LMFDB - Embedded newform 57.2.e.a.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [57,2,Mod(7,57)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(57, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("57.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 57 = 3 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	57.e (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$0.455147291521$
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			7.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	57.7
Dual form			57.2.e.a.49.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +1.00000 q^{7} -3.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +1.00000 q^{7} -3.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} -2.00000 q^{11} +1.00000 q^{12} +(-2.50000 + 4.33013i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(0.500000 + 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} +1.00000 q^{18} +(-4.00000 - 1.73205i) q^{19} +(0.500000 + 0.866025i) q^{21} +(1.00000 + 1.73205i) q^{22} +(2.00000 - 3.46410i) q^{23} +(-1.50000 - 2.59808i) q^{24} +(2.50000 - 4.33013i) q^{25} +5.00000 q^{26} -1.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +(4.00000 - 6.92820i) q^{29} -3.00000 q^{31} +(-2.50000 + 4.33013i) q^{32} +(-1.00000 - 1.73205i) q^{33} +(2.00000 - 3.46410i) q^{34} +(0.500000 + 0.866025i) q^{36} +3.00000 q^{37} +(0.500000 + 4.33013i) q^{38} -5.00000 q^{39} +(6.00000 + 10.3923i) q^{41} +(0.500000 - 0.866025i) q^{42} +(0.500000 + 0.866025i) q^{43} +(-1.00000 + 1.73205i) q^{44} -4.00000 q^{46} +(3.00000 - 5.19615i) q^{47} +(-0.500000 + 0.866025i) q^{48} -6.00000 q^{49} -5.00000 q^{50} +(-2.00000 + 3.46410i) q^{51} +(2.50000 + 4.33013i) q^{52} +(-2.00000 + 3.46410i) q^{53} +(0.500000 + 0.866025i) q^{54} -3.00000 q^{56} +(-0.500000 - 4.33013i) q^{57} -8.00000 q^{58} +(-5.00000 - 8.66025i) q^{59} +(6.50000 - 11.2583i) q^{61} +(1.50000 + 2.59808i) q^{62} +(-0.500000 + 0.866025i) q^{63} +7.00000 q^{64} +(-1.00000 + 1.73205i) q^{66} +(-5.50000 + 9.52628i) q^{67} +4.00000 q^{68} +4.00000 q^{69} +(-3.00000 - 5.19615i) q^{71} +(1.50000 - 2.59808i) q^{72} +(5.50000 + 9.52628i) q^{73} +(-1.50000 - 2.59808i) q^{74} +5.00000 q^{75} +(-3.50000 + 2.59808i) q^{76} -2.00000 q^{77} +(2.50000 + 4.33013i) q^{78} +(-0.500000 - 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(6.00000 - 10.3923i) q^{82} +1.00000 q^{84} +(0.500000 - 0.866025i) q^{86} +8.00000 q^{87} +6.00000 q^{88} +(3.00000 - 5.19615i) q^{89} +(-2.50000 + 4.33013i) q^{91} +(-2.00000 - 3.46410i) q^{92} +(-1.50000 - 2.59808i) q^{93} -6.00000 q^{94} -5.00000 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^{6} + 2 q^{7} - 6 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 + q^3 + q^4 + q^6 + 2 * q^7 - 6 * q^8 - q^9	$ 2 q - q^{2} + q^{3} + q^{4} + q^{6} + 2 q^{7} - 6 q^{8} - q^{9} - 4 q^{11} + 2 q^{12} - 5 q^{13} - q^{14} + q^{16} + 4 q^{17} + 2 q^{18} - 8 q^{19} + q^{21} + 2 q^{22} + 4 q^{23} - 3 q^{24} + 5 q^{25} + 10 q^{26} - 2 q^{27} + q^{28} + 8 q^{29} - 6 q^{31} - 5 q^{32} - 2 q^{33} + 4 q^{34} + q^{36} + 6 q^{37} + q^{38} - 10 q^{39} + 12 q^{41} + q^{42} + q^{43} - 2 q^{44} - 8 q^{46} + 6 q^{47} - q^{48} - 12 q^{49} - 10 q^{50} - 4 q^{51} + 5 q^{52} - 4 q^{53} + q^{54} - 6 q^{56} - q^{57} - 16 q^{58} - 10 q^{59} + 13 q^{61} + 3 q^{62} - q^{63} + 14 q^{64} - 2 q^{66} - 11 q^{67} + 8 q^{68} + 8 q^{69} - 6 q^{71} + 3 q^{72} + 11 q^{73} - 3 q^{74} + 10 q^{75} - 7 q^{76} - 4 q^{77} + 5 q^{78} - q^{79} - q^{81} + 12 q^{82} + 2 q^{84} + q^{86} + 16 q^{87} + 12 q^{88} + 6 q^{89} - 5 q^{91} - 4 q^{92} - 3 q^{93} - 12 q^{94} - 10 q^{96} - 2 q^{97} + 6 q^{98} + 2 q^{99}+O(q^{100}) $ 2 * q - q^2 + q^3 + q^4 + q^6 + 2 * q^7 - 6 * q^8 - q^9 - 4 * q^11 + 2 * q^12 - 5 * q^13 - q^14 + q^16 + 4 * q^17 + 2 * q^18 - 8 * q^19 + q^21 + 2 * q^22 + 4 * q^23 - 3 * q^24 + 5 * q^25 + 10 * q^26 - 2 * q^27 + q^28 + 8 * q^29 - 6 * q^31 - 5 * q^32 - 2 * q^33 + 4 * q^34 + q^36 + 6 * q^37 + q^38 - 10 * q^39 + 12 * q^41 + q^42 + q^43 - 2 * q^44 - 8 * q^46 + 6 * q^47 - q^48 - 12 * q^49 - 10 * q^50 - 4 * q^51 + 5 * q^52 - 4 * q^53 + q^54 - 6 * q^56 - q^57 - 16 * q^58 - 10 * q^59 + 13 * q^61 + 3 * q^62 - q^63 + 14 * q^64 - 2 * q^66 - 11 * q^67 + 8 * q^68 + 8 * q^69 - 6 * q^71 + 3 * q^72 + 11 * q^73 - 3 * q^74 + 10 * q^75 - 7 * q^76 - 4 * q^77 + 5 * q^78 - q^79 - q^81 + 12 * q^82 + 2 * q^84 + q^86 + 16 * q^87 + 12 * q^88 + 6 * q^89 - 5 * q^91 - 4 * q^92 - 3 * q^93 - 12 * q^94 - 10 * 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 $\left(\mathbb{Z}/57\mathbb{Z}\right)^\times$.

$n$	$20$	$40$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i	0.633316	−	0.773893i	$-0.281693\pi$
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i	−0.986869	+	0.161521i	$0.948360\pi$
$3$	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			0		0.866025	−	0.500000i	$-0.166667\pi$
$5$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$6$	0.500000	−	0.866025i	0.204124	−	0.353553i
$7$	1.00000			0.377964			0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000			0.377964			0.188982	+	0.981981i	$0.439481\pi$
$8$	−3.00000			−1.06066
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$	1.00000			0.288675
$13$	−2.50000	+	4.33013i	−0.693375	+	1.20096i	0.277350	+	0.960769i	$0.410544\pi$
$13$	−2.50000	+	4.33013i	−0.693375	+	1.20096i	−0.970725	+	0.240192i	$0.922790\pi$
$14$	−0.500000	−	0.866025i	−0.133631	−	0.231455i
$15$		0			0
$16$	0.500000	+	0.866025i	0.125000	+	0.216506i
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	0.999853	−	0.0171533i	$-0.00546033\pi$
$17$	2.00000	+	3.46410i	0.485071	+	0.840168i	−0.514782	+	0.857321i	$0.672127\pi$
$18$	1.00000			0.235702
$19$	−4.00000	−	1.73205i	−0.917663	−	0.397360i
$19$	−4.00000	−	1.73205i	−0.917663	−	0.397360i
$20$		0			0
$21$	0.500000	+	0.866025i	0.109109	+	0.188982i
$22$	1.00000	+	1.73205i	0.213201	+	0.369274i
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	−0.578610	−	0.815604i	$-0.696405\pi$
$23$	2.00000	−	3.46410i	0.417029	−	0.722315i	0.995639	+	0.0932891i	$0.0297381\pi$
$24$	−1.50000	−	2.59808i	−0.306186	−	0.530330i
$25$	2.50000	−	4.33013i	0.500000	−	0.866025i
$26$	5.00000			0.980581
$27$	−1.00000			−0.192450
$28$	0.500000	−	0.866025i	0.0944911	−	0.163663i
$29$	4.00000	−	6.92820i	0.742781	−	1.28654i	−0.208443	−	0.978035i	$-0.566840\pi$
$29$	4.00000	−	6.92820i	0.742781	−	1.28654i	0.951224	−	0.308500i	$-0.0998271\pi$
$30$		0			0
$31$	−3.00000			−0.538816			−0.269408	−	0.963026i	$-0.586828\pi$
$31$	−3.00000			−0.538816			−0.269408	+	0.963026i	$0.586828\pi$
$32$	−2.50000	+	4.33013i	−0.441942	+	0.765466i
$33$	−1.00000	−	1.73205i	−0.174078	−	0.301511i
$34$	2.00000	−	3.46410i	0.342997	−	0.594089i
$35$		0			0
$36$	0.500000	+	0.866025i	0.0833333	+	0.144338i
$37$	3.00000			0.493197			0.246598	−	0.969118i	$-0.420687\pi$
$37$	3.00000			0.493197			0.246598	+	0.969118i	$0.420687\pi$
$38$	0.500000	+	4.33013i	0.0811107	+	0.702439i
$39$	−5.00000			−0.800641
$40$		0			0
$41$	6.00000	+	10.3923i	0.937043	+	1.62301i	0.770950	+	0.636895i	$0.219782\pi$
$41$	6.00000	+	10.3923i	0.937043	+	1.62301i	0.166092	+	0.986110i	$0.446885\pi$
$42$	0.500000	−	0.866025i	0.0771517	−	0.133631i
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	0.901629	−	0.432511i	$-0.142372\pi$
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	−0.825380	+	0.564578i	$0.809039\pi$
$44$	−1.00000	+	1.73205i	−0.150756	+	0.261116i
$45$		0			0
$46$	−4.00000			−0.589768
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	−0.559908	−	0.828554i	$-0.689164\pi$
$47$	3.00000	−	5.19615i	0.437595	−	0.757937i	0.997503	+	0.0706177i	$0.0224970\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−6.00000			−0.857143
$50$	−5.00000			−0.707107
$51$	−2.00000	+	3.46410i	−0.280056	+	0.485071i
$52$	2.50000	+	4.33013i	0.346688	+	0.600481i
$53$	−2.00000	+	3.46410i	−0.274721	+	0.475831i	−0.970065	−	0.242846i	$-0.921919\pi$
$53$	−2.00000	+	3.46410i	−0.274721	+	0.475831i	0.695344	+	0.718677i	$0.255252\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$		0			0
$56$	−3.00000			−0.400892
$57$	−0.500000	−	4.33013i	−0.0662266	−	0.573539i
$58$	−8.00000			−1.05045
$59$	−5.00000	−	8.66025i	−0.650945	−	1.12747i	−0.982894	−	0.184172i	$-0.941040\pi$
$59$	−5.00000	−	8.66025i	−0.650945	−	1.12747i	0.331949	−	0.943297i	$-0.392294\pi$
$60$		0			0
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	−0.0640184	−	0.997949i	$-0.520392\pi$
$61$	6.50000	−	11.2583i	0.832240	−	1.44148i	0.896258	−	0.443533i	$-0.146275\pi$
$62$	1.50000	+	2.59808i	0.190500	+	0.329956i
$63$	−0.500000	+	0.866025i	−0.0629941	+	0.109109i
$64$	7.00000			0.875000
$65$		0			0
$66$	−1.00000	+	1.73205i	−0.123091	+	0.213201i
$67$	−5.50000	+	9.52628i	−0.671932	+	1.16382i	0.305424	+	0.952217i	$0.401202\pi$
$67$	−5.50000	+	9.52628i	−0.671932	+	1.16382i	−0.977356	+	0.211604i	$0.932131\pi$
$68$	4.00000			0.485071
$69$	4.00000			0.481543
$70$		0			0
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	0.631260	−	0.775571i	$-0.282538\pi$
$71$	−3.00000	−	5.19615i	−0.356034	−	0.616670i	−0.987294	+	0.158901i	$0.949205\pi$
$72$	1.50000	−	2.59808i	0.176777	−	0.306186i
$73$	5.50000	+	9.52628i	0.643726	+	1.11497i	0.984594	+	0.174855i	$0.0559458\pi$
$73$	5.50000	+	9.52628i	0.643726	+	1.11497i	−0.340868	+	0.940111i	$0.610721\pi$
$74$	−1.50000	−	2.59808i	−0.174371	−	0.302020i
$75$	5.00000			0.577350
$76$	−3.50000	+	2.59808i	−0.401478	+	0.298020i
$77$	−2.00000			−0.227921
$78$	2.50000	+	4.33013i	0.283069	+	0.490290i
$79$	−0.500000	−	0.866025i	−0.0562544	−	0.0974355i	0.836527	−	0.547926i	$-0.184582\pi$
$79$	−0.500000	−	0.866025i	−0.0562544	−	0.0974355i	−0.892781	+	0.450490i	$0.851249\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	6.00000	−	10.3923i	0.662589	−	1.14764i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$	1.00000			0.109109
$85$		0			0
$86$	0.500000	−	0.866025i	0.0539164	−	0.0933859i
$87$	8.00000			0.857690
$88$	6.00000			0.639602
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	−0.662071	−	0.749441i	$-0.730322\pi$
$89$	3.00000	−	5.19615i	0.317999	−	0.550791i	0.980071	+	0.198650i	$0.0636557\pi$
$90$		0			0
$91$	−2.50000	+	4.33013i	−0.262071	+	0.453921i
$92$	−2.00000	−	3.46410i	−0.208514	−	0.361158i
$93$	−1.50000	−	2.59808i	−0.155543	−	0.269408i
$94$	−6.00000			−0.618853
$95$		0			0
$96$	−5.00000			−0.510310
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	0.810782	−	0.585348i	$-0.199042\pi$
$97$	−1.00000	−	1.73205i	−0.101535	−	0.175863i	−0.912317	+	0.409484i	$0.865709\pi$
$98$	3.00000	+	5.19615i	0.303046	+	0.524891i
$99$	1.00000	−	1.73205i	0.100504	−	0.174078i
$100$	−2.50000	−	4.33013i	−0.250000	−	0.433013i
$101$	−7.00000	+	12.1244i	−0.696526	+	1.20642i	0.273138	+	0.961975i	$0.411939\pi$
$101$	−7.00000	+	12.1244i	−0.696526	+	1.20642i	−0.969664	+	0.244443i	$0.921395\pi$
$102$	4.00000			0.396059
$103$	13.0000			1.28093			0.640464	−	0.767988i	$-0.278742\pi$
$103$	13.0000			1.28093			0.640464	+	0.767988i	$0.278742\pi$
$104$	7.50000	−	12.9904i	0.735436	−	1.27381i
$105$		0			0
$106$	4.00000			0.388514
$107$	−18.0000			−1.74013			−0.870063	−	0.492941i	$-0.835922\pi$
$107$	−18.0000			−1.74013			−0.870063	+	0.492941i	$0.835922\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	0.909935	−	0.414751i	$-0.136131\pi$
$109$	1.00000	+	1.73205i	0.0957826	+	0.165900i	−0.814152	+	0.580651i	$0.802798\pi$
$110$		0			0
$111$	1.50000	+	2.59808i	0.142374	+	0.246598i
$112$	0.500000	+	0.866025i	0.0472456	+	0.0818317i
$113$	2.00000			0.188144			0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000			0.188144			0.0940721	+	0.995565i	$0.470012\pi$
$114$	−3.50000	+	2.59808i	−0.327805	+	0.243332i
$115$		0			0
$116$	−4.00000	−	6.92820i	−0.371391	−	0.643268i
$117$	−2.50000	−	4.33013i	−0.231125	−	0.400320i
$118$	−5.00000	+	8.66025i	−0.460287	+	0.797241i
$119$	2.00000	+	3.46410i	0.183340	+	0.317554i
$120$		0			0
$121$	−7.00000			−0.636364
$122$	−13.0000			−1.17696
$123$	−6.00000	+	10.3923i	−0.541002	+	0.937043i
$124$	−1.50000	+	2.59808i	−0.134704	+	0.233314i
$125$		0			0
$126$	1.00000			0.0890871
$127$	4.00000	−	6.92820i	0.354943	−	0.614779i	−0.632166	−	0.774833i	$-0.717834\pi$
$127$	4.00000	−	6.92820i	0.354943	−	0.614779i	0.987108	+	0.160055i	$0.0511671\pi$
$128$	1.50000	+	2.59808i	0.132583	+	0.229640i
$129$	−0.500000	+	0.866025i	−0.0440225	+	0.0762493i
$130$		0			0
$131$	7.00000	+	12.1244i	0.611593	+	1.05931i	0.990972	+	0.134069i	$0.0428042\pi$
$131$	7.00000	+	12.1244i	0.611593	+	1.05931i	−0.379379	+	0.925241i	$0.623862\pi$
$132$	−2.00000			−0.174078
$133$	−4.00000	−	1.73205i	−0.346844	−	0.150188i
$134$	11.0000			0.950255
$135$		0			0
$136$	−6.00000	−	10.3923i	−0.514496	−	0.891133i
$137$	−9.00000	+	15.5885i	−0.768922	+	1.33181i	0.169226	+	0.985577i	$0.445873\pi$
$137$	−9.00000	+	15.5885i	−0.768922	+	1.33181i	−0.938148	+	0.346235i	$0.887460\pi$
$138$	−2.00000	−	3.46410i	−0.170251	−	0.294884i
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	−0.952355	−	0.304991i	$-0.901346\pi$
$139$	−2.50000	+	4.33013i	−0.212047	+	0.367277i	0.740308	+	0.672268i	$0.234680\pi$
$140$		0			0
$141$	6.00000			0.505291
$142$	−3.00000	+	5.19615i	−0.251754	+	0.436051i
$143$	5.00000	−	8.66025i	0.418121	−	0.724207i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	5.50000	−	9.52628i	0.455183	−	0.788400i
$147$	−3.00000	−	5.19615i	−0.247436	−	0.428571i
$148$	1.50000	−	2.59808i	0.123299	−	0.213561i
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	0.962348	−	0.271821i	$-0.0876260\pi$
$149$	3.00000	+	5.19615i	0.245770	+	0.425685i	−0.716578	+	0.697507i	$0.754293\pi$
$150$	−2.50000	−	4.33013i	−0.204124	−	0.353553i
$151$	12.0000			0.976546			0.488273	−	0.872691i	$-0.337627\pi$
$151$	12.0000			0.976546			0.488273	+	0.872691i	$0.337627\pi$
$152$	12.0000	+	5.19615i	0.973329	+	0.421464i
$153$	−4.00000			−0.323381
$154$	1.00000	+	1.73205i	0.0805823	+	0.139573i
$155$		0			0
$156$	−2.50000	+	4.33013i	−0.200160	+	0.346688i
$157$	−1.50000	−	2.59808i	−0.119713	−	0.207349i	0.799941	−	0.600079i	$-0.204864\pi$
$157$	−1.50000	−	2.59808i	−0.119713	−	0.207349i	−0.919654	+	0.392730i	$0.871531\pi$
$158$	−0.500000	+	0.866025i	−0.0397779	+	0.0688973i
$159$	−4.00000			−0.317221
$160$		0			0
$161$	2.00000	−	3.46410i	0.157622	−	0.273009i
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	3.00000			0.234978			0.117489	−	0.993074i	$-0.462515\pi$
$163$	3.00000			0.234978			0.117489	+	0.993074i	$0.462515\pi$
$164$	12.0000			0.937043
$165$		0			0
$166$		0			0
$167$	1.00000	−	1.73205i	0.0773823	−	0.134030i	−0.824737	−	0.565516i	$-0.808677\pi$
$167$	1.00000	−	1.73205i	0.0773823	−	0.134030i	0.902120	+	0.431486i	$0.142010\pi$
$168$	−1.50000	−	2.59808i	−0.115728	−	0.200446i
$169$	−6.00000	−	10.3923i	−0.461538	−	0.799408i
$170$		0			0
$171$	3.50000	−	2.59808i	0.267652	−	0.198680i
$172$	1.00000			0.0762493
$173$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$173$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$174$	−4.00000	−	6.92820i	−0.303239	−	0.525226i
$175$	2.50000	−	4.33013i	0.188982	−	0.327327i
$176$	−1.00000	−	1.73205i	−0.0753778	−	0.130558i
$177$	5.00000	−	8.66025i	0.375823	−	0.650945i
$178$	−6.00000			−0.449719
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$		0			0
$181$	1.00000	−	1.73205i	0.0743294	−	0.128742i	−0.826465	−	0.562988i	$-0.809652\pi$
$181$	1.00000	−	1.73205i	0.0743294	−	0.128742i	0.900794	+	0.434246i	$0.142985\pi$
$182$	5.00000			0.370625
$183$	13.0000			0.960988
$184$	−6.00000	+	10.3923i	−0.442326	+	0.766131i
$185$		0			0
$186$	−1.50000	+	2.59808i	−0.109985	+	0.190500i
$187$	−4.00000	−	6.92820i	−0.292509	−	0.506640i
$188$	−3.00000	−	5.19615i	−0.218797	−	0.378968i
$189$	−1.00000			−0.0727393
$190$		0			0
$191$	24.0000			1.73658			0.868290	−	0.496058i	$-0.165220\pi$
$191$	24.0000			1.73658			0.868290	+	0.496058i	$0.165220\pi$
$192$	3.50000	+	6.06218i	0.252591	+	0.437500i
$193$	−9.50000	−	16.4545i	−0.683825	−	1.18442i	−0.973805	−	0.227387i	$-0.926982\pi$
$193$	−9.50000	−	16.4545i	−0.683825	−	1.18442i	0.289980	−	0.957033i	$-0.406351\pi$
$194$	−1.00000	+	1.73205i	−0.0717958	+	0.124354i
$195$		0			0
$196$	−3.00000	+	5.19615i	−0.214286	+	0.371154i
$197$	−26.0000			−1.85242			−0.926212	−	0.377004i	$-0.876954\pi$
$197$	−26.0000			−1.85242			−0.926212	+	0.377004i	$0.876954\pi$
$198$	−2.00000			−0.142134
$199$	−10.5000	+	18.1865i	−0.744325	+	1.28921i	0.206184	+	0.978513i	$0.433895\pi$
$199$	−10.5000	+	18.1865i	−0.744325	+	1.28921i	−0.950509	+	0.310696i	$0.899438\pi$
$200$	−7.50000	+	12.9904i	−0.530330	+	0.918559i
$201$	−11.0000			−0.775880
$202$	14.0000			0.985037
$203$	4.00000	−	6.92820i	0.280745	−	0.486265i
$204$	2.00000	+	3.46410i	0.140028	+	0.242536i
$205$		0			0
$206$	−6.50000	−	11.2583i	−0.452876	−	0.784405i
$207$	2.00000	+	3.46410i	0.139010	+	0.240772i
$208$	−5.00000			−0.346688
$209$	8.00000	+	3.46410i	0.553372	+	0.239617i
$210$		0			0
$211$	7.50000	+	12.9904i	0.516321	+	0.894295i	0.999820	+	0.0189499i	$0.00603229\pi$
$211$	7.50000	+	12.9904i	0.516321	+	0.894295i	−0.483499	+	0.875345i	$0.660634\pi$
$212$	2.00000	+	3.46410i	0.137361	+	0.237915i
$213$	3.00000	−	5.19615i	0.205557	−	0.356034i
$214$	9.00000	+	15.5885i	0.615227	+	1.06561i
$215$		0			0
$216$	3.00000			0.204124
$217$	−3.00000			−0.203653
$218$	1.00000	−	1.73205i	0.0677285	−	0.117309i
$219$	−5.50000	+	9.52628i	−0.371656	+	0.643726i
$220$		0			0
$221$	−20.0000			−1.34535
$222$	1.50000	−	2.59808i	0.100673	−	0.174371i
$223$	−4.50000	−	7.79423i	−0.301342	−	0.521940i	0.675098	−	0.737728i	$-0.264101\pi$
$223$	−4.50000	−	7.79423i	−0.301342	−	0.521940i	−0.976440	+	0.215788i	$0.930768\pi$
$224$	−2.50000	+	4.33013i	−0.167038	+	0.289319i
$225$	2.50000	+	4.33013i	0.166667	+	0.288675i
$226$	−1.00000	−	1.73205i	−0.0665190	−	0.115214i
$227$	−24.0000			−1.59294			−0.796468	−	0.604681i	$-0.793301\pi$
$227$	−24.0000			−1.59294			−0.796468	+	0.604681i	$0.793301\pi$
$228$	−4.00000	−	1.73205i	−0.264906	−	0.114708i
$229$	13.0000			0.859064			0.429532	−	0.903052i	$-0.358679\pi$
$229$	13.0000			0.859064			0.429532	+	0.903052i	$0.358679\pi$
$230$		0			0
$231$	−1.00000	−	1.73205i	−0.0657952	−	0.113961i
$232$	−12.0000	+	20.7846i	−0.787839	+	1.36458i
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	0.947403	−	0.320043i	$-0.103697\pi$
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	−0.750867	+	0.660454i	$0.770364\pi$
$234$	−2.50000	+	4.33013i	−0.163430	+	0.283069i
$235$		0			0
$236$	−10.0000			−0.650945
$237$	0.500000	−	0.866025i	0.0324785	−	0.0562544i
$238$	2.00000	−	3.46410i	0.129641	−	0.224544i
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$		0			0
$241$	3.50000	−	6.06218i	0.225455	−	0.390499i	−0.731001	−	0.682376i	$-0.760947\pi$
$241$	3.50000	−	6.06218i	0.225455	−	0.390499i	0.956456	+	0.291877i	$0.0942799\pi$
$242$	3.50000	+	6.06218i	0.224989	+	0.389692i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−6.50000	−	11.2583i	−0.416120	−	0.720741i
$245$		0			0
$246$	12.0000			0.765092
$247$	17.5000	−	12.9904i	1.11350	−	0.826558i
$248$	9.00000			0.571501
$249$		0			0
$250$		0			0
$251$	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
$253$	−4.00000	+	6.92820i	−0.251478	+	0.435572i
$254$	−8.00000			−0.501965
$255$		0			0
$256$	8.50000	−	14.7224i	0.531250	−	0.920152i
$257$	10.0000	−	17.3205i	0.623783	−	1.08042i	−0.364992	−	0.931011i	$-0.618928\pi$
$257$	10.0000	−	17.3205i	0.623783	−	1.08042i	0.988775	−	0.149413i	$-0.0477384\pi$
$258$	1.00000			0.0622573
$259$	3.00000			0.186411
$260$		0			0
$261$	4.00000	+	6.92820i	0.247594	+	0.428845i
$262$	7.00000	−	12.1244i	0.432461	−	0.749045i
$263$	−13.0000	−	22.5167i	−0.801614	−	1.38844i	−0.918553	−	0.395298i	$-0.870641\pi$
$263$	−13.0000	−	22.5167i	−0.801614	−	1.38844i	0.116939	−	0.993139i	$-0.462692\pi$
$264$	3.00000	+	5.19615i	0.184637	+	0.319801i
$265$		0			0
$266$	0.500000	+	4.33013i	0.0306570	+	0.265497i
$267$	6.00000			0.367194
$268$	5.50000	+	9.52628i	0.335966	+	0.581910i
$269$	−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			0
$271$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$271$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$272$	−2.00000	+	3.46410i	−0.121268	+	0.210042i
$273$	−5.00000			−0.302614
$274$	18.0000			1.08742
$275$	−5.00000	+	8.66025i	−0.301511	+	0.522233i
$276$	2.00000	−	3.46410i	0.120386	−	0.208514i
$277$	−2.00000			−0.120168			−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000			−0.120168			−0.0600842	+	0.998193i	$0.519137\pi$
$278$	5.00000			0.299880
$279$	1.50000	−	2.59808i	0.0898027	−	0.155543i
$280$		0			0
$281$	4.00000	−	6.92820i	0.238620	−	0.413302i	−0.721699	−	0.692207i	$-0.756638\pi$
$281$	4.00000	−	6.92820i	0.238620	−	0.413302i	0.960319	+	0.278906i	$0.0899716\pi$
$282$	−3.00000	−	5.19615i	−0.178647	−	0.309426i
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	0.919327	−	0.393494i	$-0.128734\pi$
$283$	2.00000	+	3.46410i	0.118888	+	0.205919i	−0.800439	+	0.599414i	$0.795400\pi$
$284$	−6.00000			−0.356034
$285$		0			0
$286$	−10.0000			−0.591312
$287$	6.00000	+	10.3923i	0.354169	+	0.613438i
$288$	−2.50000	−	4.33013i	−0.147314	−	0.255155i
$289$	0.500000	−	0.866025i	0.0294118	−	0.0509427i
$290$		0			0
$291$	1.00000	−	1.73205i	0.0586210	−	0.101535i
$292$	11.0000			0.643726
$293$	14.0000			0.817889			0.408944	−	0.912559i	$-0.365897\pi$
$293$	14.0000			0.817889			0.408944	+	0.912559i	$0.365897\pi$
$294$	−3.00000	+	5.19615i	−0.174964	+	0.303046i
$295$		0			0
$296$	−9.00000			−0.523114
$297$	2.00000			0.116052
$298$	3.00000	−	5.19615i	0.173785	−	0.301005i
$299$	10.0000	+	17.3205i	0.578315	+	1.00167i
$300$	2.50000	−	4.33013i	0.144338	−	0.250000i
$301$	0.500000	+	0.866025i	0.0288195	+	0.0499169i
$302$	−6.00000	−	10.3923i	−0.345261	−	0.598010i
$303$	−14.0000			−0.804279
$304$	−0.500000	−	4.33013i	−0.0286770	−	0.248350i
$305$		0			0
$306$	2.00000	+	3.46410i	0.114332	+	0.198030i
$307$	6.00000	+	10.3923i	0.342438	+	0.593120i	0.984885	−	0.173210i	$-0.0554140\pi$
$307$	6.00000	+	10.3923i	0.342438	+	0.593120i	−0.642447	+	0.766330i	$0.722081\pi$
$308$	−1.00000	+	1.73205i	−0.0569803	+	0.0986928i
$309$	6.50000	+	11.2583i	0.369772	+	0.640464i
$310$		0			0
$311$	18.0000			1.02069			0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000			1.02069			0.510343	+	0.859971i	$0.329518\pi$
$312$	15.0000			0.849208
$313$	−11.0000	+	19.0526i	−0.621757	+	1.07691i	0.367402	+	0.930062i	$0.380247\pi$
$313$	−11.0000	+	19.0526i	−0.621757	+	1.07691i	−0.989158	+	0.146852i	$0.953086\pi$
$314$	−1.50000	+	2.59808i	−0.0846499	+	0.146618i
$315$		0			0
$316$	−1.00000			−0.0562544
$317$	2.00000	−	3.46410i	0.112331	−	0.194563i	−0.804379	−	0.594117i	$-0.797502\pi$
$317$	2.00000	−	3.46410i	0.112331	−	0.194563i	0.916710	+	0.399554i	$0.130835\pi$
$318$	2.00000	+	3.46410i	0.112154	+	0.194257i
$319$	−8.00000	+	13.8564i	−0.447914	+	0.775810i
$320$		0			0
$321$	−9.00000	−	15.5885i	−0.502331	−	0.870063i
$322$	−4.00000			−0.222911
$323$	−2.00000	−	17.3205i	−0.111283	−	0.963739i
$324$	−1.00000			−0.0555556
$325$	12.5000	+	21.6506i	0.693375	+	1.20096i
$326$	−1.50000	−	2.59808i	−0.0830773	−	0.143894i
$327$	−1.00000	+	1.73205i	−0.0553001	+	0.0957826i
$328$	−18.0000	−	31.1769i	−0.993884	−	1.72146i
$329$	3.00000	−	5.19615i	0.165395	−	0.286473i
$330$		0			0
$331$	−25.0000			−1.37412			−0.687062	−	0.726599i	$-0.741100\pi$
$331$	−25.0000			−1.37412			−0.687062	+	0.726599i	$0.741100\pi$
$332$		0			0
$333$	−1.50000	+	2.59808i	−0.0821995	+	0.142374i
$334$	−2.00000			−0.109435
$335$		0			0
$336$	−0.500000	+	0.866025i	−0.0272772	+	0.0472456i
$337$	−6.50000	−	11.2583i	−0.354078	−	0.613280i	0.632882	−	0.774248i	$-0.281872\pi$
$337$	−6.50000	−	11.2583i	−0.354078	−	0.613280i	−0.986960	+	0.160968i	$0.948538\pi$
$338$	−6.00000	+	10.3923i	−0.326357	+	0.565267i
$339$	1.00000	+	1.73205i	0.0543125	+	0.0940721i
$340$		0			0
$341$	6.00000			0.324918
$342$	−4.00000	−	1.73205i	−0.216295	−	0.0936586i
$343$	−13.0000			−0.701934
$344$	−1.50000	−	2.59808i	−0.0808746	−	0.140079i
$345$		0			0
$346$		0			0
$347$	8.00000	+	13.8564i	0.429463	+	0.743851i	0.996826	−	0.0796169i	$-0.0253697\pi$
$347$	8.00000	+	13.8564i	0.429463	+	0.743851i	−0.567363	+	0.823468i	$0.692036\pi$
$348$	4.00000	−	6.92820i	0.214423	−	0.371391i
$349$	−21.0000			−1.12410			−0.562052	−	0.827102i	$-0.689988\pi$
$349$	−21.0000			−1.12410			−0.562052	+	0.827102i	$0.689988\pi$
$350$	−5.00000			−0.267261
$351$	2.50000	−	4.33013i	0.133440	−	0.231125i
$352$	5.00000	−	8.66025i	0.266501	−	0.461593i
$353$	4.00000			0.212899			0.106449	−	0.994318i	$-0.466052\pi$
$353$	4.00000			0.212899			0.106449	+	0.994318i	$0.466052\pi$
$354$	−10.0000			−0.531494
$355$		0			0
$356$	−3.00000	−	5.19615i	−0.159000	−	0.275396i
$357$	−2.00000	+	3.46410i	−0.105851	+	0.183340i
$358$	−6.00000	−	10.3923i	−0.317110	−	0.549250i
$359$	10.0000	+	17.3205i	0.527780	+	0.914141i	0.999476	+	0.0323801i	$0.0103087\pi$
$359$	10.0000	+	17.3205i	0.527780	+	0.914141i	−0.471696	+	0.881761i	$0.656358\pi$
$360$		0			0
$361$	13.0000	+	13.8564i	0.684211	+	0.729285i
$362$	−2.00000			−0.105118
$363$	−3.50000	−	6.06218i	−0.183702	−	0.318182i
$364$	2.50000	+	4.33013i	0.131036	+	0.226960i
$365$		0			0
$366$	−6.50000	−	11.2583i	−0.339760	−	0.588482i
$367$	−3.50000	+	6.06218i	−0.182699	+	0.316443i	−0.942799	−	0.333363i	$-0.891817\pi$
$367$	−3.50000	+	6.06218i	−0.182699	+	0.316443i	0.760100	+	0.649806i	$0.225150\pi$
$368$	4.00000			0.208514
$369$	−12.0000			−0.624695
$370$		0			0
$371$	−2.00000	+	3.46410i	−0.103835	+	0.179847i
$372$	−3.00000			−0.155543
$373$	10.0000			0.517780			0.258890	−	0.965907i	$-0.416643\pi$
$373$	10.0000			0.517780			0.258890	+	0.965907i	$0.416643\pi$
$374$	−4.00000	+	6.92820i	−0.206835	+	0.358249i
$375$		0			0
$376$	−9.00000	+	15.5885i	−0.464140	+	0.803913i
$377$	20.0000	+	34.6410i	1.03005	+	1.78410i
$378$	0.500000	+	0.866025i	0.0257172	+	0.0445435i
$379$	−5.00000			−0.256833			−0.128416	−	0.991720i	$-0.540989\pi$
$379$	−5.00000			−0.256833			−0.128416	+	0.991720i	$0.540989\pi$
$380$		0			0
$381$	8.00000			0.409852
$382$	−12.0000	−	20.7846i	−0.613973	−	1.06343i
$383$	−7.00000	−	12.1244i	−0.357683	−	0.619526i	0.629890	−	0.776684i	$-0.283100\pi$
$383$	−7.00000	−	12.1244i	−0.357683	−	0.619526i	−0.987573	+	0.157159i	$0.949767\pi$
$384$	−1.50000	+	2.59808i	−0.0765466	+	0.132583i
$385$		0			0
$386$	−9.50000	+	16.4545i	−0.483537	+	0.837511i
$387$	−1.00000			−0.0508329
$388$	−2.00000			−0.101535
$389$	12.0000	−	20.7846i	0.608424	−	1.05382i	−0.383076	−	0.923717i	$-0.625135\pi$
$389$	12.0000	−	20.7846i	0.608424	−	1.05382i	0.991500	−	0.130105i	$-0.0415314\pi$
$390$		0			0
$391$	16.0000			0.809155
$392$	18.0000			0.909137
$393$	−7.00000	+	12.1244i	−0.353103	+	0.611593i
$394$	13.0000	+	22.5167i	0.654931	+	1.13437i
$395$		0			0
$396$	−1.00000	−	1.73205i	−0.0502519	−	0.0870388i
$397$	−3.50000	−	6.06218i	−0.175660	−	0.304252i	0.764730	−	0.644351i	$-0.222873\pi$
$397$	−3.50000	−	6.06218i	−0.175660	−	0.304252i	−0.940389	+	0.340099i	$0.889539\pi$
$398$	21.0000			1.05263
$399$	−0.500000	−	4.33013i	−0.0250313	−	0.216777i
$400$	5.00000			0.250000
$401$	3.00000	+	5.19615i	0.149813	+	0.259483i	0.931158	−	0.364615i	$-0.118800\pi$
$401$	3.00000	+	5.19615i	0.149813	+	0.259483i	−0.781345	+	0.624099i	$0.785466\pi$
$402$	5.50000	+	9.52628i	0.274315	+	0.475128i
$403$	7.50000	−	12.9904i	0.373602	−	0.647097i
$404$	7.00000	+	12.1244i	0.348263	+	0.603209i
$405$		0			0
$406$	−8.00000			−0.397033
$407$	−6.00000			−0.297409
$408$	6.00000	−	10.3923i	0.297044	−	0.514496i
$409$	7.00000	−	12.1244i	0.346128	−	0.599511i	−0.639430	−	0.768849i	$-0.720830\pi$
$409$	7.00000	−	12.1244i	0.346128	−	0.599511i	0.985558	+	0.169338i	$0.0541630\pi$
$410$		0			0
$411$	−18.0000			−0.887875
$412$	6.50000	−	11.2583i	0.320232	−	0.554658i
$413$	−5.00000	−	8.66025i	−0.246034	−	0.426143i
$414$	2.00000	−	3.46410i	0.0982946	−	0.170251i
$415$		0			0
$416$	−12.5000	−	21.6506i	−0.612863	−	1.06151i
$417$	−5.00000			−0.244851
$418$	−1.00000	−	8.66025i	−0.0489116	−	0.423587i
$419$	−14.0000			−0.683945			−0.341972	−	0.939710i	$-0.611095\pi$
$419$	−14.0000			−0.683945			−0.341972	+	0.939710i	$0.611095\pi$
$420$		0			0
$421$	11.0000	+	19.0526i	0.536107	+	0.928565i	0.999109	+	0.0422075i	$0.0134391\pi$
$421$	11.0000	+	19.0526i	0.536107	+	0.928565i	−0.463002	+	0.886357i	$0.653228\pi$
$422$	7.50000	−	12.9904i	0.365094	−	0.632362i
$423$	3.00000	+	5.19615i	0.145865	+	0.252646i
$424$	6.00000	−	10.3923i	0.291386	−	0.504695i
$425$	20.0000			0.970143
$426$	−6.00000			−0.290701
$427$	6.50000	−	11.2583i	0.314557	−	0.544829i
$428$	−9.00000	+	15.5885i	−0.435031	+	0.753497i
$429$	10.0000			0.482805
$430$		0			0
$431$	5.00000	−	8.66025i	0.240842	−	0.417150i	−0.720113	−	0.693857i	$-0.755910\pi$
$431$	5.00000	−	8.66025i	0.240842	−	0.417150i	0.960954	+	0.276707i	$0.0892433\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	4.50000	−	7.79423i	0.216256	−	0.374567i	−0.737404	−	0.675452i	$-0.763949\pi$
$433$	4.50000	−	7.79423i	0.216256	−	0.374567i	0.953660	+	0.300885i	$0.0972820\pi$
$434$	1.50000	+	2.59808i	0.0720023	+	0.124712i
$435$		0			0
$436$	2.00000			0.0957826
$437$	−14.0000	+	10.3923i	−0.669711	+	0.497131i
$438$	11.0000			0.525600
$439$	−17.5000	−	30.3109i	−0.835229	−	1.44666i	−0.893843	−	0.448379i	$-0.852001\pi$
$439$	−17.5000	−	30.3109i	−0.835229	−	1.44666i	0.0586141	−	0.998281i	$-0.481332\pi$
$440$		0			0
$441$	3.00000	−	5.19615i	0.142857	−	0.247436i
$442$	10.0000	+	17.3205i	0.475651	+	0.823853i
$443$	16.0000	−	27.7128i	0.760183	−	1.31668i	−0.182573	−	0.983192i	$-0.558443\pi$
$443$	16.0000	−	27.7128i	0.760183	−	1.31668i	0.942756	−	0.333483i	$-0.108224\pi$
$444$	3.00000			0.142374
$445$		0			0
$446$	−4.50000	+	7.79423i	−0.213081	+	0.369067i
$447$	−3.00000	+	5.19615i	−0.141895	+	0.245770i
$448$	7.00000			0.330719
$449$	−12.0000			−0.566315			−0.283158	−	0.959073i	$-0.591382\pi$
$449$	−12.0000			−0.566315			−0.283158	+	0.959073i	$0.591382\pi$
$450$	2.50000	−	4.33013i	0.117851	−	0.204124i
$451$	−12.0000	−	20.7846i	−0.565058	−	0.978709i
$452$	1.00000	−	1.73205i	0.0470360	−	0.0814688i
$453$	6.00000	+	10.3923i	0.281905	+	0.488273i
$454$	12.0000	+	20.7846i	0.563188	+	0.975470i
$455$		0			0
$456$	1.50000	+	12.9904i	0.0702439	+	0.608330i
$457$	−11.0000			−0.514558			−0.257279	−	0.966337i	$-0.582826\pi$
$457$	−11.0000			−0.514558			−0.257279	+	0.966337i	$0.582826\pi$
$458$	−6.50000	−	11.2583i	−0.303725	−	0.526067i
$459$	−2.00000	−	3.46410i	−0.0933520	−	0.161690i
$460$		0			0
$461$	−15.0000	−	25.9808i	−0.698620	−	1.21004i	−0.968945	−	0.247276i	$-0.920465\pi$
$461$	−15.0000	−	25.9808i	−0.698620	−	1.21004i	0.270326	−	0.962769i	$-0.412869\pi$
$462$	−1.00000	+	1.73205i	−0.0465242	+	0.0805823i
$463$	23.0000			1.06890			0.534450	−	0.845200i	$-0.320519\pi$
$463$	23.0000			1.06890			0.534450	+	0.845200i	$0.320519\pi$
$464$	8.00000			0.371391
$465$		0			0
$466$	3.00000	−	5.19615i	0.138972	−	0.240707i
$467$	−8.00000			−0.370196			−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000			−0.370196			−0.185098	+	0.982720i	$0.559260\pi$
$468$	−5.00000			−0.231125
$469$	−5.50000	+	9.52628i	−0.253966	+	0.439883i
$470$		0			0
$471$	1.50000	−	2.59808i	0.0691164	−	0.119713i
$472$	15.0000	+	25.9808i	0.690431	+	1.19586i
$473$	−1.00000	−	1.73205i	−0.0459800	−	0.0796398i
$474$	−1.00000			−0.0459315
$475$	−17.5000	+	12.9904i	−0.802955	+	0.596040i
$476$	4.00000			0.183340
$477$	−2.00000	−	3.46410i	−0.0915737	−	0.158610i
$478$	6.00000	+	10.3923i	0.274434	+	0.475333i
$479$	−7.00000	+	12.1244i	−0.319838	+	0.553976i	−0.980454	−	0.196748i	$-0.936962\pi$
$479$	−7.00000	+	12.1244i	−0.319838	+	0.553976i	0.660616	+	0.750724i	$0.270295\pi$
$480$		0			0
$481$	−7.50000	+	12.9904i	−0.341971	+	0.592310i
$482$	−7.00000			−0.318841
$483$	4.00000			0.182006
$484$	−3.50000	+	6.06218i	−0.159091	+	0.275554i
$485$		0			0
$486$	−1.00000			−0.0453609
$487$	−16.0000			−0.725029			−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000			−0.725029			−0.362515	+	0.931978i	$0.618082\pi$
$488$	−19.5000	+	33.7750i	−0.882724	+	1.52892i
$489$	1.50000	+	2.59808i	0.0678323	+	0.117489i
$490$		0			0
$491$	−3.00000	−	5.19615i	−0.135388	−	0.234499i	0.790358	−	0.612646i	$-0.209895\pi$
$491$	−3.00000	−	5.19615i	−0.135388	−	0.234499i	−0.925746	+	0.378147i	$0.876561\pi$
$492$	6.00000	+	10.3923i	0.270501	+	0.468521i
$493$	32.0000			1.44121
$494$	−20.0000	−	8.66025i	−0.899843	−	0.389643i
$495$		0			0
$496$	−1.50000	−	2.59808i	−0.0673520	−	0.116657i
$497$	−3.00000	−	5.19615i	−0.134568	−	0.233079i
$498$		0			0
$499$	−14.5000	−	25.1147i	−0.649109	−	1.12429i	−0.983336	−	0.181797i	$-0.941809\pi$
$499$	−14.5000	−	25.1147i	−0.649109	−	1.12429i	0.334227	−	0.942493i	$-0.391525\pi$
$500$		0			0
$501$	2.00000			0.0893534
$502$	−2.00000			−0.0892644
$503$	−20.0000	+	34.6410i	−0.891756	+	1.54457i	−0.0539870	+	0.998542i	$0.517193\pi$
$503$	−20.0000	+	34.6410i	−0.891756	+	1.54457i	−0.837769	+	0.546025i	$0.816140\pi$
$504$	1.50000	−	2.59808i	0.0668153	−	0.115728i
$505$		0			0
$506$	8.00000			0.355643
$507$	6.00000	−	10.3923i	0.266469	−	0.461538i
$508$	−4.00000	−	6.92820i	−0.177471	−	0.307389i
$509$	3.00000	−	5.19615i	0.132973	−	0.230315i	−0.791849	−	0.610718i	$-0.790881\pi$
$509$	3.00000	−	5.19615i	0.132973	−	0.230315i	0.924821	+	0.380402i	$0.124214\pi$
$510$		0			0
$511$	5.50000	+	9.52628i	0.243306	+	0.421418i
$512$	−11.0000			−0.486136
$513$	4.00000	+	1.73205i	0.176604	+	0.0764719i
$514$	−20.0000			−0.882162
$515$		0			0
$516$	0.500000	+	0.866025i	0.0220113	+	0.0381246i
$517$	−6.00000	+	10.3923i	−0.263880	+	0.457053i
$518$	−1.50000	−	2.59808i	−0.0659062	−	0.114153i
$519$		0			0
$520$		0			0
$521$	18.0000			0.788594			0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000			0.788594			0.394297	+	0.918983i	$0.370988\pi$
$522$	4.00000	−	6.92820i	0.175075	−	0.303239i
$523$	−14.5000	+	25.1147i	−0.634041	+	1.09819i	0.352677	+	0.935745i	$0.385272\pi$
$523$	−14.5000	+	25.1147i	−0.634041	+	1.09819i	−0.986718	+	0.162446i	$0.948062\pi$
$524$	14.0000			0.611593
$525$	5.00000			0.218218
$526$	−13.0000	+	22.5167i	−0.566827	+	0.981773i
$527$	−6.00000	−	10.3923i	−0.261364	−	0.452696i
$528$	1.00000	−	1.73205i	0.0435194	−	0.0753778i
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$		0			0
$531$	10.0000			0.433963
$532$	−3.50000	+	2.59808i	−0.151744	+	0.112641i
$533$	−60.0000			−2.59889
$534$	−3.00000	−	5.19615i	−0.129823	−	0.224860i
$535$		0			0
$536$	16.5000	−	28.5788i	0.712691	−	1.23442i
$537$	6.00000	+	10.3923i	0.258919	+	0.448461i
$538$	−5.00000	+	8.66025i	−0.215565	+	0.373370i
$539$	12.0000			0.516877
$540$		0			0
$541$	19.5000	−	33.7750i	0.838370	−	1.45210i	−0.0528859	−	0.998601i	$-0.516842\pi$
$541$	19.5000	−	33.7750i	0.838370	−	1.45210i	0.891256	−	0.453500i	$-0.149825\pi$
$542$		0			0
$543$	2.00000			0.0858282
$544$	−20.0000			−0.857493
$545$		0			0
$546$	2.50000	+	4.33013i	0.106990	+	0.185312i
$547$	14.5000	−	25.1147i	0.619975	−	1.07383i	−0.369514	−	0.929225i	$-0.620476\pi$
$547$	14.5000	−	25.1147i	0.619975	−	1.07383i	0.989490	−	0.144604i	$-0.0461907\pi$
$548$	9.00000	+	15.5885i	0.384461	+	0.665906i
$549$	6.50000	+	11.2583i	0.277413	+	0.480494i
$550$	10.0000			0.426401
$551$	−28.0000	+	20.7846i	−1.19284	+	0.885454i
$552$	−12.0000			−0.510754
$553$	−0.500000	−	0.866025i	−0.0212622	−	0.0368271i
$554$	1.00000	+	1.73205i	0.0424859	+	0.0735878i
$555$		0			0
$556$	2.50000	+	4.33013i	0.106024	+	0.183638i
$557$	19.0000	−	32.9090i	0.805056	−	1.39440i	−0.111198	−	0.993798i	$-0.535469\pi$
$557$	19.0000	−	32.9090i	0.805056	−	1.39440i	0.916253	−	0.400599i	$-0.131198\pi$
$558$	−3.00000			−0.127000
$559$	−5.00000			−0.211477
$560$		0			0
$561$	4.00000	−	6.92820i	0.168880	−	0.292509i
$562$	−8.00000			−0.337460
$563$	18.0000			0.758610			0.379305	−	0.925272i	$-0.376163\pi$
$563$	18.0000			0.758610			0.379305	+	0.925272i	$0.376163\pi$
$564$	3.00000	−	5.19615i	0.126323	−	0.218797i
$565$		0			0
$566$	2.00000	−	3.46410i	0.0840663	−	0.145607i
$567$	−0.500000	−	0.866025i	−0.0209980	−	0.0363696i
$568$	9.00000	+	15.5885i	0.377632	+	0.654077i
$569$	24.0000			1.00613			0.503066	−	0.864248i	$-0.332205\pi$
$569$	24.0000			1.00613			0.503066	+	0.864248i	$0.332205\pi$
$570$		0			0
$571$	33.0000			1.38101			0.690504	−	0.723329i	$-0.257389\pi$
$571$	33.0000			1.38101			0.690504	+	0.723329i	$0.257389\pi$
$572$	−5.00000	−	8.66025i	−0.209061	−	0.362103i
$573$	12.0000	+	20.7846i	0.501307	+	0.868290i
$574$	6.00000	−	10.3923i	0.250435	−	0.433766i
$575$	−10.0000	−	17.3205i	−0.417029	−	0.722315i
$576$	−3.50000	+	6.06218i	−0.145833	+	0.252591i
$577$	18.0000			0.749350			0.374675	−	0.927156i	$-0.377754\pi$
$577$	18.0000			0.749350			0.374675	+	0.927156i	$0.377754\pi$
$578$	−1.00000			−0.0415945
$579$	9.50000	−	16.4545i	0.394807	−	0.683825i
$580$		0			0
$581$		0			0
$582$	−2.00000			−0.0829027
$583$	4.00000	−	6.92820i	0.165663	−	0.286937i
$584$	−16.5000	−	28.5788i	−0.682775	−	1.18260i
$585$		0			0
$586$	−7.00000	−	12.1244i	−0.289167	−	0.500853i
$587$	13.0000	+	22.5167i	0.536567	+	0.929362i	0.999086	+	0.0427523i	$0.0136126\pi$
$587$	13.0000	+	22.5167i	0.536567	+	0.929362i	−0.462518	+	0.886610i	$0.653054\pi$
$588$	−6.00000			−0.247436
$589$	12.0000	+	5.19615i	0.494451	+	0.214104i
$590$		0			0
$591$	−13.0000	−	22.5167i	−0.534749	−	0.926212i
$592$	1.50000	+	2.59808i	0.0616496	+	0.106780i
$593$	3.00000	−	5.19615i	0.123195	−	0.213380i	−0.797831	−	0.602881i	$-0.794019\pi$
$593$	3.00000	−	5.19615i	0.123195	−	0.213380i	0.921026	+	0.389501i	$0.127353\pi$
$594$	−1.00000	−	1.73205i	−0.0410305	−	0.0710669i
$595$		0			0
$596$	6.00000			0.245770
$597$	−21.0000			−0.859473
$598$	10.0000	−	17.3205i	0.408930	−	0.708288i
$599$	−9.00000	+	15.5885i	−0.367730	+	0.636927i	−0.989210	−	0.146503i	$-0.953198\pi$
$599$	−9.00000	+	15.5885i	−0.367730	+	0.636927i	0.621480	+	0.783430i	$0.286532\pi$
$600$	−15.0000			−0.612372
$601$	−21.0000			−0.856608			−0.428304	−	0.903635i	$-0.640889\pi$
$601$	−21.0000			−0.856608			−0.428304	+	0.903635i	$0.640889\pi$
$602$	0.500000	−	0.866025i	0.0203785	−	0.0352966i
$603$	−5.50000	−	9.52628i	−0.223977	−	0.387940i
$604$	6.00000	−	10.3923i	0.244137	−	0.422857i
$605$		0			0
$606$	7.00000	+	12.1244i	0.284356	+	0.492518i
$607$	−43.0000			−1.74532			−0.872658	−	0.488332i	$-0.837606\pi$
$607$	−43.0000			−1.74532			−0.872658	+	0.488332i	$0.837606\pi$
$608$	17.5000	−	12.9904i	0.709719	−	0.526830i
$609$	8.00000			0.324176
$610$		0			0
$611$	15.0000	+	25.9808i	0.606835	+	1.05107i
$612$	−2.00000	+	3.46410i	−0.0808452	+	0.140028i
$613$	15.0000	+	25.9808i	0.605844	+	1.04935i	0.991917	+	0.126885i	$0.0404979\pi$
$613$	15.0000	+	25.9808i	0.605844	+	1.04935i	−0.386073	+	0.922468i	$0.626169\pi$
$614$	6.00000	−	10.3923i	0.242140	−	0.419399i
$615$		0			0
$616$	6.00000			0.241747
$617$	−3.00000	+	5.19615i	−0.120775	+	0.209189i	−0.920074	−	0.391745i	$-0.871871\pi$
$617$	−3.00000	+	5.19615i	−0.120775	+	0.209189i	0.799298	+	0.600935i	$0.205205\pi$
$618$	6.50000	−	11.2583i	0.261468	−	0.452876i
$619$	25.0000			1.00483			0.502417	−	0.864625i	$-0.332444\pi$
$619$	25.0000			1.00483			0.502417	+	0.864625i	$0.332444\pi$
$620$		0			0
$621$	−2.00000	+	3.46410i	−0.0802572	+	0.139010i
$622$	−9.00000	−	15.5885i	−0.360867	−	0.625040i
$623$	3.00000	−	5.19615i	0.120192	−	0.208179i
$624$	−2.50000	−	4.33013i	−0.100080	−	0.173344i
$625$	−12.5000	−	21.6506i	−0.500000	−	0.866025i
$626$	22.0000			0.879297
$627$	1.00000	+	8.66025i	0.0399362	+	0.345857i
$628$	−3.00000			−0.119713
$629$	6.00000	+	10.3923i	0.239236	+	0.414368i
$630$		0			0
$631$	7.50000	−	12.9904i	0.298570	−	0.517139i	−0.677239	−	0.735763i	$-0.736824\pi$
$631$	7.50000	−	12.9904i	0.298570	−	0.517139i	0.975809	+	0.218624i	$0.0701569\pi$
$632$	1.50000	+	2.59808i	0.0596668	+	0.103346i
$633$	−7.50000	+	12.9904i	−0.298098	+	0.516321i
$634$	−4.00000			−0.158860
$635$		0			0
$636$	−2.00000	+	3.46410i	−0.0793052	+	0.137361i
$637$	15.0000	−	25.9808i	0.594322	−	1.02940i
$638$	16.0000			0.633446
$639$	6.00000			0.237356
$640$		0			0
$641$	15.0000	+	25.9808i	0.592464	+	1.02618i	0.993899	+	0.110291i	$0.0351782\pi$
$641$	15.0000	+	25.9808i	0.592464	+	1.02618i	−0.401435	+	0.915888i	$0.631488\pi$
$642$	−9.00000	+	15.5885i	−0.355202	+	0.615227i
$643$	9.50000	+	16.4545i	0.374643	+	0.648901i	0.990274	−	0.139134i	$-0.0444318\pi$
$643$	9.50000	+	16.4545i	0.374643	+	0.648901i	−0.615630	+	0.788035i	$0.711098\pi$
$644$	−2.00000	−	3.46410i	−0.0788110	−	0.136505i
$645$		0			0
$646$	−14.0000	+	10.3923i	−0.550823	+	0.408880i
$647$	−24.0000			−0.943537			−0.471769	−	0.881722i	$-0.656384\pi$
$647$	−24.0000			−0.943537			−0.471769	+	0.881722i	$0.656384\pi$
$648$	1.50000	+	2.59808i	0.0589256	+	0.102062i
$649$	10.0000	+	17.3205i	0.392534	+	0.679889i
$650$	12.5000	−	21.6506i	0.490290	−	0.849208i
$651$	−1.50000	−	2.59808i	−0.0587896	−	0.101827i
$652$	1.50000	−	2.59808i	0.0587445	−	0.101749i
$653$	−18.0000			−0.704394			−0.352197	−	0.935926i	$-0.614565\pi$
$653$	−18.0000			−0.704394			−0.352197	+	0.935926i	$0.614565\pi$
$654$	2.00000			0.0782062
$655$		0			0
$656$	−6.00000	+	10.3923i	−0.234261	+	0.405751i
$657$	−11.0000			−0.429151
$658$	−6.00000			−0.233904
$659$	−17.0000	+	29.4449i	−0.662226	+	1.14701i	0.317803	+	0.948157i	$0.397055\pi$
$659$	−17.0000	+	29.4449i	−0.662226	+	1.14701i	−0.980029	+	0.198852i	$0.936279\pi$
$660$		0			0
$661$	−21.0000	+	36.3731i	−0.816805	+	1.41475i	0.0912190	+	0.995831i	$0.470924\pi$
$661$	−21.0000	+	36.3731i	−0.816805	+	1.41475i	−0.908024	+	0.418917i	$0.862410\pi$
$662$	12.5000	+	21.6506i	0.485826	+	0.841476i
$663$	−10.0000	−	17.3205i	−0.388368	−	0.672673i
$664$		0			0
$665$		0			0
$666$	3.00000			0.116248
$667$	−16.0000	−	27.7128i	−0.619522	−	1.07304i
$668$	−1.00000	−	1.73205i	−0.0386912	−	0.0670151i
$669$	4.50000	−	7.79423i	0.173980	−	0.301342i
$670$		0			0
$671$	−13.0000	+	22.5167i	−0.501859	+	0.869246i
$672$	−5.00000			−0.192879
$673$	−33.0000			−1.27206			−0.636028	−	0.771666i	$-0.719424\pi$
$673$	−33.0000			−1.27206			−0.636028	+	0.771666i	$0.719424\pi$
$674$	−6.50000	+	11.2583i	−0.250371	+	0.433655i
$675$	−2.50000	+	4.33013i	−0.0962250	+	0.166667i
$676$	−12.0000			−0.461538
$677$	34.0000			1.30673			0.653363	−	0.757045i	$-0.273358\pi$
$677$	34.0000			1.30673			0.653363	+	0.757045i	$0.273358\pi$
$678$	1.00000	−	1.73205i	0.0384048	−	0.0665190i
$679$	−1.00000	−	1.73205i	−0.0383765	−	0.0664700i
$680$		0			0
$681$	−12.0000	−	20.7846i	−0.459841	−	0.796468i
$682$	−3.00000	−	5.19615i	−0.114876	−	0.198971i
$683$	12.0000			0.459167			0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000			0.459167			0.229584	+	0.973289i	$0.426264\pi$
$684$	−0.500000	−	4.33013i	−0.0191180	−	0.165567i
$685$		0			0
$686$	6.50000	+	11.2583i	0.248171	+	0.429845i
$687$	6.50000	+	11.2583i	0.247990	+	0.429532i
$688$	−0.500000	+	0.866025i	−0.0190623	+	0.0330169i
$689$	−10.0000	−	17.3205i	−0.380970	−	0.659859i
$690$		0			0
$691$	20.0000			0.760836			0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000			0.760836			0.380418	+	0.924815i	$0.375780\pi$
$692$		0			0
$693$	1.00000	−	1.73205i	0.0379869	−	0.0657952i
$694$	8.00000	−	13.8564i	0.303676	−	0.525982i
$695$		0			0
$696$	−24.0000			−0.909718
$697$	−24.0000	+	41.5692i	−0.909065	+	1.57455i
$698$	10.5000	+	18.1865i	0.397431	+	0.688370i
$699$	−3.00000	+	5.19615i	−0.113470	+	0.196537i
$700$	−2.50000	−	4.33013i	−0.0944911	−	0.163663i
$701$	−10.0000	−	17.3205i	−0.377695	−	0.654187i	0.613032	−	0.790058i	$-0.289950\pi$
$701$	−10.0000	−	17.3205i	−0.377695	−	0.654187i	−0.990726	+	0.135872i	$0.956616\pi$
$702$	−5.00000			−0.188713
$703$	−12.0000	−	5.19615i	−0.452589	−	0.195977i
$704$	−14.0000			−0.527645
$705$		0			0
$706$	−2.00000	−	3.46410i	−0.0752710	−	0.130373i
$707$	−7.00000	+	12.1244i	−0.263262	+	0.455983i
$708$	−5.00000	−	8.66025i	−0.187912	−	0.325472i
$709$	19.5000	−	33.7750i	0.732338	−	1.26845i	−0.223544	−	0.974694i	$-0.571763\pi$
$709$	19.5000	−	33.7750i	0.732338	−	1.26845i	0.955882	−	0.293752i	$-0.0949041\pi$
$710$		0			0
$711$	1.00000			0.0375029
$712$	−9.00000	+	15.5885i	−0.337289	+	0.584202i
$713$	−6.00000	+	10.3923i	−0.224702	+	0.389195i
$714$	4.00000			0.149696
$715$		0			0
$716$	6.00000	−	10.3923i	0.224231	−	0.388379i
$717$	−6.00000	−	10.3923i	−0.224074	−	0.388108i
$718$	10.0000	−	17.3205i	0.373197	−	0.646396i
$719$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$719$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$720$		0			0
$721$	13.0000			0.484145
$722$	5.50000	−	18.1865i	0.204689	−	0.676833i
$723$	7.00000			0.260333
$724$	−1.00000	−	1.73205i	−0.0371647	−	0.0643712i
$725$	−20.0000	−	34.6410i	−0.742781	−	1.28654i
$726$	−3.50000	+	6.06218i	−0.129897	+	0.224989i
$727$	23.5000	+	40.7032i	0.871567	+	1.50960i	0.860376	+	0.509661i	$0.170229\pi$
$727$	23.5000	+	40.7032i	0.871567	+	1.50960i	0.0111912	+	0.999937i	$0.496438\pi$
$728$	7.50000	−	12.9904i	0.277968	−	0.481456i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−2.00000	+	3.46410i	−0.0739727	+	0.128124i
$732$	6.50000	−	11.2583i	0.240247	−	0.416120i
$733$	−50.0000			−1.84679			−0.923396	−	0.383849i	$-0.874598\pi$
$733$	−50.0000			−1.84679			−0.923396	+	0.383849i	$0.874598\pi$
$734$	7.00000			0.258375
$735$		0			0
$736$	10.0000	+	17.3205i	0.368605	+	0.638442i
$737$	11.0000	−	19.0526i	0.405190	−	0.701810i
$738$	6.00000	+	10.3923i	0.220863	+	0.382546i
$739$	−9.50000	−	16.4545i	−0.349463	−	0.605288i	0.636691	−	0.771119i	$-0.280303\pi$
$739$	−9.50000	−	16.4545i	−0.349463	−	0.605288i	−0.986154	+	0.165831i	$0.946969\pi$
$740$		0			0
$741$	20.0000	+	8.66025i	0.734718	+	0.318142i
$742$	4.00000			0.146845
$743$	25.0000	+	43.3013i	0.917161	+	1.58857i	0.803706	+	0.595026i	$0.202858\pi$
$743$	25.0000	+	43.3013i	0.917161	+	1.58857i	0.113455	+	0.993543i	$0.463808\pi$
$744$	4.50000	+	7.79423i	0.164978	+	0.285750i
$745$		0			0
$746$	−5.00000	−	8.66025i	−0.183063	−	0.317074i
$747$		0			0
$748$	−8.00000			−0.292509
$749$	−18.0000			−0.657706
$750$		0			0
$751$	−22.5000	+	38.9711i	−0.821037	+	1.42208i	0.0838743	+	0.996476i	$0.473271\pi$
$751$	−22.5000	+	38.9711i	−0.821037	+	1.42208i	−0.904911	+	0.425601i	$0.860063\pi$
$752$	6.00000			0.218797
$753$	2.00000			0.0728841
$754$	20.0000	−	34.6410i	0.728357	−	1.26155i
$755$		0			0
$756$	−0.500000	+	0.866025i	−0.0181848	+	0.0314970i
$757$	−6.50000	−	11.2583i	−0.236247	−	0.409191i	0.723388	−	0.690442i	$-0.242584\pi$
$757$	−6.50000	−	11.2583i	−0.236247	−	0.409191i	−0.959634	+	0.281251i	$0.909251\pi$
$758$	2.50000	+	4.33013i	0.0908041	+	0.157277i
$759$	−8.00000			−0.290382
$760$		0			0
$761$	6.00000			0.217500			0.108750	−	0.994069i	$-0.465315\pi$
$761$	6.00000			0.217500			0.108750	+	0.994069i	$0.465315\pi$
$762$	−4.00000	−	6.92820i	−0.144905	−	0.250982i
$763$	1.00000	+	1.73205i	0.0362024	+	0.0627044i
$764$	12.0000	−	20.7846i	0.434145	−	0.751961i
$765$		0			0
$766$	−7.00000	+	12.1244i	−0.252920	+	0.438071i
$767$	50.0000			1.80540
$768$	17.0000			0.613435
$769$	18.5000	−	32.0429i	0.667127	−	1.15550i	−0.311577	−	0.950221i	$-0.600857\pi$
$769$	18.5000	−	32.0429i	0.667127	−	1.15550i	0.978704	−	0.205277i	$-0.0658095\pi$
$770$		0			0
$771$	20.0000			0.720282
$772$	−19.0000			−0.683825
$773$	−7.00000	+	12.1244i	−0.251773	+	0.436083i	−0.964014	−	0.265852i	$-0.914347\pi$
$773$	−7.00000	+	12.1244i	−0.251773	+	0.436083i	0.712241	+	0.701935i	$0.247680\pi$
$774$	0.500000	+	0.866025i	0.0179721	+	0.0311286i
$775$	−7.50000	+	12.9904i	−0.269408	+	0.466628i
$776$	3.00000	+	5.19615i	0.107694	+	0.186531i
$777$	1.50000	+	2.59808i	0.0538122	+	0.0932055i

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:	\( N \)	\(=\)	\( 57 = 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	57.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +1.00000 q^{7} -3.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(0.500000 - 0.866025i) q^{4} +(0.500000 - 0.866025i) q^{6} +1.00000 q^{7} -3.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} -2.00000 q^{11} +1.00000 q^{12} +(-2.50000 + 4.33013i) q^{13} +(-0.500000 - 0.866025i) q^{14} +(0.500000 + 0.866025i) q^{16} +(2.00000 + 3.46410i) q^{17} +1.00000 q^{18} +(-4.00000 - 1.73205i) q^{19} +(0.500000 + 0.866025i) q^{21} +(1.00000 + 1.73205i) q^{22} +(2.00000 - 3.46410i) q^{23} +(-1.50000 - 2.59808i) q^{24} +(2.50000 - 4.33013i) q^{25} +5.00000 q^{26} -1.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +(4.00000 - 6.92820i) q^{29} -3.00000 q^{31} +(-2.50000 + 4.33013i) q^{32} +(-1.00000 - 1.73205i) q^{33} +(2.00000 - 3.46410i) q^{34} +(0.500000 + 0.866025i) q^{36} +3.00000 q^{37} +(0.500000 + 4.33013i) q^{38} -5.00000 q^{39} +(6.00000 + 10.3923i) q^{41} +(0.500000 - 0.866025i) q^{42} +(0.500000 + 0.866025i) q^{43} +(-1.00000 + 1.73205i) q^{44} -4.00000 q^{46} +(3.00000 - 5.19615i) q^{47} +(-0.500000 + 0.866025i) q^{48} -6.00000 q^{49} -5.00000 q^{50} +(-2.00000 + 3.46410i) q^{51} +(2.50000 + 4.33013i) q^{52} +(-2.00000 + 3.46410i) q^{53} +(0.500000 + 0.866025i) q^{54} -3.00000 q^{56} +(-0.500000 - 4.33013i) q^{57} -8.00000 q^{58} +(-5.00000 - 8.66025i) q^{59} +(6.50000 - 11.2583i) q^{61} +(1.50000 + 2.59808i) q^{62} +(-0.500000 + 0.866025i) q^{63} +7.00000 q^{64} +(-1.00000 + 1.73205i) q^{66} +(-5.50000 + 9.52628i) q^{67} +4.00000 q^{68} +4.00000 q^{69} +(-3.00000 - 5.19615i) q^{71} +(1.50000 - 2.59808i) q^{72} +(5.50000 + 9.52628i) q^{73} +(-1.50000 - 2.59808i) q^{74} +5.00000 q^{75} +(-3.50000 + 2.59808i) q^{76} -2.00000 q^{77} +(2.50000 + 4.33013i) q^{78} +(-0.500000 - 0.866025i) q^{79} +(-0.500000 - 0.866025i) q^{81} +(6.00000 - 10.3923i) q^{82} +1.00000 q^{84} +(0.500000 - 0.866025i) q^{86} +8.00000 q^{87} +6.00000 q^{88} +(3.00000 - 5.19615i) q^{89} +(-2.50000 + 4.33013i) q^{91} +(-2.00000 - 3.46410i) q^{92} +(-1.50000 - 2.59808i) q^{93} -6.00000 q^{94} -5.00000 q^{96} +(-1.00000 - 1.73205i) q^{97} +(3.00000 + 5.19615i) q^{98} +(1.00000 - 1.73205i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + q^{3} + q^{4} + q^{6} + 2 q^{7} - 6 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 + q^3 + q^4 + q^6 + 2 * q^7 - 6 * q^8 - q^9	\( 2 q - q^{2} + q^{3} + q^{4} + q^{6} + 2 q^{7} - 6 q^{8} - q^{9} - 4 q^{11} + 2 q^{12} - 5 q^{13} - q^{14} + q^{16} + 4 q^{17} + 2 q^{18} - 8 q^{19} + q^{21} + 2 q^{22} + 4 q^{23} - 3 q^{24} + 5 q^{25} + 10 q^{26} - 2 q^{27} + q^{28} + 8 q^{29} - 6 q^{31} - 5 q^{32} - 2 q^{33} + 4 q^{34} + q^{36} + 6 q^{37} + q^{38} - 10 q^{39} + 12 q^{41} + q^{42} + q^{43} - 2 q^{44} - 8 q^{46} + 6 q^{47} - q^{48} - 12 q^{49} - 10 q^{50} - 4 q^{51} + 5 q^{52} - 4 q^{53} + q^{54} - 6 q^{56} - q^{57} - 16 q^{58} - 10 q^{59} + 13 q^{61} + 3 q^{62} - q^{63} + 14 q^{64} - 2 q^{66} - 11 q^{67} + 8 q^{68} + 8 q^{69} - 6 q^{71} + 3 q^{72} + 11 q^{73} - 3 q^{74} + 10 q^{75} - 7 q^{76} - 4 q^{77} + 5 q^{78} - q^{79} - q^{81} + 12 q^{82} + 2 q^{84} + q^{86} + 16 q^{87} + 12 q^{88} + 6 q^{89} - 5 q^{91} - 4 q^{92} - 3 q^{93} - 12 q^{94} - 10 q^{96} - 2 q^{97} + 6 q^{98} + 2 q^{99}+O(q^{100}) \) 2 * q - q^2 + q^3 + q^4 + q^6 + 2 * q^7 - 6 * q^8 - q^9 - 4 * q^11 + 2 * q^12 - 5 * q^13 - q^14 + q^16 + 4 * q^17 + 2 * q^18 - 8 * q^19 + q^21 + 2 * q^22 + 4 * q^23 - 3 * q^24 + 5 * q^25 + 10 * q^26 - 2 * q^27 + q^28 + 8 * q^29 - 6 * q^31 - 5 * q^32 - 2 * q^33 + 4 * q^34 + q^36 + 6 * q^37 + q^38 - 10 * q^39 + 12 * q^41 + q^42 + q^43 - 2 * q^44 - 8 * q^46 + 6 * q^47 - q^48 - 12 * q^49 - 10 * q^50 - 4 * q^51 + 5 * q^52 - 4 * q^53 + q^54 - 6 * q^56 - q^57 - 16 * q^58 - 10 * q^59 + 13 * q^61 + 3 * q^62 - q^63 + 14 * q^64 - 2 * q^66 - 11 * q^67 + 8 * q^68 + 8 * q^69 - 6 * q^71 + 3 * q^72 + 11 * q^73 - 3 * q^74 + 10 * q^75 - 7 * q^76 - 4 * q^77 + 5 * q^78 - q^79 - q^81 + 12 * q^82 + 2 * q^84 + q^86 + 16 * q^87 + 12 * q^88 + 6 * q^89 - 5 * q^91 - 4 * q^92 - 3 * q^93 - 12 * q^94 - 10 * q^96 - 2 * q^97 + 6 * q^98 + 2 * q^99

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