LMFDB - Embedded newform 546.2.l.a.211.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(211,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, 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("546.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.l (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:	$4.35983195036$
Analytic rank:	$1$
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			211.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	546.211
Dual form			546.2.l.a.295.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.50000 - 2.59808i) q^{11} +1.00000 q^{12} +(-3.50000 - 0.866025i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +1.00000 q^{18} +(-2.50000 + 4.33013i) q^{19} +1.00000 q^{21} +(-1.50000 + 2.59808i) q^{22} +(-3.00000 - 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{24} -5.00000 q^{25} +(1.00000 + 3.46410i) q^{26} +1.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} +(1.50000 + 2.59808i) q^{29} -4.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} +3.00000 q^{34} +(-0.500000 - 0.866025i) q^{36} +(2.00000 + 3.46410i) q^{37} +5.00000 q^{38} +(1.00000 + 3.46410i) q^{39} +(1.50000 + 2.59808i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(-4.00000 + 6.92820i) q^{43} +3.00000 q^{44} +(-3.00000 + 5.19615i) q^{46} +9.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(2.50000 + 4.33013i) q^{50} +3.00000 q^{51} +(2.50000 - 2.59808i) q^{52} -9.00000 q^{53} +(-0.500000 - 0.866025i) q^{54} +(-0.500000 + 0.866025i) q^{56} +5.00000 q^{57} +(1.50000 - 2.59808i) q^{58} +(3.00000 - 5.19615i) q^{59} +(-2.50000 + 4.33013i) q^{61} +(2.00000 + 3.46410i) q^{62} +(-0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +3.00000 q^{66} +(-7.00000 - 12.1244i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(-3.00000 + 5.19615i) q^{69} +(3.00000 - 5.19615i) q^{71} +(-0.500000 + 0.866025i) q^{72} -4.00000 q^{73} +(2.00000 - 3.46410i) q^{74} +(2.50000 + 4.33013i) q^{75} +(-2.50000 - 4.33013i) q^{76} +3.00000 q^{77} +(2.50000 - 2.59808i) q^{78} -1.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(1.50000 - 2.59808i) q^{82} -6.00000 q^{83} +(-0.500000 + 0.866025i) q^{84} +8.00000 q^{86} +(1.50000 - 2.59808i) q^{87} +(-1.50000 - 2.59808i) q^{88} +(4.50000 + 7.79423i) q^{89} +(2.50000 - 2.59808i) q^{91} +6.00000 q^{92} +(2.00000 + 3.46410i) q^{93} +(-4.50000 - 7.79423i) q^{94} +1.00000 q^{96} +(-4.00000 + 6.92820i) q^{97} +(-0.500000 + 0.866025i) q^{98} +3.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - q^{3} - q^{4} - q^{6} - q^{7} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q - q^2 - q^3 - q^4 - q^6 - q^7 + 2 * q^8 - q^9	$ 2 q - q^{2} - q^{3} - q^{4} - q^{6} - q^{7} + 2 q^{8} - q^{9} - 3 q^{11} + 2 q^{12} - 7 q^{13} + 2 q^{14} - q^{16} - 3 q^{17} + 2 q^{18} - 5 q^{19} + 2 q^{21} - 3 q^{22} - 6 q^{23} - q^{24} - 10 q^{25} + 2 q^{26} + 2 q^{27} - q^{28} + 3 q^{29} - 8 q^{31} - q^{32} - 3 q^{33} + 6 q^{34} - q^{36} + 4 q^{37} + 10 q^{38} + 2 q^{39} + 3 q^{41} - q^{42} - 8 q^{43} + 6 q^{44} - 6 q^{46} + 18 q^{47} - q^{48} - q^{49} + 5 q^{50} + 6 q^{51} + 5 q^{52} - 18 q^{53} - q^{54} - q^{56} + 10 q^{57} + 3 q^{58} + 6 q^{59} - 5 q^{61} + 4 q^{62} - q^{63} + 2 q^{64} + 6 q^{66} - 14 q^{67} - 3 q^{68} - 6 q^{69} + 6 q^{71} - q^{72} - 8 q^{73} + 4 q^{74} + 5 q^{75} - 5 q^{76} + 6 q^{77} + 5 q^{78} - 2 q^{79} - q^{81} + 3 q^{82} - 12 q^{83} - q^{84} + 16 q^{86} + 3 q^{87} - 3 q^{88} + 9 q^{89} + 5 q^{91} + 12 q^{92} + 4 q^{93} - 9 q^{94} + 2 q^{96} - 8 q^{97} - q^{98} + 6 q^{99}+O(q^{100}) $ 2 * q - q^2 - q^3 - q^4 - q^6 - q^7 + 2 * q^8 - q^9 - 3 * q^11 + 2 * q^12 - 7 * q^13 + 2 * q^14 - q^16 - 3 * q^17 + 2 * q^18 - 5 * q^19 + 2 * q^21 - 3 * q^22 - 6 * q^23 - q^24 - 10 * q^25 + 2 * q^26 + 2 * q^27 - q^28 + 3 * q^29 - 8 * q^31 - q^32 - 3 * q^33 + 6 * q^34 - q^36 + 4 * q^37 + 10 * q^38 + 2 * q^39 + 3 * q^41 - q^42 - 8 * q^43 + 6 * q^44 - 6 * q^46 + 18 * q^47 - q^48 - q^49 + 5 * q^50 + 6 * q^51 + 5 * q^52 - 18 * q^53 - q^54 - q^56 + 10 * q^57 + 3 * q^58 + 6 * q^59 - 5 * q^61 + 4 * q^62 - q^63 + 2 * q^64 + 6 * q^66 - 14 * q^67 - 3 * q^68 - 6 * q^69 + 6 * q^71 - q^72 - 8 * q^73 + 4 * q^74 + 5 * q^75 - 5 * q^76 + 6 * q^77 + 5 * q^78 - 2 * q^79 - q^81 + 3 * q^82 - 12 * q^83 - q^84 + 16 * q^86 + 3 * q^87 - 3 * q^88 + 9 * q^89 + 5 * q^91 + 12 * q^92 + 4 * q^93 - 9 * q^94 + 2 * q^96 - 8 * q^97 - q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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
$2$	−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			0			−	1.00000i	$-0.5\pi$
$5$		0			0				1.00000i	$0.5\pi$
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$7$	−0.500000	+	0.866025i	−0.188982	+	0.327327i
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	0.546259	−	0.837616i	$-0.316051\pi$
$11$	−1.50000	−	2.59808i	−0.452267	−	0.783349i	−0.998526	+	0.0542666i	$0.982718\pi$
$12$	1.00000			0.288675
$13$	−3.50000	−	0.866025i	−0.970725	−	0.240192i
$13$	−3.50000	−	0.866025i	−0.970725	−	0.240192i
$14$	1.00000			0.267261
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	−0.988583	−	0.150675i	$-0.951855\pi$
$17$	−1.50000	+	2.59808i	−0.363803	+	0.630126i	0.624780	+	0.780801i	$0.285189\pi$
$18$	1.00000			0.235702
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	0.422659	+	0.906289i	$0.361097\pi$
$19$	−2.50000	+	4.33013i	−0.573539	+	0.993399i	−0.996199	+	0.0871106i	$0.972237\pi$
$20$		0			0
$21$	1.00000			0.218218
$22$	−1.50000	+	2.59808i	−0.319801	+	0.553912i
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	−0.988436	−	0.151642i	$-0.951544\pi$
$23$	−3.00000	−	5.19615i	−0.625543	−	1.08347i	0.362892	−	0.931831i	$-0.381789\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−5.00000			−1.00000
$26$	1.00000	+	3.46410i	0.196116	+	0.679366i
$27$	1.00000			0.192450
$28$	−0.500000	−	0.866025i	−0.0944911	−	0.163663i
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	0.971023	−	0.238987i	$-0.0768152\pi$
$29$	1.50000	+	2.59808i	0.278543	+	0.482451i	−0.692480	+	0.721437i	$0.743482\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	−1.50000	+	2.59808i	−0.261116	+	0.452267i
$34$	3.00000			0.514496
$35$		0			0
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	0.982274	−	0.187453i	$-0.0600231\pi$
$37$	2.00000	+	3.46410i	0.328798	+	0.569495i	−0.653476	+	0.756948i	$0.726690\pi$
$38$	5.00000			0.811107
$39$	1.00000	+	3.46410i	0.160128	+	0.554700i
$40$		0			0
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	0.959058	−	0.283211i	$-0.0913998\pi$
$41$	1.50000	+	2.59808i	0.234261	+	0.405751i	−0.724797	+	0.688963i	$0.758066\pi$
$42$	−0.500000	−	0.866025i	−0.0771517	−	0.133631i
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	0.381246	+	0.924473i	$0.375495\pi$
$43$	−4.00000	+	6.92820i	−0.609994	+	1.05654i	−0.991241	+	0.132068i	$0.957838\pi$
$44$	3.00000			0.452267
$45$		0			0
$46$	−3.00000	+	5.19615i	−0.442326	+	0.766131i
$47$	9.00000			1.31278			0.656392	−	0.754420i	$-0.272082\pi$
$47$	9.00000			1.31278			0.656392	+	0.754420i	$0.272082\pi$
$48$	−0.500000	+	0.866025i	−0.0721688	+	0.125000i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	2.50000	+	4.33013i	0.353553	+	0.612372i
$51$	3.00000			0.420084
$52$	2.50000	−	2.59808i	0.346688	−	0.360288i
$53$	−9.00000			−1.23625			−0.618123	−	0.786082i	$-0.712106\pi$
$53$	−9.00000			−1.23625			−0.618123	+	0.786082i	$0.712106\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$		0			0
$56$	−0.500000	+	0.866025i	−0.0668153	+	0.115728i
$57$	5.00000			0.662266
$58$	1.50000	−	2.59808i	0.196960	−	0.341144i
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	−0.601958	−	0.798528i	$-0.705612\pi$
$59$	3.00000	−	5.19615i	0.390567	−	0.676481i	0.992524	+	0.122047i	$0.0389457\pi$
$60$		0			0
$61$	−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	$0.270381\pi$
$62$	2.00000	+	3.46410i	0.254000	+	0.439941i
$63$	−0.500000	−	0.866025i	−0.0629941	−	0.109109i
$64$	1.00000			0.125000
$65$		0			0
$66$	3.00000			0.369274
$67$	−7.00000	−	12.1244i	−0.855186	−	1.48123i	−0.876472	−	0.481452i	$-0.840109\pi$
$67$	−7.00000	−	12.1244i	−0.855186	−	1.48123i	0.0212861	−	0.999773i	$-0.493224\pi$
$68$	−1.50000	−	2.59808i	−0.181902	−	0.315063i
$69$	−3.00000	+	5.19615i	−0.361158	+	0.625543i
$70$		0			0
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	−0.631260	−	0.775571i	$-0.717462\pi$
$71$	3.00000	−	5.19615i	0.356034	−	0.616670i	0.987294	+	0.158901i	$0.0507952\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−4.00000			−0.468165			−0.234082	−	0.972217i	$-0.575209\pi$
$73$	−4.00000			−0.468165			−0.234082	+	0.972217i	$0.575209\pi$
$74$	2.00000	−	3.46410i	0.232495	−	0.402694i
$75$	2.50000	+	4.33013i	0.288675	+	0.500000i
$76$	−2.50000	−	4.33013i	−0.286770	−	0.496700i
$77$	3.00000			0.341882
$78$	2.50000	−	2.59808i	0.283069	−	0.294174i
$79$	−1.00000			−0.112509			−0.0562544	−	0.998416i	$-0.517916\pi$
$79$	−1.00000			−0.112509			−0.0562544	+	0.998416i	$0.517916\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.50000	−	2.59808i	0.165647	−	0.286910i
$83$	−6.00000			−0.658586			−0.329293	−	0.944228i	$-0.606810\pi$
$83$	−6.00000			−0.658586			−0.329293	+	0.944228i	$0.606810\pi$
$84$	−0.500000	+	0.866025i	−0.0545545	+	0.0944911i
$85$		0			0
$86$	8.00000			0.862662
$87$	1.50000	−	2.59808i	0.160817	−	0.278543i
$88$	−1.50000	−	2.59808i	−0.159901	−	0.276956i
$89$	4.50000	+	7.79423i	0.476999	+	0.826187i	0.999653	−	0.0263586i	$-0.00839118\pi$
$89$	4.50000	+	7.79423i	0.476999	+	0.826187i	−0.522654	+	0.852545i	$0.675058\pi$
$90$		0			0
$91$	2.50000	−	2.59808i	0.262071	−	0.272352i
$92$	6.00000			0.625543
$93$	2.00000	+	3.46410i	0.207390	+	0.359211i
$94$	−4.50000	−	7.79423i	−0.464140	−	0.803913i
$95$		0			0
$96$	1.00000			0.102062
$97$	−4.00000	+	6.92820i	−0.406138	+	0.703452i	−0.994453	−	0.105180i	$-0.966458\pi$
$97$	−4.00000	+	6.92820i	−0.406138	+	0.703452i	0.588315	+	0.808632i	$0.299792\pi$
$98$	−0.500000	+	0.866025i	−0.0505076	+	0.0874818i
$99$	3.00000			0.301511
$100$	2.50000	−	4.33013i	0.250000	−	0.433013i
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	0.677284	−	0.735721i	$-0.263157\pi$
$101$	−3.00000	−	5.19615i	−0.298511	−	0.517036i	−0.975796	+	0.218685i	$0.929823\pi$
$102$	−1.50000	−	2.59808i	−0.148522	−	0.257248i
$103$	8.00000			0.788263			0.394132	−	0.919054i	$-0.371045\pi$
$103$	8.00000			0.788263			0.394132	+	0.919054i	$0.371045\pi$
$104$	−3.50000	−	0.866025i	−0.343203	−	0.0849208i
$105$		0			0
$106$	4.50000	+	7.79423i	0.437079	+	0.757042i
$107$	−7.50000	−	12.9904i	−0.725052	−	1.25583i	−0.958952	−	0.283567i	$-0.908482\pi$
$107$	−7.50000	−	12.9904i	−0.725052	−	1.25583i	0.233900	−	0.972261i	$-0.424851\pi$
$108$	−0.500000	+	0.866025i	−0.0481125	+	0.0833333i
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$		0			0
$111$	2.00000	−	3.46410i	0.189832	−	0.328798i
$112$	1.00000			0.0944911
$113$	6.00000	−	10.3923i	0.564433	−	0.977626i	−0.432670	−	0.901553i	$-0.642428\pi$
$113$	6.00000	−	10.3923i	0.564433	−	0.977626i	0.997102	−	0.0760733i	$-0.0242383\pi$
$114$	−2.50000	−	4.33013i	−0.234146	−	0.405554i
$115$		0			0
$116$	−3.00000			−0.278543
$117$	2.50000	−	2.59808i	0.231125	−	0.240192i
$118$	−6.00000			−0.552345
$119$	−1.50000	−	2.59808i	−0.137505	−	0.238165i
$120$		0			0
$121$	1.00000	−	1.73205i	0.0909091	−	0.157459i
$122$	5.00000			0.452679
$123$	1.50000	−	2.59808i	0.135250	−	0.234261i
$124$	2.00000	−	3.46410i	0.179605	−	0.311086i
$125$		0			0
$126$	−0.500000	+	0.866025i	−0.0445435	+	0.0771517i
$127$	−4.00000	−	6.92820i	−0.354943	−	0.614779i	0.632166	−	0.774833i	$-0.282166\pi$
$127$	−4.00000	−	6.92820i	−0.354943	−	0.614779i	−0.987108	+	0.160055i	$0.948833\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	8.00000			0.704361
$130$		0			0
$131$		0			0			−	1.00000i	$-0.5\pi$
$131$		0			0				1.00000i	$0.5\pi$
$132$	−1.50000	−	2.59808i	−0.130558	−	0.226134i
$133$	−2.50000	−	4.33013i	−0.216777	−	0.375470i
$134$	−7.00000	+	12.1244i	−0.604708	+	1.04738i
$135$		0			0
$136$	−1.50000	+	2.59808i	−0.128624	+	0.222783i
$137$	9.00000	−	15.5885i	0.768922	−	1.33181i	−0.169226	−	0.985577i	$-0.554127\pi$
$137$	9.00000	−	15.5885i	0.768922	−	1.33181i	0.938148	−	0.346235i	$-0.112540\pi$
$138$	6.00000			0.510754
$139$	6.50000	−	11.2583i	0.551323	−	0.954919i	−0.446857	−	0.894606i	$-0.647457\pi$
$139$	6.50000	−	11.2583i	0.551323	−	0.954919i	0.998179	−	0.0603135i	$-0.0192101\pi$
$140$		0			0
$141$	−4.50000	−	7.79423i	−0.378968	−	0.656392i
$142$	−6.00000			−0.503509
$143$	3.00000	+	10.3923i	0.250873	+	0.869048i
$144$	1.00000			0.0833333
$145$		0			0
$146$	2.00000	+	3.46410i	0.165521	+	0.286691i
$147$	−0.500000	+	0.866025i	−0.0412393	+	0.0714286i
$148$	−4.00000			−0.328798
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	−0.962348	−	0.271821i	$-0.912374\pi$
$149$	−3.00000	+	5.19615i	−0.245770	+	0.425685i	0.716578	+	0.697507i	$0.245707\pi$
$150$	2.50000	−	4.33013i	0.204124	−	0.353553i
$151$	17.0000			1.38344			0.691720	−	0.722166i	$-0.256853\pi$
$151$	17.0000			1.38344			0.691720	+	0.722166i	$0.256853\pi$
$152$	−2.50000	+	4.33013i	−0.202777	+	0.351220i
$153$	−1.50000	−	2.59808i	−0.121268	−	0.210042i
$154$	−1.50000	−	2.59808i	−0.120873	−	0.209359i
$155$		0			0
$156$	−3.50000	−	0.866025i	−0.280224	−	0.0693375i
$157$	−22.0000			−1.75579			−0.877896	−	0.478852i	$-0.841053\pi$
$157$	−22.0000			−1.75579			−0.877896	+	0.478852i	$0.841053\pi$
$158$	0.500000	+	0.866025i	0.0397779	+	0.0688973i
$159$	4.50000	+	7.79423i	0.356873	+	0.618123i
$160$		0			0
$161$	6.00000			0.472866
$162$	−0.500000	+	0.866025i	−0.0392837	+	0.0680414i
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	−0.361619	−	0.932326i	$-0.617776\pi$
$163$	8.00000	−	13.8564i	0.626608	−	1.08532i	0.988227	−	0.152992i	$-0.0488907\pi$
$164$	−3.00000			−0.234261
$165$		0			0
$166$	3.00000	+	5.19615i	0.232845	+	0.403300i
$167$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$167$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$168$	1.00000			0.0771517
$169$	11.5000	+	6.06218i	0.884615	+	0.466321i
$170$		0			0
$171$	−2.50000	−	4.33013i	−0.191180	−	0.331133i
$172$	−4.00000	−	6.92820i	−0.304997	−	0.528271i
$173$	−9.00000	+	15.5885i	−0.684257	+	1.18517i	0.289412	+	0.957205i	$0.406540\pi$
$173$	−9.00000	+	15.5885i	−0.684257	+	1.18517i	−0.973670	+	0.227964i	$0.926793\pi$
$174$	−3.00000			−0.227429
$175$	2.50000	−	4.33013i	0.188982	−	0.327327i
$176$	−1.50000	+	2.59808i	−0.113067	+	0.195837i
$177$	−6.00000			−0.450988
$178$	4.50000	−	7.79423i	0.337289	−	0.584202i
$179$	−12.0000	−	20.7846i	−0.896922	−	1.55351i	−0.831408	−	0.555663i	$-0.812464\pi$
$179$	−12.0000	−	20.7846i	−0.896922	−	1.55351i	−0.0655145	−	0.997852i	$-0.520869\pi$
$180$		0			0
$181$	17.0000			1.26360			0.631800	−	0.775131i	$-0.282316\pi$
$181$	17.0000			1.26360			0.631800	+	0.775131i	$0.282316\pi$
$182$	−3.50000	−	0.866025i	−0.259437	−	0.0641941i
$183$	5.00000			0.369611
$184$	−3.00000	−	5.19615i	−0.221163	−	0.383065i
$185$		0			0
$186$	2.00000	−	3.46410i	0.146647	−	0.254000i
$187$	9.00000			0.658145
$188$	−4.50000	+	7.79423i	−0.328196	+	0.568453i
$189$	−0.500000	+	0.866025i	−0.0363696	+	0.0629941i
$190$		0			0
$191$	−9.00000	+	15.5885i	−0.651217	+	1.12794i	0.331611	+	0.943416i	$0.392408\pi$
$191$	−9.00000	+	15.5885i	−0.651217	+	1.12794i	−0.982828	+	0.184525i	$0.940925\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	9.50000	+	16.4545i	0.683825	+	1.18442i	0.973805	+	0.227387i	$0.0730182\pi$
$193$	9.50000	+	16.4545i	0.683825	+	1.18442i	−0.289980	+	0.957033i	$0.593649\pi$
$194$	8.00000			0.574367
$195$		0			0
$196$	1.00000			0.0714286
$197$	4.50000	+	7.79423i	0.320612	+	0.555316i	0.980614	−	0.195947i	$-0.0627782\pi$
$197$	4.50000	+	7.79423i	0.320612	+	0.555316i	−0.660003	+	0.751263i	$0.729445\pi$
$198$	−1.50000	−	2.59808i	−0.106600	−	0.184637i
$199$	−10.0000	+	17.3205i	−0.708881	+	1.22782i	0.256391	+	0.966573i	$0.417466\pi$
$199$	−10.0000	+	17.3205i	−0.708881	+	1.22782i	−0.965272	+	0.261245i	$0.915867\pi$
$200$	−5.00000			−0.353553
$201$	−7.00000	+	12.1244i	−0.493742	+	0.855186i
$202$	−3.00000	+	5.19615i	−0.211079	+	0.365600i
$203$	−3.00000			−0.210559
$204$	−1.50000	+	2.59808i	−0.105021	+	0.181902i
$205$		0			0
$206$	−4.00000	−	6.92820i	−0.278693	−	0.482711i
$207$	6.00000			0.417029
$208$	1.00000	+	3.46410i	0.0693375	+	0.240192i
$209$	15.0000			1.03757
$210$		0			0
$211$	5.00000	+	8.66025i	0.344214	+	0.596196i	0.985211	−	0.171347i	$-0.0548120\pi$
$211$	5.00000	+	8.66025i	0.344214	+	0.596196i	−0.640996	+	0.767544i	$0.721479\pi$
$212$	4.50000	−	7.79423i	0.309061	−	0.535310i
$213$	−6.00000			−0.411113
$214$	−7.50000	+	12.9904i	−0.512689	+	0.888004i
$215$		0			0
$216$	1.00000			0.0680414
$217$	2.00000	−	3.46410i	0.135769	−	0.235159i
$218$	5.00000	+	8.66025i	0.338643	+	0.586546i
$219$	2.00000	+	3.46410i	0.135147	+	0.234082i
$220$		0			0
$221$	7.50000	−	7.79423i	0.504505	−	0.524297i
$222$	−4.00000			−0.268462
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	0.700449	−	0.713702i	$-0.252983\pi$
$223$	−4.00000	−	6.92820i	−0.267860	−	0.463947i	−0.968309	+	0.249756i	$0.919650\pi$
$224$	−0.500000	−	0.866025i	−0.0334077	−	0.0578638i
$225$	2.50000	−	4.33013i	0.166667	−	0.288675i
$226$	−12.0000			−0.798228
$227$	9.00000	−	15.5885i	0.597351	−	1.03464i	−0.395860	−	0.918311i	$-0.629553\pi$
$227$	9.00000	−	15.5885i	0.597351	−	1.03464i	0.993210	−	0.116331i	$-0.0371134\pi$
$228$	−2.50000	+	4.33013i	−0.165567	+	0.286770i
$229$	17.0000			1.12339			0.561696	−	0.827344i	$-0.310149\pi$
$229$	17.0000			1.12339			0.561696	+	0.827344i	$0.310149\pi$
$230$		0			0
$231$	−1.50000	−	2.59808i	−0.0986928	−	0.170941i
$232$	1.50000	+	2.59808i	0.0984798	+	0.170572i
$233$	−12.0000			−0.786146			−0.393073	−	0.919507i	$-0.628588\pi$
$233$	−12.0000			−0.786146			−0.393073	+	0.919507i	$0.628588\pi$
$234$	−3.50000	−	0.866025i	−0.228802	−	0.0566139i
$235$		0			0
$236$	3.00000	+	5.19615i	0.195283	+	0.338241i
$237$	0.500000	+	0.866025i	0.0324785	+	0.0562544i
$238$	−1.50000	+	2.59808i	−0.0972306	+	0.168408i
$239$	6.00000			0.388108			0.194054	−	0.980991i	$-0.437836\pi$
$239$	6.00000			0.388108			0.194054	+	0.980991i	$0.437836\pi$
$240$		0			0
$241$	−4.00000	+	6.92820i	−0.257663	+	0.446285i	−0.965615	−	0.259975i	$-0.916286\pi$
$241$	−4.00000	+	6.92820i	−0.257663	+	0.446285i	0.707953	+	0.706260i	$0.249619\pi$
$242$	−2.00000			−0.128565
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−2.50000	−	4.33013i	−0.160046	−	0.277208i
$245$		0			0
$246$	−3.00000			−0.191273
$247$	12.5000	−	12.9904i	0.795356	−	0.826558i
$248$	−4.00000			−0.254000
$249$	3.00000	+	5.19615i	0.190117	+	0.329293i
$250$		0			0
$251$	−15.0000	+	25.9808i	−0.946792	+	1.63989i	−0.194668	+	0.980869i	$0.562363\pi$
$251$	−15.0000	+	25.9808i	−0.946792	+	1.63989i	−0.752124	+	0.659022i	$0.770970\pi$
$252$	1.00000			0.0629941
$253$	−9.00000	+	15.5885i	−0.565825	+	0.980038i
$254$	−4.00000	+	6.92820i	−0.250982	+	0.434714i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−7.50000	−	12.9904i	−0.467837	−	0.810318i	0.531487	−	0.847066i	$-0.321633\pi$
$257$	−7.50000	−	12.9904i	−0.467837	−	0.810318i	−0.999325	+	0.0367485i	$0.988300\pi$
$258$	−4.00000	−	6.92820i	−0.249029	−	0.431331i
$259$	−4.00000			−0.248548
$260$		0			0
$261$	−3.00000			−0.185695
$262$		0			0
$263$	−9.00000	−	15.5885i	−0.554964	−	0.961225i	−0.997906	−	0.0646755i	$-0.979399\pi$
$263$	−9.00000	−	15.5885i	−0.554964	−	0.961225i	0.442943	−	0.896550i	$-0.353935\pi$
$264$	−1.50000	+	2.59808i	−0.0923186	+	0.159901i
$265$		0			0
$266$	−2.50000	+	4.33013i	−0.153285	+	0.265497i
$267$	4.50000	−	7.79423i	0.275396	−	0.476999i
$268$	14.0000			0.855186
$269$	−12.0000	+	20.7846i	−0.731653	+	1.26726i	0.224523	+	0.974469i	$0.427917\pi$
$269$	−12.0000	+	20.7846i	−0.731653	+	1.26726i	−0.956176	+	0.292791i	$0.905416\pi$
$270$		0			0
$271$	14.0000	+	24.2487i	0.850439	+	1.47300i	0.880812	+	0.473466i	$0.156997\pi$
$271$	14.0000	+	24.2487i	0.850439	+	1.47300i	−0.0303728	+	0.999539i	$0.509669\pi$
$272$	3.00000			0.181902
$273$	−3.50000	−	0.866025i	−0.211830	−	0.0524142i
$274$	−18.0000			−1.08742
$275$	7.50000	+	12.9904i	0.452267	+	0.783349i
$276$	−3.00000	−	5.19615i	−0.180579	−	0.312772i
$277$	−1.00000	+	1.73205i	−0.0600842	+	0.104069i	−0.894503	−	0.447062i	$-0.852470\pi$
$277$	−1.00000	+	1.73205i	−0.0600842	+	0.104069i	0.834419	+	0.551131i	$0.185804\pi$
$278$	−13.0000			−0.779688
$279$	2.00000	−	3.46410i	0.119737	−	0.207390i
$280$		0			0
$281$	6.00000			0.357930			0.178965	−	0.983855i	$-0.442725\pi$
$281$	6.00000			0.357930			0.178965	+	0.983855i	$0.442725\pi$
$282$	−4.50000	+	7.79423i	−0.267971	+	0.464140i
$283$	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	$0.795400\pi$
$284$	3.00000	+	5.19615i	0.178017	+	0.308335i
$285$		0			0
$286$	7.50000	−	7.79423i	0.443484	−	0.460882i
$287$	−3.00000			−0.177084
$288$	−0.500000	−	0.866025i	−0.0294628	−	0.0510310i
$289$	4.00000	+	6.92820i	0.235294	+	0.407541i
$290$		0			0
$291$	8.00000			0.468968
$292$	2.00000	−	3.46410i	0.117041	−	0.202721i
$293$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$293$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$294$	1.00000			0.0583212
$295$		0			0
$296$	2.00000	+	3.46410i	0.116248	+	0.201347i
$297$	−1.50000	−	2.59808i	−0.0870388	−	0.150756i
$298$	6.00000			0.347571
$299$	6.00000	+	20.7846i	0.346989	+	1.20201i
$300$	−5.00000			−0.288675
$301$	−4.00000	−	6.92820i	−0.230556	−	0.399335i
$302$	−8.50000	−	14.7224i	−0.489120	−	0.847181i
$303$	−3.00000	+	5.19615i	−0.172345	+	0.298511i
$304$	5.00000			0.286770
$305$		0			0
$306$	−1.50000	+	2.59808i	−0.0857493	+	0.148522i
$307$	11.0000			0.627803			0.313902	−	0.949456i	$-0.398364\pi$
$307$	11.0000			0.627803			0.313902	+	0.949456i	$0.398364\pi$
$308$	−1.50000	+	2.59808i	−0.0854704	+	0.148039i
$309$	−4.00000	−	6.92820i	−0.227552	−	0.394132i
$310$		0			0
$311$	−15.0000			−0.850572			−0.425286	−	0.905059i	$-0.639826\pi$
$311$	−15.0000			−0.850572			−0.425286	+	0.905059i	$0.639826\pi$
$312$	1.00000	+	3.46410i	0.0566139	+	0.196116i
$313$	−22.0000			−1.24351			−0.621757	−	0.783210i	$-0.713581\pi$
$313$	−22.0000			−1.24351			−0.621757	+	0.783210i	$0.713581\pi$
$314$	11.0000	+	19.0526i	0.620766	+	1.07520i
$315$		0			0
$316$	0.500000	−	0.866025i	0.0281272	−	0.0487177i
$317$	−6.00000			−0.336994			−0.168497	−	0.985702i	$-0.553891\pi$
$317$	−6.00000			−0.336994			−0.168497	+	0.985702i	$0.553891\pi$
$318$	4.50000	−	7.79423i	0.252347	−	0.437079i
$319$	4.50000	−	7.79423i	0.251952	−	0.436393i
$320$		0			0
$321$	−7.50000	+	12.9904i	−0.418609	+	0.725052i
$322$	−3.00000	−	5.19615i	−0.167183	−	0.289570i
$323$	−7.50000	−	12.9904i	−0.417311	−	0.722804i
$324$	1.00000			0.0555556
$325$	17.5000	+	4.33013i	0.970725	+	0.240192i
$326$	−16.0000			−0.886158
$327$	5.00000	+	8.66025i	0.276501	+	0.478913i
$328$	1.50000	+	2.59808i	0.0828236	+	0.143455i
$329$	−4.50000	+	7.79423i	−0.248093	+	0.429710i
$330$		0			0
$331$	5.00000	−	8.66025i	0.274825	−	0.476011i	−0.695266	−	0.718752i	$-0.744713\pi$
$331$	5.00000	−	8.66025i	0.274825	−	0.476011i	0.970091	+	0.242742i	$0.0780468\pi$
$332$	3.00000	−	5.19615i	0.164646	−	0.285176i
$333$	−4.00000			−0.219199
$334$		0			0
$335$		0			0
$336$	−0.500000	−	0.866025i	−0.0272772	−	0.0472456i
$337$	−25.0000			−1.36184			−0.680918	−	0.732359i	$-0.738419\pi$
$337$	−25.0000			−1.36184			−0.680918	+	0.732359i	$0.738419\pi$
$338$	−0.500000	−	12.9904i	−0.0271964	−	0.706584i
$339$	−12.0000			−0.651751
$340$		0			0
$341$	6.00000	+	10.3923i	0.324918	+	0.562775i
$342$	−2.50000	+	4.33013i	−0.135185	+	0.234146i
$343$	1.00000			0.0539949
$344$	−4.00000	+	6.92820i	−0.215666	+	0.373544i
$345$		0			0
$346$	18.0000			0.967686
$347$	13.5000	−	23.3827i	0.724718	−	1.25525i	−0.234372	−	0.972147i	$-0.575303\pi$
$347$	13.5000	−	23.3827i	0.724718	−	1.25525i	0.959090	−	0.283101i	$-0.0913633\pi$
$348$	1.50000	+	2.59808i	0.0804084	+	0.139272i
$349$	−1.00000	−	1.73205i	−0.0535288	−	0.0927146i	0.838019	−	0.545640i	$-0.183714\pi$
$349$	−1.00000	−	1.73205i	−0.0535288	−	0.0927146i	−0.891548	+	0.452926i	$0.850380\pi$
$350$	−5.00000			−0.267261
$351$	−3.50000	−	0.866025i	−0.186816	−	0.0462250i
$352$	3.00000			0.159901
$353$	9.00000	+	15.5885i	0.479022	+	0.829690i	0.999711	−	0.0240566i	$-0.00765819\pi$
$353$	9.00000	+	15.5885i	0.479022	+	0.829690i	−0.520689	+	0.853746i	$0.674325\pi$
$354$	3.00000	+	5.19615i	0.159448	+	0.276172i
$355$		0			0
$356$	−9.00000			−0.476999
$357$	−1.50000	+	2.59808i	−0.0793884	+	0.137505i
$358$	−12.0000	+	20.7846i	−0.634220	+	1.09850i
$359$	−12.0000			−0.633336			−0.316668	−	0.948536i	$-0.602564\pi$
$359$	−12.0000			−0.633336			−0.316668	+	0.948536i	$0.602564\pi$
$360$		0			0
$361$	−3.00000	−	5.19615i	−0.157895	−	0.273482i
$362$	−8.50000	−	14.7224i	−0.446750	−	0.773794i
$363$	−2.00000			−0.104973
$364$	1.00000	+	3.46410i	0.0524142	+	0.181568i
$365$		0			0
$366$	−2.50000	−	4.33013i	−0.130677	−	0.226339i
$367$	−1.00000	−	1.73205i	−0.0521996	−	0.0904123i	0.838745	−	0.544524i	$-0.183290\pi$
$367$	−1.00000	−	1.73205i	−0.0521996	−	0.0904123i	−0.890945	+	0.454112i	$0.849957\pi$
$368$	−3.00000	+	5.19615i	−0.156386	+	0.270868i
$369$	−3.00000			−0.156174
$370$		0			0
$371$	4.50000	−	7.79423i	0.233628	−	0.404656i
$372$	−4.00000			−0.207390
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	−0.988363	−	0.152115i	$-0.951392\pi$
$373$	−7.00000	+	12.1244i	−0.362446	+	0.627775i	0.625917	+	0.779890i	$0.284725\pi$
$374$	−4.50000	−	7.79423i	−0.232689	−	0.403030i
$375$		0			0
$376$	9.00000			0.464140
$377$	−3.00000	−	10.3923i	−0.154508	−	0.535231i
$378$	1.00000			0.0514344
$379$	17.0000	+	29.4449i	0.873231	+	1.51248i	0.858635	+	0.512588i	$0.171313\pi$
$379$	17.0000	+	29.4449i	0.873231	+	1.51248i	0.0145964	+	0.999893i	$0.495354\pi$
$380$		0			0
$381$	−4.00000	+	6.92820i	−0.204926	+	0.354943i
$382$	18.0000			0.920960
$383$	−4.50000	+	7.79423i	−0.229939	+	0.398266i	−0.957790	−	0.287469i	$-0.907186\pi$
$383$	−4.50000	+	7.79423i	−0.229939	+	0.398266i	0.727851	+	0.685736i	$0.240519\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$		0			0
$386$	9.50000	−	16.4545i	0.483537	−	0.837511i
$387$	−4.00000	−	6.92820i	−0.203331	−	0.352180i
$388$	−4.00000	−	6.92820i	−0.203069	−	0.351726i
$389$	−6.00000			−0.304212			−0.152106	−	0.988364i	$-0.548606\pi$
$389$	−6.00000			−0.304212			−0.152106	+	0.988364i	$0.548606\pi$
$390$		0			0
$391$	18.0000			0.910299
$392$	−0.500000	−	0.866025i	−0.0252538	−	0.0437409i
$393$		0			0
$394$	4.50000	−	7.79423i	0.226707	−	0.392668i
$395$		0			0
$396$	−1.50000	+	2.59808i	−0.0753778	+	0.130558i
$397$	18.5000	−	32.0429i	0.928488	−	1.60819i	0.142636	−	0.989775i	$-0.454442\pi$
$397$	18.5000	−	32.0429i	0.928488	−	1.60819i	0.785853	−	0.618414i	$-0.212224\pi$
$398$	20.0000			1.00251
$399$	−2.50000	+	4.33013i	−0.125157	+	0.216777i
$400$	2.50000	+	4.33013i	0.125000	+	0.216506i
$401$	−15.0000	−	25.9808i	−0.749064	−	1.29742i	−0.948272	−	0.317460i	$-0.897170\pi$
$401$	−15.0000	−	25.9808i	−0.749064	−	1.29742i	0.199207	−	0.979957i	$-0.436163\pi$
$402$	14.0000			0.698257
$403$	14.0000	+	3.46410i	0.697390	+	0.172559i
$404$	6.00000			0.298511
$405$		0			0
$406$	1.50000	+	2.59808i	0.0744438	+	0.128940i
$407$	6.00000	−	10.3923i	0.297409	−	0.515127i
$408$	3.00000			0.148522
$409$	−7.00000	+	12.1244i	−0.346128	+	0.599511i	−0.985558	−	0.169338i	$-0.945837\pi$
$409$	−7.00000	+	12.1244i	−0.346128	+	0.599511i	0.639430	+	0.768849i	$0.279170\pi$
$410$		0			0
$411$	−18.0000			−0.887875
$412$	−4.00000	+	6.92820i	−0.197066	+	0.341328i
$413$	3.00000	+	5.19615i	0.147620	+	0.255686i
$414$	−3.00000	−	5.19615i	−0.147442	−	0.255377i
$415$		0			0
$416$	2.50000	−	2.59808i	0.122573	−	0.127381i
$417$	−13.0000			−0.636613
$418$	−7.50000	−	12.9904i	−0.366837	−	0.635380i
$419$	−3.00000	−	5.19615i	−0.146560	−	0.253849i	0.783394	−	0.621525i	$-0.213487\pi$
$419$	−3.00000	−	5.19615i	−0.146560	−	0.253849i	−0.929954	+	0.367677i	$0.880153\pi$
$420$		0			0
$421$	−10.0000			−0.487370			−0.243685	−	0.969854i	$-0.578356\pi$
$421$	−10.0000			−0.487370			−0.243685	+	0.969854i	$0.578356\pi$
$422$	5.00000	−	8.66025i	0.243396	−	0.421575i
$423$	−4.50000	+	7.79423i	−0.218797	+	0.378968i
$424$	−9.00000			−0.437079
$425$	7.50000	−	12.9904i	0.363803	−	0.630126i
$426$	3.00000	+	5.19615i	0.145350	+	0.251754i
$427$	−2.50000	−	4.33013i	−0.120983	−	0.209550i
$428$	15.0000			0.725052
$429$	7.50000	−	7.79423i	0.362103	−	0.376309i
$430$		0			0
$431$	15.0000	+	25.9808i	0.722525	+	1.25145i	0.959985	+	0.280052i	$0.0903517\pi$
$431$	15.0000	+	25.9808i	0.722525	+	1.25145i	−0.237460	+	0.971397i	$0.576315\pi$
$432$	−0.500000	−	0.866025i	−0.0240563	−	0.0416667i
$433$	17.0000	−	29.4449i	0.816968	−	1.41503i	−0.0909384	−	0.995857i	$-0.528987\pi$
$433$	17.0000	−	29.4449i	0.816968	−	1.41503i	0.907906	−	0.419173i	$-0.137680\pi$
$434$	−4.00000			−0.192006
$435$		0			0
$436$	5.00000	−	8.66025i	0.239457	−	0.414751i
$437$	30.0000			1.43509
$438$	2.00000	−	3.46410i	0.0955637	−	0.165521i
$439$	2.00000	+	3.46410i	0.0954548	+	0.165333i	0.909798	−	0.415051i	$-0.136236\pi$
$439$	2.00000	+	3.46410i	0.0954548	+	0.165333i	−0.814344	+	0.580383i	$0.802903\pi$
$440$		0			0
$441$	1.00000			0.0476190
$442$	−10.5000	−	2.59808i	−0.499434	−	0.123578i
$443$	−9.00000			−0.427603			−0.213801	−	0.976877i	$-0.568585\pi$
$443$	−9.00000			−0.427603			−0.213801	+	0.976877i	$0.568585\pi$
$444$	2.00000	+	3.46410i	0.0949158	+	0.164399i
$445$		0			0
$446$	−4.00000	+	6.92820i	−0.189405	+	0.328060i
$447$	6.00000			0.283790
$448$	−0.500000	+	0.866025i	−0.0236228	+	0.0409159i
$449$	−6.00000	+	10.3923i	−0.283158	+	0.490443i	−0.972161	−	0.234315i	$-0.924715\pi$
$449$	−6.00000	+	10.3923i	−0.283158	+	0.490443i	0.689003	+	0.724758i	$0.258049\pi$
$450$	−5.00000			−0.235702
$451$	4.50000	−	7.79423i	0.211897	−	0.367016i
$452$	6.00000	+	10.3923i	0.282216	+	0.488813i
$453$	−8.50000	−	14.7224i	−0.399365	−	0.691720i
$454$	−18.0000			−0.844782
$455$		0			0
$456$	5.00000			0.234146
$457$	5.00000	+	8.66025i	0.233890	+	0.405110i	0.958950	−	0.283577i	$-0.0915211\pi$
$457$	5.00000	+	8.66025i	0.233890	+	0.405110i	−0.725059	+	0.688686i	$0.758188\pi$
$458$	−8.50000	−	14.7224i	−0.397179	−	0.687934i
$459$	−1.50000	+	2.59808i	−0.0700140	+	0.121268i
$460$		0			0
$461$	6.00000	−	10.3923i	0.279448	−	0.484018i	−0.691800	−	0.722089i	$-0.743182\pi$
$461$	6.00000	−	10.3923i	0.279448	−	0.484018i	0.971248	+	0.238071i	$0.0765153\pi$
$462$	−1.50000	+	2.59808i	−0.0697863	+	0.120873i
$463$	5.00000			0.232370			0.116185	−	0.993228i	$-0.462933\pi$
$463$	5.00000			0.232370			0.116185	+	0.993228i	$0.462933\pi$
$464$	1.50000	−	2.59808i	0.0696358	−	0.120613i
$465$		0			0
$466$	6.00000	+	10.3923i	0.277945	+	0.481414i
$467$		0			0			−	1.00000i	$-0.5\pi$
$467$		0			0				1.00000i	$0.5\pi$
$468$	1.00000	+	3.46410i	0.0462250	+	0.160128i
$469$	14.0000			0.646460
$470$		0			0
$471$	11.0000	+	19.0526i	0.506853	+	0.877896i
$472$	3.00000	−	5.19615i	0.138086	−	0.239172i
$473$	24.0000			1.10352
$474$	0.500000	−	0.866025i	0.0229658	−	0.0397779i
$475$	12.5000	−	21.6506i	0.573539	−	0.993399i
$476$	3.00000			0.137505
$477$	4.50000	−	7.79423i	0.206041	−	0.356873i
$478$	−3.00000	−	5.19615i	−0.137217	−	0.237666i
$479$	−13.5000	−	23.3827i	−0.616831	−	1.06838i	−0.990060	−	0.140643i	$-0.955083\pi$
$479$	−13.5000	−	23.3827i	−0.616831	−	1.06838i	0.373230	−	0.927739i	$-0.378250\pi$
$480$		0			0
$481$	−4.00000	−	13.8564i	−0.182384	−	0.631798i
$482$	8.00000			0.364390
$483$	−3.00000	−	5.19615i	−0.136505	−	0.236433i
$484$	1.00000	+	1.73205i	0.0454545	+	0.0787296i
$485$		0			0
$486$	1.00000			0.0453609
$487$	−11.5000	+	19.9186i	−0.521115	+	0.902597i	0.478584	+	0.878042i	$0.341150\pi$
$487$	−11.5000	+	19.9186i	−0.521115	+	0.902597i	−0.999698	+	0.0245553i	$0.992183\pi$
$488$	−2.50000	+	4.33013i	−0.113170	+	0.196016i
$489$	−16.0000			−0.723545
$490$		0			0
$491$	−18.0000	−	31.1769i	−0.812329	−	1.40699i	−0.911230	−	0.411897i	$-0.864866\pi$
$491$	−18.0000	−	31.1769i	−0.812329	−	1.40699i	0.0989017	−	0.995097i	$-0.468467\pi$
$492$	1.50000	+	2.59808i	0.0676252	+	0.117130i
$493$	−9.00000			−0.405340
$494$	−17.5000	−	4.33013i	−0.787362	−	0.194822i
$495$		0			0
$496$	2.00000	+	3.46410i	0.0898027	+	0.155543i
$497$	3.00000	+	5.19615i	0.134568	+	0.233079i
$498$	3.00000	−	5.19615i	0.134433	−	0.232845i
$499$	−40.0000			−1.79065			−0.895323	−	0.445418i	$-0.853055\pi$
$499$	−40.0000			−1.79065			−0.895323	+	0.445418i	$0.853055\pi$
$500$		0			0
$501$		0			0
$502$	30.0000			1.33897
$503$	−12.0000	+	20.7846i	−0.535054	+	0.926740i	0.464107	+	0.885779i	$0.346375\pi$
$503$	−12.0000	+	20.7846i	−0.535054	+	0.926740i	−0.999161	+	0.0409609i	$0.986958\pi$
$504$	−0.500000	−	0.866025i	−0.0222718	−	0.0385758i
$505$		0			0
$506$	18.0000			0.800198
$507$	−0.500000	−	12.9904i	−0.0222058	−	0.576923i
$508$	8.00000			0.354943
$509$	−15.0000	−	25.9808i	−0.664863	−	1.15158i	−0.979322	−	0.202306i	$-0.935156\pi$
$509$	−15.0000	−	25.9808i	−0.664863	−	1.15158i	0.314459	−	0.949271i	$-0.398177\pi$
$510$		0			0
$511$	2.00000	−	3.46410i	0.0884748	−	0.153243i
$512$	1.00000			0.0441942
$513$	−2.50000	+	4.33013i	−0.110378	+	0.191180i
$514$	−7.50000	+	12.9904i	−0.330811	+	0.572981i
$515$		0			0
$516$	−4.00000	+	6.92820i	−0.176090	+	0.304997i
$517$	−13.5000	−	23.3827i	−0.593729	−	1.02837i
$518$	2.00000	+	3.46410i	0.0878750	+	0.152204i
$519$	18.0000			0.790112
$520$		0			0
$521$	27.0000			1.18289			0.591446	−	0.806345i	$-0.298557\pi$
$521$	27.0000			1.18289			0.591446	+	0.806345i	$0.298557\pi$
$522$	1.50000	+	2.59808i	0.0656532	+	0.113715i
$523$	−14.5000	−	25.1147i	−0.634041	−	1.09819i	−0.986718	−	0.162446i	$-0.948062\pi$
$523$	−14.5000	−	25.1147i	−0.634041	−	1.09819i	0.352677	−	0.935745i	$-0.385272\pi$
$524$		0			0
$525$	−5.00000			−0.218218
$526$	−9.00000	+	15.5885i	−0.392419	+	0.679689i
$527$	6.00000	−	10.3923i	0.261364	−	0.452696i
$528$	3.00000			0.130558
$529$	−6.50000	+	11.2583i	−0.282609	+	0.489493i
$530$		0			0
$531$	3.00000	+	5.19615i	0.130189	+	0.225494i
$532$	5.00000			0.216777
$533$	−3.00000	−	10.3923i	−0.129944	−	0.450141i
$534$	−9.00000			−0.389468
$535$		0			0
$536$	−7.00000	−	12.1244i	−0.302354	−	0.523692i
$537$	−12.0000	+	20.7846i	−0.517838	+	0.896922i
$538$	24.0000			1.03471
$539$	−1.50000	+	2.59808i	−0.0646096	+	0.111907i
$540$		0			0
$541$	−10.0000			−0.429934			−0.214967	−	0.976621i	$-0.568964\pi$
$541$	−10.0000			−0.429934			−0.214967	+	0.976621i	$0.568964\pi$
$542$	14.0000	−	24.2487i	0.601351	−	1.04157i
$543$	−8.50000	−	14.7224i	−0.364770	−	0.631800i
$544$	−1.50000	−	2.59808i	−0.0643120	−	0.111392i
$545$		0			0
$546$	1.00000	+	3.46410i	0.0427960	+	0.148250i
$547$	−22.0000			−0.940652			−0.470326	−	0.882493i	$-0.655864\pi$
$547$	−22.0000			−0.940652			−0.470326	+	0.882493i	$0.655864\pi$
$548$	9.00000	+	15.5885i	0.384461	+	0.665906i
$549$	−2.50000	−	4.33013i	−0.106697	−	0.184805i
$550$	7.50000	−	12.9904i	0.319801	−	0.553912i
$551$	−15.0000			−0.639021
$552$	−3.00000	+	5.19615i	−0.127688	+	0.221163i
$553$	0.500000	−	0.866025i	0.0212622	−	0.0368271i
$554$	2.00000			0.0849719
$555$		0			0
$556$	6.50000	+	11.2583i	0.275661	+	0.477460i
$557$	7.50000	+	12.9904i	0.317785	+	0.550420i	0.980026	−	0.198871i	$-0.0637276\pi$
$557$	7.50000	+	12.9904i	0.317785	+	0.550420i	−0.662240	+	0.749291i	$0.730394\pi$
$558$	−4.00000			−0.169334
$559$	20.0000	−	20.7846i	0.845910	−	0.879095i
$560$		0			0
$561$	−4.50000	−	7.79423i	−0.189990	−	0.329073i
$562$	−3.00000	−	5.19615i	−0.126547	−	0.219186i
$563$	−12.0000	+	20.7846i	−0.505740	+	0.875967i	0.494238	+	0.869326i	$0.335447\pi$
$563$	−12.0000	+	20.7846i	−0.505740	+	0.875967i	−0.999978	+	0.00664037i	$0.997886\pi$
$564$	9.00000			0.378968
$565$		0			0
$566$	2.00000	−	3.46410i	0.0840663	−	0.145607i
$567$	1.00000			0.0419961
$568$	3.00000	−	5.19615i	0.125877	−	0.218026i
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	0.922032	−	0.387113i	$-0.126528\pi$
$569$	3.00000	+	5.19615i	0.125767	+	0.217834i	−0.796266	+	0.604947i	$0.793194\pi$
$570$		0			0
$571$	2.00000			0.0836974			0.0418487	−	0.999124i	$-0.486675\pi$
$571$	2.00000			0.0836974			0.0418487	+	0.999124i	$0.486675\pi$
$572$	−10.5000	−	2.59808i	−0.439027	−	0.108631i
$573$	18.0000			0.751961
$574$	1.50000	+	2.59808i	0.0626088	+	0.108442i
$575$	15.0000	+	25.9808i	0.625543	+	1.08347i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	2.00000			0.0832611			0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000			0.0832611			0.0416305	+	0.999133i	$0.486745\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$	9.50000	−	16.4545i	0.394807	−	0.683825i
$580$		0			0
$581$	3.00000	−	5.19615i	0.124461	−	0.215573i
$582$	−4.00000	−	6.92820i	−0.165805	−	0.287183i
$583$	13.5000	+	23.3827i	0.559113	+	0.968412i
$584$	−4.00000			−0.165521
$585$		0			0
$586$		0			0
$587$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$587$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$588$	−0.500000	−	0.866025i	−0.0206197	−	0.0357143i
$589$	10.0000	−	17.3205i	0.412043	−	0.713679i
$590$		0			0
$591$	4.50000	−	7.79423i	0.185105	−	0.320612i
$592$	2.00000	−	3.46410i	0.0821995	−	0.142374i
$593$	−15.0000			−0.615976			−0.307988	−	0.951390i	$-0.599656\pi$
$593$	−15.0000			−0.615976			−0.307988	+	0.951390i	$0.599656\pi$
$594$	−1.50000	+	2.59808i	−0.0615457	+	0.106600i
$595$		0			0
$596$	−3.00000	−	5.19615i	−0.122885	−	0.212843i
$597$	20.0000			0.818546
$598$	15.0000	−	15.5885i	0.613396	−	0.637459i
$599$	6.00000			0.245153			0.122577	−	0.992459i	$-0.460884\pi$
$599$	6.00000			0.245153			0.122577	+	0.992459i	$0.460884\pi$
$600$	2.50000	+	4.33013i	0.102062	+	0.176777i
$601$	20.0000	+	34.6410i	0.815817	+	1.41304i	0.908740	+	0.417363i	$0.137046\pi$
$601$	20.0000	+	34.6410i	0.815817	+	1.41304i	−0.0929227	+	0.995673i	$0.529621\pi$
$602$	−4.00000	+	6.92820i	−0.163028	+	0.282372i
$603$	14.0000			0.570124
$604$	−8.50000	+	14.7224i	−0.345860	+	0.599047i
$605$		0			0
$606$	6.00000			0.243733
$607$	8.00000	−	13.8564i	0.324710	−	0.562414i	−0.656744	−	0.754114i	$-0.728067\pi$
$607$	8.00000	−	13.8564i	0.324710	−	0.562414i	0.981454	+	0.191700i	$0.0614000\pi$
$608$	−2.50000	−	4.33013i	−0.101388	−	0.175610i
$609$	1.50000	+	2.59808i	0.0607831	+	0.105279i
$610$		0			0
$611$	−31.5000	−	7.79423i	−1.27435	−	0.315321i
$612$	3.00000			0.121268
$613$	−4.00000	−	6.92820i	−0.161558	−	0.279827i	0.773869	−	0.633345i	$-0.218319\pi$
$613$	−4.00000	−	6.92820i	−0.161558	−	0.279827i	−0.935428	+	0.353518i	$0.884985\pi$
$614$	−5.50000	−	9.52628i	−0.221962	−	0.384449i
$615$		0			0
$616$	3.00000			0.120873
$617$	9.00000	−	15.5885i	0.362326	−	0.627568i	−0.626017	−	0.779809i	$-0.715316\pi$
$617$	9.00000	−	15.5885i	0.362326	−	0.627568i	0.988343	+	0.152242i	$0.0486493\pi$
$618$	−4.00000	+	6.92820i	−0.160904	+	0.278693i
$619$	−25.0000			−1.00483			−0.502417	−	0.864625i	$-0.667556\pi$
$619$	−25.0000			−1.00483			−0.502417	+	0.864625i	$0.667556\pi$
$620$		0			0
$621$	−3.00000	−	5.19615i	−0.120386	−	0.208514i
$622$	7.50000	+	12.9904i	0.300723	+	0.520867i
$623$	−9.00000			−0.360577
$624$	2.50000	−	2.59808i	0.100080	−	0.104006i
$625$	25.0000			1.00000
$626$	11.0000	+	19.0526i	0.439648	+	0.761493i
$627$	−7.50000	−	12.9904i	−0.299521	−	0.518786i
$628$	11.0000	−	19.0526i	0.438948	−	0.760280i
$629$	−12.0000			−0.478471
$630$		0			0
$631$	−11.5000	+	19.9186i	−0.457808	+	0.792946i	−0.998845	−	0.0480524i	$-0.984699\pi$
$631$	−11.5000	+	19.9186i	−0.457808	+	0.792946i	0.541037	+	0.840999i	$0.318032\pi$
$632$	−1.00000			−0.0397779
$633$	5.00000	−	8.66025i	0.198732	−	0.344214i
$634$	3.00000	+	5.19615i	0.119145	+	0.206366i
$635$		0			0
$636$	−9.00000			−0.356873
$637$	1.00000	+	3.46410i	0.0396214	+	0.137253i
$638$	−9.00000			−0.356313
$639$	3.00000	+	5.19615i	0.118678	+	0.205557i
$640$		0			0
$641$	−3.00000	+	5.19615i	−0.118493	+	0.205236i	−0.919171	−	0.393860i	$-0.871140\pi$
$641$	−3.00000	+	5.19615i	−0.118493	+	0.205236i	0.800678	+	0.599095i	$0.204473\pi$
$642$	15.0000			0.592003
$643$	−8.50000	+	14.7224i	−0.335207	+	0.580596i	−0.983525	−	0.180774i	$-0.942140\pi$
$643$	−8.50000	+	14.7224i	−0.335207	+	0.580596i	0.648317	+	0.761370i	$0.275473\pi$
$644$	−3.00000	+	5.19615i	−0.118217	+	0.204757i
$645$		0			0
$646$	−7.50000	+	12.9904i	−0.295084	+	0.511100i
$647$	22.5000	+	38.9711i	0.884566	+	1.53211i	0.846210	+	0.532850i	$0.178879\pi$
$647$	22.5000	+	38.9711i	0.884566	+	1.53211i	0.0383563	+	0.999264i	$0.487788\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	−18.0000			−0.706562
$650$	−5.00000	−	17.3205i	−0.196116	−	0.679366i
$651$	−4.00000			−0.156772
$652$	8.00000	+	13.8564i	0.313304	+	0.542659i
$653$	16.5000	+	28.5788i	0.645695	+	1.11838i	0.984141	+	0.177390i	$0.0567655\pi$
$653$	16.5000	+	28.5788i	0.645695	+	1.11838i	−0.338446	+	0.940986i	$0.609901\pi$
$654$	5.00000	−	8.66025i	0.195515	−	0.338643i
$655$		0			0
$656$	1.50000	−	2.59808i	0.0585652	−	0.101438i
$657$	2.00000	−	3.46410i	0.0780274	−	0.135147i
$658$	9.00000			0.350857
$659$	7.50000	−	12.9904i	0.292159	−	0.506033i	−0.682161	−	0.731202i	$-0.738960\pi$
$659$	7.50000	−	12.9904i	0.292159	−	0.506033i	0.974320	+	0.225168i	$0.0722932\pi$
$660$		0			0
$661$	11.0000	+	19.0526i	0.427850	+	0.741059i	0.996682	−	0.0813955i	$-0.0259377\pi$
$661$	11.0000	+	19.0526i	0.427850	+	0.741059i	−0.568831	+	0.822454i	$0.692604\pi$
$662$	−10.0000			−0.388661
$663$	−10.5000	−	2.59808i	−0.407786	−	0.100901i
$664$	−6.00000			−0.232845
$665$		0			0
$666$	2.00000	+	3.46410i	0.0774984	+	0.134231i
$667$	9.00000	−	15.5885i	0.348481	−	0.603587i
$668$		0			0
$669$	−4.00000	+	6.92820i	−0.154649	+	0.267860i
$670$		0			0
$671$	15.0000			0.579069
$672$	−0.500000	+	0.866025i	−0.0192879	+	0.0334077i
$673$	0.500000	+	0.866025i	0.0192736	+	0.0333828i	0.875501	−	0.483216i	$-0.160531\pi$
$673$	0.500000	+	0.866025i	0.0192736	+	0.0333828i	−0.856228	+	0.516599i	$0.827198\pi$
$674$	12.5000	+	21.6506i	0.481482	+	0.833951i
$675$	−5.00000			−0.192450
$676$	−11.0000	+	6.92820i	−0.423077	+	0.266469i
$677$	6.00000			0.230599			0.115299	−	0.993331i	$-0.463217\pi$
$677$	6.00000			0.230599			0.115299	+	0.993331i	$0.463217\pi$
$678$	6.00000	+	10.3923i	0.230429	+	0.399114i
$679$	−4.00000	−	6.92820i	−0.153506	−	0.265880i
$680$		0			0
$681$	−18.0000			−0.689761
$682$	6.00000	−	10.3923i	0.229752	−	0.397942i
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	−0.957685	−	0.287819i	$-0.907070\pi$
$683$	−6.00000	+	10.3923i	−0.229584	+	0.397650i	0.728101	+	0.685470i	$0.240403\pi$
$684$	5.00000			0.191180
$685$		0			0
$686$	−0.500000	−	0.866025i	−0.0190901	−	0.0330650i
$687$	−8.50000	−	14.7224i	−0.324295	−	0.561696i
$688$	8.00000			0.304997
$689$	31.5000	+	7.79423i	1.20005	+	0.296936i
$690$		0			0
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	0.779857	−	0.625958i	$-0.215292\pi$
$691$	−4.00000	−	6.92820i	−0.152167	−	0.263561i	−0.932024	+	0.362397i	$0.881959\pi$
$692$	−9.00000	−	15.5885i	−0.342129	−	0.592584i
$693$	−1.50000	+	2.59808i	−0.0569803	+	0.0986928i
$694$	−27.0000			−1.02491
$695$		0			0
$696$	1.50000	−	2.59808i	0.0568574	−	0.0984798i
$697$	−9.00000			−0.340899
$698$	−1.00000	+	1.73205i	−0.0378506	+	0.0655591i
$699$	6.00000	+	10.3923i	0.226941	+	0.393073i
$700$	2.50000	+	4.33013i	0.0944911	+	0.163663i
$701$	−15.0000			−0.566542			−0.283271	−	0.959040i	$-0.591420\pi$
$701$	−15.0000			−0.566542			−0.283271	+	0.959040i	$0.591420\pi$
$702$	1.00000	+	3.46410i	0.0377426	+	0.130744i
$703$	−20.0000			−0.754314
$704$	−1.50000	−	2.59808i	−0.0565334	−	0.0979187i
$705$		0			0
$706$	9.00000	−	15.5885i	0.338719	−	0.586679i
$707$	6.00000			0.225653
$708$	3.00000	−	5.19615i	0.112747	−	0.195283i
$709$	−1.00000	+	1.73205i	−0.0375558	+	0.0650485i	−0.884192	−	0.467123i	$-0.845291\pi$
$709$	−1.00000	+	1.73205i	−0.0375558	+	0.0650485i	0.846637	+	0.532172i	$0.178624\pi$
$710$		0			0
$711$	0.500000	−	0.866025i	0.0187515	−	0.0324785i
$712$	4.50000	+	7.79423i	0.168645	+	0.292101i
$713$	12.0000	+	20.7846i	0.449404	+	0.778390i
$714$	3.00000			0.112272
$715$		0			0
$716$	24.0000			0.896922
$717$	−3.00000	−	5.19615i	−0.112037	−	0.194054i
$718$	6.00000	+	10.3923i	0.223918	+	0.387837i
$719$	−13.5000	+	23.3827i	−0.503465	+	0.872027i	0.496527	+	0.868021i	$0.334608\pi$
$719$	−13.5000	+	23.3827i	−0.503465	+	0.872027i	−0.999992	+	0.00400572i	$0.998725\pi$
$720$		0			0
$721$	−4.00000	+	6.92820i	−0.148968	+	0.258020i
$722$	−3.00000	+	5.19615i	−0.111648	+	0.193381i
$723$	8.00000			0.297523
$724$	−8.50000	+	14.7224i	−0.315900	+	0.547155i
$725$	−7.50000	−	12.9904i	−0.278543	−	0.482451i
$726$	1.00000	+	1.73205i	0.0371135	+	0.0642824i
$727$	−28.0000			−1.03846			−0.519231	−	0.854634i	$-0.673782\pi$
$727$	−28.0000			−1.03846			−0.519231	+	0.854634i	$0.673782\pi$
$728$	2.50000	−	2.59808i	0.0926562	−	0.0962911i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−12.0000	−	20.7846i	−0.443836	−	0.768747i
$732$	−2.50000	+	4.33013i	−0.0924027	+	0.160046i
$733$	−49.0000			−1.80986			−0.904928	−	0.425564i	$-0.860076\pi$
$733$	−49.0000			−1.80986			−0.904928	+	0.425564i	$0.860076\pi$
$734$	−1.00000	+	1.73205i	−0.0369107	+	0.0639312i
$735$		0			0
$736$	6.00000			0.221163
$737$	−21.0000	+	36.3731i	−0.773545	+	1.33982i
$738$	1.50000	+	2.59808i	0.0552158	+	0.0956365i
$739$	5.00000	+	8.66025i	0.183928	+	0.318573i	0.943215	−	0.332184i	$-0.107785\pi$
$739$	5.00000	+	8.66025i	0.183928	+	0.318573i	−0.759287	+	0.650756i	$0.774452\pi$
$740$		0			0
$741$	−17.5000	−	4.33013i	−0.642879	−	0.159071i
$742$	−9.00000			−0.330400
$743$	12.0000	+	20.7846i	0.440237	+	0.762513i	0.997707	−	0.0676840i	$-0.0215610\pi$
$743$	12.0000	+	20.7846i	0.440237	+	0.762513i	−0.557470	+	0.830197i	$0.688228\pi$
$744$	2.00000	+	3.46410i	0.0733236	+	0.127000i
$745$		0			0
$746$	14.0000			0.512576
$747$	3.00000	−	5.19615i	0.109764	−	0.190117i
$748$	−4.50000	+	7.79423i	−0.164536	+	0.284985i
$749$	15.0000			0.548088
$750$		0			0
$751$	−5.50000	−	9.52628i	−0.200698	−	0.347619i	0.748056	−	0.663636i	$-0.230988\pi$
$751$	−5.50000	−	9.52628i	−0.200698	−	0.347619i	−0.948753	+	0.316017i	$0.897654\pi$
$752$	−4.50000	−	7.79423i	−0.164098	−	0.284226i
$753$	30.0000			1.09326
$754$	−7.50000	+	7.79423i	−0.273134	+	0.283849i
$755$		0			0
$756$	−0.500000	−	0.866025i	−0.0181848	−	0.0314970i
$757$	−1.00000	−	1.73205i	−0.0363456	−	0.0629525i	0.847280	−	0.531146i	$-0.178238\pi$
$757$	−1.00000	−	1.73205i	−0.0363456	−	0.0629525i	−0.883626	+	0.468193i	$0.844905\pi$
$758$	17.0000	−	29.4449i	0.617468	−	1.06949i
$759$	18.0000			0.653359
$760$		0			0
$761$	21.0000	−	36.3731i	0.761249	−	1.31852i	−0.180957	−	0.983491i	$-0.557920\pi$
$761$	21.0000	−	36.3731i	0.761249	−	1.31852i	0.942207	−	0.335032i	$-0.108747\pi$
$762$	8.00000			0.289809
$763$	5.00000	−	8.66025i	0.181012	−	0.313522i
$764$	−9.00000	−	15.5885i	−0.325609	−	0.563971i
$765$		0			0
$766$	9.00000			0.325183
$767$	−15.0000	+	15.5885i	−0.541619	+	0.562867i
$768$	1.00000			0.0360844
$769$	−22.0000	−	38.1051i	−0.793340	−	1.37411i	−0.923888	−	0.382664i	$-0.875007\pi$
$769$	−22.0000	−	38.1051i	−0.793340	−	1.37411i	0.130547	−	0.991442i	$-0.458327\pi$
$770$		0			0
$771$	−7.50000	+	12.9904i	−0.270106	+	0.467837i
$772$	−19.0000			−0.683825
$773$	−9.00000	+	15.5885i	−0.323708	+	0.560678i	−0.981250	−	0.192740i	$-0.938263\pi$
$773$	−9.00000	+	15.5885i	−0.323708	+	0.560678i	0.657542	+	0.753418i	$0.271596\pi$
$774$	−4.00000	+	6.92820i	−0.143777	+	0.249029i
$775$	20.0000			0.718421
$776$	−4.00000	+	6.92820i	−0.143592	+	0.248708i
$777$	2.00000	+	3.46410i	0.0717496	+	0.124274i
$778$	3.00000	+	5.19615i	0.107555	+	0.186291i
$779$	−15.0000			−0.537431
$780$		0			0
$781$	−18.0000			−0.644091
$782$	−9.00000	−	15.5885i	−0.321839	−	0.557442i
$783$	1.50000	+	2.59808i	0.0536056	+	0.0928477i
$784$	−0.500000	+	0.866025i	−0.0178571	+	0.0309295i
$785$		0			0
$786$		0			0
$787$	−5.50000	+	9.52628i	−0.196054	+	0.339575i	−0.947245	−	0.320509i	$-0.896146\pi$
$787$	−5.50000	+	9.52628i	−0.196054	+	0.339575i	0.751192	+	0.660084i	$0.229479\pi$
$788$	−9.00000			−0.320612
$789$	−9.00000	+	15.5885i	−0.320408	+	0.554964i
$790$		0			0
$791$	6.00000	+	10.3923i	0.213335	+	0.369508i
$792$	3.00000			0.106600
$793$	12.5000	−	12.9904i	0.443888	−	0.461302i
$794$	−37.0000			−1.31308
$795$		0			0
$796$	−10.0000	−	17.3205i	−0.354441	−	0.613909i
$797$	3.00000	−	5.19615i	0.106265	−	0.184057i	−0.807989	−	0.589197i	$-0.799444\pi$
$797$	3.00000	−	5.19615i	0.106265	−	0.184057i	0.914255	+	0.405140i	$0.132777\pi$
$798$	5.00000			0.176998
$799$	−13.5000	+	23.3827i	−0.477596	+	0.827220i
$800$	2.50000	−	4.33013i	0.0883883	−	0.153093i
$801$	−9.00000			−0.317999
$802$	−15.0000	+	25.9808i	−0.529668	+	0.917413i
$803$	6.00000	+	10.3923i	0.211735	+	0.366736i
$804$	−7.00000	−	12.1244i	−0.246871	−	0.427593i
$805$		0			0
$806$	−4.00000	−	13.8564i	−0.140894	−	0.488071i
$807$	24.0000			0.844840
$808$	−3.00000	−	5.19615i	−0.105540	−	0.182800i
$809$	21.0000	+	36.3731i	0.738321	+	1.27881i	0.953251	+	0.302180i	$0.0977142\pi$
$809$	21.0000	+	36.3731i	0.738321	+	1.27881i	−0.214930	+	0.976629i	$0.568952\pi$
$810$		0			0
$811$	−40.0000			−1.40459			−0.702295	−	0.711886i	$-0.747841\pi$
$811$	−40.0000			−1.40459			−0.702295	+	0.711886i	$0.747841\pi$
$812$	1.50000	−	2.59808i	0.0526397	−	0.0911746i
$813$	14.0000	−	24.2487i	0.491001	−	0.850439i
$814$	−12.0000			−0.420600
$815$		0			0
$816$	−1.50000	−	2.59808i	−0.0525105	−	0.0909509i
$817$	−20.0000	−	34.6410i	−0.699711	−	1.21194i
$818$	14.0000			0.489499
$819$	1.00000	+	3.46410i	0.0349428	+	0.121046i
$820$		0			0
$821$	22.5000	+	38.9711i	0.785255	+	1.36010i	0.928846	+	0.370465i	$0.120802\pi$
$821$	22.5000	+	38.9711i	0.785255	+	1.36010i	−0.143591	+	0.989637i	$0.545865\pi$
$822$	9.00000	+	15.5885i	0.313911	+	0.543710i
$823$	−16.0000	+	27.7128i	−0.557725	+	0.966008i	0.439961	+	0.898017i	$0.354992\pi$
$823$	−16.0000	+	27.7128i	−0.557725	+	0.966008i	−0.997686	+	0.0679910i	$0.978341\pi$
$824$	8.00000			0.278693
$825$	7.50000	−	12.9904i	0.261116	−	0.452267i
$826$	3.00000	−	5.19615i	0.104383	−	0.180797i
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$	−3.00000	+	5.19615i	−0.104257	+	0.180579i
$829$	12.5000	+	21.6506i	0.434143	+	0.751958i	0.997225	−	0.0744432i	$-0.0237179\pi$
$829$	12.5000	+	21.6506i	0.434143	+	0.751958i	−0.563082	+	0.826401i	$0.690385\pi$
$830$		0			0
$831$	2.00000			0.0693792
$832$	−3.50000	−	0.866025i	−0.121341	−	0.0300240i
$833$	3.00000			0.103944
$834$	6.50000	+	11.2583i	0.225077	+	0.389844i
$835$		0			0
$836$	−7.50000	+	12.9904i	−0.259393	+	0.449282i
$837$	−4.00000			−0.138260
$838$	−3.00000	+	5.19615i	−0.103633	+	0.179498i
$839$	−18.0000	+	31.1769i	−0.621429	+	1.07635i	0.367791	+	0.929909i	$0.380114\pi$
$839$	−18.0000	+	31.1769i	−0.621429	+	1.07635i	−0.989220	+	0.146438i	$0.953219\pi$
$840$		0			0
$841$	10.0000	−	17.3205i	0.344828	−	0.597259i
$842$	5.00000	+	8.66025i	0.172311	+	0.298452i
$843$	−3.00000	−	5.19615i	−0.103325	−	0.178965i
$844$	−10.0000			−0.344214
$845$		0			0
$846$	9.00000			0.309426
$847$	1.00000	+	1.73205i	0.0343604	+	0.0595140i
$848$	4.50000	+	7.79423i	0.154531	+	0.267655i
$849$	2.00000	−	3.46410i	0.0686398	−	0.118888i
$850$	−15.0000			−0.514496
$851$	12.0000	−	20.7846i	0.411355	−	0.712487i
$852$	3.00000	−	5.19615i	0.102778	−	0.178017i
$853$	−37.0000			−1.26686			−0.633428	−	0.773802i	$-0.718353\pi$
$853$	−37.0000			−1.26686			−0.633428	+	0.773802i	$0.718353\pi$
$854$	−2.50000	+	4.33013i	−0.0855482	+	0.148174i
$855$		0			0
$856$	−7.50000	−	12.9904i	−0.256345	−	0.444002i
$857$	18.0000			0.614868			0.307434	−	0.951569i	$-0.400530\pi$
$857$	18.0000			0.614868			0.307434	+	0.951569i	$0.400530\pi$
$858$	−10.5000	−	2.59808i	−0.358464	−	0.0886969i
$859$	5.00000			0.170598			0.0852989	−	0.996355i	$-0.472815\pi$
$859$	5.00000			0.170598			0.0852989	+	0.996355i	$0.472815\pi$
$860$		0			0
$861$	1.50000	+	2.59808i	0.0511199	+	0.0885422i
$862$	15.0000	−	25.9808i	0.510902	−	0.884908i
$863$	−30.0000			−1.02121			−0.510606	−	0.859815i	$-0.670579\pi$
$863$	−30.0000			−1.02121			−0.510606	+	0.859815i	$0.670579\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$		0			0
$866$	−34.0000			−1.15537
$867$	4.00000	−	6.92820i	0.135847	−	0.235294i
$868$	2.00000	+	3.46410i	0.0678844	+	0.117579i
$869$	1.50000	+	2.59808i	0.0508840	+	0.0881337i
$870$		0			0
$871$	14.0000	+	48.4974i	0.474372	+	1.64327i
$872$	−10.0000			−0.338643
$873$	−4.00000	−	6.92820i	−0.135379	−	0.234484i
$874$	−15.0000	−	25.9808i	−0.507383	−	0.878812i
$875$		0			0
$876$	−4.00000			−0.135147
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	−0.618344	−	0.785907i	$-0.712196\pi$
$877$	11.0000	−	19.0526i	0.371444	−	0.643359i	0.989788	+	0.142548i	$0.0455296\pi$
$878$	2.00000	−	3.46410i	0.0674967	−	0.116908i
$879$		0			0
$880$		0			0
$881$	−21.0000	−	36.3731i	−0.707508	−	1.22544i	−0.965779	−	0.259367i	$-0.916486\pi$
$881$	−21.0000	−	36.3731i	−0.707508	−	1.22544i	0.258271	−	0.966073i	$-0.416847\pi$
$882$	−0.500000	−	0.866025i	−0.0168359	−	0.0291606i
$883$	−52.0000			−1.74994			−0.874970	−	0.484178i	$-0.839119\pi$
$883$	−52.0000			−1.74994			−0.874970	+	0.484178i	$0.839119\pi$
$884$	3.00000	+	10.3923i	0.100901	+	0.349531i
$885$		0			0
$886$	4.50000	+	7.79423i	0.151180	+	0.261852i
$887$	−1.50000	−	2.59808i	−0.0503651	−	0.0872349i	0.839744	−	0.542983i	$-0.182705\pi$
$887$	−1.50000	−	2.59808i	−0.0503651	−	0.0872349i	−0.890109	+	0.455748i	$0.849372\pi$
$888$	2.00000	−	3.46410i	0.0671156	−	0.116248i
$889$	8.00000			0.268311
$890$		0			0
$891$	−1.50000	+	2.59808i	−0.0502519	+	0.0870388i
$892$	8.00000			0.267860
$893$	−22.5000	+	38.9711i	−0.752934	+	1.30412i
$894$	−3.00000	−	5.19615i	−0.100335	−	0.173785i
$895$		0			0
$896$	1.00000			0.0334077
$897$	15.0000	−	15.5885i	0.500835	−	0.520483i
$898$	12.0000			0.400445
$899$	−6.00000	−	10.3923i	−0.200111	−	0.346603i
$900$	2.50000	+	4.33013i	0.0833333	+	0.144338i
$901$	13.5000	−	23.3827i	0.449750	−	0.778990i
$902$	−9.00000			−0.299667
$903$	−4.00000	+	6.92820i	−0.133112	+	0.230556i
$904$	6.00000	−	10.3923i	0.199557	−	0.345643i
$905$		0			0
$906$	−8.50000	+	14.7224i	−0.282394	+	0.489120i
$907$	−25.0000	−	43.3013i	−0.830111	−	1.43780i	−0.897949	−	0.440099i	$-0.854943\pi$
$907$	−25.0000	−	43.3013i	−0.830111	−	1.43780i	0.0678380	−	0.997696i	$-0.478390\pi$
$908$	9.00000	+	15.5885i	0.298675	+	0.517321i
$909$	6.00000			0.199007
$910$		0			0
$911$	6.00000			0.198789			0.0993944	−	0.995048i	$-0.468309\pi$
$911$	6.00000			0.198789			0.0993944	+	0.995048i	$0.468309\pi$
$912$	−2.50000	−	4.33013i	−0.0827833	−	0.143385i
$913$	9.00000	+	15.5885i	0.297857	+	0.515903i
$914$	5.00000	−	8.66025i	0.165385	−	0.286456i
$915$		0			0
$916$	−8.50000	+	14.7224i	−0.280848	+	0.486443i
$917$		0			0
$918$	3.00000			0.0990148
$919$	3.50000	−	6.06218i	0.115454	−	0.199973i	−0.802507	−	0.596643i	$-0.796501\pi$
$919$	3.50000	−	6.06218i	0.115454	−	0.199973i	0.917961	+	0.396670i	$0.129834\pi$
$920$		0			0
$921$	−5.50000	−	9.52628i	−0.181231	−	0.313902i
$922$	−12.0000			−0.395199
$923$	−15.0000	+	15.5885i	−0.493731	+	0.513100i
$924$	3.00000			0.0986928
$925$	−10.0000	−	17.3205i	−0.328798	−	0.569495i
$926$	−2.50000	−	4.33013i	−0.0821551	−	0.142297i
$927$	−4.00000	+	6.92820i	−0.131377	+	0.227552i
$928$	−3.00000			−0.0984798
$929$	19.5000	−	33.7750i	0.639774	−	1.10812i	−0.345708	−	0.938342i	$-0.612361\pi$
$929$	19.5000	−	33.7750i	0.639774	−	1.10812i	0.985482	−	0.169779i	$-0.0543055\pi$
$930$		0			0
$931$	5.00000			0.163868
$932$	6.00000	−	10.3923i	0.196537	−	0.340411i
$933$	7.50000	+	12.9904i	0.245539	+	0.425286i
$934$		0			0
$935$		0			0
$936$	2.50000	−	2.59808i	0.0817151	−	0.0849208i
$937$	32.0000			1.04539			0.522697	−	0.852518i	$-0.324926\pi$
$937$	32.0000			1.04539			0.522697	+	0.852518i	$0.324926\pi$
$938$	−7.00000	−	12.1244i	−0.228558	−	0.395874i
$939$	11.0000	+	19.0526i	0.358971	+	0.621757i
$940$		0			0
$941$	12.0000			0.391189			0.195594	−	0.980685i	$-0.437336\pi$
$941$	12.0000			0.391189			0.195594	+	0.980685i	$0.437336\pi$
$942$	11.0000	−	19.0526i	0.358399	−	0.620766i
$943$	9.00000	−	15.5885i	0.293080	−	0.507630i
$944$	−6.00000			−0.195283
$945$		0			0
$946$	−12.0000	−	20.7846i	−0.390154	−	0.675766i
$947$	13.5000	+	23.3827i	0.438691	+	0.759835i	0.997589	−	0.0694014i	$-0.0221089\pi$
$947$	13.5000	+	23.3827i	0.438691	+	0.759835i	−0.558898	+	0.829237i	$0.688776\pi$
$948$	−1.00000			−0.0324785
$949$	14.0000	+	3.46410i	0.454459	+	0.112449i
$950$	−25.0000			−0.811107
$951$	3.00000	+	5.19615i	0.0972817	+	0.168497i
$952$	−1.50000	−	2.59808i	−0.0486153	−	0.0842041i
$953$	18.0000	−	31.1769i	0.583077	−	1.00992i	−0.412035	−	0.911168i	$-0.635182\pi$
$953$	18.0000	−	31.1769i	0.583077	−	1.00992i	0.995112	−	0.0987513i	$-0.0314848\pi$
$954$	−9.00000			−0.291386
$955$		0			0
$956$	−3.00000	+	5.19615i	−0.0970269	+	0.168056i
$957$	−9.00000			−0.290929
$958$	−13.5000	+	23.3827i	−0.436165	+	0.755460i
$959$	9.00000	+	15.5885i	0.290625	+	0.503378i
$960$		0			0
$961$	−15.0000			−0.483871
$962$	−10.0000	+	10.3923i	−0.322413	+	0.335061i
$963$	15.0000			0.483368
$964$	−4.00000	−	6.92820i	−0.128831	−	0.223142i
$965$		0			0
$966$	−3.00000	+	5.19615i	−0.0965234	+	0.167183i
$967$	32.0000			1.02905			0.514525	−	0.857475i	$-0.327968\pi$
$967$	32.0000			1.02905			0.514525	+	0.857475i	$0.327968\pi$
$968$	1.00000	−	1.73205i	0.0321412	−	0.0556702i
$969$	−7.50000	+	12.9904i	−0.240935	+	0.417311i
$970$		0			0
$971$	−21.0000	+	36.3731i	−0.673922	+	1.16727i	0.302861	+	0.953035i	$0.402058\pi$
$971$	−21.0000	+	36.3731i	−0.673922	+	1.16727i	−0.976783	+	0.214232i	$0.931275\pi$
$972$	−0.500000	−	0.866025i	−0.0160375	−	0.0277778i
$973$	6.50000	+	11.2583i	0.208380	+	0.360925i
$974$	23.0000			0.736968
$975$	−5.00000	−	17.3205i	−0.160128	−	0.554700i
$976$	5.00000			0.160046
$977$	12.0000	+	20.7846i	0.383914	+	0.664959i	0.991618	−	0.129205i	$-0.0412426\pi$
$977$	12.0000	+	20.7846i	0.383914	+	0.664959i	−0.607704	+	0.794164i	$0.707909\pi$
$978$	8.00000	+	13.8564i	0.255812	+	0.443079i
$979$	13.5000	−	23.3827i	0.431462	−	0.747314i
$980$		0			0
$981$	5.00000	−	8.66025i	0.159638	−	0.276501i
$982$	−18.0000	+	31.1769i	−0.574403	+	0.994895i
$983$	−48.0000			−1.53096			−0.765481	−	0.643458i	$-0.777499\pi$
$983$	−48.0000			−1.53096			−0.765481	+	0.643458i	$0.777499\pi$
$984$	1.50000	−	2.59808i	0.0478183	−	0.0828236i
$985$		0			0
$986$	4.50000	+	7.79423i	0.143309	+	0.248219i
$987$	9.00000			0.286473
$988$	5.00000	+	17.3205i	0.159071	+	0.551039i
$989$	48.0000			1.52631
$990$		0			0
$991$	21.5000	+	37.2391i	0.682970	+	1.18294i	0.974070	+	0.226246i	$0.0726454\pi$
$991$	21.5000	+	37.2391i	0.682970	+	1.18294i	−0.291100	+	0.956693i	$0.594021\pi$
$992$	2.00000	−	3.46410i	0.0635001	−	0.109985i
$993$	−10.0000			−0.317340
$994$	3.00000	−	5.19615i	0.0951542	−	0.164812i
$995$		0			0
$996$	−6.00000			−0.190117
$997$	3.50000	−	6.06218i	0.110846	−	0.191991i	−0.805266	−	0.592914i	$-0.797977\pi$
$997$	3.50000	−	6.06218i	0.110846	−	0.191991i	0.916112	+	0.400923i	$0.131311\pi$
$998$	20.0000	+	34.6410i	0.633089	+	1.09654i
$999$	2.00000	+	3.46410i	0.0632772	+	0.109599i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.l.a.211.1	✓	2
3.2	odd	2		1638.2.r.r.757.1		2
13.3	even	3		7098.2.a.bb.1.1		1
13.9	even	3	inner	546.2.l.a.295.1	yes	2
13.10	even	6		7098.2.a.l.1.1		1
39.35	odd	6		1638.2.r.r.1387.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.l.a.211.1	✓	2	1.1	even	1	trivial
546.2.l.a.295.1	yes	2	13.9	even	3	inner
1638.2.r.r.757.1		2	3.2	odd	2
1638.2.r.r.1387.1		2	39.35	odd	6
7098.2.a.l.1.1		1	13.10	even	6
7098.2.a.bb.1.1		1	13.3	even	3

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{6} +(-0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.50000 - 2.59808i) q^{11} +1.00000 q^{12} +(-3.50000 - 0.866025i) q^{13} +1.00000 q^{14} +(-0.500000 - 0.866025i) q^{16} +(-1.50000 + 2.59808i) q^{17} +1.00000 q^{18} +(-2.50000 + 4.33013i) q^{19} +1.00000 q^{21} +(-1.50000 + 2.59808i) q^{22} +(-3.00000 - 5.19615i) q^{23} +(-0.500000 - 0.866025i) q^{24} -5.00000 q^{25} +(1.00000 + 3.46410i) q^{26} +1.00000 q^{27} +(-0.500000 - 0.866025i) q^{28} +(1.50000 + 2.59808i) q^{29} -4.00000 q^{31} +(-0.500000 + 0.866025i) q^{32} +(-1.50000 + 2.59808i) q^{33} +3.00000 q^{34} +(-0.500000 - 0.866025i) q^{36} +(2.00000 + 3.46410i) q^{37} +5.00000 q^{38} +(1.00000 + 3.46410i) q^{39} +(1.50000 + 2.59808i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(-4.00000 + 6.92820i) q^{43} +3.00000 q^{44} +(-3.00000 + 5.19615i) q^{46} +9.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(2.50000 + 4.33013i) q^{50} +3.00000 q^{51} +(2.50000 - 2.59808i) q^{52} -9.00000 q^{53} +(-0.500000 - 0.866025i) q^{54} +(-0.500000 + 0.866025i) q^{56} +5.00000 q^{57} +(1.50000 - 2.59808i) q^{58} +(3.00000 - 5.19615i) q^{59} +(-2.50000 + 4.33013i) q^{61} +(2.00000 + 3.46410i) q^{62} +(-0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +3.00000 q^{66} +(-7.00000 - 12.1244i) q^{67} +(-1.50000 - 2.59808i) q^{68} +(-3.00000 + 5.19615i) q^{69} +(3.00000 - 5.19615i) q^{71} +(-0.500000 + 0.866025i) q^{72} -4.00000 q^{73} +(2.00000 - 3.46410i) q^{74} +(2.50000 + 4.33013i) q^{75} +(-2.50000 - 4.33013i) q^{76} +3.00000 q^{77} +(2.50000 - 2.59808i) q^{78} -1.00000 q^{79} +(-0.500000 - 0.866025i) q^{81} +(1.50000 - 2.59808i) q^{82} -6.00000 q^{83} +(-0.500000 + 0.866025i) q^{84} +8.00000 q^{86} +(1.50000 - 2.59808i) q^{87} +(-1.50000 - 2.59808i) q^{88} +(4.50000 + 7.79423i) q^{89} +(2.50000 - 2.59808i) q^{91} +6.00000 q^{92} +(2.00000 + 3.46410i) q^{93} +(-4.50000 - 7.79423i) q^{94} +1.00000 q^{96} +(-4.00000 + 6.92820i) q^{97} +(-0.500000 + 0.866025i) q^{98} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - q^{3} - q^{4} - q^{6} - q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q - q^2 - q^3 - q^4 - q^6 - q^7 + 2 * q^8 - q^9	\( 2 q - q^{2} - q^{3} - q^{4} - q^{6} - q^{7} + 2 q^{8} - q^{9} - 3 q^{11} + 2 q^{12} - 7 q^{13} + 2 q^{14} - q^{16} - 3 q^{17} + 2 q^{18} - 5 q^{19} + 2 q^{21} - 3 q^{22} - 6 q^{23} - q^{24} - 10 q^{25} + 2 q^{26} + 2 q^{27} - q^{28} + 3 q^{29} - 8 q^{31} - q^{32} - 3 q^{33} + 6 q^{34} - q^{36} + 4 q^{37} + 10 q^{38} + 2 q^{39} + 3 q^{41} - q^{42} - 8 q^{43} + 6 q^{44} - 6 q^{46} + 18 q^{47} - q^{48} - q^{49} + 5 q^{50} + 6 q^{51} + 5 q^{52} - 18 q^{53} - q^{54} - q^{56} + 10 q^{57} + 3 q^{58} + 6 q^{59} - 5 q^{61} + 4 q^{62} - q^{63} + 2 q^{64} + 6 q^{66} - 14 q^{67} - 3 q^{68} - 6 q^{69} + 6 q^{71} - q^{72} - 8 q^{73} + 4 q^{74} + 5 q^{75} - 5 q^{76} + 6 q^{77} + 5 q^{78} - 2 q^{79} - q^{81} + 3 q^{82} - 12 q^{83} - q^{84} + 16 q^{86} + 3 q^{87} - 3 q^{88} + 9 q^{89} + 5 q^{91} + 12 q^{92} + 4 q^{93} - 9 q^{94} + 2 q^{96} - 8 q^{97} - q^{98} + 6 q^{99}+O(q^{100}) \) 2 * q - q^2 - q^3 - q^4 - q^6 - q^7 + 2 * q^8 - q^9 - 3 * q^11 + 2 * q^12 - 7 * q^13 + 2 * q^14 - q^16 - 3 * q^17 + 2 * q^18 - 5 * q^19 + 2 * q^21 - 3 * q^22 - 6 * q^23 - q^24 - 10 * q^25 + 2 * q^26 + 2 * q^27 - q^28 + 3 * q^29 - 8 * q^31 - q^32 - 3 * q^33 + 6 * q^34 - q^36 + 4 * q^37 + 10 * q^38 + 2 * q^39 + 3 * q^41 - q^42 - 8 * q^43 + 6 * q^44 - 6 * q^46 + 18 * q^47 - q^48 - q^49 + 5 * q^50 + 6 * q^51 + 5 * q^52 - 18 * q^53 - q^54 - q^56 + 10 * q^57 + 3 * q^58 + 6 * q^59 - 5 * q^61 + 4 * q^62 - q^63 + 2 * q^64 + 6 * q^66 - 14 * q^67 - 3 * q^68 - 6 * q^69 + 6 * q^71 - q^72 - 8 * q^73 + 4 * q^74 + 5 * q^75 - 5 * q^76 + 6 * q^77 + 5 * q^78 - 2 * q^79 - q^81 + 3 * q^82 - 12 * q^83 - q^84 + 16 * q^86 + 3 * q^87 - 3 * q^88 + 9 * q^89 + 5 * q^91 + 12 * q^92 + 4 * q^93 - 9 * q^94 + 2 * q^96 - 8 * q^97 - q^98 + 6 * q^99

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