LMFDB - Embedded newform 546.2.j.a.529.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(289,546)]

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, 2]))

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

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

chi := DirichletCharacter("546.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.j (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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			529.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	546.529
Dual form			546.2.j.a.289.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{6} +(0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{6} +(0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{11} +(0.500000 + 0.866025i) q^{12} +(3.50000 + 0.866025i) q^{13} +(0.500000 - 2.59808i) q^{14} +1.00000 q^{16} +4.00000 q^{17} +(-0.500000 + 0.866025i) q^{18} +(-0.500000 + 0.866025i) q^{19} +(2.50000 - 0.866025i) q^{21} +(1.00000 + 1.73205i) q^{22} -4.00000 q^{23} +(0.500000 + 0.866025i) q^{24} +(2.50000 - 4.33013i) q^{25} +(3.50000 + 0.866025i) q^{26} -1.00000 q^{27} +(0.500000 - 2.59808i) q^{28} +(-3.00000 + 5.19615i) q^{29} +1.00000 q^{32} +(-1.00000 + 1.73205i) q^{33} +4.00000 q^{34} +(-0.500000 + 0.866025i) q^{36} -11.0000 q^{37} +(-0.500000 + 0.866025i) q^{38} +(1.00000 + 3.46410i) q^{39} +(1.00000 - 1.73205i) q^{41} +(2.50000 - 0.866025i) q^{42} +(0.500000 + 0.866025i) q^{43} +(1.00000 + 1.73205i) q^{44} -4.00000 q^{46} +(0.500000 + 0.866025i) q^{48} +(-6.50000 - 2.59808i) q^{49} +(2.50000 - 4.33013i) q^{50} +(2.00000 + 3.46410i) q^{51} +(3.50000 + 0.866025i) q^{52} +(-2.00000 + 3.46410i) q^{53} -1.00000 q^{54} +(0.500000 - 2.59808i) q^{56} -1.00000 q^{57} +(-3.00000 + 5.19615i) q^{58} +4.00000 q^{59} +(-0.500000 + 0.866025i) q^{61} +(2.00000 + 1.73205i) q^{63} +1.00000 q^{64} +(-1.00000 + 1.73205i) q^{66} +(-6.00000 - 10.3923i) q^{67} +4.00000 q^{68} +(-2.00000 - 3.46410i) q^{69} +(-3.00000 - 5.19615i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(3.50000 - 6.06218i) q^{73} -11.0000 q^{74} +5.00000 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} +(-0.500000 - 0.866025i) q^{81} +(1.00000 - 1.73205i) q^{82} -14.0000 q^{83} +(2.50000 - 0.866025i) q^{84} +(0.500000 + 0.866025i) q^{86} -6.00000 q^{87} +(1.00000 + 1.73205i) q^{88} +6.00000 q^{89} +(4.00000 - 8.66025i) q^{91} -4.00000 q^{92} +(0.500000 + 0.866025i) q^{96} +(-4.50000 - 7.79423i) q^{97} +(-6.50000 - 2.59808i) q^{98} -2.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} + q^{3} + 2 q^{4} + q^{6} + q^{7} + 2 q^{8} - q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 + q^3 + 2 * q^4 + q^6 + q^7 + 2 * q^8 - q^9	$ 2 q + 2 q^{2} + q^{3} + 2 q^{4} + q^{6} + q^{7} + 2 q^{8} - q^{9} + 2 q^{11} + q^{12} + 7 q^{13} + q^{14} + 2 q^{16} + 8 q^{17} - q^{18} - q^{19} + 5 q^{21} + 2 q^{22} - 8 q^{23} + q^{24} + 5 q^{25} + 7 q^{26} - 2 q^{27} + q^{28} - 6 q^{29} + 2 q^{32} - 2 q^{33} + 8 q^{34} - q^{36} - 22 q^{37} - q^{38} + 2 q^{39} + 2 q^{41} + 5 q^{42} + q^{43} + 2 q^{44} - 8 q^{46} + q^{48} - 13 q^{49} + 5 q^{50} + 4 q^{51} + 7 q^{52} - 4 q^{53} - 2 q^{54} + q^{56} - 2 q^{57} - 6 q^{58} + 8 q^{59} - q^{61} + 4 q^{63} + 2 q^{64} - 2 q^{66} - 12 q^{67} + 8 q^{68} - 4 q^{69} - 6 q^{71} - q^{72} + 7 q^{73} - 22 q^{74} + 10 q^{75} - q^{76} + 10 q^{77} + 2 q^{78} - 8 q^{79} - q^{81} + 2 q^{82} - 28 q^{83} + 5 q^{84} + q^{86} - 12 q^{87} + 2 q^{88} + 12 q^{89} + 8 q^{91} - 8 q^{92} + q^{96} - 9 q^{97} - 13 q^{98} - 4 q^{99}+O(q^{100}) $ 2 * q + 2 * q^2 + q^3 + 2 * q^4 + q^6 + q^7 + 2 * q^8 - q^9 + 2 * q^11 + q^12 + 7 * q^13 + q^14 + 2 * q^16 + 8 * q^17 - q^18 - q^19 + 5 * q^21 + 2 * q^22 - 8 * q^23 + q^24 + 5 * q^25 + 7 * q^26 - 2 * q^27 + q^28 - 6 * q^29 + 2 * q^32 - 2 * q^33 + 8 * q^34 - q^36 - 22 * q^37 - q^38 + 2 * q^39 + 2 * q^41 + 5 * q^42 + q^43 + 2 * q^44 - 8 * q^46 + q^48 - 13 * q^49 + 5 * q^50 + 4 * q^51 + 7 * q^52 - 4 * q^53 - 2 * q^54 + q^56 - 2 * q^57 - 6 * q^58 + 8 * q^59 - q^61 + 4 * q^63 + 2 * q^64 - 2 * q^66 - 12 * q^67 + 8 * q^68 - 4 * q^69 - 6 * q^71 - q^72 + 7 * q^73 - 22 * q^74 + 10 * q^75 - q^76 + 10 * q^77 + 2 * q^78 - 8 * q^79 - q^81 + 2 * q^82 - 28 * q^83 + 5 * q^84 + q^86 - 12 * q^87 + 2 * q^88 + 12 * q^89 + 8 * q^91 - 8 * q^92 + q^96 - 9 * q^97 - 13 * q^98 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	1.00000			0.500000
$5$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$5$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$7$	0.500000	−	2.59808i	0.188982	−	0.981981i
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$		0			0
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	0.976478	−	0.215615i	$-0.0691756\pi$
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	−0.674967	+	0.737848i	$0.735842\pi$
$12$	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
$16$	1.00000			0.250000
$17$	4.00000			0.970143			0.485071	−	0.874475i	$-0.338794\pi$
$17$	4.00000			0.970143			0.485071	+	0.874475i	$0.338794\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	−0.917663	−	0.397360i	$-0.869927\pi$
$19$	−0.500000	+	0.866025i	−0.114708	+	0.198680i	0.802955	+	0.596040i	$0.203260\pi$
$20$		0			0
$21$	2.50000	−	0.866025i	0.545545	−	0.188982i
$22$	1.00000	+	1.73205i	0.213201	+	0.369274i
$23$	−4.00000			−0.834058			−0.417029	−	0.908893i	$-0.636929\pi$
$23$	−4.00000			−0.834058			−0.417029	+	0.908893i	$0.636929\pi$
$24$	0.500000	+	0.866025i	0.102062	+	0.176777i
$25$	2.50000	−	4.33013i	0.500000	−	0.866025i
$26$	3.50000	+	0.866025i	0.686406	+	0.169842i
$27$	−1.00000			−0.192450
$28$	0.500000	−	2.59808i	0.0944911	−	0.490990i
$29$	−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	$-0.833333\pi$
$31$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$32$	1.00000			0.176777
$33$	−1.00000	+	1.73205i	−0.174078	+	0.301511i
$34$	4.00000			0.685994
$35$		0			0
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−11.0000			−1.80839			−0.904194	−	0.427121i	$-0.859528\pi$
$37$	−11.0000			−1.80839			−0.904194	+	0.427121i	$0.859528\pi$
$38$	−0.500000	+	0.866025i	−0.0811107	+	0.140488i
$39$	1.00000	+	3.46410i	0.160128	+	0.554700i
$40$		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	$0.116751\pi$
$42$	2.50000	−	0.866025i	0.385758	−	0.133631i
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	0.901629	−	0.432511i	$-0.142372\pi$
$43$	0.500000	+	0.866025i	0.0762493	+	0.132068i	−0.825380	+	0.564578i	$0.809039\pi$
$44$	1.00000	+	1.73205i	0.150756	+	0.261116i
$45$		0			0
$46$	−4.00000			−0.589768
$47$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$47$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	−6.50000	−	2.59808i	−0.928571	−	0.371154i
$50$	2.50000	−	4.33013i	0.353553	−	0.612372i
$51$	2.00000	+	3.46410i	0.280056	+	0.485071i
$52$	3.50000	+	0.866025i	0.485363	+	0.120096i
$53$	−2.00000	+	3.46410i	−0.274721	+	0.475831i	−0.970065	−	0.242846i	$-0.921919\pi$
$53$	−2.00000	+	3.46410i	−0.274721	+	0.475831i	0.695344	+	0.718677i	$0.255252\pi$
$54$	−1.00000			−0.136083
$55$		0			0
$56$	0.500000	−	2.59808i	0.0668153	−	0.347183i
$57$	−1.00000			−0.132453
$58$	−3.00000	+	5.19615i	−0.393919	+	0.682288i
$59$	4.00000			0.520756			0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000			0.520756			0.260378	+	0.965507i	$0.416153\pi$
$60$		0			0
$61$	−0.500000	+	0.866025i	−0.0640184	+	0.110883i	−0.896258	−	0.443533i	$-0.853725\pi$
$61$	−0.500000	+	0.866025i	−0.0640184	+	0.110883i	0.832240	+	0.554416i	$0.187058\pi$
$62$		0			0
$63$	2.00000	+	1.73205i	0.251976	+	0.218218i
$64$	1.00000			0.125000
$65$		0			0
$66$	−1.00000	+	1.73205i	−0.123091	+	0.213201i
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	−0.955588	−	0.294706i	$-0.904778\pi$
$67$	−6.00000	−	10.3923i	−0.733017	−	1.26962i	0.222571	−	0.974916i	$-0.428555\pi$
$68$	4.00000			0.485071
$69$	−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	$0.949205\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	3.50000	−	6.06218i	0.409644	−	0.709524i	−0.585206	−	0.810885i	$-0.698986\pi$
$73$	3.50000	−	6.06218i	0.409644	−	0.709524i	0.994850	+	0.101361i	$0.0323196\pi$
$74$	−11.0000			−1.27872
$75$	5.00000			0.577350
$76$	−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	0.548352	−	0.836247i	$-0.315255\pi$
$79$	−4.00000	−	6.92820i	−0.450035	−	0.779484i	−0.998388	+	0.0567635i	$0.981922\pi$
$80$		0			0
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	1.00000	−	1.73205i	0.110432	−	0.191273i
$83$	−14.0000			−1.53670			−0.768350	−	0.640030i	$-0.778922\pi$
$83$	−14.0000			−1.53670			−0.768350	+	0.640030i	$0.778922\pi$
$84$	2.50000	−	0.866025i	0.272772	−	0.0944911i
$85$		0			0
$86$	0.500000	+	0.866025i	0.0539164	+	0.0933859i
$87$	−6.00000			−0.643268
$88$	1.00000	+	1.73205i	0.106600	+	0.184637i
$89$	6.00000			0.635999			0.317999	−	0.948091i	$-0.396989\pi$
$89$	6.00000			0.635999			0.317999	+	0.948091i	$0.396989\pi$
$90$		0			0
$91$	4.00000	−	8.66025i	0.419314	−	0.907841i
$92$	−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	$0.984376\pi$
$98$	−6.50000	−	2.59808i	−0.656599	−	0.262445i
$99$	−2.00000			−0.201008
$100$	2.50000	−	4.33013i	0.250000	−	0.433013i
$101$	9.00000	+	15.5885i	0.895533	+	1.55111i	0.833143	+	0.553058i	$0.186539\pi$
$101$	9.00000	+	15.5885i	0.895533	+	1.55111i	0.0623905	+	0.998052i	$0.480128\pi$
$102$	2.00000	+	3.46410i	0.198030	+	0.342997i
$103$	3.50000	+	6.06218i	0.344865	+	0.597324i	0.985329	−	0.170664i	$-0.0545913\pi$
$103$	3.50000	+	6.06218i	0.344865	+	0.597324i	−0.640464	+	0.767988i	$0.721258\pi$
$104$	3.50000	+	0.866025i	0.343203	+	0.0849208i
$105$		0			0
$106$	−2.00000	+	3.46410i	−0.194257	+	0.336463i
$107$	−18.0000			−1.74013			−0.870063	−	0.492941i	$-0.835922\pi$
$107$	−18.0000			−1.74013			−0.870063	+	0.492941i	$0.835922\pi$
$108$	−1.00000			−0.0962250
$109$	−5.50000	+	9.52628i	−0.526804	+	0.912452i	0.472708	+	0.881219i	$0.343277\pi$
$109$	−5.50000	+	9.52628i	−0.526804	+	0.912452i	−0.999512	+	0.0312328i	$0.990057\pi$
$110$		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	$0.710534\pi$
$114$	−1.00000			−0.0936586
$115$		0			0
$116$	−3.00000	+	5.19615i	−0.278543	+	0.482451i
$117$	−2.50000	+	2.59808i	−0.231125	+	0.240192i
$118$	4.00000			0.368230
$119$	2.00000	−	10.3923i	0.183340	−	0.952661i
$120$		0			0
$121$	3.50000	−	6.06218i	0.318182	−	0.551107i
$122$	−0.500000	+	0.866025i	−0.0452679	+	0.0784063i
$123$	2.00000			0.180334
$124$		0			0
$125$		0			0
$126$	2.00000	+	1.73205i	0.178174	+	0.154303i
$127$	−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	$0.970975\pi$
$128$	1.00000			0.0883883
$129$	−0.500000	+	0.866025i	−0.0440225	+	0.0762493i
$130$		0			0
$131$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$131$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$132$	−1.00000	+	1.73205i	−0.0870388	+	0.150756i
$133$	2.00000	+	1.73205i	0.173422	+	0.150188i
$134$	−6.00000	−	10.3923i	−0.518321	−	0.897758i
$135$		0			0
$136$	4.00000			0.342997
$137$	12.0000			1.02523			0.512615	−	0.858619i	$-0.328677\pi$
$137$	12.0000			1.02523			0.512615	+	0.858619i	$0.328677\pi$
$138$	−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
$143$	2.00000	+	6.92820i	0.167248	+	0.579365i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$		0			0
$146$	3.50000	−	6.06218i	0.289662	−	0.501709i
$147$	−1.00000	−	6.92820i	−0.0824786	−	0.571429i
$148$	−11.0000			−0.904194
$149$	−5.00000	+	8.66025i	−0.409616	+	0.709476i	−0.994847	−	0.101391i	$-0.967671\pi$
$149$	−5.00000	+	8.66025i	−0.409616	+	0.709476i	0.585231	+	0.810867i	$0.301004\pi$
$150$	5.00000			0.408248
$151$	−2.00000	+	3.46410i	−0.162758	+	0.281905i	−0.935857	−	0.352381i	$-0.885372\pi$
$151$	−2.00000	+	3.46410i	−0.162758	+	0.281905i	0.773099	+	0.634285i	$0.218706\pi$
$152$	−0.500000	+	0.866025i	−0.0405554	+	0.0702439i
$153$	−2.00000	+	3.46410i	−0.161690	+	0.280056i
$154$	5.00000	−	1.73205i	0.402911	−	0.139573i
$155$		0			0
$156$	1.00000	+	3.46410i	0.0800641	+	0.277350i
$157$	3.50000	−	6.06218i	0.279330	−	0.483814i	−0.691888	−	0.722005i	$-0.743221\pi$
$157$	3.50000	−	6.06218i	0.279330	−	0.483814i	0.971219	+	0.238190i	$0.0765542\pi$
$158$	−4.00000	−	6.92820i	−0.318223	−	0.551178i
$159$	−4.00000			−0.317221
$160$		0			0
$161$	−2.00000	+	10.3923i	−0.157622	+	0.819028i
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	5.50000	−	9.52628i	0.430793	−	0.746156i	−0.566149	−	0.824303i	$-0.691567\pi$
$163$	5.50000	−	9.52628i	0.430793	−	0.746156i	0.996942	+	0.0781474i	$0.0249005\pi$
$164$	1.00000	−	1.73205i	0.0780869	−	0.135250i
$165$		0			0
$166$	−14.0000			−1.08661
$167$	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
$171$	−0.500000	−	0.866025i	−0.0382360	−	0.0662266i
$172$	0.500000	+	0.866025i	0.0381246	+	0.0660338i
$173$	−4.00000	+	6.92820i	−0.304114	+	0.526742i	−0.977064	−	0.212947i	$-0.931694\pi$
$173$	−4.00000	+	6.92820i	−0.304114	+	0.526742i	0.672949	+	0.739689i	$0.265027\pi$
$174$	−6.00000			−0.454859
$175$	−10.0000	−	8.66025i	−0.755929	−	0.654654i
$176$	1.00000	+	1.73205i	0.0753778	+	0.130558i
$177$	2.00000	+	3.46410i	0.150329	+	0.260378i
$178$	6.00000			0.449719
$179$	8.00000	+	13.8564i	0.597948	+	1.03568i	0.993124	+	0.117071i	$0.0373504\pi$
$179$	8.00000	+	13.8564i	0.597948	+	1.03568i	−0.395175	+	0.918606i	$0.629316\pi$
$180$		0			0
$181$	7.00000			0.520306			0.260153	−	0.965567i	$-0.416227\pi$
$181$	7.00000			0.520306			0.260153	+	0.965567i	$0.416227\pi$
$182$	4.00000	−	8.66025i	0.296500	−	0.641941i
$183$	−1.00000			−0.0739221
$184$	−4.00000			−0.294884
$185$		0			0
$186$		0			0
$187$	4.00000	+	6.92820i	0.292509	+	0.506640i
$188$		0			0
$189$	−0.500000	+	2.59808i	−0.0363696	+	0.188982i
$190$		0			0
$191$	−12.0000	+	20.7846i	−0.868290	+	1.50392i	−0.00454614	+	0.999990i	$0.501447\pi$
$191$	−12.0000	+	20.7846i	−0.868290	+	1.50392i	−0.863743	+	0.503932i	$0.831886\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	−9.50000	−	16.4545i	−0.683825	−	1.18442i	−0.973805	−	0.227387i	$-0.926982\pi$
$193$	−9.50000	−	16.4545i	−0.683825	−	1.18442i	0.289980	−	0.957033i	$-0.406351\pi$
$194$	−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	$0.0746770\pi$
$198$	−2.00000			−0.142134
$199$	−3.00000			−0.212664			−0.106332	−	0.994331i	$-0.533911\pi$
$199$	−3.00000			−0.212664			−0.106332	+	0.994331i	$0.533911\pi$
$200$	2.50000	−	4.33013i	0.176777	−	0.306186i
$201$	6.00000	−	10.3923i	0.423207	−	0.733017i
$202$	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
$206$	3.50000	+	6.06218i	0.243857	+	0.422372i
$207$	2.00000	−	3.46410i	0.139010	−	0.240772i
$208$	3.50000	+	0.866025i	0.242681	+	0.0600481i
$209$	−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	$0.314345\pi$
$212$	−2.00000	+	3.46410i	−0.137361	+	0.237915i
$213$	3.00000	−	5.19615i	0.205557	−	0.356034i
$214$	−18.0000			−1.23045
$215$		0			0
$216$	−1.00000			−0.0680414
$217$		0			0
$218$	−5.50000	+	9.52628i	−0.372507	+	0.645201i
$219$	7.00000			0.473016
$220$		0			0
$221$	14.0000	+	3.46410i	0.941742	+	0.233021i
$222$	−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	$-0.0132929\pi$
$224$	0.500000	−	2.59808i	0.0334077	−	0.173591i
$225$	2.50000	+	4.33013i	0.166667	+	0.288675i
$226$	4.00000	+	6.92820i	0.266076	+	0.460857i
$227$	18.0000			1.19470			0.597351	−	0.801980i	$-0.296220\pi$
$227$	18.0000			1.19470			0.597351	+	0.801980i	$0.296220\pi$
$228$	−1.00000			−0.0662266
$229$	10.5000	+	18.1865i	0.693860	+	1.20180i	0.970564	+	0.240845i	$0.0774245\pi$
$229$	10.5000	+	18.1865i	0.693860	+	1.20180i	−0.276704	+	0.960955i	$0.589242\pi$
$230$		0			0
$231$	4.00000	+	3.46410i	0.263181	+	0.227921i
$232$	−3.00000	+	5.19615i	−0.196960	+	0.341144i
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	0.947403	−	0.320043i	$-0.103697\pi$
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	−0.750867	+	0.660454i	$0.770364\pi$
$234$	−2.50000	+	2.59808i	−0.163430	+	0.169842i
$235$		0			0
$236$	4.00000			0.260378
$237$	4.00000	−	6.92820i	0.259828	−	0.450035i
$238$	2.00000	−	10.3923i	0.129641	−	0.673633i
$239$	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
$241$	18.0000			1.15948			0.579741	−	0.814801i	$-0.303154\pi$
$241$	18.0000			1.15948			0.579741	+	0.814801i	$0.303154\pi$
$242$	3.50000	−	6.06218i	0.224989	−	0.389692i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−0.500000	+	0.866025i	−0.0320092	+	0.0554416i
$245$		0			0
$246$	2.00000			0.127515
$247$	−2.50000	+	2.59808i	−0.159071	+	0.165312i
$248$		0			0
$249$	−7.00000	−	12.1244i	−0.443607	−	0.768350i
$250$		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
$254$	−6.50000	+	11.2583i	−0.407846	+	0.706410i
$255$		0			0
$256$	1.00000			0.0625000
$257$	−8.00000			−0.499026			−0.249513	−	0.968371i	$-0.580271\pi$
$257$	−8.00000			−0.499026			−0.249513	+	0.968371i	$0.580271\pi$
$258$	−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
$263$	−13.0000	−	22.5167i	−0.801614	−	1.38844i	−0.918553	−	0.395298i	$-0.870641\pi$
$263$	−13.0000	−	22.5167i	−0.801614	−	1.38844i	0.116939	−	0.993139i	$-0.462692\pi$
$264$	−1.00000	+	1.73205i	−0.0615457	+	0.106600i
$265$		0			0
$266$	2.00000	+	1.73205i	0.122628	+	0.106199i
$267$	3.00000	+	5.19615i	0.183597	+	0.317999i
$268$	−6.00000	−	10.3923i	−0.366508	−	0.634811i
$269$	−10.0000			−0.609711			−0.304855	−	0.952399i	$-0.598608\pi$
$269$	−10.0000			−0.609711			−0.304855	+	0.952399i	$0.598608\pi$
$270$		0			0
$271$	−15.0000			−0.911185			−0.455593	−	0.890188i	$-0.650573\pi$
$271$	−15.0000			−0.911185			−0.455593	+	0.890188i	$0.650573\pi$
$272$	4.00000			0.242536
$273$	9.50000	−	0.866025i	0.574966	−	0.0524142i
$274$	12.0000			0.724947
$275$	10.0000			0.603023
$276$	−2.00000	−	3.46410i	−0.120386	−	0.208514i
$277$	19.0000			1.14160			0.570800	−	0.821089i	$-0.306633\pi$
$277$	19.0000			1.14160			0.570800	+	0.821089i	$0.306633\pi$
$278$	−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
$283$	12.5000	+	21.6506i	0.743048	+	1.28700i	0.951101	+	0.308879i	$0.0999539\pi$
$283$	12.5000	+	21.6506i	0.743048	+	1.28700i	−0.208053	+	0.978117i	$0.566713\pi$
$284$	−3.00000	−	5.19615i	−0.178017	−	0.308335i
$285$		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
$289$	−1.00000			−0.0588235
$290$		0			0
$291$	4.50000	−	7.79423i	0.263795	−	0.456906i
$292$	3.50000	−	6.06218i	0.204822	−	0.354762i
$293$	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
$296$	−11.0000			−0.639362
$297$	−1.00000	−	1.73205i	−0.0580259	−	0.100504i
$298$	−5.00000	+	8.66025i	−0.289642	+	0.501675i
$299$	−14.0000	−	3.46410i	−0.809641	−	0.200334i
$300$	5.00000			0.288675
$301$	2.50000	−	0.866025i	0.144098	−	0.0499169i
$302$	−2.00000	+	3.46410i	−0.115087	+	0.199337i
$303$	−9.00000	+	15.5885i	−0.517036	+	0.895533i
$304$	−0.500000	+	0.866025i	−0.0286770	+	0.0496700i
$305$		0			0
$306$	−2.00000	+	3.46410i	−0.114332	+	0.198030i
$307$	28.0000			1.59804			0.799022	−	0.601302i	$-0.205351\pi$
$307$	28.0000			1.59804			0.799022	+	0.601302i	$0.205351\pi$
$308$	5.00000	−	1.73205i	0.284901	−	0.0986928i
$309$	−3.50000	+	6.06218i	−0.199108	+	0.344865i
$310$		0			0
$311$	14.0000	−	24.2487i	0.793867	−	1.37502i	−0.129689	−	0.991555i	$-0.541398\pi$
$311$	14.0000	−	24.2487i	0.793867	−	1.37502i	0.923556	−	0.383464i	$-0.125269\pi$
$312$	1.00000	+	3.46410i	0.0566139	+	0.196116i
$313$	10.5000	+	18.1865i	0.593495	+	1.02796i	0.993757	+	0.111563i	$0.0355857\pi$
$313$	10.5000	+	18.1865i	0.593495	+	1.02796i	−0.400262	+	0.916401i	$0.631081\pi$
$314$	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	0.731556	−	0.681782i	$-0.238795\pi$
$317$	−4.00000	−	6.92820i	−0.224662	−	0.389127i	−0.956218	+	0.292655i	$0.905461\pi$
$318$	−4.00000			−0.224309
$319$	−12.0000			−0.671871
$320$		0			0
$321$	−9.00000	−	15.5885i	−0.502331	−	0.870063i
$322$	−2.00000	+	10.3923i	−0.111456	+	0.579141i
$323$	−2.00000	+	3.46410i	−0.111283	+	0.192748i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	12.5000	−	12.9904i	0.693375	−	0.720577i
$326$	5.50000	−	9.52628i	0.304617	−	0.527612i
$327$	−11.0000			−0.608301
$328$	1.00000	−	1.73205i	0.0552158	−	0.0956365i
$329$		0			0
$330$		0			0
$331$	5.50000	−	9.52628i	0.302307	−	0.523612i	−0.674351	−	0.738411i	$-0.735576\pi$
$331$	5.50000	−	9.52628i	0.302307	−	0.523612i	0.976658	+	0.214799i	$0.0689098\pi$
$332$	−14.0000			−0.768350
$333$	5.50000	−	9.52628i	0.301398	−	0.522037i
$334$	1.00000	−	1.73205i	0.0547176	−	0.0947736i
$335$		0			0
$336$	2.50000	−	0.866025i	0.136386	−	0.0472456i
$337$	9.00000			0.490261			0.245131	−	0.969490i	$-0.421169\pi$
$337$	9.00000			0.490261			0.245131	+	0.969490i	$0.421169\pi$
$338$	11.5000	+	6.06218i	0.625518	+	0.329739i
$339$	−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
$347$	26.0000			1.39575			0.697877	−	0.716218i	$-0.254128\pi$
$347$	26.0000			1.39575			0.697877	+	0.716218i	$0.254128\pi$
$348$	−6.00000			−0.321634
$349$	−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
$353$	2.00000	+	3.46410i	0.106449	+	0.184376i	0.914329	−	0.404971i	$-0.132718\pi$
$353$	2.00000	+	3.46410i	0.106449	+	0.184376i	−0.807880	+	0.589347i	$0.799385\pi$
$354$	2.00000	+	3.46410i	0.106299	+	0.184115i
$355$		0			0
$356$	6.00000			0.317999
$357$	10.0000	−	3.46410i	0.529256	−	0.183340i
$358$	8.00000	+	13.8564i	0.422813	+	0.732334i
$359$	3.00000	+	5.19615i	0.158334	+	0.274242i	0.934268	−	0.356572i	$-0.116054\pi$
$359$	3.00000	+	5.19615i	0.158334	+	0.274242i	−0.775934	+	0.630814i	$0.782721\pi$
$360$		0			0
$361$	9.00000	+	15.5885i	0.473684	+	0.820445i
$362$	7.00000			0.367912
$363$	7.00000			0.367405
$364$	4.00000	−	8.66025i	0.209657	−	0.453921i
$365$		0			0
$366$	−1.00000			−0.0522708
$367$	12.5000	+	21.6506i	0.652495	+	1.13015i	0.982516	+	0.186180i	$0.0596109\pi$
$367$	12.5000	+	21.6506i	0.652495	+	1.13015i	−0.330021	+	0.943974i	$0.607056\pi$
$368$	−4.00000			−0.208514
$369$	1.00000	+	1.73205i	0.0520579	+	0.0901670i
$370$		0			0
$371$	8.00000	+	6.92820i	0.415339	+	0.359694i
$372$		0			0
$373$	9.00000	−	15.5885i	0.466002	−	0.807140i	−0.533244	−	0.845962i	$-0.679027\pi$
$373$	9.00000	−	15.5885i	0.466002	−	0.807140i	0.999246	+	0.0388219i	$0.0123605\pi$
$374$	4.00000	+	6.92820i	0.206835	+	0.358249i
$375$		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
$381$	−13.0000			−0.666010
$382$	−12.0000	+	20.7846i	−0.613973	+	1.06343i
$383$	−4.00000	+	6.92820i	−0.204390	+	0.354015i	−0.949938	−	0.312437i	$-0.898855\pi$
$383$	−4.00000	+	6.92820i	−0.204390	+	0.354015i	0.745548	+	0.666452i	$0.232188\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$		0			0
$386$	−9.50000	−	16.4545i	−0.483537	−	0.837511i
$387$	−1.00000			−0.0508329
$388$	−4.50000	−	7.79423i	−0.228453	−	0.395692i
$389$	−2.00000	+	3.46410i	−0.101404	+	0.175637i	−0.912263	−	0.409604i	$-0.865667\pi$
$389$	−2.00000	+	3.46410i	−0.101404	+	0.175637i	0.810859	+	0.585241i	$0.199000\pi$
$390$		0			0
$391$	−16.0000			−0.809155
$392$	−6.50000	−	2.59808i	−0.328300	−	0.131223i
$393$		0			0
$394$	4.00000	−	6.92820i	0.201517	−	0.349038i
$395$		0			0
$396$	−2.00000			−0.100504
$397$	−0.500000	+	0.866025i	−0.0250943	+	0.0434646i	−0.878300	−	0.478110i	$-0.841322\pi$
$397$	−0.500000	+	0.866025i	−0.0250943	+	0.0434646i	0.853206	+	0.521575i	$0.174655\pi$
$398$	−3.00000			−0.150376
$399$	−0.500000	+	2.59808i	−0.0250313	+	0.130066i
$400$	2.50000	−	4.33013i	0.125000	−	0.216506i
$401$	10.0000			0.499376			0.249688	−	0.968326i	$-0.419672\pi$
$401$	10.0000			0.499376			0.249688	+	0.968326i	$0.419672\pi$
$402$	6.00000	−	10.3923i	0.299253	−	0.518321i
$403$		0			0
$404$	9.00000	+	15.5885i	0.447767	+	0.775555i
$405$		0			0
$406$	12.0000	+	10.3923i	0.595550	+	0.515761i
$407$	−11.0000	−	19.0526i	−0.545250	−	0.944400i
$408$	2.00000	+	3.46410i	0.0990148	+	0.171499i
$409$	−31.0000			−1.53285			−0.766426	−	0.642333i	$-0.777967\pi$
$409$	−31.0000			−1.53285			−0.766426	+	0.642333i	$0.777967\pi$
$410$		0			0
$411$	6.00000	+	10.3923i	0.295958	+	0.512615i
$412$	3.50000	+	6.06218i	0.172433	+	0.298662i
$413$	2.00000	−	10.3923i	0.0984136	−	0.511372i
$414$	2.00000	−	3.46410i	0.0982946	−	0.170251i
$415$		0			0
$416$	3.50000	+	0.866025i	0.171602	+	0.0424604i
$417$	8.00000	−	13.8564i	0.391762	−	0.678551i
$418$	−2.00000			−0.0978232
$419$	−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	$0.484480\pi$
$422$	−6.50000	+	11.2583i	−0.316415	+	0.548047i
$423$		0			0
$424$	−2.00000	+	3.46410i	−0.0971286	+	0.168232i
$425$	10.0000	−	17.3205i	0.485071	−	0.840168i
$426$	3.00000	−	5.19615i	0.145350	−	0.251754i
$427$	2.00000	+	1.73205i	0.0967868	+	0.0838198i
$428$	−18.0000			−0.870063
$429$	−5.00000	+	5.19615i	−0.241402	+	0.250873i
$430$		0			0
$431$	−13.0000	−	22.5167i	−0.626188	−	1.08459i	−0.988310	−	0.152459i	$-0.951281\pi$
$431$	−13.0000	−	22.5167i	−0.626188	−	1.08459i	0.362122	−	0.932131i	$-0.382052\pi$
$432$	−1.00000			−0.0481125
$433$	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
$436$	−5.50000	+	9.52628i	−0.263402	+	0.456226i
$437$	2.00000	−	3.46410i	0.0956730	−	0.165710i
$438$	7.00000			0.334473
$439$	−1.00000			−0.0477274			−0.0238637	−	0.999715i	$-0.507597\pi$
$439$	−1.00000			−0.0477274			−0.0238637	+	0.999715i	$0.507597\pi$
$440$		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	0.755219	−	0.655472i	$-0.227530\pi$
$443$	−4.00000	−	6.92820i	−0.190046	−	0.329169i	−0.945265	+	0.326303i	$0.894197\pi$
$444$	−5.50000	−	9.52628i	−0.261018	−	0.452097i
$445$		0			0
$446$	8.00000	−	13.8564i	0.378811	−	0.656120i
$447$	−10.0000			−0.472984
$448$	0.500000	−	2.59808i	0.0236228	−	0.122748i
$449$	−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
$451$	4.00000			0.188353
$452$	4.00000	+	6.92820i	0.188144	+	0.325875i
$453$	−4.00000			−0.187936
$454$	18.0000			0.844782
$455$		0			0
$456$	−1.00000			−0.0468293
$457$	38.0000			1.77757			0.888783	−	0.458329i	$-0.151552\pi$
$457$	38.0000			1.77757			0.888783	+	0.458329i	$0.151552\pi$
$458$	10.5000	+	18.1865i	0.490633	+	0.849801i
$459$	−4.00000			−0.186704
$460$		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	$0.954866\pi$
$462$	4.00000	+	3.46410i	0.186097	+	0.161165i
$463$	23.0000			1.06890			0.534450	−	0.845200i	$-0.320519\pi$
$463$	23.0000			1.06890			0.534450	+	0.845200i	$0.320519\pi$
$464$	−3.00000	+	5.19615i	−0.139272	+	0.241225i
$465$		0			0
$466$	3.00000	+	5.19615i	0.138972	+	0.240707i
$467$	−21.0000	−	36.3731i	−0.971764	−	1.68314i	−0.690225	−	0.723595i	$-0.742488\pi$
$467$	−21.0000	−	36.3731i	−0.971764	−	1.68314i	−0.281539	−	0.959550i	$-0.590845\pi$
$468$	−2.50000	+	2.59808i	−0.115563	+	0.120096i
$469$	−30.0000	+	10.3923i	−1.38527	+	0.479872i
$470$		0			0
$471$	7.00000			0.322543
$472$	4.00000			0.184115
$473$	−1.00000	+	1.73205i	−0.0459800	+	0.0796398i
$474$	4.00000	−	6.92820i	0.183726	−	0.318223i
$475$	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
$478$	2.00000			0.0914779
$479$	−5.00000	−	8.66025i	−0.228456	−	0.395697i	0.728895	−	0.684626i	$-0.240034\pi$
$479$	−5.00000	−	8.66025i	−0.228456	−	0.395697i	−0.957351	+	0.288929i	$0.906701\pi$
$480$		0			0
$481$	−38.5000	−	9.52628i	−1.75545	−	0.434361i
$482$	18.0000			0.819878
$483$	−10.0000	+	3.46410i	−0.455016	+	0.157622i
$484$	3.50000	−	6.06218i	0.159091	−	0.275554i
$485$		0			0
$486$	0.500000	−	0.866025i	0.0226805	−	0.0392837i
$487$	−23.0000			−1.04223			−0.521115	−	0.853487i	$-0.674484\pi$
$487$	−23.0000			−1.04223			−0.521115	+	0.853487i	$0.674484\pi$
$488$	−0.500000	+	0.866025i	−0.0226339	+	0.0392031i
$489$	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	$0.00131316\pi$
$492$	2.00000			0.0901670
$493$	−12.0000	+	20.7846i	−0.540453	+	0.936092i
$494$	−2.50000	+	2.59808i	−0.112480	+	0.116893i
$495$		0			0
$496$		0			0
$497$	−15.0000	+	5.19615i	−0.672842	+	0.233079i
$498$	−7.00000	−	12.1244i	−0.313678	−	0.543305i
$499$	−0.500000	−	0.866025i	−0.0223831	−	0.0387686i	0.854617	−	0.519259i	$-0.173792\pi$
$499$	−0.500000	−	0.866025i	−0.0223831	−	0.0387686i	−0.877000	+	0.480490i	$0.840459\pi$
$500$		0			0
$501$	2.00000			0.0893534
$502$	−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	$-0.399866\pi$
$504$	2.00000	+	1.73205i	0.0890871	+	0.0771517i
$505$		0			0
$506$	−4.00000	−	6.92820i	−0.177822	−	0.307996i
$507$	0.500000	+	12.9904i	0.0222058	+	0.576923i
$508$	−6.50000	+	11.2583i	−0.288391	+	0.499508i
$509$	6.00000			0.265945			0.132973	−	0.991120i	$-0.457548\pi$
$509$	6.00000			0.265945			0.132973	+	0.991120i	$0.457548\pi$
$510$		0			0
$511$	−14.0000	−	12.1244i	−0.619324	−	0.536350i
$512$	1.00000			0.0441942
$513$	0.500000	−	0.866025i	0.0220755	−	0.0382360i
$514$	−8.00000			−0.352865
$515$		0			0
$516$	−0.500000	+	0.866025i	−0.0220113	+	0.0381246i
$517$		0			0
$518$	−5.50000	+	28.5788i	−0.241656	+	1.25568i
$519$	−8.00000			−0.351161
$520$		0			0
$521$	−14.0000	+	24.2487i	−0.613351	+	1.06236i	0.377320	+	0.926083i	$0.376846\pi$
$521$	−14.0000	+	24.2487i	−0.613351	+	1.06236i	−0.990671	+	0.136272i	$0.956488\pi$
$522$	−3.00000	−	5.19615i	−0.131306	−	0.227429i
$523$	−1.00000			−0.0437269			−0.0218635	−	0.999761i	$-0.506960\pi$
$523$	−1.00000			−0.0437269			−0.0218635	+	0.999761i	$0.506960\pi$
$524$		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
$529$	−7.00000			−0.304348
$530$		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
$536$	−6.00000	−	10.3923i	−0.259161	−	0.448879i
$537$	−8.00000	+	13.8564i	−0.345225	+	0.597948i
$538$	−10.0000			−0.431131
$539$	−2.00000	−	13.8564i	−0.0861461	−	0.596838i
$540$		0			0
$541$	−21.5000	−	37.2391i	−0.924357	−	1.60103i	−0.792592	−	0.609753i	$-0.791269\pi$
$541$	−21.5000	−	37.2391i	−0.924357	−	1.60103i	−0.131765	−	0.991281i	$-0.542065\pi$
$542$	−15.0000			−0.644305
$543$	3.50000	+	6.06218i	0.150199	+	0.260153i
$544$	4.00000			0.171499
$545$		0			0
$546$	9.50000	−	0.866025i	0.406562	−	0.0370625i
$547$	−5.00000			−0.213785			−0.106892	−	0.994271i	$-0.534090\pi$
$547$	−5.00000			−0.213785			−0.106892	+	0.994271i	$0.534090\pi$
$548$	12.0000			0.512615
$549$	−0.500000	−	0.866025i	−0.0213395	−	0.0369611i
$550$	10.0000			0.426401
$551$	−3.00000	−	5.19615i	−0.127804	−	0.221364i
$552$	−2.00000	−	3.46410i	−0.0851257	−	0.147442i
$553$	−20.0000	+	6.92820i	−0.850487	+	0.294617i
$554$	19.0000			0.807233
$555$		0			0
$556$	−8.00000	−	13.8564i	−0.339276	−	0.587643i
$557$	15.0000	+	25.9808i	0.635570	+	1.10084i	0.986394	+	0.164399i	$0.0525683\pi$
$557$	15.0000	+	25.9808i	0.635570	+	1.10084i	−0.350824	+	0.936442i	$0.614098\pi$
$558$		0			0
$559$	1.00000	+	3.46410i	0.0422955	+	0.146516i
$560$		0			0
$561$	−4.00000	+	6.92820i	−0.168880	+	0.292509i
$562$	30.0000			1.26547
$563$	−24.0000			−1.01148			−0.505740	−	0.862686i	$-0.668780\pi$
$563$	−24.0000			−1.01148			−0.505740	+	0.862686i	$0.668780\pi$
$564$		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
$569$	−4.00000			−0.167689			−0.0838444	−	0.996479i	$-0.526720\pi$
$569$	−4.00000			−0.167689			−0.0838444	+	0.996479i	$0.526720\pi$
$570$		0			0
$571$	−12.5000	+	21.6506i	−0.523109	+	0.906051i	0.476530	+	0.879158i	$0.341895\pi$
$571$	−12.5000	+	21.6506i	−0.523109	+	0.906051i	−0.999638	+	0.0268925i	$0.991439\pi$
$572$	2.00000	+	6.92820i	0.0836242	+	0.289683i
$573$	−24.0000			−1.00261
$574$	−4.00000	−	3.46410i	−0.166957	−	0.144589i
$575$	−10.0000	+	17.3205i	−0.417029	+	0.722315i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−3.50000	+	6.06218i	−0.145707	+	0.252372i	−0.929636	−	0.368478i	$-0.879879\pi$
$577$	−3.50000	+	6.06218i	−0.145707	+	0.252372i	0.783930	+	0.620850i	$0.213212\pi$
$578$	−1.00000			−0.0415945
$579$	9.50000	−	16.4545i	0.394807	−	0.683825i
$580$		0			0
$581$	−7.00000	+	36.3731i	−0.290409	+	1.50901i
$582$	4.50000	−	7.79423i	0.186531	−	0.323081i
$583$	−8.00000			−0.331326
$584$	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	$-0.0458424\pi$
$588$	−1.00000	−	6.92820i	−0.0412393	−	0.285714i
$589$		0			0
$590$		0			0
$591$	8.00000			0.329076
$592$	−11.0000			−0.452097
$593$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$593$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$594$	−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
$598$	−14.0000	−	3.46410i	−0.572503	−	0.141658i
$599$	5.00000	−	8.66025i	0.204294	−	0.353848i	−0.745613	−	0.666379i	$-0.767843\pi$
$599$	5.00000	−	8.66025i	0.204294	−	0.353848i	0.949908	+	0.312531i	$0.101177\pi$
$600$	5.00000			0.204124
$601$	−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	$0.293332\pi$
$602$	2.50000	−	0.866025i	0.101892	−	0.0352966i
$603$	12.0000			0.488678
$604$	−2.00000	+	3.46410i	−0.0813788	+	0.140952i
$605$		0			0
$606$	−9.00000	+	15.5885i	−0.365600	+	0.633238i
$607$	−0.500000	+	0.866025i	−0.0202944	+	0.0351509i	−0.875994	−	0.482322i	$-0.839794\pi$
$607$	−0.500000	+	0.866025i	−0.0202944	+	0.0351509i	0.855700	+	0.517472i	$0.173127\pi$
$608$	−0.500000	+	0.866025i	−0.0202777	+	0.0351220i
$609$	−3.00000	+	15.5885i	−0.121566	+	0.631676i
$610$		0			0
$611$		0			0
$612$	−2.00000	+	3.46410i	−0.0808452	+	0.140028i
$613$	−2.50000	−	4.33013i	−0.100974	−	0.174892i	0.811112	−	0.584891i	$-0.198863\pi$
$613$	−2.50000	−	4.33013i	−0.100974	−	0.174892i	−0.912086	+	0.409998i	$0.865529\pi$
$614$	28.0000			1.12999
$615$		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	$0.871871\pi$
$618$	−3.50000	+	6.06218i	−0.140791	+	0.243857i
$619$	17.5000	−	30.3109i	0.703384	−	1.21830i	−0.263887	−	0.964554i	$-0.585005\pi$
$619$	17.5000	−	30.3109i	0.703384	−	1.21830i	0.967271	−	0.253744i	$-0.0816620\pi$
$620$		0			0
$621$	4.00000			0.160514
$622$	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
$626$	10.5000	+	18.1865i	0.419664	+	0.726880i
$627$	−1.00000	−	1.73205i	−0.0399362	−	0.0691714i
$628$	3.50000	−	6.06218i	0.139665	−	0.241907i
$629$	−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
$633$	−13.0000			−0.516704
$634$	−4.00000	−	6.92820i	−0.158860	−	0.275154i
$635$		0			0
$636$	−4.00000			−0.158610
$637$	−20.5000	−	14.7224i	−0.812240	−	0.583324i
$638$	−12.0000			−0.475085
$639$	6.00000			0.237356
$640$		0			0
$641$	−30.0000			−1.18493			−0.592464	−	0.805597i	$-0.701845\pi$
$641$	−30.0000			−1.18493			−0.592464	+	0.805597i	$0.701845\pi$
$642$	−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	$0.607810\pi$
$644$	−2.00000	+	10.3923i	−0.0788110	+	0.409514i
$645$		0			0
$646$	−2.00000	+	3.46410i	−0.0786889	+	0.136293i
$647$	−12.0000	−	20.7846i	−0.471769	−	0.817127i	0.527710	−	0.849425i	$-0.323051\pi$
$647$	−12.0000	−	20.7846i	−0.471769	−	0.817127i	−0.999478	+	0.0322975i	$0.989718\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	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
$653$	−4.00000			−0.156532			−0.0782660	−	0.996933i	$-0.524938\pi$
$653$	−4.00000			−0.156532			−0.0782660	+	0.996933i	$0.524938\pi$
$654$	−11.0000			−0.430134
$655$		0			0
$656$	1.00000	−	1.73205i	0.0390434	−	0.0676252i
$657$	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
$661$	−19.0000	−	32.9090i	−0.739014	−	1.28001i	−0.952940	−	0.303160i	$-0.901958\pi$
$661$	−19.0000	−	32.9090i	−0.739014	−	1.28001i	0.213925	−	0.976850i	$-0.431375\pi$
$662$	5.50000	−	9.52628i	0.213764	−	0.370249i
$663$	4.00000	+	13.8564i	0.155347	+	0.538138i
$664$	−14.0000			−0.543305
$665$		0			0
$666$	5.50000	−	9.52628i	0.213121	−	0.369136i
$667$	12.0000	−	20.7846i	0.464642	−	0.804783i
$668$	1.00000	−	1.73205i	0.0386912	−	0.0670151i
$669$	16.0000			0.618596
$670$		0			0
$671$	−2.00000			−0.0772091
$672$	2.50000	−	0.866025i	0.0964396	−	0.0334077i
$673$	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	$-0.0221228\pi$
$674$	9.00000			0.346667
$675$	−2.50000	+	4.33013i	−0.0962250	+	0.166667i
$676$	11.5000	+	6.06218i	0.442308	+	0.233161i
$677$	7.00000	+	12.1244i	0.269032	+	0.465977i	0.968612	−	0.248577i	$-0.0799630\pi$
$677$	7.00000	+	12.1244i	0.269032	+	0.465977i	−0.699580	+	0.714554i	$0.746630\pi$
$678$	−4.00000	+	6.92820i	−0.153619	+	0.266076i
$679$	−22.5000	+	7.79423i	−0.863471	+	0.299115i
$680$		0			0
$681$	9.00000	+	15.5885i	0.344881	+	0.597351i
$682$		0			0
$683$	−16.0000			−0.612223			−0.306111	−	0.951996i	$-0.599028\pi$
$683$	−16.0000			−0.612223			−0.306111	+	0.951996i	$0.599028\pi$
$684$	−0.500000	−	0.866025i	−0.0191180	−	0.0331133i
$685$		0			0
$686$	−10.0000	+	15.5885i	−0.381802	+	0.595170i
$687$	−10.5000	+	18.1865i	−0.400600	+	0.693860i
$688$	0.500000	+	0.866025i	0.0190623	+	0.0330169i
$689$	−10.0000	+	10.3923i	−0.380970	+	0.395915i
$690$		0			0
$691$	41.0000			1.55971			0.779857	−	0.625958i	$-0.215292\pi$
$691$	41.0000			1.55971			0.779857	+	0.625958i	$0.215292\pi$
$692$	−4.00000	+	6.92820i	−0.152057	+	0.263371i
$693$	−1.00000	+	5.19615i	−0.0379869	+	0.197386i
$694$	26.0000			0.986947
$695$		0			0
$696$	−6.00000			−0.227429
$697$	4.00000	−	6.92820i	0.151511	−	0.262424i
$698$	−2.50000	+	4.33013i	−0.0946264	+	0.163898i
$699$	−3.00000	+	5.19615i	−0.113470	+	0.196537i
$700$	−10.0000	−	8.66025i	−0.377964	−	0.327327i
$701$	30.0000			1.13308			0.566542	−	0.824033i	$-0.308281\pi$
$701$	30.0000			1.13308			0.566542	+	0.824033i	$0.308281\pi$
$702$	−3.50000	−	0.866025i	−0.132099	−	0.0326860i
$703$	5.50000	−	9.52628i	0.207436	−	0.359290i
$704$	1.00000	+	1.73205i	0.0376889	+	0.0652791i
$705$		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
$709$	12.5000	−	21.6506i	0.469447	−	0.813107i	−0.529943	−	0.848034i	$-0.677787\pi$
$709$	12.5000	−	21.6506i	0.469447	−	0.813107i	0.999390	+	0.0349269i	$0.0111198\pi$
$710$		0			0
$711$	8.00000			0.300023
$712$	6.00000			0.224860
$713$		0			0
$714$	10.0000	−	3.46410i	0.374241	−	0.129641i
$715$		0			0
$716$	8.00000	+	13.8564i	0.298974	+	0.517838i
$717$	1.00000	+	1.73205i	0.0373457	+	0.0646846i
$718$	3.00000	+	5.19615i	0.111959	+	0.193919i
$719$	−18.0000	+	31.1769i	−0.671287	+	1.16270i	0.306253	+	0.951950i	$0.400925\pi$
$719$	−18.0000	+	31.1769i	−0.671287	+	1.16270i	−0.977539	+	0.210752i	$0.932409\pi$
$720$		0			0
$721$	17.5000	−	6.06218i	0.651734	−	0.225767i
$722$	9.00000	+	15.5885i	0.334945	+	0.580142i
$723$	9.00000	+	15.5885i	0.334714	+	0.579741i
$724$	7.00000			0.260153
$725$	15.0000	+	25.9808i	0.557086	+	0.964901i
$726$	7.00000			0.259794
$727$	28.0000			1.03846			0.519231	−	0.854634i	$-0.326218\pi$
$727$	28.0000			1.03846			0.519231	+	0.854634i	$0.326218\pi$
$728$	4.00000	−	8.66025i	0.148250	−	0.320970i
$729$	1.00000			0.0370370
$730$		0			0
$731$	2.00000	+	3.46410i	0.0739727	+	0.128124i
$732$	−1.00000			−0.0369611
$733$	−7.00000	−	12.1244i	−0.258551	−	0.447823i	0.707303	−	0.706910i	$-0.249912\pi$
$733$	−7.00000	−	12.1244i	−0.258551	−	0.447823i	−0.965854	+	0.259087i	$0.916578\pi$
$734$	12.5000	+	21.6506i	0.461383	+	0.799140i
$735$		0			0
$736$	−4.00000			−0.147442
$737$	12.0000	−	20.7846i	0.442026	−	0.765611i
$738$	1.00000	+	1.73205i	0.0368105	+	0.0637577i
$739$	−2.50000	−	4.33013i	−0.0919640	−	0.159286i	0.816373	−	0.577524i	$-0.195981\pi$
$739$	−2.50000	−	4.33013i	−0.0919640	−	0.159286i	−0.908337	+	0.418238i	$0.862648\pi$
$740$		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
$747$	7.00000	−	12.1244i	0.256117	−	0.443607i
$748$	4.00000	+	6.92820i	0.146254	+	0.253320i
$749$	−9.00000	+	46.7654i	−0.328853	+	1.70877i
$750$		0			0
$751$	−25.0000			−0.912263			−0.456131	−	0.889912i	$-0.650765\pi$
$751$	−25.0000			−0.912263			−0.456131	+	0.889912i	$0.650765\pi$
$752$		0			0
$753$	15.0000	−	25.9808i	0.546630	−	0.946792i
$754$	−15.0000	+	15.5885i	−0.546268	+	0.567698i
$755$		0			0
$756$	−0.500000	+	2.59808i	−0.0181848	+	0.0944911i
$757$	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	$0.0357456\pi$
$758$	−10.0000	+	17.3205i	−0.363216	+	0.629109i
$759$	4.00000	−	6.92820i	0.145191	−	0.251478i
$760$		0			0
$761$	10.0000	−	17.3205i	0.362500	−	0.627868i	−0.625872	−	0.779926i	$-0.715257\pi$
$761$	10.0000	−	17.3205i	0.362500	−	0.627868i	0.988372	+	0.152058i	$0.0485900\pi$
$762$	−13.0000			−0.470940
$763$	22.0000	+	19.0526i	0.796453	+	0.689749i
$764$	−12.0000	+	20.7846i	−0.434145	+	0.751961i
$765$		0			0
$766$	−4.00000	+	6.92820i	−0.144526	+	0.250326i
$767$	14.0000	+	3.46410i	0.505511	+	0.125081i
$768$	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
$773$	−52.0000			−1.87031			−0.935155	−	0.354239i	$-0.884740\pi$
$773$	−52.0000			−1.87031			−0.935155	+	0.354239i	$0.884740\pi$
$774$	−1.00000			−0.0359443
$775$		0			0
$776$	−4.50000	−	7.79423i	−0.161541	−	0.279797i
$777$	−27.5000	+	9.52628i	−0.986557	+	0.341753i
$778$	−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
$782$	−16.0000			−0.572159
$783$	3.00000	−	5.19615i	0.107211	−	0.185695i
$784$	−6.50000	−	2.59808i	−0.232143	−	0.0927884i
$785$		0			0
$786$		0			0
$787$	53.0000			1.88925			0.944623	−	0.328158i	$-0.106428\pi$
$787$	53.0000			1.88925			0.944623	+	0.328158i	$0.106428\pi$
$788$	4.00000	−	6.92820i	0.142494	−	0.246807i
$789$	13.0000	−	22.5167i	0.462812	−	0.801614i
$790$		0			0
$791$	20.0000	−	6.92820i	0.711118	−	0.246339i
$792$	−2.00000			−0.0710669
$793$	−2.50000	+	2.59808i	−0.0887776	+	0.0922604i
$794$	−0.500000	+	0.866025i	−0.0177443	+	0.0307341i
$795$		0			0
$796$	−3.00000			−0.106332
$797$	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
$800$	2.50000	−	4.33013i	0.0883883	−	0.153093i
$801$	−3.00000	+	5.19615i	−0.106000	+	0.183597i
$802$	10.0000			0.353112
$803$	14.0000			0.494049
$804$	6.00000	−	10.3923i	0.211604	−	0.366508i
$805$		0			0
$806$		0			0
$807$	−5.00000	−	8.66025i	−0.176008	−	0.304855i
$808$	9.00000	+	15.5885i	0.316619	+	0.548400i
$809$	1.00000	+	1.73205i	0.0351581	+	0.0608957i	0.883069	−	0.469243i	$-0.155473\pi$
$809$	1.00000	+	1.73205i	0.0351581	+	0.0608957i	−0.847911	+	0.530139i	$0.822140\pi$
$810$		0			0
$811$	−21.0000			−0.737410			−0.368705	−	0.929547i	$-0.620199\pi$
$811$	−21.0000			−0.737410			−0.368705	+	0.929547i	$0.620199\pi$
$812$	12.0000	+	10.3923i	0.421117	+	0.364698i
$813$	−7.50000	−	12.9904i	−0.263036	−	0.455593i
$814$	−11.0000	−	19.0526i	−0.385550	−	0.667792i
$815$		0			0
$816$	2.00000	+	3.46410i	0.0700140	+	0.121268i
$817$	−1.00000			−0.0349856
$818$	−31.0000			−1.08389
$819$	5.50000	+	7.79423i	0.192186	+	0.272352i
$820$		0			0
$821$	52.0000			1.81481			0.907406	−	0.420255i	$-0.138059\pi$
$821$	52.0000			1.81481			0.907406	+	0.420255i	$0.138059\pi$
$822$	6.00000	+	10.3923i	0.209274	+	0.362473i
$823$	40.0000			1.39431			0.697156	−	0.716919i	$-0.254448\pi$
$823$	40.0000			1.39431			0.697156	+	0.716919i	$0.254448\pi$
$824$	3.50000	+	6.06218i	0.121928	+	0.211186i
$825$	5.00000	+	8.66025i	0.174078	+	0.301511i
$826$	2.00000	−	10.3923i	0.0695889	−	0.361595i
$827$	−12.0000			−0.417281			−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000			−0.417281			−0.208640	+	0.977992i	$0.566904\pi$
$828$	2.00000	−	3.46410i	0.0695048	−	0.120386i
$829$	−15.5000	−	26.8468i	−0.538337	−	0.932427i	−0.998994	−	0.0448490i	$-0.985719\pi$
$829$	−15.5000	−	26.8468i	−0.538337	−	0.932427i	0.460657	−	0.887578i	$-0.347614\pi$
$830$		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
$836$	−2.00000			−0.0691714
$837$		0			0
$838$	−13.0000	+	22.5167i	−0.449078	+	0.777825i
$839$	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
$842$	2.00000			0.0689246
$843$	15.0000	+	25.9808i	0.516627	+	0.894825i
$844$	−6.50000	+	11.2583i	−0.223739	+	0.387528i
$845$		0			0
$846$		0			0
$847$	−14.0000	−	12.1244i	−0.481046	−	0.416598i
$848$	−2.00000	+	3.46410i	−0.0686803	+	0.118958i
$849$	−12.5000	+	21.6506i	−0.428999	+	0.743048i
$850$	10.0000	−	17.3205i	0.342997	−	0.594089i
$851$	44.0000			1.50830
$852$	3.00000	−	5.19615i	0.102778	−	0.178017i
$853$	14.0000			0.479351			0.239675	−	0.970853i	$-0.422959\pi$
$853$	14.0000			0.479351			0.239675	+	0.970853i	$0.422959\pi$
$854$	2.00000	+	1.73205i	0.0684386	+	0.0592696i
$855$		0			0
$856$	−18.0000			−0.615227
$857$	7.00000	−	12.1244i	0.239115	−	0.414160i	−0.721345	−	0.692576i	$-0.756476\pi$
$857$	7.00000	−	12.1244i	0.239115	−	0.414160i	0.960461	+	0.278416i	$0.0898092\pi$
$858$	−5.00000	+	5.19615i	−0.170697	+	0.177394i
$859$	17.5000	+	30.3109i	0.597092	+	1.03419i	0.993248	+	0.116011i	$0.0370107\pi$
$859$	17.5000	+	30.3109i	0.597092	+	1.03419i	−0.396156	+	0.918183i	$0.629656\pi$
$860$		0			0
$861$	1.00000	−	5.19615i	0.0340799	−	0.177084i
$862$	−13.0000	−	22.5167i	−0.442782	−	0.766921i
$863$	3.00000	+	5.19615i	0.102121	+	0.176879i	0.912558	−	0.408946i	$-0.134104\pi$
$863$	3.00000	+	5.19615i	0.102121	+	0.176879i	−0.810437	+	0.585826i	$0.800770\pi$
$864$	−1.00000			−0.0340207
$865$		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
$871$	−12.0000	−	41.5692i	−0.406604	−	1.40852i
$872$	−5.50000	+	9.52628i	−0.186254	+	0.322601i
$873$	9.00000			0.304604
$874$	2.00000	−	3.46410i	0.0676510	−	0.117175i
$875$		0			0
$876$	7.00000			0.236508
$877$	9.00000	−	15.5885i	0.303908	−	0.526385i	−0.673109	−	0.739543i	$-0.735042\pi$
$877$	9.00000	−	15.5885i	0.303908	−	0.526385i	0.977018	+	0.213158i	$0.0683750\pi$
$878$	−1.00000			−0.0337484
$879$	−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	$0.155941\pi$
$882$	5.50000	−	4.33013i	0.185195	−	0.145803i
$883$	−19.0000			−0.639401			−0.319700	−	0.947519i	$-0.603582\pi$
$883$	−19.0000			−0.639401			−0.319700	+	0.947519i	$0.603582\pi$
$884$	14.0000	+	3.46410i	0.470871	+	0.116510i
$885$		0			0
$886$	−4.00000	−	6.92820i	−0.134383	−	0.232758i
$887$	6.00000			0.201460			0.100730	−	0.994914i	$-0.467882\pi$
$887$	6.00000			0.201460			0.100730	+	0.994914i	$0.467882\pi$
$888$	−5.50000	−	9.52628i	−0.184568	−	0.319681i
$889$	26.0000	+	22.5167i	0.872012	+	0.755185i
$890$		0			0
$891$	1.00000	−	1.73205i	0.0335013	−	0.0580259i
$892$	8.00000	−	13.8564i	0.267860	−	0.463947i
$893$		0			0
$894$	−10.0000			−0.334450
$895$		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
$900$	2.50000	+	4.33013i	0.0833333	+	0.144338i
$901$	−8.00000	+	13.8564i	−0.266519	+	0.461624i
$902$	4.00000			0.133185
$903$	2.00000	+	1.73205i	0.0665558	+	0.0576390i
$904$	4.00000	+	6.92820i	0.133038	+	0.230429i
$905$		0			0
$906$	−4.00000			−0.132891
$907$	4.50000	+	7.79423i	0.149420	+	0.258803i	0.931013	−	0.364985i	$-0.118926\pi$
$907$	4.50000	+	7.79423i	0.149420	+	0.258803i	−0.781593	+	0.623788i	$0.785593\pi$
$908$	18.0000			0.597351
$909$	−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	$0.334445\pi$
$912$	−1.00000			−0.0331133
$913$	−14.0000	−	24.2487i	−0.463332	−	0.802515i
$914$	38.0000			1.25693
$915$		0			0
$916$	10.5000	+	18.1865i	0.346930	+	0.600900i
$917$		0			0
$918$	−4.00000			−0.132020
$919$	5.50000	−	9.52628i	0.181428	−	0.314243i	−0.760939	−	0.648824i	$-0.775261\pi$
$919$	5.50000	−	9.52628i	0.181428	−	0.314243i	0.942367	+	0.334581i	$0.108595\pi$
$920$		0			0
$921$	14.0000	+	24.2487i	0.461316	+	0.799022i
$922$	−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
$926$	23.0000			0.755827
$927$	−7.00000			−0.229910
$928$	−3.00000	+	5.19615i	−0.0984798	+	0.170572i
$929$	3.00000	−	5.19615i	0.0984268	−	0.170480i	−0.812607	−	0.582812i	$-0.801952\pi$
$929$	3.00000	−	5.19615i	0.0984268	−	0.170480i	0.911034	+	0.412332i	$0.135286\pi$
$930$		0			0
$931$	5.50000	−	4.33013i	0.180255	−	0.141914i
$932$	3.00000	+	5.19615i	0.0982683	+	0.170206i
$933$	28.0000			0.916679
$934$	−21.0000	−	36.3731i	−0.687141	−	1.19016i
$935$		0			0
$936$	−2.50000	+	2.59808i	−0.0817151	+	0.0849208i
$937$	35.0000			1.14340			0.571700	−	0.820463i	$-0.306284\pi$
$937$	35.0000			1.14340			0.571700	+	0.820463i	$0.306284\pi$
$938$	−30.0000	+	10.3923i	−0.979535	+	0.339321i
$939$	−10.5000	+	18.1865i	−0.342655	+	0.593495i
$940$		0			0
$941$	28.0000	−	48.4974i	0.912774	−	1.58097i	0.102646	−	0.994718i	$-0.467269\pi$
$941$	28.0000	−	48.4974i	0.912774	−	1.58097i	0.810128	−	0.586253i	$-0.199397\pi$
$942$	7.00000			0.228072
$943$	−4.00000	+	6.92820i	−0.130258	+	0.225613i
$944$	4.00000			0.130189
$945$		0			0
$946$	−1.00000	+	1.73205i	−0.0325128	+	0.0563138i
$947$	10.0000			0.324956			0.162478	−	0.986712i	$-0.448051\pi$
$947$	10.0000			0.324956			0.162478	+	0.986712i	$0.448051\pi$
$948$	4.00000	−	6.92820i	0.129914	−	0.225018i
$949$	17.5000	−	18.1865i	0.568074	−	0.590360i
$950$	2.50000	+	4.33013i	0.0811107	+	0.140488i
$951$	4.00000	−	6.92820i	0.129709	−	0.224662i
$952$	2.00000	−	10.3923i	0.0648204	−	0.336817i
$953$	−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
$956$	2.00000			0.0646846
$957$	−6.00000	−	10.3923i	−0.193952	−	0.335936i
$958$	−5.00000	−	8.66025i	−0.161543	−	0.279800i
$959$	6.00000	−	31.1769i	0.193750	−	1.00676i
$960$		0			0
$961$	15.5000	+	26.8468i	0.500000	+	0.866025i
$962$	−38.5000	−	9.52628i	−1.24129	−	0.307140i
$963$	9.00000	−	15.5885i	0.290021	−	0.502331i
$964$	18.0000			0.579741
$965$		0			0
$966$	−10.0000	+	3.46410i	−0.321745	+	0.111456i
$967$	37.0000			1.18984			0.594920	−	0.803785i	$-0.297184\pi$
$967$	37.0000			1.18984			0.594920	+	0.803785i	$0.297184\pi$
$968$	3.50000	−	6.06218i	0.112494	−	0.194846i
$969$	−4.00000			−0.128499
$970$		0			0
$971$	−18.0000	+	31.1769i	−0.577647	+	1.00051i	0.418101	+	0.908401i	$0.362696\pi$
$971$	−18.0000	+	31.1769i	−0.577647	+	1.00051i	−0.995748	+	0.0921142i	$0.970638\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−40.0000	+	13.8564i	−1.28234	+	0.444216i
$974$	−23.0000			−0.736968
$975$	17.5000	+	4.33013i	0.560449	+	0.138675i
$976$	−0.500000	+	0.866025i	−0.0160046	+	0.0277208i
$977$	8.00000	+	13.8564i	0.255943	+	0.443306i	0.965151	−	0.261693i	$-0.0842808\pi$
$977$	8.00000	+	13.8564i	0.255943	+	0.443306i	−0.709208	+	0.704999i	$0.750947\pi$
$978$	11.0000			0.351741
$979$	6.00000	+	10.3923i	0.191761	+	0.332140i
$980$		0			0
$981$	−5.50000	−	9.52628i	−0.175601	−	0.304151i
$982$	11.0000	−	19.0526i	0.351024	−	0.607992i
$983$	−7.00000	+	12.1244i	−0.223265	+	0.386707i	−0.955798	−	0.294025i	$-0.905005\pi$
$983$	−7.00000	+	12.1244i	−0.223265	+	0.386707i	0.732532	+	0.680732i	$0.238338\pi$
$984$	2.00000			0.0637577
$985$		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
$991$	−9.50000	−	16.4545i	−0.301777	−	0.522694i	0.674761	−	0.738036i	$-0.264247\pi$
$991$	−9.50000	−	16.4545i	−0.301777	−	0.522694i	−0.976539	+	0.215342i	$0.930913\pi$
$992$		0			0
$993$	11.0000			0.349074
$994$	−15.0000	+	5.19615i	−0.475771	+	0.164812i
$995$		0			0
$996$	−7.00000	−	12.1244i	−0.221803	−	0.384175i
$997$	−3.00000			−0.0950110			−0.0475055	−	0.998871i	$-0.515127\pi$
$997$	−3.00000			−0.0950110			−0.0475055	+	0.998871i	$0.515127\pi$
$998$	−0.500000	−	0.866025i	−0.0158272	−	0.0274136i
$999$	11.0000			0.348025

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.j.a.289.1	✓	2	91.16	even	3	inner
546.2.j.a.529.1	yes	2	1.1	even	1	trivial
546.2.k.a.373.1	yes	2	7.2	even	3
546.2.k.a.445.1	yes	2	13.3	even	3
1638.2.m.a.289.1		2	273.107	odd	6
1638.2.m.a.1621.1		2	3.2	odd	2
1638.2.p.d.919.1		2	21.2	odd	6
1638.2.p.d.991.1		2	39.29	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.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{6} +(0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(0.500000 + 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 + 0.866025i) q^{6} +(0.500000 - 2.59808i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.00000 + 1.73205i) q^{11} +(0.500000 + 0.866025i) q^{12} +(3.50000 + 0.866025i) q^{13} +(0.500000 - 2.59808i) q^{14} +1.00000 q^{16} +4.00000 q^{17} +(-0.500000 + 0.866025i) q^{18} +(-0.500000 + 0.866025i) q^{19} +(2.50000 - 0.866025i) q^{21} +(1.00000 + 1.73205i) q^{22} -4.00000 q^{23} +(0.500000 + 0.866025i) q^{24} +(2.50000 - 4.33013i) q^{25} +(3.50000 + 0.866025i) q^{26} -1.00000 q^{27} +(0.500000 - 2.59808i) q^{28} +(-3.00000 + 5.19615i) q^{29} +1.00000 q^{32} +(-1.00000 + 1.73205i) q^{33} +4.00000 q^{34} +(-0.500000 + 0.866025i) q^{36} -11.0000 q^{37} +(-0.500000 + 0.866025i) q^{38} +(1.00000 + 3.46410i) q^{39} +(1.00000 - 1.73205i) q^{41} +(2.50000 - 0.866025i) q^{42} +(0.500000 + 0.866025i) q^{43} +(1.00000 + 1.73205i) q^{44} -4.00000 q^{46} +(0.500000 + 0.866025i) q^{48} +(-6.50000 - 2.59808i) q^{49} +(2.50000 - 4.33013i) q^{50} +(2.00000 + 3.46410i) q^{51} +(3.50000 + 0.866025i) q^{52} +(-2.00000 + 3.46410i) q^{53} -1.00000 q^{54} +(0.500000 - 2.59808i) q^{56} -1.00000 q^{57} +(-3.00000 + 5.19615i) q^{58} +4.00000 q^{59} +(-0.500000 + 0.866025i) q^{61} +(2.00000 + 1.73205i) q^{63} +1.00000 q^{64} +(-1.00000 + 1.73205i) q^{66} +(-6.00000 - 10.3923i) q^{67} +4.00000 q^{68} +(-2.00000 - 3.46410i) q^{69} +(-3.00000 - 5.19615i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(3.50000 - 6.06218i) q^{73} -11.0000 q^{74} +5.00000 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} +(-0.500000 - 0.866025i) q^{81} +(1.00000 - 1.73205i) q^{82} -14.0000 q^{83} +(2.50000 - 0.866025i) q^{84} +(0.500000 + 0.866025i) q^{86} -6.00000 q^{87} +(1.00000 + 1.73205i) q^{88} +6.00000 q^{89} +(4.00000 - 8.66025i) q^{91} -4.00000 q^{92} +(0.500000 + 0.866025i) q^{96} +(-4.50000 - 7.79423i) q^{97} +(-6.50000 - 2.59808i) q^{98} -2.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} + q^{3} + 2 q^{4} + q^{6} + q^{7} + 2 q^{8} - q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 + q^3 + 2 * q^4 + q^6 + q^7 + 2 * q^8 - q^9	\( 2 q + 2 q^{2} + q^{3} + 2 q^{4} + q^{6} + q^{7} + 2 q^{8} - q^{9} + 2 q^{11} + q^{12} + 7 q^{13} + q^{14} + 2 q^{16} + 8 q^{17} - q^{18} - q^{19} + 5 q^{21} + 2 q^{22} - 8 q^{23} + q^{24} + 5 q^{25} + 7 q^{26} - 2 q^{27} + q^{28} - 6 q^{29} + 2 q^{32} - 2 q^{33} + 8 q^{34} - q^{36} - 22 q^{37} - q^{38} + 2 q^{39} + 2 q^{41} + 5 q^{42} + q^{43} + 2 q^{44} - 8 q^{46} + q^{48} - 13 q^{49} + 5 q^{50} + 4 q^{51} + 7 q^{52} - 4 q^{53} - 2 q^{54} + q^{56} - 2 q^{57} - 6 q^{58} + 8 q^{59} - q^{61} + 4 q^{63} + 2 q^{64} - 2 q^{66} - 12 q^{67} + 8 q^{68} - 4 q^{69} - 6 q^{71} - q^{72} + 7 q^{73} - 22 q^{74} + 10 q^{75} - q^{76} + 10 q^{77} + 2 q^{78} - 8 q^{79} - q^{81} + 2 q^{82} - 28 q^{83} + 5 q^{84} + q^{86} - 12 q^{87} + 2 q^{88} + 12 q^{89} + 8 q^{91} - 8 q^{92} + q^{96} - 9 q^{97} - 13 q^{98} - 4 q^{99}+O(q^{100}) \) 2 * q + 2 * q^2 + q^3 + 2 * q^4 + q^6 + q^7 + 2 * q^8 - q^9 + 2 * q^11 + q^12 + 7 * q^13 + q^14 + 2 * q^16 + 8 * q^17 - q^18 - q^19 + 5 * q^21 + 2 * q^22 - 8 * q^23 + q^24 + 5 * q^25 + 7 * q^26 - 2 * q^27 + q^28 - 6 * q^29 + 2 * q^32 - 2 * q^33 + 8 * q^34 - q^36 - 22 * q^37 - q^38 + 2 * q^39 + 2 * q^41 + 5 * q^42 + q^43 + 2 * q^44 - 8 * q^46 + q^48 - 13 * q^49 + 5 * q^50 + 4 * q^51 + 7 * q^52 - 4 * q^53 - 2 * q^54 + q^56 - 2 * q^57 - 6 * q^58 + 8 * q^59 - q^61 + 4 * q^63 + 2 * q^64 - 2 * q^66 - 12 * q^67 + 8 * q^68 - 4 * q^69 - 6 * q^71 - q^72 + 7 * q^73 - 22 * q^74 + 10 * q^75 - q^76 + 10 * q^77 + 2 * q^78 - 8 * q^79 - q^81 + 2 * q^82 - 28 * q^83 + 5 * q^84 + q^86 - 12 * q^87 + 2 * q^88 + 12 * q^89 + 8 * q^91 - 8 * q^92 + q^96 - 9 * q^97 - 13 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more