LMFDB - Embedded newform 546.2.k.a.373.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(373,546)]

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, 2, 4]))

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

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

chi := DirichletCharacter("546.373");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.k (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:	$0$
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			373.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	546.373
Dual form			546.2.k.a.445.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 - 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(-2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-0.500000 - 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(-2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.00000 q^{11} +(0.500000 - 0.866025i) q^{12} +(3.50000 + 0.866025i) q^{13} +(0.500000 + 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} +(-0.500000 - 0.866025i) q^{18} +1.00000 q^{19} +(2.50000 + 0.866025i) q^{21} +(1.00000 + 1.73205i) q^{22} +(2.00000 + 3.46410i) q^{23} -1.00000 q^{24} +(2.50000 + 4.33013i) q^{25} +(-1.00000 - 3.46410i) q^{26} -1.00000 q^{27} +(2.00000 - 1.73205i) q^{28} +(-3.00000 + 5.19615i) q^{29} +(-0.500000 + 0.866025i) q^{32} +2.00000 q^{33} +4.00000 q^{34} +(-0.500000 + 0.866025i) q^{36} +(5.50000 + 9.52628i) q^{37} +(-0.500000 - 0.866025i) q^{38} +(-3.50000 - 0.866025i) q^{39} +(1.00000 - 1.73205i) q^{41} +(-0.500000 - 2.59808i) q^{42} +(0.500000 + 0.866025i) q^{43} +(1.00000 - 1.73205i) q^{44} +(2.00000 - 3.46410i) q^{46} +(0.500000 + 0.866025i) q^{48} +(5.50000 + 4.33013i) q^{49} +(2.50000 - 4.33013i) q^{50} +(2.00000 - 3.46410i) q^{51} +(-2.50000 + 2.59808i) q^{52} +(-2.00000 - 3.46410i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-2.50000 - 0.866025i) q^{56} -1.00000 q^{57} +6.00000 q^{58} +(-2.00000 + 3.46410i) q^{59} +1.00000 q^{61} +(-2.50000 - 0.866025i) q^{63} +1.00000 q^{64} +(-1.00000 - 1.73205i) q^{66} +12.0000 q^{67} +(-2.00000 - 3.46410i) q^{68} +(-2.00000 - 3.46410i) q^{69} +(-3.00000 - 5.19615i) q^{71} +1.00000 q^{72} +(3.50000 + 6.06218i) q^{73} +(5.50000 - 9.52628i) q^{74} +(-2.50000 - 4.33013i) q^{75} +(-0.500000 + 0.866025i) q^{76} +(5.00000 + 1.73205i) q^{77} +(1.00000 + 3.46410i) q^{78} +(-4.00000 + 6.92820i) q^{79} +1.00000 q^{81} -2.00000 q^{82} -14.0000 q^{83} +(-2.00000 + 1.73205i) q^{84} +(0.500000 - 0.866025i) q^{86} +(3.00000 - 5.19615i) q^{87} -2.00000 q^{88} +(-3.00000 - 5.19615i) q^{89} +(-8.00000 - 5.19615i) q^{91} -4.00000 q^{92} +(0.500000 - 0.866025i) q^{96} +(-4.50000 - 7.79423i) q^{97} +(1.00000 - 6.92820i) q^{98} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} - 2 q^{3} - q^{4} + q^{6} - 5 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - q^2 - 2 * q^3 - q^4 + q^6 - 5 * q^7 + 2 * q^8 + 2 * q^9	$ 2 q - q^{2} - 2 q^{3} - q^{4} + q^{6} - 5 q^{7} + 2 q^{8} + 2 q^{9} - 4 q^{11} + q^{12} + 7 q^{13} + q^{14} - q^{16} - 4 q^{17} - q^{18} + 2 q^{19} + 5 q^{21} + 2 q^{22} + 4 q^{23} - 2 q^{24} + 5 q^{25} - 2 q^{26} - 2 q^{27} + 4 q^{28} - 6 q^{29} - q^{32} + 4 q^{33} + 8 q^{34} - q^{36} + 11 q^{37} - q^{38} - 7 q^{39} + 2 q^{41} - q^{42} + q^{43} + 2 q^{44} + 4 q^{46} + q^{48} + 11 q^{49} + 5 q^{50} + 4 q^{51} - 5 q^{52} - 4 q^{53} + q^{54} - 5 q^{56} - 2 q^{57} + 12 q^{58} - 4 q^{59} + 2 q^{61} - 5 q^{63} + 2 q^{64} - 2 q^{66} + 24 q^{67} - 4 q^{68} - 4 q^{69} - 6 q^{71} + 2 q^{72} + 7 q^{73} + 11 q^{74} - 5 q^{75} - q^{76} + 10 q^{77} + 2 q^{78} - 8 q^{79} + 2 q^{81} - 4 q^{82} - 28 q^{83} - 4 q^{84} + q^{86} + 6 q^{87} - 4 q^{88} - 6 q^{89} - 16 q^{91} - 8 q^{92} + q^{96} - 9 q^{97} + 2 q^{98} - 4 q^{99}+O(q^{100}) $ 2 * q - q^2 - 2 * q^3 - q^4 + q^6 - 5 * q^7 + 2 * q^8 + 2 * q^9 - 4 * q^11 + q^12 + 7 * q^13 + q^14 - q^16 - 4 * q^17 - q^18 + 2 * q^19 + 5 * q^21 + 2 * q^22 + 4 * q^23 - 2 * q^24 + 5 * q^25 - 2 * q^26 - 2 * q^27 + 4 * q^28 - 6 * q^29 - q^32 + 4 * q^33 + 8 * q^34 - q^36 + 11 * q^37 - q^38 - 7 * q^39 + 2 * q^41 - q^42 + q^43 + 2 * q^44 + 4 * q^46 + q^48 + 11 * q^49 + 5 * q^50 + 4 * q^51 - 5 * q^52 - 4 * q^53 + q^54 - 5 * q^56 - 2 * q^57 + 12 * q^58 - 4 * q^59 + 2 * q^61 - 5 * q^63 + 2 * q^64 - 2 * q^66 + 24 * q^67 - 4 * q^68 - 4 * q^69 - 6 * q^71 + 2 * q^72 + 7 * q^73 + 11 * q^74 - 5 * q^75 - q^76 + 10 * q^77 + 2 * q^78 - 8 * q^79 + 2 * q^81 - 4 * q^82 - 28 * q^83 - 4 * q^84 + q^86 + 6 * q^87 - 4 * q^88 - 6 * q^89 - 16 * q^91 - 8 * q^92 + q^96 - 9 * q^97 + 2 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$2$	−0.500000	−	0.866025i	−0.353553	−	0.612372i
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$5$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$7$	−2.50000	−	0.866025i	−0.944911	−	0.327327i
$8$	1.00000			0.353553
$9$	1.00000			0.333333
$10$		0			0
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	3.50000	+	0.866025i	0.970725	+	0.240192i
$13$	3.50000	+	0.866025i	0.970725	+	0.240192i
$14$	0.500000	+	2.59808i	0.133631	+	0.694365i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	−0.999853	−	0.0171533i	$-0.994540\pi$
$17$	−2.00000	+	3.46410i	−0.485071	+	0.840168i	0.514782	+	0.857321i	$0.327873\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	1.00000			0.229416			0.114708	−	0.993399i	$-0.463407\pi$
$19$	1.00000			0.229416			0.114708	+	0.993399i	$0.463407\pi$
$20$		0			0
$21$	2.50000	+	0.866025i	0.545545	+	0.188982i
$22$	1.00000	+	1.73205i	0.213201	+	0.369274i
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	0.995639	−	0.0932891i	$-0.0297381\pi$
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	−0.578610	+	0.815604i	$0.696405\pi$
$24$	−1.00000			−0.204124
$25$	2.50000	+	4.33013i	0.500000	+	0.866025i
$26$	−1.00000	−	3.46410i	−0.196116	−	0.679366i
$27$	−1.00000			−0.192450
$28$	2.00000	−	1.73205i	0.377964	−	0.327327i
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	0.440652	+	0.897678i	$0.354747\pi$
$29$	−3.00000	+	5.19615i	−0.557086	+	0.964901i	−0.997738	+	0.0672232i	$0.978586\pi$
$30$		0			0
$31$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$31$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$32$	−0.500000	+	0.866025i	−0.0883883	+	0.153093i
$33$	2.00000			0.348155
$34$	4.00000			0.685994
$35$		0			0
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	5.50000	+	9.52628i	0.904194	+	1.56611i	0.821995	+	0.569495i	$0.192861\pi$
$37$	5.50000	+	9.52628i	0.904194	+	1.56611i	0.0821995	+	0.996616i	$0.473806\pi$
$38$	−0.500000	−	0.866025i	−0.0811107	−	0.140488i
$39$	−3.50000	−	0.866025i	−0.560449	−	0.138675i
$40$		0			0
$41$	1.00000	−	1.73205i	0.156174	−	0.270501i	−0.777312	−	0.629115i	$-0.783417\pi$
$41$	1.00000	−	1.73205i	0.156174	−	0.270501i	0.933486	+	0.358614i	$0.116751\pi$
$42$	−0.500000	−	2.59808i	−0.0771517	−	0.400892i
$43$	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
$46$	2.00000	−	3.46410i	0.294884	−	0.510754i
$47$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$47$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	5.50000	+	4.33013i	0.785714	+	0.618590i
$50$	2.50000	−	4.33013i	0.353553	−	0.612372i
$51$	2.00000	−	3.46410i	0.280056	−	0.485071i
$52$	−2.50000	+	2.59808i	−0.346688	+	0.360288i
$53$	−2.00000	−	3.46410i	−0.274721	−	0.475831i	0.695344	−	0.718677i	$-0.255252\pi$
$53$	−2.00000	−	3.46410i	−0.274721	−	0.475831i	−0.970065	+	0.242846i	$0.921919\pi$
$54$	0.500000	+	0.866025i	0.0680414	+	0.117851i
$55$		0			0
$56$	−2.50000	−	0.866025i	−0.334077	−	0.115728i
$57$	−1.00000			−0.132453
$58$	6.00000			0.787839
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	−0.966342	−	0.257260i	$-0.917180\pi$
$59$	−2.00000	+	3.46410i	−0.260378	+	0.450988i	0.705965	+	0.708247i	$0.250514\pi$
$60$		0			0
$61$	1.00000			0.128037			0.0640184	−	0.997949i	$-0.479608\pi$
$61$	1.00000			0.128037			0.0640184	+	0.997949i	$0.479608\pi$
$62$		0			0
$63$	−2.50000	−	0.866025i	−0.314970	−	0.109109i
$64$	1.00000			0.125000
$65$		0			0
$66$	−1.00000	−	1.73205i	−0.123091	−	0.213201i
$67$	12.0000			1.46603			0.733017	−	0.680211i	$-0.238112\pi$
$67$	12.0000			1.46603			0.733017	+	0.680211i	$0.238112\pi$
$68$	−2.00000	−	3.46410i	−0.242536	−	0.420084i
$69$	−2.00000	−	3.46410i	−0.240772	−	0.417029i
$70$		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	$0.949205\pi$
$72$	1.00000			0.117851
$73$	3.50000	+	6.06218i	0.409644	+	0.709524i	0.994850	−	0.101361i	$-0.0323196\pi$
$73$	3.50000	+	6.06218i	0.409644	+	0.709524i	−0.585206	+	0.810885i	$0.698986\pi$
$74$	5.50000	−	9.52628i	0.639362	−	1.10741i
$75$	−2.50000	−	4.33013i	−0.288675	−	0.500000i
$76$	−0.500000	+	0.866025i	−0.0573539	+	0.0993399i
$77$	5.00000	+	1.73205i	0.569803	+	0.197386i
$78$	1.00000	+	3.46410i	0.113228	+	0.392232i
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	−0.998388	−	0.0567635i	$-0.981922\pi$
$79$	−4.00000	+	6.92820i	−0.450035	+	0.779484i	0.548352	+	0.836247i	$0.315255\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$	−2.00000			−0.220863
$83$	−14.0000			−1.53670			−0.768350	−	0.640030i	$-0.778922\pi$
$83$	−14.0000			−1.53670			−0.768350	+	0.640030i	$0.778922\pi$
$84$	−2.00000	+	1.73205i	−0.218218	+	0.188982i
$85$		0			0
$86$	0.500000	−	0.866025i	0.0539164	−	0.0933859i
$87$	3.00000	−	5.19615i	0.321634	−	0.557086i
$88$	−2.00000			−0.213201
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	0.662071	−	0.749441i	$-0.269678\pi$
$89$	−3.00000	−	5.19615i	−0.317999	−	0.550791i	−0.980071	+	0.198650i	$0.936344\pi$
$90$		0			0
$91$	−8.00000	−	5.19615i	−0.838628	−	0.544705i
$92$	−4.00000			−0.417029
$93$		0			0
$94$		0			0
$95$		0			0
$96$	0.500000	−	0.866025i	0.0510310	−	0.0883883i
$97$	−4.50000	−	7.79423i	−0.456906	−	0.791384i	0.541890	−	0.840450i	$-0.317709\pi$
$97$	−4.50000	−	7.79423i	−0.456906	−	0.791384i	−0.998796	+	0.0490655i	$0.984376\pi$
$98$	1.00000	−	6.92820i	0.101015	−	0.699854i
$99$	−2.00000			−0.201008
$100$	−5.00000			−0.500000
$101$	−18.0000			−1.79107			−0.895533	−	0.444994i	$-0.853206\pi$
$101$	−18.0000			−1.79107			−0.895533	+	0.444994i	$0.853206\pi$
$102$	−4.00000			−0.396059
$103$	3.50000	−	6.06218i	0.344865	−	0.597324i	−0.640464	−	0.767988i	$-0.721258\pi$
$103$	3.50000	−	6.06218i	0.344865	−	0.597324i	0.985329	+	0.170664i	$0.0545913\pi$
$104$	3.50000	+	0.866025i	0.343203	+	0.0849208i
$105$		0			0
$106$	−2.00000	+	3.46410i	−0.194257	+	0.336463i
$107$	9.00000	+	15.5885i	0.870063	+	1.50699i	0.861931	+	0.507026i	$0.169255\pi$
$107$	9.00000	+	15.5885i	0.870063	+	1.50699i	0.00813215	+	0.999967i	$0.497411\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−5.50000	−	9.52628i	−0.526804	−	0.912452i	−0.999512	−	0.0312328i	$-0.990057\pi$
$109$	−5.50000	−	9.52628i	−0.526804	−	0.912452i	0.472708	−	0.881219i	$-0.343277\pi$
$110$		0			0
$111$	−5.50000	−	9.52628i	−0.522037	−	0.904194i
$112$	0.500000	+	2.59808i	0.0472456	+	0.245495i
$113$	4.00000	+	6.92820i	0.376288	+	0.651751i	0.990519	−	0.137376i	$-0.0438669\pi$
$113$	4.00000	+	6.92820i	0.376288	+	0.651751i	−0.614231	+	0.789127i	$0.710534\pi$
$114$	0.500000	+	0.866025i	0.0468293	+	0.0811107i
$115$		0			0
$116$	−3.00000	−	5.19615i	−0.278543	−	0.482451i
$117$	3.50000	+	0.866025i	0.323575	+	0.0800641i
$118$	4.00000			0.368230
$119$	8.00000	−	6.92820i	0.733359	−	0.635107i
$120$		0			0
$121$	−7.00000			−0.636364
$122$	−0.500000	−	0.866025i	−0.0452679	−	0.0784063i
$123$	−1.00000	+	1.73205i	−0.0901670	+	0.156174i
$124$		0			0
$125$		0			0
$126$	0.500000	+	2.59808i	0.0445435	+	0.231455i
$127$	−6.50000	+	11.2583i	−0.576782	+	0.999015i	0.419064	+	0.907957i	$0.362358\pi$
$127$	−6.50000	+	11.2583i	−0.576782	+	0.999015i	−0.995846	+	0.0910585i	$0.970975\pi$
$128$	−0.500000	−	0.866025i	−0.0441942	−	0.0765466i
$129$	−0.500000	−	0.866025i	−0.0440225	−	0.0762493i
$130$		0			0
$131$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$131$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$132$	−1.00000	+	1.73205i	−0.0870388	+	0.150756i
$133$	−2.50000	−	0.866025i	−0.216777	−	0.0750939i
$134$	−6.00000	−	10.3923i	−0.518321	−	0.897758i
$135$		0			0
$136$	−2.00000	+	3.46410i	−0.171499	+	0.297044i
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	0.487278	+	0.873247i	$0.337990\pi$
$137$	−6.00000	+	10.3923i	−0.512615	+	0.887875i	−0.999893	+	0.0146279i	$0.995344\pi$
$138$	−2.00000	+	3.46410i	−0.170251	+	0.294884i
$139$	−8.00000	−	13.8564i	−0.678551	−	1.17529i	−0.975417	−	0.220366i	$-0.929275\pi$
$139$	−8.00000	−	13.8564i	−0.678551	−	1.17529i	0.296866	−	0.954919i	$-0.404058\pi$
$140$		0			0
$141$		0			0
$142$	−3.00000	+	5.19615i	−0.251754	+	0.436051i
$143$	−7.00000	−	1.73205i	−0.585369	−	0.144841i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$		0			0
$146$	3.50000	−	6.06218i	0.289662	−	0.501709i
$147$	−5.50000	−	4.33013i	−0.453632	−	0.357143i
$148$	−11.0000			−0.904194
$149$	10.0000			0.819232			0.409616	−	0.912258i	$-0.365663\pi$
$149$	10.0000			0.819232			0.409616	+	0.912258i	$0.365663\pi$
$150$	−2.50000	+	4.33013i	−0.204124	+	0.353553i
$151$	−2.00000	−	3.46410i	−0.162758	−	0.281905i	0.773099	−	0.634285i	$-0.218706\pi$
$151$	−2.00000	−	3.46410i	−0.162758	−	0.281905i	−0.935857	+	0.352381i	$0.885372\pi$
$152$	1.00000			0.0811107
$153$	−2.00000	+	3.46410i	−0.161690	+	0.280056i
$154$	−1.00000	−	5.19615i	−0.0805823	−	0.418718i
$155$		0			0
$156$	2.50000	−	2.59808i	0.200160	−	0.208013i
$157$	3.50000	+	6.06218i	0.279330	+	0.483814i	0.971219	−	0.238190i	$-0.0765542\pi$
$157$	3.50000	+	6.06218i	0.279330	+	0.483814i	−0.691888	+	0.722005i	$0.743221\pi$
$158$	8.00000			0.636446
$159$	2.00000	+	3.46410i	0.158610	+	0.274721i
$160$		0			0
$161$	−2.00000	−	10.3923i	−0.157622	−	0.819028i
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	−11.0000			−0.861586			−0.430793	−	0.902451i	$-0.641766\pi$
$163$	−11.0000			−0.861586			−0.430793	+	0.902451i	$0.641766\pi$
$164$	1.00000	+	1.73205i	0.0780869	+	0.135250i
$165$		0			0
$166$	7.00000	+	12.1244i	0.543305	+	0.941033i
$167$	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	$0.142010\pi$
$168$	2.50000	+	0.866025i	0.192879	+	0.0668153i
$169$	11.5000	+	6.06218i	0.884615	+	0.466321i
$170$		0			0
$171$	1.00000			0.0764719
$172$	−1.00000			−0.0762493
$173$	8.00000			0.608229			0.304114	−	0.952636i	$-0.401639\pi$
$173$	8.00000			0.608229			0.304114	+	0.952636i	$0.401639\pi$
$174$	−6.00000			−0.454859
$175$	−2.50000	−	12.9904i	−0.188982	−	0.981981i
$176$	1.00000	+	1.73205i	0.0753778	+	0.130558i
$177$	2.00000	−	3.46410i	0.150329	−	0.260378i
$178$	−3.00000	+	5.19615i	−0.224860	+	0.389468i
$179$	−16.0000			−1.19590			−0.597948	−	0.801535i	$-0.704017\pi$
$179$	−16.0000			−1.19590			−0.597948	+	0.801535i	$0.704017\pi$
$180$		0			0
$181$	7.00000			0.520306			0.260153	−	0.965567i	$-0.416227\pi$
$181$	7.00000			0.520306			0.260153	+	0.965567i	$0.416227\pi$
$182$	−0.500000	+	9.52628i	−0.0370625	+	0.706135i
$183$	−1.00000			−0.0739221
$184$	2.00000	+	3.46410i	0.147442	+	0.255377i
$185$		0			0
$186$		0			0
$187$	4.00000	−	6.92820i	0.292509	−	0.506640i
$188$		0			0
$189$	2.50000	+	0.866025i	0.181848	+	0.0629941i
$190$		0			0
$191$	24.0000			1.73658			0.868290	−	0.496058i	$-0.165220\pi$
$191$	24.0000			1.73658			0.868290	+	0.496058i	$0.165220\pi$
$192$	−1.00000			−0.0721688
$193$	19.0000			1.36765			0.683825	−	0.729646i	$-0.260315\pi$
$193$	19.0000			1.36765			0.683825	+	0.729646i	$0.260315\pi$
$194$	−4.50000	+	7.79423i	−0.323081	+	0.559593i
$195$		0			0
$196$	−6.50000	+	2.59808i	−0.464286	+	0.185577i
$197$	4.00000	−	6.92820i	0.284988	−	0.493614i	−0.687618	−	0.726073i	$-0.741344\pi$
$197$	4.00000	−	6.92820i	0.284988	−	0.493614i	0.972606	+	0.232458i	$0.0746770\pi$
$198$	1.00000	+	1.73205i	0.0710669	+	0.123091i
$199$	1.50000	−	2.59808i	0.106332	−	0.184173i	−0.807950	−	0.589252i	$-0.799423\pi$
$199$	1.50000	−	2.59808i	0.106332	−	0.184173i	0.914282	+	0.405079i	$0.132756\pi$
$200$	2.50000	+	4.33013i	0.176777	+	0.306186i
$201$	−12.0000			−0.846415
$202$	9.00000	+	15.5885i	0.633238	+	1.09680i
$203$	12.0000	−	10.3923i	0.842235	−	0.729397i
$204$	2.00000	+	3.46410i	0.140028	+	0.242536i
$205$		0			0
$206$	−7.00000			−0.487713
$207$	2.00000	+	3.46410i	0.139010	+	0.240772i
$208$	−1.00000	−	3.46410i	−0.0693375	−	0.240192i
$209$	−2.00000			−0.138343
$210$		0			0
$211$	−6.50000	+	11.2583i	−0.447478	+	0.775055i	−0.998221	−	0.0596196i	$-0.981011\pi$
$211$	−6.50000	+	11.2583i	−0.447478	+	0.775055i	0.550743	+	0.834675i	$0.314345\pi$
$212$	4.00000			0.274721
$213$	3.00000	+	5.19615i	0.205557	+	0.356034i
$214$	9.00000	−	15.5885i	0.615227	−	1.06561i
$215$		0			0
$216$	−1.00000			−0.0680414
$217$		0			0
$218$	−5.50000	+	9.52628i	−0.372507	+	0.645201i
$219$	−3.50000	−	6.06218i	−0.236508	−	0.409644i
$220$		0			0
$221$	−10.0000	+	10.3923i	−0.672673	+	0.699062i
$222$	−5.50000	+	9.52628i	−0.369136	+	0.639362i
$223$	8.00000	−	13.8564i	0.535720	−	0.927894i	−0.463409	−	0.886145i	$-0.653374\pi$
$223$	8.00000	−	13.8564i	0.535720	−	0.927894i	0.999128	−	0.0417488i	$-0.0132929\pi$
$224$	2.00000	−	1.73205i	0.133631	−	0.115728i
$225$	2.50000	+	4.33013i	0.166667	+	0.288675i
$226$	4.00000	−	6.92820i	0.266076	−	0.460857i
$227$	−9.00000	+	15.5885i	−0.597351	+	1.03464i	0.395860	+	0.918311i	$0.370447\pi$
$227$	−9.00000	+	15.5885i	−0.597351	+	1.03464i	−0.993210	+	0.116331i	$0.962887\pi$
$228$	0.500000	−	0.866025i	0.0331133	−	0.0573539i
$229$	10.5000	−	18.1865i	0.693860	−	1.20180i	−0.276704	−	0.960955i	$-0.589242\pi$
$229$	10.5000	−	18.1865i	0.693860	−	1.20180i	0.970564	−	0.240845i	$-0.0774245\pi$
$230$		0			0
$231$	−5.00000	−	1.73205i	−0.328976	−	0.113961i
$232$	−3.00000	+	5.19615i	−0.196960	+	0.341144i
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	−0.750867	−	0.660454i	$-0.770364\pi$
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	0.947403	+	0.320043i	$0.103697\pi$
$234$	−1.00000	−	3.46410i	−0.0653720	−	0.226455i
$235$		0			0
$236$	−2.00000	−	3.46410i	−0.130189	−	0.225494i
$237$	4.00000	−	6.92820i	0.259828	−	0.450035i
$238$	−10.0000	−	3.46410i	−0.648204	−	0.224544i
$239$	2.00000			0.129369			0.0646846	−	0.997906i	$-0.479396\pi$
$239$	2.00000			0.129369			0.0646846	+	0.997906i	$0.479396\pi$
$240$		0			0
$241$	−9.00000	+	15.5885i	−0.579741	+	1.00414i	0.415768	+	0.909471i	$0.363513\pi$
$241$	−9.00000	+	15.5885i	−0.579741	+	1.00414i	−0.995509	+	0.0946700i	$0.969820\pi$
$242$	3.50000	+	6.06218i	0.224989	+	0.389692i
$243$	−1.00000			−0.0641500
$244$	−0.500000	+	0.866025i	−0.0320092	+	0.0554416i
$245$		0			0
$246$	2.00000			0.127515
$247$	3.50000	+	0.866025i	0.222700	+	0.0551039i
$248$		0			0
$249$	14.0000			0.887214
$250$		0			0
$251$	−15.0000	−	25.9808i	−0.946792	−	1.63989i	−0.752124	−	0.659022i	$-0.770970\pi$
$251$	−15.0000	−	25.9808i	−0.946792	−	1.63989i	−0.194668	−	0.980869i	$-0.562363\pi$
$252$	2.00000	−	1.73205i	0.125988	−	0.109109i
$253$	−4.00000	−	6.92820i	−0.251478	−	0.435572i
$254$	13.0000			0.815693
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	4.00000	+	6.92820i	0.249513	+	0.432169i	0.963391	−	0.268101i	$-0.0863961\pi$
$257$	4.00000	+	6.92820i	0.249513	+	0.432169i	−0.713878	+	0.700270i	$0.753063\pi$
$258$	−0.500000	+	0.866025i	−0.0311286	+	0.0539164i
$259$	−5.50000	−	28.5788i	−0.341753	−	1.77580i
$260$		0			0
$261$	−3.00000	+	5.19615i	−0.185695	+	0.321634i
$262$		0			0
$263$	26.0000			1.60323			0.801614	−	0.597841i	$-0.203975\pi$
$263$	26.0000			1.60323			0.801614	+	0.597841i	$0.203975\pi$
$264$	2.00000			0.123091
$265$		0			0
$266$	0.500000	+	2.59808i	0.0306570	+	0.159298i
$267$	3.00000	+	5.19615i	0.183597	+	0.317999i
$268$	−6.00000	+	10.3923i	−0.366508	+	0.634811i
$269$	5.00000	−	8.66025i	0.304855	−	0.528025i	−0.672374	−	0.740212i	$-0.734725\pi$
$269$	5.00000	−	8.66025i	0.304855	−	0.528025i	0.977229	+	0.212187i	$0.0680585\pi$
$270$		0			0
$271$	7.50000	+	12.9904i	0.455593	+	0.789109i	0.998722	−	0.0505395i	$-0.0160941\pi$
$271$	7.50000	+	12.9904i	0.455593	+	0.789109i	−0.543130	+	0.839649i	$0.682761\pi$
$272$	4.00000			0.242536
$273$	8.00000	+	5.19615i	0.484182	+	0.314485i
$274$	12.0000			0.724947
$275$	−5.00000	−	8.66025i	−0.301511	−	0.522233i
$276$	4.00000			0.240772
$277$	−9.50000	+	16.4545i	−0.570800	+	0.988654i	0.425684	+	0.904872i	$0.360033\pi$
$277$	−9.50000	+	16.4545i	−0.570800	+	0.988654i	−0.996484	+	0.0837823i	$0.973300\pi$
$278$	−8.00000	+	13.8564i	−0.479808	+	0.831052i
$279$		0			0
$280$		0			0
$281$	30.0000			1.78965			0.894825	−	0.446417i	$-0.147300\pi$
$281$	30.0000			1.78965			0.894825	+	0.446417i	$0.147300\pi$
$282$		0			0
$283$	−25.0000			−1.48610			−0.743048	−	0.669238i	$-0.766621\pi$
$283$	−25.0000			−1.48610			−0.743048	+	0.669238i	$0.766621\pi$
$284$	6.00000			0.356034
$285$		0			0
$286$	2.00000	+	6.92820i	0.118262	+	0.409673i
$287$	−4.00000	+	3.46410i	−0.236113	+	0.204479i
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$		0			0
$291$	4.50000	+	7.79423i	0.263795	+	0.456906i
$292$	−7.00000			−0.409644
$293$	6.00000	+	10.3923i	0.350524	+	0.607125i	0.986341	−	0.164714i	$-0.0526703\pi$
$293$	6.00000	+	10.3923i	0.350524	+	0.607125i	−0.635818	+	0.771839i	$0.719337\pi$
$294$	−1.00000	+	6.92820i	−0.0583212	+	0.404061i
$295$		0			0
$296$	5.50000	+	9.52628i	0.319681	+	0.553704i
$297$	2.00000			0.116052
$298$	−5.00000	−	8.66025i	−0.289642	−	0.501675i
$299$	4.00000	+	13.8564i	0.231326	+	0.801337i
$300$	5.00000			0.288675
$301$	−0.500000	−	2.59808i	−0.0288195	−	0.149751i
$302$	−2.00000	+	3.46410i	−0.115087	+	0.199337i
$303$	18.0000			1.03407
$304$	−0.500000	−	0.866025i	−0.0286770	−	0.0496700i
$305$		0			0
$306$	4.00000			0.228665
$307$	28.0000			1.59804			0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000			1.59804			0.799022	+	0.601302i	$0.205351\pi$
$308$	−4.00000	+	3.46410i	−0.227921	+	0.197386i
$309$	−3.50000	+	6.06218i	−0.199108	+	0.344865i
$310$		0			0
$311$	14.0000	+	24.2487i	0.793867	+	1.37502i	0.923556	+	0.383464i	$0.125269\pi$
$311$	14.0000	+	24.2487i	0.793867	+	1.37502i	−0.129689	+	0.991555i	$0.541398\pi$
$312$	−3.50000	−	0.866025i	−0.198148	−	0.0490290i
$313$	10.5000	−	18.1865i	0.593495	−	1.02796i	−0.400262	−	0.916401i	$-0.631081\pi$
$313$	10.5000	−	18.1865i	0.593495	−	1.02796i	0.993757	−	0.111563i	$-0.0355857\pi$
$314$	3.50000	−	6.06218i	0.197516	−	0.342108i
$315$		0			0
$316$	−4.00000	−	6.92820i	−0.225018	−	0.389742i
$317$	−4.00000	+	6.92820i	−0.224662	+	0.389127i	−0.956218	−	0.292655i	$-0.905461\pi$
$317$	−4.00000	+	6.92820i	−0.224662	+	0.389127i	0.731556	+	0.681782i	$0.238795\pi$
$318$	2.00000	−	3.46410i	0.112154	−	0.194257i
$319$	6.00000	−	10.3923i	0.335936	−	0.581857i
$320$		0			0
$321$	−9.00000	−	15.5885i	−0.502331	−	0.870063i
$322$	−8.00000	+	6.92820i	−0.445823	+	0.386094i
$323$	−2.00000	+	3.46410i	−0.111283	+	0.192748i
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	5.00000	+	17.3205i	0.277350	+	0.960769i
$326$	5.50000	+	9.52628i	0.304617	+	0.527612i
$327$	5.50000	+	9.52628i	0.304151	+	0.526804i
$328$	1.00000	−	1.73205i	0.0552158	−	0.0956365i
$329$		0			0
$330$		0			0
$331$	−11.0000			−0.604615			−0.302307	−	0.953211i	$-0.597757\pi$
$331$	−11.0000			−0.604615			−0.302307	+	0.953211i	$0.597757\pi$
$332$	7.00000	−	12.1244i	0.384175	−	0.665410i
$333$	5.50000	+	9.52628i	0.301398	+	0.522037i
$334$	−2.00000			−0.109435
$335$		0			0
$336$	−0.500000	−	2.59808i	−0.0272772	−	0.141737i
$337$	9.00000			0.490261			0.245131	−	0.969490i	$-0.421169\pi$
$337$	9.00000			0.490261			0.245131	+	0.969490i	$0.421169\pi$
$338$	−0.500000	−	12.9904i	−0.0271964	−	0.706584i
$339$	−4.00000	−	6.92820i	−0.217250	−	0.376288i
$340$		0			0
$341$		0			0
$342$	−0.500000	−	0.866025i	−0.0270369	−	0.0468293i
$343$	−10.0000	−	15.5885i	−0.539949	−	0.841698i
$344$	0.500000	+	0.866025i	0.0269582	+	0.0466930i
$345$		0			0
$346$	−4.00000	−	6.92820i	−0.215041	−	0.372463i
$347$	−13.0000	+	22.5167i	−0.697877	+	1.20876i	0.271325	+	0.962488i	$0.412538\pi$
$347$	−13.0000	+	22.5167i	−0.697877	+	1.20876i	−0.969201	+	0.246270i	$0.920795\pi$
$348$	3.00000	+	5.19615i	0.160817	+	0.278543i
$349$	−2.50000	+	4.33013i	−0.133822	+	0.231786i	−0.925147	−	0.379610i	$-0.876058\pi$
$349$	−2.50000	+	4.33013i	−0.133822	+	0.231786i	0.791325	+	0.611396i	$0.209392\pi$
$350$	−10.0000	+	8.66025i	−0.534522	+	0.462910i
$351$	−3.50000	−	0.866025i	−0.186816	−	0.0462250i
$352$	1.00000	−	1.73205i	0.0533002	−	0.0923186i
$353$	−4.00000			−0.212899			−0.106449	−	0.994318i	$-0.533948\pi$
$353$	−4.00000			−0.212899			−0.106449	+	0.994318i	$0.533948\pi$
$354$	−4.00000			−0.212598
$355$		0			0
$356$	6.00000			0.317999
$357$	−8.00000	+	6.92820i	−0.423405	+	0.366679i
$358$	8.00000	+	13.8564i	0.422813	+	0.732334i
$359$	3.00000	−	5.19615i	0.158334	−	0.274242i	−0.775934	−	0.630814i	$-0.782721\pi$
$359$	3.00000	−	5.19615i	0.158334	−	0.274242i	0.934268	+	0.356572i	$0.116054\pi$
$360$		0			0
$361$	−18.0000			−0.947368
$362$	−3.50000	−	6.06218i	−0.183956	−	0.318621i
$363$	7.00000			0.367405
$364$	8.50000	−	4.33013i	0.445521	−	0.226960i
$365$		0			0
$366$	0.500000	+	0.866025i	0.0261354	+	0.0452679i
$367$	−25.0000			−1.30499			−0.652495	−	0.757793i	$-0.726278\pi$
$367$	−25.0000			−1.30499			−0.652495	+	0.757793i	$0.726278\pi$
$368$	2.00000	−	3.46410i	0.104257	−	0.180579i
$369$	1.00000	−	1.73205i	0.0520579	−	0.0901670i
$370$		0			0
$371$	2.00000	+	10.3923i	0.103835	+	0.539542i
$372$		0			0
$373$	−18.0000			−0.932005			−0.466002	−	0.884783i	$-0.654306\pi$
$373$	−18.0000			−0.932005			−0.466002	+	0.884783i	$0.654306\pi$
$374$	−8.00000			−0.413670
$375$		0			0
$376$		0			0
$377$	−15.0000	+	15.5885i	−0.772539	+	0.802846i
$378$	−0.500000	−	2.59808i	−0.0257172	−	0.133631i
$379$	−10.0000	+	17.3205i	−0.513665	+	0.889695i	0.486209	+	0.873843i	$0.338379\pi$
$379$	−10.0000	+	17.3205i	−0.513665	+	0.889695i	−0.999874	+	0.0158521i	$0.994954\pi$
$380$		0			0
$381$	6.50000	−	11.2583i	0.333005	−	0.576782i
$382$	−12.0000	−	20.7846i	−0.613973	−	1.06343i
$383$	8.00000			0.408781			0.204390	−	0.978889i	$-0.434479\pi$
$383$	8.00000			0.408781			0.204390	+	0.978889i	$0.434479\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$		0			0
$386$	−9.50000	−	16.4545i	−0.483537	−	0.837511i
$387$	0.500000	+	0.866025i	0.0254164	+	0.0440225i
$388$	9.00000			0.456906
$389$	−2.00000	−	3.46410i	−0.101404	−	0.175637i	0.810859	−	0.585241i	$-0.199000\pi$
$389$	−2.00000	−	3.46410i	−0.101404	−	0.175637i	−0.912263	+	0.409604i	$0.865667\pi$
$390$		0			0
$391$	−16.0000			−0.809155
$392$	5.50000	+	4.33013i	0.277792	+	0.218704i
$393$		0			0
$394$	−8.00000			−0.403034
$395$		0			0
$396$	1.00000	−	1.73205i	0.0502519	−	0.0870388i
$397$	1.00000			0.0501886			0.0250943	−	0.999685i	$-0.492011\pi$
$397$	1.00000			0.0501886			0.0250943	+	0.999685i	$0.492011\pi$
$398$	−3.00000			−0.150376
$399$	2.50000	+	0.866025i	0.125157	+	0.0433555i
$400$	2.50000	−	4.33013i	0.125000	−	0.216506i
$401$	−5.00000	−	8.66025i	−0.249688	−	0.432472i	0.713751	−	0.700399i	$-0.246995\pi$
$401$	−5.00000	−	8.66025i	−0.249688	−	0.432472i	−0.963439	+	0.267927i	$0.913661\pi$
$402$	6.00000	+	10.3923i	0.299253	+	0.518321i
$403$		0			0
$404$	9.00000	−	15.5885i	0.447767	−	0.775555i
$405$		0			0
$406$	−15.0000	−	5.19615i	−0.744438	−	0.257881i
$407$	−11.0000	−	19.0526i	−0.545250	−	0.944400i
$408$	2.00000	−	3.46410i	0.0990148	−	0.171499i
$409$	15.5000	−	26.8468i	0.766426	−	1.32749i	−0.173064	−	0.984911i	$-0.555367\pi$
$409$	15.5000	−	26.8468i	0.766426	−	1.32749i	0.939490	−	0.342578i	$-0.111300\pi$
$410$		0			0
$411$	6.00000	−	10.3923i	0.295958	−	0.512615i
$412$	3.50000	+	6.06218i	0.172433	+	0.298662i
$413$	8.00000	−	6.92820i	0.393654	−	0.340915i
$414$	2.00000	−	3.46410i	0.0982946	−	0.170251i
$415$		0			0
$416$	−2.50000	+	2.59808i	−0.122573	+	0.127381i
$417$	8.00000	+	13.8564i	0.391762	+	0.678551i
$418$	1.00000	+	1.73205i	0.0489116	+	0.0847174i
$419$	−13.0000	+	22.5167i	−0.635092	+	1.10001i	0.351404	+	0.936224i	$0.385704\pi$
$419$	−13.0000	+	22.5167i	−0.635092	+	1.10001i	−0.986496	+	0.163787i	$0.947629\pi$
$420$		0			0
$421$	2.00000			0.0974740			0.0487370	−	0.998812i	$-0.484480\pi$
$421$	2.00000			0.0974740			0.0487370	+	0.998812i	$0.484480\pi$
$422$	13.0000			0.632830
$423$		0			0
$424$	−2.00000	−	3.46410i	−0.0971286	−	0.168232i
$425$	−20.0000			−0.970143
$426$	3.00000	−	5.19615i	0.145350	−	0.251754i
$427$	−2.50000	−	0.866025i	−0.120983	−	0.0419099i
$428$	−18.0000			−0.870063
$429$	7.00000	+	1.73205i	0.337963	+	0.0836242i
$430$		0			0
$431$	26.0000			1.25238			0.626188	−	0.779672i	$-0.284614\pi$
$431$	26.0000			1.25238			0.626188	+	0.779672i	$0.284614\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	13.0000	+	22.5167i	0.624740	+	1.08208i	0.988591	+	0.150624i	$0.0481284\pi$
$433$	13.0000	+	22.5167i	0.624740	+	1.08208i	−0.363851	+	0.931457i	$0.618538\pi$
$434$		0			0
$435$		0			0
$436$	11.0000			0.526804
$437$	2.00000	+	3.46410i	0.0956730	+	0.165710i
$438$	−3.50000	+	6.06218i	−0.167236	+	0.289662i
$439$	0.500000	+	0.866025i	0.0238637	+	0.0413331i	0.877711	−	0.479191i	$-0.159070\pi$
$439$	0.500000	+	0.866025i	0.0238637	+	0.0413331i	−0.853847	+	0.520524i	$0.825737\pi$
$440$		0			0
$441$	5.50000	+	4.33013i	0.261905	+	0.206197i
$442$	14.0000	+	3.46410i	0.665912	+	0.164771i
$443$	−4.00000	+	6.92820i	−0.190046	+	0.329169i	−0.945265	−	0.326303i	$-0.894197\pi$
$443$	−4.00000	+	6.92820i	−0.190046	+	0.329169i	0.755219	+	0.655472i	$0.227530\pi$
$444$	11.0000			0.522037
$445$		0			0
$446$	−16.0000			−0.757622
$447$	−10.0000			−0.472984
$448$	−2.50000	−	0.866025i	−0.118114	−	0.0409159i
$449$	−17.0000	−	29.4449i	−0.802280	−	1.38959i	−0.918112	−	0.396320i	$-0.870287\pi$
$449$	−17.0000	−	29.4449i	−0.802280	−	1.38959i	0.115833	−	0.993269i	$-0.463046\pi$
$450$	2.50000	−	4.33013i	0.117851	−	0.204124i
$451$	−2.00000	+	3.46410i	−0.0941763	+	0.163118i
$452$	−8.00000			−0.376288
$453$	2.00000	+	3.46410i	0.0939682	+	0.162758i
$454$	18.0000			0.844782
$455$		0			0
$456$	−1.00000			−0.0468293
$457$	−19.0000	−	32.9090i	−0.888783	−	1.53942i	−0.841316	−	0.540544i	$-0.818219\pi$
$457$	−19.0000	−	32.9090i	−0.888783	−	1.53942i	−0.0474665	−	0.998873i	$-0.515115\pi$
$458$	−21.0000			−0.981266
$459$	2.00000	−	3.46410i	0.0933520	−	0.161690i
$460$		0			0
$461$	−8.00000	−	13.8564i	−0.372597	−	0.645357i	0.617367	−	0.786675i	$-0.288199\pi$
$461$	−8.00000	−	13.8564i	−0.372597	−	0.645357i	−0.989964	+	0.141318i	$0.954866\pi$
$462$	1.00000	+	5.19615i	0.0465242	+	0.241747i
$463$	23.0000			1.06890			0.534450	−	0.845200i	$-0.320519\pi$
$463$	23.0000			1.06890			0.534450	+	0.845200i	$0.320519\pi$
$464$	6.00000			0.278543
$465$		0			0
$466$	−6.00000			−0.277945
$467$	−21.0000	+	36.3731i	−0.971764	+	1.68314i	−0.281539	+	0.959550i	$0.590845\pi$
$467$	−21.0000	+	36.3731i	−0.971764	+	1.68314i	−0.690225	+	0.723595i	$0.742488\pi$
$468$	−2.50000	+	2.59808i	−0.115563	+	0.120096i
$469$	−30.0000	−	10.3923i	−1.38527	−	0.479872i
$470$		0			0
$471$	−3.50000	−	6.06218i	−0.161271	−	0.279330i
$472$	−2.00000	+	3.46410i	−0.0920575	+	0.159448i
$473$	−1.00000	−	1.73205i	−0.0459800	−	0.0796398i
$474$	−8.00000			−0.367452
$475$	2.50000	+	4.33013i	0.114708	+	0.198680i
$476$	2.00000	+	10.3923i	0.0916698	+	0.476331i
$477$	−2.00000	−	3.46410i	−0.0915737	−	0.158610i
$478$	−1.00000	−	1.73205i	−0.0457389	−	0.0792222i
$479$	10.0000			0.456912			0.228456	−	0.973554i	$-0.426632\pi$
$479$	10.0000			0.456912			0.228456	+	0.973554i	$0.426632\pi$
$480$		0			0
$481$	11.0000	+	38.1051i	0.501557	+	1.73744i
$482$	18.0000			0.819878
$483$	2.00000	+	10.3923i	0.0910032	+	0.472866i
$484$	3.50000	−	6.06218i	0.159091	−	0.275554i
$485$		0			0
$486$	0.500000	+	0.866025i	0.0226805	+	0.0392837i
$487$	11.5000	−	19.9186i	0.521115	−	0.902597i	−0.478584	−	0.878042i	$-0.658850\pi$
$487$	11.5000	−	19.9186i	0.521115	−	0.902597i	0.999698	−	0.0245553i	$-0.00781698\pi$
$488$	1.00000			0.0452679
$489$	11.0000			0.497437
$490$		0			0
$491$	11.0000	−	19.0526i	0.496423	−	0.859830i	−0.503568	−	0.863955i	$-0.667980\pi$
$491$	11.0000	−	19.0526i	0.496423	−	0.859830i	0.999991	+	0.00412539i	$0.00131316\pi$
$492$	−1.00000	−	1.73205i	−0.0450835	−	0.0780869i
$493$	−12.0000	−	20.7846i	−0.540453	−	0.936092i
$494$	−1.00000	−	3.46410i	−0.0449921	−	0.155857i
$495$		0			0
$496$		0			0
$497$	3.00000	+	15.5885i	0.134568	+	0.699238i
$498$	−7.00000	−	12.1244i	−0.313678	−	0.543305i
$499$	−0.500000	+	0.866025i	−0.0223831	+	0.0387686i	−0.877000	−	0.480490i	$-0.840459\pi$
$499$	−0.500000	+	0.866025i	−0.0223831	+	0.0387686i	0.854617	+	0.519259i	$0.173792\pi$
$500$		0			0
$501$	−1.00000	+	1.73205i	−0.0446767	+	0.0773823i
$502$	−15.0000	+	25.9808i	−0.669483	+	1.15958i
$503$	−15.0000	−	25.9808i	−0.668817	−	1.15842i	−0.978235	−	0.207499i	$-0.933468\pi$
$503$	−15.0000	−	25.9808i	−0.668817	−	1.15842i	0.309418	−	0.950926i	$-0.399866\pi$
$504$	−2.50000	−	0.866025i	−0.111359	−	0.0385758i
$505$		0			0
$506$	−4.00000	+	6.92820i	−0.177822	+	0.307996i
$507$	−11.5000	−	6.06218i	−0.510733	−	0.269231i
$508$	−6.50000	−	11.2583i	−0.288391	−	0.499508i
$509$	−3.00000	−	5.19615i	−0.132973	−	0.230315i	0.791849	−	0.610718i	$-0.209119\pi$
$509$	−3.00000	−	5.19615i	−0.132973	−	0.230315i	−0.924821	+	0.380402i	$0.875786\pi$
$510$		0			0
$511$	−3.50000	−	18.1865i	−0.154831	−	0.804525i
$512$	1.00000			0.0441942
$513$	−1.00000			−0.0441511
$514$	4.00000	−	6.92820i	0.176432	−	0.305590i
$515$		0			0
$516$	1.00000			0.0440225
$517$		0			0
$518$	−22.0000	+	19.0526i	−0.966625	+	0.837121i
$519$	−8.00000			−0.351161
$520$		0			0
$521$	−14.0000	−	24.2487i	−0.613351	−	1.06236i	−0.990671	−	0.136272i	$-0.956488\pi$
$521$	−14.0000	−	24.2487i	−0.613351	−	1.06236i	0.377320	−	0.926083i	$-0.376846\pi$
$522$	6.00000			0.262613
$523$	0.500000	+	0.866025i	0.0218635	+	0.0378686i	0.876750	−	0.480946i	$-0.159707\pi$
$523$	0.500000	+	0.866025i	0.0218635	+	0.0378686i	−0.854887	+	0.518815i	$0.826373\pi$
$524$		0			0
$525$	2.50000	+	12.9904i	0.109109	+	0.566947i
$526$	−13.0000	−	22.5167i	−0.566827	−	0.981773i
$527$		0			0
$528$	−1.00000	−	1.73205i	−0.0435194	−	0.0753778i
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$		0			0
$531$	−2.00000	+	3.46410i	−0.0867926	+	0.150329i
$532$	2.00000	−	1.73205i	0.0867110	−	0.0750939i
$533$	5.00000	−	5.19615i	0.216574	−	0.225070i
$534$	3.00000	−	5.19615i	0.129823	−	0.224860i
$535$		0			0
$536$	12.0000			0.518321
$537$	16.0000			0.690451
$538$	−10.0000			−0.431131
$539$	−11.0000	−	8.66025i	−0.473804	−	0.373024i
$540$		0			0
$541$	−21.5000	+	37.2391i	−0.924357	+	1.60103i	−0.131765	+	0.991281i	$0.542065\pi$
$541$	−21.5000	+	37.2391i	−0.924357	+	1.60103i	−0.792592	+	0.609753i	$0.791269\pi$
$542$	7.50000	−	12.9904i	0.322153	−	0.557985i
$543$	−7.00000			−0.300399
$544$	−2.00000	−	3.46410i	−0.0857493	−	0.148522i
$545$		0			0
$546$	0.500000	−	9.52628i	0.0213980	−	0.407687i
$547$	−5.00000			−0.213785			−0.106892	−	0.994271i	$-0.534090\pi$
$547$	−5.00000			−0.213785			−0.106892	+	0.994271i	$0.534090\pi$
$548$	−6.00000	−	10.3923i	−0.256307	−	0.443937i
$549$	1.00000			0.0426790
$550$	−5.00000	+	8.66025i	−0.213201	+	0.369274i
$551$	−3.00000	+	5.19615i	−0.127804	+	0.221364i
$552$	−2.00000	−	3.46410i	−0.0851257	−	0.147442i
$553$	16.0000	−	13.8564i	0.680389	−	0.589234i
$554$	19.0000			0.807233
$555$		0			0
$556$	16.0000			0.678551
$557$	−30.0000			−1.27114			−0.635570	−	0.772043i	$-0.719235\pi$
$557$	−30.0000			−1.27114			−0.635570	+	0.772043i	$0.719235\pi$
$558$		0			0
$559$	1.00000	+	3.46410i	0.0422955	+	0.146516i
$560$		0			0
$561$	−4.00000	+	6.92820i	−0.168880	+	0.292509i
$562$	−15.0000	−	25.9808i	−0.632737	−	1.09593i
$563$	12.0000	−	20.7846i	0.505740	−	0.875967i	−0.494238	−	0.869326i	$-0.664553\pi$
$563$	12.0000	−	20.7846i	0.505740	−	0.875967i	0.999978	−	0.00664037i	$-0.00211371\pi$
$564$		0			0
$565$		0			0
$566$	12.5000	+	21.6506i	0.525414	+	0.910044i
$567$	−2.50000	−	0.866025i	−0.104990	−	0.0363696i
$568$	−3.00000	−	5.19615i	−0.125877	−	0.218026i
$569$	2.00000	+	3.46410i	0.0838444	+	0.145223i	0.904898	−	0.425628i	$-0.139947\pi$
$569$	2.00000	+	3.46410i	0.0838444	+	0.145223i	−0.821054	+	0.570851i	$0.806613\pi$
$570$		0			0
$571$	−12.5000	−	21.6506i	−0.523109	−	0.906051i	−0.999638	−	0.0268925i	$-0.991439\pi$
$571$	−12.5000	−	21.6506i	−0.523109	−	0.906051i	0.476530	−	0.879158i	$-0.341895\pi$
$572$	5.00000	−	5.19615i	0.209061	−	0.217262i
$573$	−24.0000			−1.00261
$574$	5.00000	+	1.73205i	0.208696	+	0.0722944i
$575$	−10.0000	+	17.3205i	−0.417029	+	0.722315i
$576$	1.00000			0.0416667
$577$	−3.50000	−	6.06218i	−0.145707	−	0.252372i	0.783930	−	0.620850i	$-0.213212\pi$
$577$	−3.50000	−	6.06218i	−0.145707	−	0.252372i	−0.929636	+	0.368478i	$0.879879\pi$
$578$	0.500000	−	0.866025i	0.0207973	−	0.0360219i
$579$	−19.0000			−0.789613
$580$		0			0
$581$	35.0000	+	12.1244i	1.45204	+	0.503003i
$582$	4.50000	−	7.79423i	0.186531	−	0.323081i
$583$	4.00000	+	6.92820i	0.165663	+	0.286937i
$584$	3.50000	+	6.06218i	0.144831	+	0.250855i
$585$		0			0
$586$	6.00000	−	10.3923i	0.247858	−	0.429302i
$587$	15.0000	−	25.9808i	0.619116	−	1.07234i	−0.370531	−	0.928820i	$-0.620824\pi$
$587$	15.0000	−	25.9808i	0.619116	−	1.07234i	0.989647	−	0.143521i	$-0.0458424\pi$
$588$	6.50000	−	2.59808i	0.268055	−	0.107143i
$589$		0			0
$590$		0			0
$591$	−4.00000	+	6.92820i	−0.164538	+	0.284988i
$592$	5.50000	−	9.52628i	0.226049	−	0.391528i
$593$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$593$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$594$	−1.00000	−	1.73205i	−0.0410305	−	0.0710669i
$595$		0			0
$596$	−5.00000	+	8.66025i	−0.204808	+	0.354738i
$597$	−1.50000	+	2.59808i	−0.0613909	+	0.106332i
$598$	10.0000	−	10.3923i	0.408930	−	0.424973i
$599$	5.00000	+	8.66025i	0.204294	+	0.353848i	0.949908	−	0.312531i	$-0.101177\pi$
$599$	5.00000	+	8.66025i	0.204294	+	0.353848i	−0.745613	+	0.666379i	$0.767843\pi$
$600$	−2.50000	−	4.33013i	−0.102062	−	0.176777i
$601$	−9.50000	+	16.4545i	−0.387513	+	0.671192i	−0.992114	−	0.125336i	$-0.959999\pi$
$601$	−9.50000	+	16.4545i	−0.387513	+	0.671192i	0.604601	+	0.796528i	$0.293332\pi$
$602$	−2.00000	+	1.73205i	−0.0815139	+	0.0705931i
$603$	12.0000			0.488678
$604$	4.00000			0.162758
$605$		0			0
$606$	−9.00000	−	15.5885i	−0.365600	−	0.633238i
$607$	1.00000			0.0405887			0.0202944	−	0.999794i	$-0.493540\pi$
$607$	1.00000			0.0405887			0.0202944	+	0.999794i	$0.493540\pi$
$608$	−0.500000	+	0.866025i	−0.0202777	+	0.0351220i
$609$	−12.0000	+	10.3923i	−0.486265	+	0.421117i
$610$		0			0
$611$		0			0
$612$	−2.00000	−	3.46410i	−0.0808452	−	0.140028i
$613$	5.00000			0.201948			0.100974	−	0.994889i	$-0.467804\pi$
$613$	5.00000			0.201948			0.100974	+	0.994889i	$0.467804\pi$
$614$	−14.0000	−	24.2487i	−0.564994	−	0.978598i
$615$		0			0
$616$	5.00000	+	1.73205i	0.201456	+	0.0697863i
$617$	−3.00000	−	5.19615i	−0.120775	−	0.209189i	0.799298	−	0.600935i	$-0.205205\pi$
$617$	−3.00000	−	5.19615i	−0.120775	−	0.209189i	−0.920074	+	0.391745i	$0.871871\pi$
$618$	7.00000			0.281581
$619$	17.5000	+	30.3109i	0.703384	+	1.21830i	0.967271	+	0.253744i	$0.0816620\pi$
$619$	17.5000	+	30.3109i	0.703384	+	1.21830i	−0.263887	+	0.964554i	$0.585005\pi$
$620$		0			0
$621$	−2.00000	−	3.46410i	−0.0802572	−	0.139010i
$622$	14.0000	−	24.2487i	0.561349	−	0.972285i
$623$	3.00000	+	15.5885i	0.120192	+	0.624538i
$624$	1.00000	+	3.46410i	0.0400320	+	0.138675i
$625$	−12.5000	+	21.6506i	−0.500000	+	0.866025i
$626$	−21.0000			−0.839329
$627$	2.00000			0.0798723
$628$	−7.00000			−0.279330
$629$	−44.0000			−1.75439
$630$		0			0
$631$	0.500000	+	0.866025i	0.0199047	+	0.0344759i	0.875806	−	0.482663i	$-0.160330\pi$
$631$	0.500000	+	0.866025i	0.0199047	+	0.0344759i	−0.855901	+	0.517139i	$0.826997\pi$
$632$	−4.00000	+	6.92820i	−0.159111	+	0.275589i
$633$	6.50000	−	11.2583i	0.258352	−	0.447478i
$634$	8.00000			0.317721
$635$		0			0
$636$	−4.00000			−0.158610
$637$	15.5000	+	19.9186i	0.614132	+	0.789203i
$638$	−12.0000			−0.475085
$639$	−3.00000	−	5.19615i	−0.118678	−	0.205557i
$640$		0			0
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	−0.401435	−	0.915888i	$-0.631488\pi$
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	0.993899	−	0.110291i	$-0.0351782\pi$
$642$	−9.00000	+	15.5885i	−0.355202	+	0.615227i
$643$	16.5000	+	28.5788i	0.650696	+	1.12704i	0.982954	+	0.183851i	$0.0588563\pi$
$643$	16.5000	+	28.5788i	0.650696	+	1.12704i	−0.332258	+	0.943189i	$0.607810\pi$
$644$	10.0000	+	3.46410i	0.394055	+	0.136505i
$645$		0			0
$646$	4.00000			0.157378
$647$	24.0000			0.943537			0.471769	−	0.881722i	$-0.343616\pi$
$647$	24.0000			0.943537			0.471769	+	0.881722i	$0.343616\pi$
$648$	1.00000			0.0392837
$649$	4.00000	−	6.92820i	0.157014	−	0.271956i
$650$	12.5000	−	12.9904i	0.490290	−	0.509525i
$651$		0			0
$652$	5.50000	−	9.52628i	0.215397	−	0.373078i
$653$	2.00000	+	3.46410i	0.0782660	+	0.135561i	0.902502	−	0.430686i	$-0.141728\pi$
$653$	2.00000	+	3.46410i	0.0782660	+	0.135561i	−0.824236	+	0.566247i	$0.808395\pi$
$654$	5.50000	−	9.52628i	0.215067	−	0.372507i
$655$		0			0
$656$	−2.00000			−0.0780869
$657$	3.50000	+	6.06218i	0.136548	+	0.236508i
$658$		0			0
$659$	18.0000	+	31.1769i	0.701180	+	1.21448i	0.968052	+	0.250748i	$0.0806766\pi$
$659$	18.0000	+	31.1769i	0.701180	+	1.21448i	−0.266872	+	0.963732i	$0.585990\pi$
$660$		0			0
$661$	38.0000			1.47803			0.739014	−	0.673690i	$-0.235292\pi$
$661$	38.0000			1.47803			0.739014	+	0.673690i	$0.235292\pi$
$662$	5.50000	+	9.52628i	0.213764	+	0.370249i
$663$	10.0000	−	10.3923i	0.388368	−	0.403604i
$664$	−14.0000			−0.543305
$665$		0			0
$666$	5.50000	−	9.52628i	0.213121	−	0.369136i
$667$	−24.0000			−0.929284
$668$	1.00000	+	1.73205i	0.0386912	+	0.0670151i
$669$	−8.00000	+	13.8564i	−0.309298	+	0.535720i
$670$		0			0
$671$	−2.00000			−0.0772091
$672$	−2.00000	+	1.73205i	−0.0771517	+	0.0668153i
$673$	14.5000	−	25.1147i	0.558934	−	0.968102i	−0.438652	−	0.898657i	$-0.644544\pi$
$673$	14.5000	−	25.1147i	0.558934	−	0.968102i	0.997586	−	0.0694449i	$-0.0221228\pi$
$674$	−4.50000	−	7.79423i	−0.173334	−	0.300222i
$675$	−2.50000	−	4.33013i	−0.0962250	−	0.166667i
$676$	−11.0000	+	6.92820i	−0.423077	+	0.266469i
$677$	7.00000	−	12.1244i	0.269032	−	0.465977i	−0.699580	−	0.714554i	$-0.746630\pi$
$677$	7.00000	−	12.1244i	0.269032	−	0.465977i	0.968612	+	0.248577i	$0.0799630\pi$
$678$	−4.00000	+	6.92820i	−0.153619	+	0.266076i
$679$	4.50000	+	23.3827i	0.172694	+	0.897345i
$680$		0			0
$681$	9.00000	−	15.5885i	0.344881	−	0.597351i
$682$		0			0
$683$	8.00000	−	13.8564i	0.306111	−	0.530201i	−0.671397	−	0.741098i	$-0.734305\pi$
$683$	8.00000	−	13.8564i	0.306111	−	0.530201i	0.977508	+	0.210898i	$0.0676386\pi$
$684$	−0.500000	+	0.866025i	−0.0191180	+	0.0331133i
$685$		0			0
$686$	−8.50000	+	16.4545i	−0.324532	+	0.628235i
$687$	−10.5000	+	18.1865i	−0.400600	+	0.693860i
$688$	0.500000	−	0.866025i	0.0190623	−	0.0330169i
$689$	−4.00000	−	13.8564i	−0.152388	−	0.527887i
$690$		0			0
$691$	−20.5000	−	35.5070i	−0.779857	−	1.35075i	−0.932024	−	0.362397i	$-0.881959\pi$
$691$	−20.5000	−	35.5070i	−0.779857	−	1.35075i	0.152167	−	0.988355i	$-0.451375\pi$
$692$	−4.00000	+	6.92820i	−0.152057	+	0.263371i
$693$	5.00000	+	1.73205i	0.189934	+	0.0657952i
$694$	26.0000			0.986947
$695$		0			0
$696$	3.00000	−	5.19615i	0.113715	−	0.196960i
$697$	4.00000	+	6.92820i	0.151511	+	0.262424i
$698$	5.00000			0.189253
$699$	−3.00000	+	5.19615i	−0.113470	+	0.196537i
$700$	12.5000	+	4.33013i	0.472456	+	0.163663i
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$	1.00000	+	3.46410i	0.0377426	+	0.130744i
$703$	5.50000	+	9.52628i	0.207436	+	0.359290i
$704$	−2.00000			−0.0753778
$705$		0			0
$706$	2.00000	+	3.46410i	0.0752710	+	0.130373i
$707$	45.0000	+	15.5885i	1.69240	+	0.586264i
$708$	2.00000	+	3.46410i	0.0751646	+	0.130189i
$709$	−25.0000			−0.938895			−0.469447	−	0.882960i	$-0.655547\pi$
$709$	−25.0000			−0.938895			−0.469447	+	0.882960i	$0.655547\pi$
$710$		0			0
$711$	−4.00000	+	6.92820i	−0.150012	+	0.259828i
$712$	−3.00000	−	5.19615i	−0.112430	−	0.194734i
$713$		0			0
$714$	10.0000	+	3.46410i	0.374241	+	0.129641i
$715$		0			0
$716$	8.00000	−	13.8564i	0.298974	−	0.517838i
$717$	−2.00000			−0.0746914
$718$	−6.00000			−0.223918
$719$	36.0000			1.34257			0.671287	−	0.741198i	$-0.265742\pi$
$719$	36.0000			1.34257			0.671287	+	0.741198i	$0.265742\pi$
$720$		0			0
$721$	−14.0000	+	12.1244i	−0.521387	+	0.451535i
$722$	9.00000	+	15.5885i	0.334945	+	0.580142i
$723$	9.00000	−	15.5885i	0.334714	−	0.579741i
$724$	−3.50000	+	6.06218i	−0.130076	+	0.225299i
$725$	−30.0000			−1.11417
$726$	−3.50000	−	6.06218i	−0.129897	−	0.224989i
$727$	28.0000			1.03846			0.519231	−	0.854634i	$-0.326218\pi$
$727$	28.0000			1.03846			0.519231	+	0.854634i	$0.326218\pi$
$728$	−8.00000	−	5.19615i	−0.296500	−	0.192582i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−4.00000			−0.147945
$732$	0.500000	−	0.866025i	0.0184805	−	0.0320092i
$733$	−7.00000	+	12.1244i	−0.258551	+	0.447823i	−0.965854	−	0.259087i	$-0.916578\pi$
$733$	−7.00000	+	12.1244i	−0.258551	+	0.447823i	0.707303	+	0.706910i	$0.249912\pi$
$734$	12.5000	+	21.6506i	0.461383	+	0.799140i
$735$		0			0
$736$	−4.00000			−0.147442
$737$	−24.0000			−0.884051
$738$	−2.00000			−0.0736210
$739$	5.00000			0.183928			0.0919640	−	0.995762i	$-0.470686\pi$
$739$	5.00000			0.183928			0.0919640	+	0.995762i	$0.470686\pi$
$740$		0			0
$741$	−3.50000	−	0.866025i	−0.128576	−	0.0318142i
$742$	8.00000	−	6.92820i	0.293689	−	0.254342i
$743$	4.00000	−	6.92820i	0.146746	−	0.254171i	−0.783277	−	0.621673i	$-0.786453\pi$
$743$	4.00000	−	6.92820i	0.146746	−	0.254171i	0.930023	+	0.367502i	$0.119787\pi$
$744$		0			0
$745$		0			0
$746$	9.00000	+	15.5885i	0.329513	+	0.570734i
$747$	−14.0000			−0.512233
$748$	4.00000	+	6.92820i	0.146254	+	0.253320i
$749$	−9.00000	−	46.7654i	−0.328853	−	1.70877i
$750$		0			0
$751$	12.5000	+	21.6506i	0.456131	+	0.790043i	0.998752	−	0.0499348i	$-0.0159013\pi$
$751$	12.5000	+	21.6506i	0.456131	+	0.790043i	−0.542621	+	0.839978i	$0.682568\pi$
$752$		0			0
$753$	15.0000	+	25.9808i	0.546630	+	0.946792i
$754$	21.0000	+	5.19615i	0.764775	+	0.189233i
$755$		0			0
$756$	−2.00000	+	1.73205i	−0.0727393	+	0.0629941i
$757$	11.0000	−	19.0526i	0.399802	−	0.692477i	−0.593899	−	0.804539i	$-0.702412\pi$
$757$	11.0000	−	19.0526i	0.399802	−	0.692477i	0.993701	+	0.112062i	$0.0357456\pi$
$758$	20.0000			0.726433
$759$	4.00000	+	6.92820i	0.145191	+	0.251478i
$760$		0			0
$761$	−20.0000			−0.724999			−0.362500	−	0.931984i	$-0.618077\pi$
$761$	−20.0000			−0.724999			−0.362500	+	0.931984i	$0.618077\pi$
$762$	−13.0000			−0.470940
$763$	5.50000	+	28.5788i	0.199113	+	1.03462i
$764$	−12.0000	+	20.7846i	−0.434145	+	0.751961i
$765$		0			0
$766$	−4.00000	−	6.92820i	−0.144526	−	0.250326i
$767$	−10.0000	+	10.3923i	−0.361079	+	0.375244i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	−23.5000	+	40.7032i	−0.847432	+	1.46779i	0.0360609	+	0.999350i	$0.488519\pi$
$769$	−23.5000	+	40.7032i	−0.847432	+	1.46779i	−0.883493	+	0.468445i	$0.844814\pi$
$770$		0			0
$771$	−4.00000	−	6.92820i	−0.144056	−	0.249513i
$772$	−9.50000	+	16.4545i	−0.341912	+	0.592210i
$773$	26.0000	−	45.0333i	0.935155	−	1.61974i	0.160798	−	0.986987i	$-0.448593\pi$
$773$	26.0000	−	45.0333i	0.935155	−	1.61974i	0.774357	−	0.632749i	$-0.218073\pi$
$774$	0.500000	−	0.866025i	0.0179721	−	0.0311286i
$775$		0			0
$776$	−4.50000	−	7.79423i	−0.161541	−	0.279797i
$777$	5.50000	+	28.5788i	0.197311	+	1.02526i
$778$	−2.00000	+	3.46410i	−0.0717035	+	0.124194i
$779$	1.00000	−	1.73205i	0.0358287	−	0.0620572i
$780$		0			0
$781$	6.00000	+	10.3923i	0.214697	+	0.371866i
$782$	8.00000	+	13.8564i	0.286079	+	0.495504i
$783$	3.00000	−	5.19615i	0.107211	−	0.185695i
$784$	1.00000	−	6.92820i	0.0357143	−	0.247436i
$785$		0			0
$786$		0			0
$787$	−26.5000	+	45.8993i	−0.944623	+	1.63614i	−0.188119	+	0.982146i	$0.560239\pi$
$787$	−26.5000	+	45.8993i	−0.944623	+	1.63614i	−0.756504	+	0.653989i	$0.773094\pi$
$788$	4.00000	+	6.92820i	0.142494	+	0.246807i
$789$	−26.0000			−0.925625
$790$		0			0
$791$	−4.00000	−	20.7846i	−0.142224	−	0.739016i
$792$	−2.00000			−0.0710669
$793$	3.50000	+	0.866025i	0.124289	+	0.0307535i
$794$	−0.500000	−	0.866025i	−0.0177443	−	0.0307341i
$795$		0			0
$796$	1.50000	+	2.59808i	0.0531661	+	0.0920864i
$797$	27.0000	+	46.7654i	0.956389	+	1.65651i	0.731157	+	0.682209i	$0.238981\pi$
$797$	27.0000	+	46.7654i	0.956389	+	1.65651i	0.225232	+	0.974305i	$0.427686\pi$
$798$	−0.500000	−	2.59808i	−0.0176998	−	0.0919709i
$799$		0			0
$800$	−5.00000			−0.176777
$801$	−3.00000	−	5.19615i	−0.106000	−	0.183597i
$802$	−5.00000	+	8.66025i	−0.176556	+	0.305804i
$803$	−7.00000	−	12.1244i	−0.247025	−	0.427859i
$804$	6.00000	−	10.3923i	0.211604	−	0.366508i
$805$		0			0
$806$		0			0
$807$	−5.00000	+	8.66025i	−0.176008	+	0.304855i
$808$	−18.0000			−0.633238
$809$	−2.00000			−0.0703163			−0.0351581	−	0.999382i	$-0.511193\pi$
$809$	−2.00000			−0.0703163			−0.0351581	+	0.999382i	$0.511193\pi$
$810$		0			0
$811$	−21.0000			−0.737410			−0.368705	−	0.929547i	$-0.620199\pi$
$811$	−21.0000			−0.737410			−0.368705	+	0.929547i	$0.620199\pi$
$812$	3.00000	+	15.5885i	0.105279	+	0.547048i
$813$	−7.50000	−	12.9904i	−0.263036	−	0.455593i
$814$	−11.0000	+	19.0526i	−0.385550	+	0.667792i
$815$		0			0
$816$	−4.00000			−0.140028
$817$	0.500000	+	0.866025i	0.0174928	+	0.0302984i
$818$	−31.0000			−1.08389
$819$	−8.00000	−	5.19615i	−0.279543	−	0.181568i
$820$		0			0
$821$	−26.0000	−	45.0333i	−0.907406	−	1.57167i	−0.817654	−	0.575710i	$-0.804726\pi$
$821$	−26.0000	−	45.0333i	−0.907406	−	1.57167i	−0.0897520	−	0.995964i	$-0.528607\pi$
$822$	−12.0000			−0.418548
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	0.272292	+	0.962215i	$0.412218\pi$
$823$	−20.0000	+	34.6410i	−0.697156	+	1.20751i	−0.969448	+	0.245295i	$0.921115\pi$
$824$	3.50000	−	6.06218i	0.121928	−	0.211186i
$825$	5.00000	+	8.66025i	0.174078	+	0.301511i
$826$	−10.0000	−	3.46410i	−0.347945	−	0.120532i
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$	−4.00000			−0.139010
$829$	31.0000			1.07667			0.538337	−	0.842729i	$-0.319053\pi$
$829$	31.0000			1.07667			0.538337	+	0.842729i	$0.319053\pi$
$830$		0			0
$831$	9.50000	−	16.4545i	0.329551	−	0.570800i
$832$	3.50000	+	0.866025i	0.121341	+	0.0300240i
$833$	−26.0000	+	10.3923i	−0.900847	+	0.360072i
$834$	8.00000	−	13.8564i	0.277017	−	0.479808i
$835$		0			0
$836$	1.00000	−	1.73205i	0.0345857	−	0.0599042i
$837$		0			0
$838$	26.0000			0.898155
$839$	20.0000	+	34.6410i	0.690477	+	1.19594i	0.971682	+	0.236293i	$0.0759325\pi$
$839$	20.0000	+	34.6410i	0.690477	+	1.19594i	−0.281205	+	0.959648i	$0.590734\pi$
$840$		0			0
$841$	−3.50000	−	6.06218i	−0.120690	−	0.209041i
$842$	−1.00000	−	1.73205i	−0.0344623	−	0.0596904i
$843$	−30.0000			−1.03325
$844$	−6.50000	−	11.2583i	−0.223739	−	0.387528i
$845$		0			0
$846$		0			0
$847$	17.5000	+	6.06218i	0.601307	+	0.208299i
$848$	−2.00000	+	3.46410i	−0.0686803	+	0.118958i
$849$	25.0000			0.857998
$850$	10.0000	+	17.3205i	0.342997	+	0.594089i
$851$	−22.0000	+	38.1051i	−0.754150	+	1.30623i
$852$	−6.00000			−0.205557
$853$	14.0000			0.479351			0.239675	−	0.970853i	$-0.422959\pi$
$853$	14.0000			0.479351			0.239675	+	0.970853i	$0.422959\pi$
$854$	0.500000	+	2.59808i	0.0171096	+	0.0889043i
$855$		0			0
$856$	9.00000	+	15.5885i	0.307614	+	0.532803i
$857$	7.00000	+	12.1244i	0.239115	+	0.414160i	0.960461	−	0.278416i	$-0.0898092\pi$
$857$	7.00000	+	12.1244i	0.239115	+	0.414160i	−0.721345	+	0.692576i	$0.756476\pi$
$858$	−2.00000	−	6.92820i	−0.0682789	−	0.236525i
$859$	17.5000	−	30.3109i	0.597092	−	1.03419i	−0.396156	−	0.918183i	$-0.629656\pi$
$859$	17.5000	−	30.3109i	0.597092	−	1.03419i	0.993248	−	0.116011i	$-0.0370107\pi$
$860$		0			0
$861$	4.00000	−	3.46410i	0.136320	−	0.118056i
$862$	−13.0000	−	22.5167i	−0.442782	−	0.766921i
$863$	3.00000	−	5.19615i	0.102121	−	0.176879i	−0.810437	−	0.585826i	$-0.800770\pi$
$863$	3.00000	−	5.19615i	0.102121	−	0.176879i	0.912558	+	0.408946i	$0.134104\pi$
$864$	0.500000	−	0.866025i	0.0170103	−	0.0294628i
$865$		0			0
$866$	13.0000	−	22.5167i	0.441758	−	0.765147i
$867$	−0.500000	−	0.866025i	−0.0169809	−	0.0294118i
$868$		0			0
$869$	8.00000	−	13.8564i	0.271381	−	0.470046i
$870$		0			0
$871$	42.0000	+	10.3923i	1.42312	+	0.352130i
$872$	−5.50000	−	9.52628i	−0.186254	−	0.322601i
$873$	−4.50000	−	7.79423i	−0.152302	−	0.263795i
$874$	2.00000	−	3.46410i	0.0676510	−	0.117175i
$875$		0			0
$876$	7.00000			0.236508
$877$	−18.0000			−0.607817			−0.303908	−	0.952701i	$-0.598292\pi$
$877$	−18.0000			−0.607817			−0.303908	+	0.952701i	$0.598292\pi$
$878$	0.500000	−	0.866025i	0.0168742	−	0.0292269i
$879$	−6.00000	−	10.3923i	−0.202375	−	0.350524i
$880$		0			0
$881$	1.00000	−	1.73205i	0.0336909	−	0.0583543i	−0.848688	−	0.528893i	$-0.822607\pi$
$881$	1.00000	−	1.73205i	0.0336909	−	0.0583543i	0.882379	+	0.470539i	$0.155941\pi$
$882$	1.00000	−	6.92820i	0.0336718	−	0.233285i
$883$	−19.0000			−0.639401			−0.319700	−	0.947519i	$-0.603582\pi$
$883$	−19.0000			−0.639401			−0.319700	+	0.947519i	$0.603582\pi$
$884$	−4.00000	−	13.8564i	−0.134535	−	0.466041i
$885$		0			0
$886$	8.00000			0.268765
$887$	−3.00000	−	5.19615i	−0.100730	−	0.174470i	0.811256	−	0.584692i	$-0.198785\pi$
$887$	−3.00000	−	5.19615i	−0.100730	−	0.174470i	−0.911986	+	0.410222i	$0.865451\pi$
$888$	−5.50000	−	9.52628i	−0.184568	−	0.319681i
$889$	26.0000	−	22.5167i	0.872012	−	0.755185i
$890$		0			0
$891$	−2.00000			−0.0670025
$892$	8.00000	+	13.8564i	0.267860	+	0.463947i
$893$		0			0
$894$	5.00000	+	8.66025i	0.167225	+	0.289642i
$895$		0			0
$896$	0.500000	+	2.59808i	0.0167038	+	0.0867956i
$897$	−4.00000	−	13.8564i	−0.133556	−	0.462652i
$898$	−17.0000	+	29.4449i	−0.567297	+	0.982588i
$899$		0			0
$900$	−5.00000			−0.166667
$901$	16.0000			0.533037
$902$	4.00000			0.133185
$903$	0.500000	+	2.59808i	0.0166390	+	0.0864586i
$904$	4.00000	+	6.92820i	0.133038	+	0.230429i
$905$		0			0
$906$	2.00000	−	3.46410i	0.0664455	−	0.115087i
$907$	−9.00000			−0.298840			−0.149420	−	0.988774i	$-0.547741\pi$
$907$	−9.00000			−0.298840			−0.149420	+	0.988774i	$0.547741\pi$
$908$	−9.00000	−	15.5885i	−0.298675	−	0.517321i
$909$	−18.0000			−0.597022
$910$		0			0
$911$	30.0000			0.993944			0.496972	−	0.867766i	$-0.334445\pi$
$911$	30.0000			0.993944			0.496972	+	0.867766i	$0.334445\pi$
$912$	0.500000	+	0.866025i	0.0165567	+	0.0286770i
$913$	28.0000			0.926665
$914$	−19.0000	+	32.9090i	−0.628464	+	1.08853i
$915$		0			0
$916$	10.5000	+	18.1865i	0.346930	+	0.600900i
$917$		0			0
$918$	−4.00000			−0.132020
$919$	−11.0000			−0.362857			−0.181428	−	0.983404i	$-0.558072\pi$
$919$	−11.0000			−0.362857			−0.181428	+	0.983404i	$0.558072\pi$
$920$		0			0
$921$	−28.0000			−0.922631
$922$	−8.00000	+	13.8564i	−0.263466	+	0.456336i
$923$	−6.00000	−	20.7846i	−0.197492	−	0.684134i
$924$	4.00000	−	3.46410i	0.131590	−	0.113961i
$925$	−27.5000	+	47.6314i	−0.904194	+	1.56611i
$926$	−11.5000	−	19.9186i	−0.377913	−	0.654565i
$927$	3.50000	−	6.06218i	0.114955	−	0.199108i
$928$	−3.00000	−	5.19615i	−0.0984798	−	0.170572i
$929$	−6.00000			−0.196854			−0.0984268	−	0.995144i	$-0.531381\pi$
$929$	−6.00000			−0.196854			−0.0984268	+	0.995144i	$0.531381\pi$
$930$		0			0
$931$	5.50000	+	4.33013i	0.180255	+	0.141914i
$932$	3.00000	+	5.19615i	0.0982683	+	0.170206i
$933$	−14.0000	−	24.2487i	−0.458339	−	0.793867i
$934$	42.0000			1.37428
$935$		0			0
$936$	3.50000	+	0.866025i	0.114401	+	0.0283069i
$937$	35.0000			1.14340			0.571700	−	0.820463i	$-0.306284\pi$
$937$	35.0000			1.14340			0.571700	+	0.820463i	$0.306284\pi$
$938$	6.00000	+	31.1769i	0.195907	+	1.01796i
$939$	−10.5000	+	18.1865i	−0.342655	+	0.593495i
$940$		0			0
$941$	28.0000	+	48.4974i	0.912774	+	1.58097i	0.810128	+	0.586253i	$0.199397\pi$
$941$	28.0000	+	48.4974i	0.912774	+	1.58097i	0.102646	+	0.994718i	$0.467269\pi$
$942$	−3.50000	+	6.06218i	−0.114036	+	0.197516i
$943$	8.00000			0.260516
$944$	4.00000			0.130189
$945$		0			0
$946$	−1.00000	+	1.73205i	−0.0325128	+	0.0563138i
$947$	−5.00000	−	8.66025i	−0.162478	−	0.281420i	0.773279	−	0.634066i	$-0.218615\pi$
$947$	−5.00000	−	8.66025i	−0.162478	−	0.281420i	−0.935757	+	0.352646i	$0.885282\pi$
$948$	4.00000	+	6.92820i	0.129914	+	0.225018i
$949$	7.00000	+	24.2487i	0.227230	+	0.787146i
$950$	2.50000	−	4.33013i	0.0811107	−	0.140488i
$951$	4.00000	−	6.92820i	0.129709	−	0.224662i
$952$	8.00000	−	6.92820i	0.259281	−	0.224544i
$953$	−24.0000	−	41.5692i	−0.777436	−	1.34656i	−0.933415	−	0.358799i	$-0.883186\pi$
$953$	−24.0000	−	41.5692i	−0.777436	−	1.34656i	0.155979	−	0.987760i	$-0.450147\pi$
$954$	−2.00000	+	3.46410i	−0.0647524	+	0.112154i
$955$		0			0
$956$	−1.00000	+	1.73205i	−0.0323423	+	0.0560185i
$957$	−6.00000	+	10.3923i	−0.193952	+	0.335936i
$958$	−5.00000	−	8.66025i	−0.161543	−	0.279800i
$959$	24.0000	−	20.7846i	0.775000	−	0.671170i
$960$		0			0
$961$	15.5000	−	26.8468i	0.500000	−	0.866025i
$962$	27.5000	−	28.5788i	0.886636	−	0.921419i
$963$	9.00000	+	15.5885i	0.290021	+	0.502331i
$964$	−9.00000	−	15.5885i	−0.289870	−	0.502070i
$965$		0			0
$966$	8.00000	−	6.92820i	0.257396	−	0.222911i
$967$	37.0000			1.18984			0.594920	−	0.803785i	$-0.297184\pi$
$967$	37.0000			1.18984			0.594920	+	0.803785i	$0.297184\pi$
$968$	−7.00000			−0.224989
$969$	2.00000	−	3.46410i	0.0642493	−	0.111283i
$970$		0			0
$971$	36.0000			1.15529			0.577647	−	0.816286i	$-0.303971\pi$
$971$	36.0000			1.15529			0.577647	+	0.816286i	$0.303971\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	8.00000	+	41.5692i	0.256468	+	1.33265i
$974$	−23.0000			−0.736968
$975$	−5.00000	−	17.3205i	−0.160128	−	0.554700i
$976$	−0.500000	−	0.866025i	−0.0160046	−	0.0277208i
$977$	−16.0000			−0.511885			−0.255943	−	0.966692i	$-0.582386\pi$
$977$	−16.0000			−0.511885			−0.255943	+	0.966692i	$0.582386\pi$
$978$	−5.50000	−	9.52628i	−0.175871	−	0.304617i
$979$	6.00000	+	10.3923i	0.191761	+	0.332140i
$980$		0			0
$981$	−5.50000	−	9.52628i	−0.175601	−	0.304151i
$982$	−22.0000			−0.702048
$983$	−7.00000	−	12.1244i	−0.223265	−	0.386707i	0.732532	−	0.680732i	$-0.238338\pi$
$983$	−7.00000	−	12.1244i	−0.223265	−	0.386707i	−0.955798	+	0.294025i	$0.905005\pi$
$984$	−1.00000	+	1.73205i	−0.0318788	+	0.0552158i
$985$		0			0
$986$	−12.0000	+	20.7846i	−0.382158	+	0.661917i
$987$		0			0
$988$	−2.50000	+	2.59808i	−0.0795356	+	0.0826558i
$989$	−2.00000	+	3.46410i	−0.0635963	+	0.110152i
$990$		0			0
$991$	19.0000			0.603555			0.301777	−	0.953378i	$-0.402420\pi$
$991$	19.0000			0.603555			0.301777	+	0.953378i	$0.402420\pi$
$992$		0			0
$993$	11.0000			0.349074
$994$	12.0000	−	10.3923i	0.380617	−	0.329624i
$995$		0			0
$996$	−7.00000	+	12.1244i	−0.221803	+	0.384175i
$997$	1.50000	−	2.59808i	0.0475055	−	0.0822819i	−0.841295	−	0.540576i	$-0.818206\pi$
$997$	1.50000	−	2.59808i	0.0475055	−	0.0822819i	0.888800	+	0.458295i	$0.151540\pi$
$998$	1.00000			0.0316544
$999$	−5.50000	−	9.52628i	−0.174012	−	0.301398i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.k.a.373.1	yes	2
3.2	odd	2		1638.2.p.d.919.1		2
7.4	even	3		546.2.j.a.529.1	yes	2
13.3	even	3		546.2.j.a.289.1	✓	2
21.11	odd	6		1638.2.m.a.1621.1		2
39.29	odd	6		1638.2.m.a.289.1		2
91.81	even	3	inner	546.2.k.a.445.1	yes	2
273.263	odd	6		1638.2.p.d.991.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.a.289.1	✓	2	13.3	even	3
546.2.j.a.529.1	yes	2	7.4	even	3
546.2.k.a.373.1	yes	2	1.1	even	1	trivial
546.2.k.a.445.1	yes	2	91.81	even	3	inner
1638.2.m.a.289.1		2	39.29	odd	6
1638.2.m.a.1621.1		2	21.11	odd	6
1638.2.p.d.919.1		2	3.2	odd	2
1638.2.p.d.991.1		2	273.263	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.500000 - 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(-2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-0.500000 - 0.866025i) q^{2} -1.00000 q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{6} +(-2.50000 - 0.866025i) q^{7} +1.00000 q^{8} +1.00000 q^{9} -2.00000 q^{11} +(0.500000 - 0.866025i) q^{12} +(3.50000 + 0.866025i) q^{13} +(0.500000 + 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-2.00000 + 3.46410i) q^{17} +(-0.500000 - 0.866025i) q^{18} +1.00000 q^{19} +(2.50000 + 0.866025i) q^{21} +(1.00000 + 1.73205i) q^{22} +(2.00000 + 3.46410i) q^{23} -1.00000 q^{24} +(2.50000 + 4.33013i) q^{25} +(-1.00000 - 3.46410i) q^{26} -1.00000 q^{27} +(2.00000 - 1.73205i) q^{28} +(-3.00000 + 5.19615i) q^{29} +(-0.500000 + 0.866025i) q^{32} +2.00000 q^{33} +4.00000 q^{34} +(-0.500000 + 0.866025i) q^{36} +(5.50000 + 9.52628i) q^{37} +(-0.500000 - 0.866025i) q^{38} +(-3.50000 - 0.866025i) q^{39} +(1.00000 - 1.73205i) q^{41} +(-0.500000 - 2.59808i) q^{42} +(0.500000 + 0.866025i) q^{43} +(1.00000 - 1.73205i) q^{44} +(2.00000 - 3.46410i) q^{46} +(0.500000 + 0.866025i) q^{48} +(5.50000 + 4.33013i) q^{49} +(2.50000 - 4.33013i) q^{50} +(2.00000 - 3.46410i) q^{51} +(-2.50000 + 2.59808i) q^{52} +(-2.00000 - 3.46410i) q^{53} +(0.500000 + 0.866025i) q^{54} +(-2.50000 - 0.866025i) q^{56} -1.00000 q^{57} +6.00000 q^{58} +(-2.00000 + 3.46410i) q^{59} +1.00000 q^{61} +(-2.50000 - 0.866025i) q^{63} +1.00000 q^{64} +(-1.00000 - 1.73205i) q^{66} +12.0000 q^{67} +(-2.00000 - 3.46410i) q^{68} +(-2.00000 - 3.46410i) q^{69} +(-3.00000 - 5.19615i) q^{71} +1.00000 q^{72} +(3.50000 + 6.06218i) q^{73} +(5.50000 - 9.52628i) q^{74} +(-2.50000 - 4.33013i) q^{75} +(-0.500000 + 0.866025i) q^{76} +(5.00000 + 1.73205i) q^{77} +(1.00000 + 3.46410i) q^{78} +(-4.00000 + 6.92820i) q^{79} +1.00000 q^{81} -2.00000 q^{82} -14.0000 q^{83} +(-2.00000 + 1.73205i) q^{84} +(0.500000 - 0.866025i) q^{86} +(3.00000 - 5.19615i) q^{87} -2.00000 q^{88} +(-3.00000 - 5.19615i) q^{89} +(-8.00000 - 5.19615i) q^{91} -4.00000 q^{92} +(0.500000 - 0.866025i) q^{96} +(-4.50000 - 7.79423i) q^{97} +(1.00000 - 6.92820i) q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} - 2 q^{3} - q^{4} + q^{6} - 5 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - q^2 - 2 * q^3 - q^4 + q^6 - 5 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q - q^{2} - 2 q^{3} - q^{4} + q^{6} - 5 q^{7} + 2 q^{8} + 2 q^{9} - 4 q^{11} + q^{12} + 7 q^{13} + q^{14} - q^{16} - 4 q^{17} - q^{18} + 2 q^{19} + 5 q^{21} + 2 q^{22} + 4 q^{23} - 2 q^{24} + 5 q^{25} - 2 q^{26} - 2 q^{27} + 4 q^{28} - 6 q^{29} - q^{32} + 4 q^{33} + 8 q^{34} - q^{36} + 11 q^{37} - q^{38} - 7 q^{39} + 2 q^{41} - q^{42} + q^{43} + 2 q^{44} + 4 q^{46} + q^{48} + 11 q^{49} + 5 q^{50} + 4 q^{51} - 5 q^{52} - 4 q^{53} + q^{54} - 5 q^{56} - 2 q^{57} + 12 q^{58} - 4 q^{59} + 2 q^{61} - 5 q^{63} + 2 q^{64} - 2 q^{66} + 24 q^{67} - 4 q^{68} - 4 q^{69} - 6 q^{71} + 2 q^{72} + 7 q^{73} + 11 q^{74} - 5 q^{75} - q^{76} + 10 q^{77} + 2 q^{78} - 8 q^{79} + 2 q^{81} - 4 q^{82} - 28 q^{83} - 4 q^{84} + q^{86} + 6 q^{87} - 4 q^{88} - 6 q^{89} - 16 q^{91} - 8 q^{92} + q^{96} - 9 q^{97} + 2 q^{98} - 4 q^{99}+O(q^{100}) \) 2 * q - q^2 - 2 * q^3 - q^4 + q^6 - 5 * q^7 + 2 * q^8 + 2 * q^9 - 4 * q^11 + q^12 + 7 * q^13 + q^14 - q^16 - 4 * q^17 - q^18 + 2 * q^19 + 5 * q^21 + 2 * q^22 + 4 * q^23 - 2 * q^24 + 5 * q^25 - 2 * q^26 - 2 * q^27 + 4 * q^28 - 6 * q^29 - q^32 + 4 * q^33 + 8 * q^34 - q^36 + 11 * q^37 - q^38 - 7 * q^39 + 2 * q^41 - q^42 + q^43 + 2 * q^44 + 4 * q^46 + q^48 + 11 * q^49 + 5 * q^50 + 4 * q^51 - 5 * q^52 - 4 * q^53 + q^54 - 5 * q^56 - 2 * q^57 + 12 * q^58 - 4 * q^59 + 2 * q^61 - 5 * q^63 + 2 * q^64 - 2 * q^66 + 24 * q^67 - 4 * q^68 - 4 * q^69 - 6 * q^71 + 2 * q^72 + 7 * q^73 + 11 * q^74 - 5 * q^75 - q^76 + 10 * q^77 + 2 * q^78 - 8 * q^79 + 2 * q^81 - 4 * q^82 - 28 * q^83 - 4 * q^84 + q^86 + 6 * q^87 - 4 * q^88 - 6 * q^89 - 16 * q^91 - 8 * q^92 + q^96 - 9 * q^97 + 2 * q^98 - 4 * q^99

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