$	1.50000	+	2.59808i	0.0497245	+	0.0861254i
$911$	30.0000			0.993944			0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000			0.993944			0.496972	+	0.867766i	$0.334445\pi$
$912$	−3.50000	+	2.59808i	−0.115897	+	0.0860309i
$913$	4.00000			0.132381
$914$	−11.5000	−	19.9186i	−0.380386	−	0.658848i
$915$	2.50000	+	4.33013i	0.0826475	+	0.143150i
$916$	2.50000	−	4.33013i	0.0826023	−	0.143071i
$917$	−3.00000	−	5.19615i	−0.0990687	−	0.171592i
$918$	−2.00000	+	3.46410i	−0.0660098	+	0.114332i
$919$	43.0000			1.41844			0.709220	−	0.704988i	$-0.249047\pi$
$919$	43.0000			1.41844			0.709220	+	0.704988i	$0.249047\pi$
$920$	6.00000			0.197814
$921$	−2.00000	+	3.46410i	−0.0659022	+	0.114146i
$922$		0			0
$923$		0			0
$924$	−2.00000			−0.0657952
$925$	2.50000	−	4.33013i	0.0821995	−	0.142374i
$926$	−0.500000	−	0.866025i	−0.0164310	−	0.0284594i
$927$	−9.50000	+	16.4545i	−0.312021	+	0.540436i
$928$	5.00000	+	8.66025i	0.164133	+	0.284287i
$929$	24.0000	+	41.5692i	0.787414	+	1.36384i	0.927546	+	0.373709i	$0.121914\pi$
$929$	24.0000	+	41.5692i	0.787414	+	1.36384i	−0.140132	+	0.990133i	$0.544753\pi$
$930$	−1.00000			−0.0327913
$931$	−24.0000	−	10.3923i	−0.786568	−	0.340594i
$932$	−4.00000			−0.131024
$933$	5.00000	+	8.66025i	0.163693	+	0.283524i
$934$	−15.0000	−	25.9808i	−0.490815	−	0.850117i
$935$	4.00000	−	6.92820i	0.130814	−	0.226576i
$936$	1.50000	+	2.59808i	0.0490290	+	0.0849208i
$937$	−10.5000	+	18.1865i	−0.343020	+	0.594128i	−0.984992	−	0.172600i	$-0.944783\pi$
$937$	−10.5000	+	18.1865i	−0.343020	+	0.594128i	0.641972	+	0.766728i	$0.278117\pi$
$938$	5.00000			0.163256
$939$	18.0000			0.587408
$940$		0			0
$941$	17.0000	−	29.4449i	0.554184	−	0.959875i	−0.443782	−	0.896135i	$-0.646364\pi$
$941$	17.0000	−	29.4449i	0.554184	−	0.959875i	0.997967	−	0.0637405i	$-0.0203030\pi$
$942$	−13.0000			−0.423563
$943$	−12.0000			−0.390774
$944$	1.00000	−	1.73205i	0.0325472	−	0.0563735i
$945$	−0.500000	−	0.866025i	−0.0162650	−	0.0281718i
$946$	5.00000	−	8.66025i	0.162564	−	0.281569i
$947$	11.0000	+	19.0526i	0.357452	+	0.619125i	0.987534	−	0.157403i	$-0.0503122\pi$
$947$	11.0000	+	19.0526i	0.357452	+	0.619125i	−0.630082	+	0.776528i	$0.716979\pi$
$948$	5.50000	+	9.52628i	0.178632	+	0.309399i
$949$	−33.0000			−1.07123
$950$	4.00000	+	1.73205i	0.129777	+	0.0561951i
$951$	30.0000			0.972817
$952$	2.00000	+	3.46410i	0.0648204	+	0.112272i
$953$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$953$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$954$	6.00000	−	10.3923i	0.194257	−	0.336463i
$955$	8.00000	+	13.8564i	0.258874	+	0.448383i
$956$	9.00000	−	15.5885i	0.291081	−	0.504167i
$957$	−20.0000			−0.646508
$958$	42.0000			1.35696
$959$	−1.00000	+	1.73205i	−0.0322917	+	0.0559308i
$960$	0.500000	−	0.866025i	0.0161374	−	0.0279508i
$961$	−30.0000			−0.967742
$962$	15.0000			0.483619
$963$	2.00000	−	3.46410i	0.0644491	−	0.111629i
$964$	−2.50000	−	4.33013i	−0.0805196	−	0.139464i
$965$	12.5000	−	21.6506i	0.402389	−	0.696959i
$966$	−3.00000	−	5.19615i	−0.0965234	−	0.167183i
$967$	−14.5000	−	25.1147i	−0.466289	−	0.807635i	0.532970	−	0.846134i	$-0.321076\pi$
$967$	−14.5000	−	25.1147i	−0.466289	−	0.807635i	−0.999259	+	0.0384986i	$0.987742\pi$
$968$	−7.00000			−0.224989
$969$	−14.0000	+	10.3923i	−0.449745	+	0.333849i
$970$	2.00000			0.0642161
$971$	4.00000	+	6.92820i	0.128366	+	0.222337i	0.923044	−	0.384695i	$-0.125693\pi$
$971$	4.00000	+	6.92820i	0.128366	+	0.222337i	−0.794678	+	0.607032i	$0.792360\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	−4.50000	+	7.79423i	−0.144263	+	0.249871i
$974$	−8.00000	−	13.8564i	−0.256337	−	0.443988i
$975$	1.50000	−	2.59808i	0.0480384	−	0.0832050i
$976$	5.00000			0.160046
$977$	−34.0000			−1.08776			−0.543878	−	0.839164i	$-0.683045\pi$
$977$	−34.0000			−1.08776			−0.543878	+	0.839164i	$0.683045\pi$
$978$	8.50000	−	14.7224i	0.271800	−	0.470771i
$979$		0			0
$980$	6.00000			0.191663
$981$	−18.0000			−0.574696
$982$	−14.0000	+	24.2487i	−0.446758	+	0.773807i
$983$	−12.0000	−	20.7846i	−0.382741	−	0.662926i	0.608712	−	0.793391i	$-0.291686\pi$
$983$	−12.0000	−	20.7846i	−0.382741	−	0.662926i	−0.991453	+	0.130465i	$0.958353\pi$
$984$	−1.00000	+	1.73205i	−0.0318788	+	0.0552158i
$985$	−9.00000	−	15.5885i	−0.286764	−	0.496690i
$986$	20.0000	+	34.6410i	0.636930	+	1.10319i
$987$		0			0
$988$	1.50000	+	12.9904i	0.0477214	+	0.413279i
$989$	30.0000			0.953945
$990$	1.00000	+	1.73205i	0.0317821	+	0.0550482i
$991$	−11.5000	−	19.9186i	−0.365310	−	0.632735i	0.623516	−	0.781810i	$-0.285704\pi$
$991$	−11.5000	−	19.9186i	−0.365310	−	0.632735i	−0.988826	+	0.149076i	$0.952370\pi$
$992$	−0.500000	+	0.866025i	−0.0158750	+	0.0274963i
$993$	−2.50000	−	4.33013i	−0.0793351	−	0.137412i
$994$		0			0
$995$	−5.00000			−0.158511
$996$	2.00000			0.0633724
$997$	−5.50000	+	9.52628i	−0.174187	+	0.301700i	−0.939880	−	0.341506i	$-0.889063\pi$
$997$	−5.50000	+	9.52628i	−0.174187	+	0.301700i	0.765693	+	0.643206i	$0.222396\pi$
$998$	12.5000	−	21.6506i	0.395681	−	0.685339i
$999$	−5.00000			−0.158193

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	570.2.i.b.121.1	✓	2
3.2	odd	2		1710.2.l.f.1261.1		2
19.11	even	3	inner	570.2.i.b.391.1	yes	2
57.11	odd	6		1710.2.l.f.1531.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
570.2.i.b.121.1	✓	2	1.1	even	1	trivial
570.2.i.b.391.1	yes	2	19.11	even	3	inner
1710.2.l.f.1261.1		2	3.2	odd	2
1710.2.l.f.1531.1		2	57.11	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:	\( N \)	\(=\)	\( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	570.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} -1.00000 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} +(-0.500000 + 0.866025i) q^{6} -1.00000 q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +2.00000 q^{11} +1.00000 q^{12} +(1.50000 - 2.59808i) q^{13} +(0.500000 + 0.866025i) q^{14} +(0.500000 - 0.866025i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 - 3.46410i) q^{17} +1.00000 q^{18} +(4.00000 + 1.73205i) q^{19} -1.00000 q^{20} +(0.500000 + 0.866025i) q^{21} +(-1.00000 - 1.73205i) q^{22} +(3.00000 - 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 + 0.866025i) q^{25} -3.00000 q^{26} +1.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +(5.00000 - 8.66025i) q^{29} -1.00000 q^{30} +1.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.00000 - 1.73205i) q^{33} +(-2.00000 + 3.46410i) q^{34} +(-0.500000 - 0.866025i) q^{35} +(-0.500000 - 0.866025i) q^{36} -5.00000 q^{37} +(-0.500000 - 4.33013i) q^{38} -3.00000 q^{39} +(0.500000 + 0.866025i) q^{40} +(-1.00000 - 1.73205i) q^{41} +(0.500000 - 0.866025i) q^{42} +(2.50000 + 4.33013i) q^{43} +(-1.00000 + 1.73205i) q^{44} -1.00000 q^{45} -6.00000 q^{46} +(-0.500000 + 0.866025i) q^{48} -6.00000 q^{49} +1.00000 q^{50} +(-2.00000 + 3.46410i) q^{51} +(1.50000 + 2.59808i) q^{52} +(6.00000 - 10.3923i) q^{53} +(-0.500000 - 0.866025i) q^{54} +(1.00000 + 1.73205i) q^{55} -1.00000 q^{56} +(-0.500000 - 4.33013i) q^{57} -10.0000 q^{58} +(1.00000 + 1.73205i) q^{59} +(0.500000 + 0.866025i) q^{60} +(-2.50000 + 4.33013i) q^{61} +(-0.500000 - 0.866025i) q^{62} +(0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +3.00000 q^{65} +(-1.00000 + 1.73205i) q^{66} +(2.50000 - 4.33013i) q^{67} +4.00000 q^{68} -6.00000 q^{69} +(-0.500000 + 0.866025i) q^{70} +(-0.500000 + 0.866025i) q^{72} +(-5.50000 - 9.52628i) q^{73} +(2.50000 + 4.33013i) q^{74} +1.00000 q^{75} +(-3.50000 + 2.59808i) q^{76} -2.00000 q^{77} +(1.50000 + 2.59808i) q^{78} +(5.50000 + 9.52628i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-1.00000 + 1.73205i) q^{82} +2.00000 q^{83} -1.00000 q^{84} +(2.00000 - 3.46410i) q^{85} +(2.50000 - 4.33013i) q^{86} -10.0000 q^{87} +2.00000 q^{88} +(0.500000 + 0.866025i) q^{90} +(-1.50000 + 2.59808i) q^{91} +(3.00000 + 5.19615i) q^{92} +(-0.500000 - 0.866025i) q^{93} +(0.500000 + 4.33013i) q^{95} +1.00000 q^{96} +(1.00000 + 1.73205i) q^{97} +(3.00000 + 5.19615i) q^{98} +(-1.00000 + 1.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - 2 q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 - q^3 - q^4 + q^5 - q^6 - 2 * q^7 + 2 * q^8 - q^9	\( 2 q - q^{2} - q^{3} - q^{4} + q^{5} - q^{6} - 2 q^{7} + 2 q^{8} - q^{9} + q^{10} + 4 q^{11} + 2 q^{12} + 3 q^{13} + q^{14} + q^{15} - q^{16} - 4 q^{17} + 2 q^{18} + 8 q^{19} - 2 q^{20} + q^{21} - 2 q^{22} + 6 q^{23} - q^{24} - q^{25} - 6 q^{26} + 2 q^{27} + q^{28} + 10 q^{29} - 2 q^{30} + 2 q^{31} - q^{32} - 2 q^{33} - 4 q^{34} - q^{35} - q^{36} - 10 q^{37} - q^{38} - 6 q^{39} + q^{40} - 2 q^{41} + q^{42} + 5 q^{43} - 2 q^{44} - 2 q^{45} - 12 q^{46} - q^{48} - 12 q^{49} + 2 q^{50} - 4 q^{51} + 3 q^{52} + 12 q^{53} - q^{54} + 2 q^{55} - 2 q^{56} - q^{57} - 20 q^{58} + 2 q^{59} + q^{60} - 5 q^{61} - q^{62} + q^{63} + 2 q^{64} + 6 q^{65} - 2 q^{66} + 5 q^{67} + 8 q^{68} - 12 q^{69} - q^{70} - q^{72} - 11 q^{73} + 5 q^{74} + 2 q^{75} - 7 q^{76} - 4 q^{77} + 3 q^{78} + 11 q^{79} + q^{80} - q^{81} - 2 q^{82} + 4 q^{83} - 2 q^{84} + 4 q^{85} + 5 q^{86} - 20 q^{87} + 4 q^{88} + q^{90} - 3 q^{91} + 6 q^{92} - q^{93} + q^{95} + 2 q^{96} + 2 q^{97} + 6 q^{98} - 2 q^{99}+O(q^{100}) \) 2 * q - q^2 - q^3 - q^4 + q^5 - q^6 - 2 * q^7 + 2 * q^8 - q^9 + q^10 + 4 * q^11 + 2 * q^12 + 3 * q^13 + q^14 + q^15 - q^16 - 4 * q^17 + 2 * q^18 + 8 * q^19 - 2 * q^20 + q^21 - 2 * q^22 + 6 * q^23 - q^24 - q^25 - 6 * q^26 + 2 * q^27 + q^28 + 10 * q^29 - 2 * q^30 + 2 * q^31 - q^32 - 2 * q^33 - 4 * q^34 - q^35 - q^36 - 10 * q^37 - q^38 - 6 * q^39 + q^40 - 2 * q^41 + q^42 + 5 * q^43 - 2 * q^44 - 2 * q^45 - 12 * q^46 - q^48 - 12 * q^49 + 2 * q^50 - 4 * q^51 + 3 * q^52 + 12 * q^53 - q^54 + 2 * q^55 - 2 * q^56 - q^57 - 20 * q^58 + 2 * q^59 + q^60 - 5 * q^61 - q^62 + q^63 + 2 * q^64 + 6 * q^65 - 2 * q^66 + 5 * q^67 + 8 * q^68 - 12 * q^69 - q^70 - q^72 - 11 * q^73 + 5 * q^74 + 2 * q^75 - 7 * q^76 - 4 * q^77 + 3 * q^78 + 11 * q^79 + q^80 - q^81 - 2 * q^82 + 4 * q^83 - 2 * q^84 + 4 * q^85 + 5 * q^86 - 20 * q^87 + 4 * q^88 + q^90 - 3 * q^91 + 6 * q^92 - q^93 + q^95 + 2 * q^96 + 2 * q^97 + 6 * q^98 - 2 * q^99

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