LMFDB - Embedded newform 57.2.e.a.49.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [57,2,Mod(7,57)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("57.7"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(57, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 2])) N = Newforms(chi, 2, names="a")

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

Newform invariants

comment:select newform

sage:traces = [2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$0.455147291521$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			49.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	57.49
Dual form			57.2.e.a.7.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

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

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/57\mathbb{Z}\right)^\times$.

$n$	$20$	$40$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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	−0.986869	−	0.161521i	$-0.948360\pi$
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i	0.633316	+	0.773893i	$0.281693\pi$
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$5$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	1.00000			0.377964			0.188982	−	0.981981i	$-0.439481\pi$
$7$	1.00000			0.377964			0.188982	+	0.981981i	$0.439481\pi$
$8$	−3.00000			−1.06066
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$		0			0
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$	1.00000			0.288675
$13$	−2.50000	−	4.33013i	−0.693375	−	1.20096i	−0.970725	−	0.240192i	$-0.922790\pi$
$13$	−2.50000	−	4.33013i	−0.693375	−	1.20096i	0.277350	−	0.960769i	$-0.410544\pi$
$14$	−0.500000	+	0.866025i	−0.133631	+	0.231455i
$15$		0			0
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	−0.514782	−	0.857321i	$-0.672127\pi$
$17$	2.00000	−	3.46410i	0.485071	−	0.840168i	0.999853	+	0.0171533i	$0.00546033\pi$
$18$	1.00000			0.235702
$19$	−4.00000	+	1.73205i	−0.917663	+	0.397360i
$19$	−4.00000	+	1.73205i	−0.917663	+	0.397360i
$20$		0			0
$21$	0.500000	−	0.866025i	0.109109	−	0.188982i
$22$	1.00000	−	1.73205i	0.213201	−	0.369274i
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	0.995639	−	0.0932891i	$-0.0297381\pi$
$23$	2.00000	+	3.46410i	0.417029	+	0.722315i	−0.578610	+	0.815604i	$0.696405\pi$
$24$	−1.50000	+	2.59808i	−0.306186	+	0.530330i
$25$	2.50000	+	4.33013i	0.500000	+	0.866025i
$26$	5.00000			0.980581
$27$	−1.00000			−0.192450
$28$	0.500000	+	0.866025i	0.0944911	+	0.163663i
$29$	4.00000	+	6.92820i	0.742781	+	1.28654i	0.951224	+	0.308500i	$0.0998271\pi$
$29$	4.00000	+	6.92820i	0.742781	+	1.28654i	−0.208443	+	0.978035i	$0.566840\pi$
$30$		0			0
$31$	−3.00000			−0.538816			−0.269408	−	0.963026i	$-0.586828\pi$
$31$	−3.00000			−0.538816			−0.269408	+	0.963026i	$0.586828\pi$
$32$	−2.50000	−	4.33013i	−0.441942	−	0.765466i
$33$	−1.00000	+	1.73205i	−0.174078	+	0.301511i
$34$	2.00000	+	3.46410i	0.342997	+	0.594089i
$35$		0			0
$36$	0.500000	−	0.866025i	0.0833333	−	0.144338i
$37$	3.00000			0.493197			0.246598	−	0.969118i	$-0.420687\pi$
$37$	3.00000			0.493197			0.246598	+	0.969118i	$0.420687\pi$
$38$	0.500000	−	4.33013i	0.0811107	−	0.702439i
$39$	−5.00000			−0.800641
$40$		0			0
$41$	6.00000	−	10.3923i	0.937043	−	1.62301i	0.166092	−	0.986110i	$-0.446885\pi$
$41$	6.00000	−	10.3923i	0.937043	−	1.62301i	0.770950	−	0.636895i	$-0.219782\pi$
$42$	0.500000	+	0.866025i	0.0771517	+	0.133631i
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	−0.825380	−	0.564578i	$-0.809039\pi$
$43$	0.500000	−	0.866025i	0.0762493	−	0.132068i	0.901629	+	0.432511i	$0.142372\pi$
$44$	−1.00000	−	1.73205i	−0.150756	−	0.261116i
$45$		0			0
$46$	−4.00000			−0.589768
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	0.997503	−	0.0706177i	$-0.0224970\pi$
$47$	3.00000	+	5.19615i	0.437595	+	0.757937i	−0.559908	+	0.828554i	$0.689164\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	−6.00000			−0.857143
$50$	−5.00000			−0.707107
$51$	−2.00000	−	3.46410i	−0.280056	−	0.485071i
$52$	2.50000	−	4.33013i	0.346688	−	0.600481i
$53$	−2.00000	−	3.46410i	−0.274721	−	0.475831i	0.695344	−	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
$56$	−3.00000			−0.400892
$57$	−0.500000	+	4.33013i	−0.0662266	+	0.573539i
$58$	−8.00000			−1.05045
$59$	−5.00000	+	8.66025i	−0.650945	+	1.12747i	0.331949	+	0.943297i	$0.392294\pi$
$59$	−5.00000	+	8.66025i	−0.650945	+	1.12747i	−0.982894	+	0.184172i	$0.941040\pi$
$60$		0			0
$61$	6.50000	+	11.2583i	0.832240	+	1.44148i	0.896258	+	0.443533i	$0.146275\pi$
$61$	6.50000	+	11.2583i	0.832240	+	1.44148i	−0.0640184	+	0.997949i	$0.520392\pi$
$62$	1.50000	−	2.59808i	0.190500	−	0.329956i
$63$	−0.500000	−	0.866025i	−0.0629941	−	0.109109i
$64$	7.00000			0.875000
$65$		0			0
$66$	−1.00000	−	1.73205i	−0.123091	−	0.213201i
$67$	−5.50000	−	9.52628i	−0.671932	−	1.16382i	−0.977356	−	0.211604i	$-0.932131\pi$
$67$	−5.50000	−	9.52628i	−0.671932	−	1.16382i	0.305424	−	0.952217i	$-0.401202\pi$
$68$	4.00000			0.485071
$69$	4.00000			0.481543
$70$		0			0
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	−0.987294	−	0.158901i	$-0.949205\pi$
$71$	−3.00000	+	5.19615i	−0.356034	+	0.616670i	0.631260	+	0.775571i	$0.282538\pi$
$72$	1.50000	+	2.59808i	0.176777	+	0.306186i
$73$	5.50000	−	9.52628i	0.643726	−	1.11497i	−0.340868	−	0.940111i	$-0.610721\pi$
$73$	5.50000	−	9.52628i	0.643726	−	1.11497i	0.984594	−	0.174855i	$-0.0559458\pi$
$74$	−1.50000	+	2.59808i	−0.174371	+	0.302020i
$75$	5.00000			0.577350
$76$	−3.50000	−	2.59808i	−0.401478	−	0.298020i
$77$	−2.00000			−0.227921
$78$	2.50000	−	4.33013i	0.283069	−	0.490290i
$79$	−0.500000	+	0.866025i	−0.0562544	+	0.0974355i	−0.892781	−	0.450490i	$-0.851249\pi$
$79$	−0.500000	+	0.866025i	−0.0562544	+	0.0974355i	0.836527	+	0.547926i	$0.184582\pi$
$80$		0			0
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	6.00000	+	10.3923i	0.662589	+	1.14764i
$83$		0			0			−	1.00000i	$-0.5\pi$
$83$		0			0				1.00000i	$0.5\pi$
$84$	1.00000			0.109109
$85$		0			0
$86$	0.500000	+	0.866025i	0.0539164	+	0.0933859i
$87$	8.00000			0.857690
$88$	6.00000			0.639602
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	0.980071	−	0.198650i	$-0.0636557\pi$
$89$	3.00000	+	5.19615i	0.317999	+	0.550791i	−0.662071	+	0.749441i	$0.730322\pi$
$90$		0			0
$91$	−2.50000	−	4.33013i	−0.262071	−	0.453921i
$92$	−2.00000	+	3.46410i	−0.208514	+	0.361158i
$93$	−1.50000	+	2.59808i	−0.155543	+	0.269408i
$94$	−6.00000			−0.618853
$95$		0			0
$96$	−5.00000			−0.510310
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	−0.912317	−	0.409484i	$-0.865709\pi$
$97$	−1.00000	+	1.73205i	−0.101535	+	0.175863i	0.810782	+	0.585348i	$0.199042\pi$
$98$	3.00000	−	5.19615i	0.303046	−	0.524891i
$99$	1.00000	+	1.73205i	0.100504	+	0.174078i
$100$	−2.50000	+	4.33013i	−0.250000	+	0.433013i
$101$	−7.00000	−	12.1244i	−0.696526	−	1.20642i	−0.969664	−	0.244443i	$-0.921395\pi$
$101$	−7.00000	−	12.1244i	−0.696526	−	1.20642i	0.273138	−	0.961975i	$-0.411939\pi$
$102$	4.00000			0.396059
$103$	13.0000			1.28093			0.640464	−	0.767988i	$-0.278742\pi$
$103$	13.0000			1.28093			0.640464	+	0.767988i	$0.278742\pi$
$104$	7.50000	+	12.9904i	0.735436	+	1.27381i
$105$		0			0
$106$	4.00000			0.388514
$107$	−18.0000			−1.74013			−0.870063	−	0.492941i	$-0.835922\pi$
$107$	−18.0000			−1.74013			−0.870063	+	0.492941i	$0.835922\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	−0.814152	−	0.580651i	$-0.802798\pi$
$109$	1.00000	−	1.73205i	0.0957826	−	0.165900i	0.909935	+	0.414751i	$0.136131\pi$
$110$		0			0
$111$	1.50000	−	2.59808i	0.142374	−	0.246598i
$112$	0.500000	−	0.866025i	0.0472456	−	0.0818317i
$113$	2.00000			0.188144			0.0940721	−	0.995565i	$-0.470012\pi$
$113$	2.00000			0.188144			0.0940721	+	0.995565i	$0.470012\pi$
$114$	−3.50000	−	2.59808i	−0.327805	−	0.243332i
$115$		0			0
$116$	−4.00000	+	6.92820i	−0.371391	+	0.643268i
$117$	−2.50000	+	4.33013i	−0.231125	+	0.400320i
$118$	−5.00000	−	8.66025i	−0.460287	−	0.797241i
$119$	2.00000	−	3.46410i	0.183340	−	0.317554i
$120$		0			0
$121$	−7.00000			−0.636364
$122$	−13.0000			−1.17696
$123$	−6.00000	−	10.3923i	−0.541002	−	0.937043i
$124$	−1.50000	−	2.59808i	−0.134704	−	0.233314i
$125$		0			0
$126$	1.00000			0.0890871
$127$	4.00000	+	6.92820i	0.354943	+	0.614779i	0.987108	−	0.160055i	$-0.0511671\pi$
$127$	4.00000	+	6.92820i	0.354943	+	0.614779i	−0.632166	+	0.774833i	$0.717834\pi$
$128$	1.50000	−	2.59808i	0.132583	−	0.229640i
$129$	−0.500000	−	0.866025i	−0.0440225	−	0.0762493i
$130$		0			0
$131$	7.00000	−	12.1244i	0.611593	−	1.05931i	−0.379379	−	0.925241i	$-0.623862\pi$
$131$	7.00000	−	12.1244i	0.611593	−	1.05931i	0.990972	−	0.134069i	$-0.0428042\pi$
$132$	−2.00000			−0.174078
$133$	−4.00000	+	1.73205i	−0.346844	+	0.150188i
$134$	11.0000			0.950255
$135$		0			0
$136$	−6.00000	+	10.3923i	−0.514496	+	0.891133i
$137$	−9.00000	−	15.5885i	−0.768922	−	1.33181i	−0.938148	−	0.346235i	$-0.887460\pi$
$137$	−9.00000	−	15.5885i	−0.768922	−	1.33181i	0.169226	−	0.985577i	$-0.445873\pi$
$138$	−2.00000	+	3.46410i	−0.170251	+	0.294884i
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	0.740308	−	0.672268i	$-0.234680\pi$
$139$	−2.50000	−	4.33013i	−0.212047	−	0.367277i	−0.952355	+	0.304991i	$0.901346\pi$
$140$		0			0
$141$	6.00000			0.505291
$142$	−3.00000	−	5.19615i	−0.251754	−	0.436051i
$143$	5.00000	+	8.66025i	0.418121	+	0.724207i
$144$	−1.00000			−0.0833333
$145$		0			0
$146$	5.50000	+	9.52628i	0.455183	+	0.788400i
$147$	−3.00000	+	5.19615i	−0.247436	+	0.428571i
$148$	1.50000	+	2.59808i	0.123299	+	0.213561i
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	−0.716578	−	0.697507i	$-0.754293\pi$
$149$	3.00000	−	5.19615i	0.245770	−	0.425685i	0.962348	+	0.271821i	$0.0876260\pi$
$150$	−2.50000	+	4.33013i	−0.204124	+	0.353553i
$151$	12.0000			0.976546			0.488273	−	0.872691i	$-0.337627\pi$
$151$	12.0000			0.976546			0.488273	+	0.872691i	$0.337627\pi$
$152$	12.0000	−	5.19615i	0.973329	−	0.421464i
$153$	−4.00000			−0.323381
$154$	1.00000	−	1.73205i	0.0805823	−	0.139573i
$155$		0			0
$156$	−2.50000	−	4.33013i	−0.200160	−	0.346688i
$157$	−1.50000	+	2.59808i	−0.119713	+	0.207349i	−0.919654	−	0.392730i	$-0.871531\pi$
$157$	−1.50000	+	2.59808i	−0.119713	+	0.207349i	0.799941	+	0.600079i	$0.204864\pi$
$158$	−0.500000	−	0.866025i	−0.0397779	−	0.0688973i
$159$	−4.00000			−0.317221
$160$		0			0
$161$	2.00000	+	3.46410i	0.157622	+	0.273009i
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	3.00000			0.234978			0.117489	−	0.993074i	$-0.462515\pi$
$163$	3.00000			0.234978			0.117489	+	0.993074i	$0.462515\pi$
$164$	12.0000			0.937043
$165$		0			0
$166$		0			0
$167$	1.00000	+	1.73205i	0.0773823	+	0.134030i	0.902120	−	0.431486i	$-0.142010\pi$
$167$	1.00000	+	1.73205i	0.0773823	+	0.134030i	−0.824737	+	0.565516i	$0.808677\pi$
$168$	−1.50000	+	2.59808i	−0.115728	+	0.200446i
$169$	−6.00000	+	10.3923i	−0.461538	+	0.799408i
$170$		0			0
$171$	3.50000	+	2.59808i	0.267652	+	0.198680i
$172$	1.00000			0.0762493
$173$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$173$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$174$	−4.00000	+	6.92820i	−0.303239	+	0.525226i
$175$	2.50000	+	4.33013i	0.188982	+	0.327327i
$176$	−1.00000	+	1.73205i	−0.0753778	+	0.130558i
$177$	5.00000	+	8.66025i	0.375823	+	0.650945i
$178$	−6.00000			−0.449719
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$		0			0
$181$	1.00000	+	1.73205i	0.0743294	+	0.128742i	0.900794	−	0.434246i	$-0.142985\pi$
$181$	1.00000	+	1.73205i	0.0743294	+	0.128742i	−0.826465	+	0.562988i	$0.809652\pi$
$182$	5.00000			0.370625
$183$	13.0000			0.960988
$184$	−6.00000	−	10.3923i	−0.442326	−	0.766131i
$185$		0			0
$186$	−1.50000	−	2.59808i	−0.109985	−	0.190500i
$187$	−4.00000	+	6.92820i	−0.292509	+	0.506640i
$188$	−3.00000	+	5.19615i	−0.218797	+	0.378968i
$189$	−1.00000			−0.0727393
$190$		0			0
$191$	24.0000			1.73658			0.868290	−	0.496058i	$-0.165220\pi$
$191$	24.0000			1.73658			0.868290	+	0.496058i	$0.165220\pi$
$192$	3.50000	−	6.06218i	0.252591	−	0.437500i
$193$	−9.50000	+	16.4545i	−0.683825	+	1.18442i	0.289980	+	0.957033i	$0.406351\pi$
$193$	−9.50000	+	16.4545i	−0.683825	+	1.18442i	−0.973805	+	0.227387i	$0.926982\pi$
$194$	−1.00000	−	1.73205i	−0.0717958	−	0.124354i
$195$		0			0
$196$	−3.00000	−	5.19615i	−0.214286	−	0.371154i
$197$	−26.0000			−1.85242			−0.926212	−	0.377004i	$-0.876954\pi$
$197$	−26.0000			−1.85242			−0.926212	+	0.377004i	$0.876954\pi$
$198$	−2.00000			−0.142134
$199$	−10.5000	−	18.1865i	−0.744325	−	1.28921i	−0.950509	−	0.310696i	$-0.899438\pi$
$199$	−10.5000	−	18.1865i	−0.744325	−	1.28921i	0.206184	−	0.978513i	$-0.433895\pi$
$200$	−7.50000	−	12.9904i	−0.530330	−	0.918559i
$201$	−11.0000			−0.775880
$202$	14.0000			0.985037
$203$	4.00000	+	6.92820i	0.280745	+	0.486265i
$204$	2.00000	−	3.46410i	0.140028	−	0.242536i
$205$		0			0
$206$	−6.50000	+	11.2583i	−0.452876	+	0.784405i
$207$	2.00000	−	3.46410i	0.139010	−	0.240772i
$208$	−5.00000			−0.346688
$209$	8.00000	−	3.46410i	0.553372	−	0.239617i
$210$		0			0
$211$	7.50000	−	12.9904i	0.516321	−	0.894295i	−0.483499	−	0.875345i	$-0.660634\pi$
$211$	7.50000	−	12.9904i	0.516321	−	0.894295i	0.999820	−	0.0189499i	$-0.00603229\pi$
$212$	2.00000	−	3.46410i	0.137361	−	0.237915i
$213$	3.00000	+	5.19615i	0.205557	+	0.356034i
$214$	9.00000	−	15.5885i	0.615227	−	1.06561i
$215$		0			0
$216$	3.00000			0.204124
$217$	−3.00000			−0.203653
$218$	1.00000	+	1.73205i	0.0677285	+	0.117309i
$219$	−5.50000	−	9.52628i	−0.371656	−	0.643726i
$220$		0			0
$221$	−20.0000			−1.34535
$222$	1.50000	+	2.59808i	0.100673	+	0.174371i
$223$	−4.50000	+	7.79423i	−0.301342	+	0.521940i	−0.976440	−	0.215788i	$-0.930768\pi$
$223$	−4.50000	+	7.79423i	−0.301342	+	0.521940i	0.675098	+	0.737728i	$0.264101\pi$
$224$	−2.50000	−	4.33013i	−0.167038	−	0.289319i
$225$	2.50000	−	4.33013i	0.166667	−	0.288675i
$226$	−1.00000	+	1.73205i	−0.0665190	+	0.115214i
$227$	−24.0000			−1.59294			−0.796468	−	0.604681i	$-0.793301\pi$
$227$	−24.0000			−1.59294			−0.796468	+	0.604681i	$0.793301\pi$
$228$	−4.00000	+	1.73205i	−0.264906	+	0.114708i
$229$	13.0000			0.859064			0.429532	−	0.903052i	$-0.358679\pi$
$229$	13.0000			0.859064			0.429532	+	0.903052i	$0.358679\pi$
$230$		0			0
$231$	−1.00000	+	1.73205i	−0.0657952	+	0.113961i
$232$	−12.0000	−	20.7846i	−0.787839	−	1.36458i
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	−0.750867	−	0.660454i	$-0.770364\pi$
$233$	3.00000	−	5.19615i	0.196537	−	0.340411i	0.947403	+	0.320043i	$0.103697\pi$
$234$	−2.50000	−	4.33013i	−0.163430	−	0.283069i
$235$		0			0
$236$	−10.0000			−0.650945
$237$	0.500000	+	0.866025i	0.0324785	+	0.0562544i
$238$	2.00000	+	3.46410i	0.129641	+	0.224544i
$239$	−12.0000			−0.776215			−0.388108	−	0.921614i	$-0.626871\pi$
$239$	−12.0000			−0.776215			−0.388108	+	0.921614i	$0.626871\pi$
$240$		0			0
$241$	3.50000	+	6.06218i	0.225455	+	0.390499i	0.956456	−	0.291877i	$-0.0942799\pi$
$241$	3.50000	+	6.06218i	0.225455	+	0.390499i	−0.731001	+	0.682376i	$0.760947\pi$
$242$	3.50000	−	6.06218i	0.224989	−	0.389692i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	−6.50000	+	11.2583i	−0.416120	+	0.720741i
$245$		0			0
$246$	12.0000			0.765092
$247$	17.5000	+	12.9904i	1.11350	+	0.826558i
$248$	9.00000			0.571501
$249$		0			0
$250$		0			0
$251$	1.00000	+	1.73205i	0.0631194	+	0.109326i	0.895858	−	0.444340i	$-0.146562\pi$
$251$	1.00000	+	1.73205i	0.0631194	+	0.109326i	−0.832739	+	0.553666i	$0.813228\pi$
$252$	0.500000	−	0.866025i	0.0314970	−	0.0545545i
$253$	−4.00000	−	6.92820i	−0.251478	−	0.435572i
$254$	−8.00000			−0.501965
$255$		0			0
$256$	8.50000	+	14.7224i	0.531250	+	0.920152i
$257$	10.0000	+	17.3205i	0.623783	+	1.08042i	0.988775	+	0.149413i	$0.0477384\pi$
$257$	10.0000	+	17.3205i	0.623783	+	1.08042i	−0.364992	+	0.931011i	$0.618928\pi$
$258$	1.00000			0.0622573
$259$	3.00000			0.186411
$260$		0			0
$261$	4.00000	−	6.92820i	0.247594	−	0.428845i
$262$	7.00000	+	12.1244i	0.432461	+	0.749045i
$263$	−13.0000	+	22.5167i	−0.801614	+	1.38844i	0.116939	+	0.993139i	$0.462692\pi$
$263$	−13.0000	+	22.5167i	−0.801614	+	1.38844i	−0.918553	+	0.395298i	$0.870641\pi$
$264$	3.00000	−	5.19615i	0.184637	−	0.319801i
$265$		0			0
$266$	0.500000	−	4.33013i	0.0306570	−	0.265497i
$267$	6.00000			0.367194
$268$	5.50000	−	9.52628i	0.335966	−	0.581910i
$269$	−5.00000	+	8.66025i	−0.304855	+	0.528025i	−0.977229	−	0.212187i	$-0.931941\pi$
$269$	−5.00000	+	8.66025i	−0.304855	+	0.528025i	0.672374	+	0.740212i	$0.265275\pi$
$270$		0			0
$271$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$271$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$272$	−2.00000	−	3.46410i	−0.121268	−	0.210042i
$273$	−5.00000			−0.302614
$274$	18.0000			1.08742
$275$	−5.00000	−	8.66025i	−0.301511	−	0.522233i
$276$	2.00000	+	3.46410i	0.120386	+	0.208514i
$277$	−2.00000			−0.120168			−0.0600842	−	0.998193i	$-0.519137\pi$
$277$	−2.00000			−0.120168			−0.0600842	+	0.998193i	$0.519137\pi$
$278$	5.00000			0.299880
$279$	1.50000	+	2.59808i	0.0898027	+	0.155543i
$280$		0			0
$281$	4.00000	+	6.92820i	0.238620	+	0.413302i	0.960319	−	0.278906i	$-0.0899716\pi$
$281$	4.00000	+	6.92820i	0.238620	+	0.413302i	−0.721699	+	0.692207i	$0.756638\pi$
$282$	−3.00000	+	5.19615i	−0.178647	+	0.309426i
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	−0.800439	−	0.599414i	$-0.795400\pi$
$283$	2.00000	−	3.46410i	0.118888	−	0.205919i	0.919327	+	0.393494i	$0.128734\pi$
$284$	−6.00000			−0.356034
$285$		0			0
$286$	−10.0000			−0.591312
$287$	6.00000	−	10.3923i	0.354169	−	0.613438i
$288$	−2.50000	+	4.33013i	−0.147314	+	0.255155i
$289$	0.500000	+	0.866025i	0.0294118	+	0.0509427i
$290$		0			0
$291$	1.00000	+	1.73205i	0.0586210	+	0.101535i
$292$	11.0000			0.643726
$293$	14.0000			0.817889			0.408944	−	0.912559i	$-0.365897\pi$
$293$	14.0000			0.817889			0.408944	+	0.912559i	$0.365897\pi$
$294$	−3.00000	−	5.19615i	−0.174964	−	0.303046i
$295$		0			0
$296$	−9.00000			−0.523114
$297$	2.00000			0.116052
$298$	3.00000	+	5.19615i	0.173785	+	0.301005i
$299$	10.0000	−	17.3205i	0.578315	−	1.00167i
$300$	2.50000	+	4.33013i	0.144338	+	0.250000i
$301$	0.500000	−	0.866025i	0.0288195	−	0.0499169i
$302$	−6.00000	+	10.3923i	−0.345261	+	0.598010i
$303$	−14.0000			−0.804279
$304$	−0.500000	+	4.33013i	−0.0286770	+	0.248350i
$305$		0			0
$306$	2.00000	−	3.46410i	0.114332	−	0.198030i
$307$	6.00000	−	10.3923i	0.342438	−	0.593120i	−0.642447	−	0.766330i	$-0.722081\pi$
$307$	6.00000	−	10.3923i	0.342438	−	0.593120i	0.984885	+	0.173210i	$0.0554140\pi$
$308$	−1.00000	−	1.73205i	−0.0569803	−	0.0986928i
$309$	6.50000	−	11.2583i	0.369772	−	0.640464i
$310$		0			0
$311$	18.0000			1.02069			0.510343	−	0.859971i	$-0.329518\pi$
$311$	18.0000			1.02069			0.510343	+	0.859971i	$0.329518\pi$
$312$	15.0000			0.849208
$313$	−11.0000	−	19.0526i	−0.621757	−	1.07691i	−0.989158	−	0.146852i	$-0.953086\pi$
$313$	−11.0000	−	19.0526i	−0.621757	−	1.07691i	0.367402	−	0.930062i	$-0.380247\pi$
$314$	−1.50000	−	2.59808i	−0.0846499	−	0.146618i
$315$		0			0
$316$	−1.00000			−0.0562544
$317$	2.00000	+	3.46410i	0.112331	+	0.194563i	0.916710	−	0.399554i	$-0.130835\pi$
$317$	2.00000	+	3.46410i	0.112331	+	0.194563i	−0.804379	+	0.594117i	$0.797502\pi$
$318$	2.00000	−	3.46410i	0.112154	−	0.194257i
$319$	−8.00000	−	13.8564i	−0.447914	−	0.775810i
$320$		0			0
$321$	−9.00000	+	15.5885i	−0.502331	+	0.870063i
$322$	−4.00000			−0.222911
$323$	−2.00000	+	17.3205i	−0.111283	+	0.963739i
$324$	−1.00000			−0.0555556
$325$	12.5000	−	21.6506i	0.693375	−	1.20096i
$326$	−1.50000	+	2.59808i	−0.0830773	+	0.143894i
$327$	−1.00000	−	1.73205i	−0.0553001	−	0.0957826i
$328$	−18.0000	+	31.1769i	−0.993884	+	1.72146i
$329$	3.00000	+	5.19615i	0.165395	+	0.286473i
$330$		0			0
$331$	−25.0000			−1.37412			−0.687062	−	0.726599i	$-0.741100\pi$
$331$	−25.0000			−1.37412			−0.687062	+	0.726599i	$0.741100\pi$
$332$		0			0
$333$	−1.50000	−	2.59808i	−0.0821995	−	0.142374i
$334$	−2.00000			−0.109435
$335$		0			0
$336$	−0.500000	−	0.866025i	−0.0272772	−	0.0472456i
$337$	−6.50000	+	11.2583i	−0.354078	+	0.613280i	−0.986960	−	0.160968i	$-0.948538\pi$
$337$	−6.50000	+	11.2583i	−0.354078	+	0.613280i	0.632882	+	0.774248i	$0.281872\pi$
$338$	−6.00000	−	10.3923i	−0.326357	−	0.565267i
$339$	1.00000	−	1.73205i	0.0543125	−	0.0940721i
$340$		0			0
$341$	6.00000			0.324918
$342$	−4.00000	+	1.73205i	−0.216295	+	0.0936586i
$343$	−13.0000			−0.701934
$344$	−1.50000	+	2.59808i	−0.0808746	+	0.140079i
$345$		0			0
$346$		0			0
$347$	8.00000	−	13.8564i	0.429463	−	0.743851i	−0.567363	−	0.823468i	$-0.692036\pi$
$347$	8.00000	−	13.8564i	0.429463	−	0.743851i	0.996826	+	0.0796169i	$0.0253697\pi$
$348$	4.00000	+	6.92820i	0.214423	+	0.371391i
$349$	−21.0000			−1.12410			−0.562052	−	0.827102i	$-0.689988\pi$
$349$	−21.0000			−1.12410			−0.562052	+	0.827102i	$0.689988\pi$
$350$	−5.00000			−0.267261
$351$	2.50000	+	4.33013i	0.133440	+	0.231125i
$352$	5.00000	+	8.66025i	0.266501	+	0.461593i
$353$	4.00000			0.212899			0.106449	−	0.994318i	$-0.466052\pi$
$353$	4.00000			0.212899			0.106449	+	0.994318i	$0.466052\pi$
$354$	−10.0000			−0.531494
$355$		0			0
$356$	−3.00000	+	5.19615i	−0.159000	+	0.275396i
$357$	−2.00000	−	3.46410i	−0.105851	−	0.183340i
$358$	−6.00000	+	10.3923i	−0.317110	+	0.549250i
$359$	10.0000	−	17.3205i	0.527780	−	0.914141i	−0.471696	−	0.881761i	$-0.656358\pi$
$359$	10.0000	−	17.3205i	0.527780	−	0.914141i	0.999476	−	0.0323801i	$-0.0103087\pi$
$360$		0			0
$361$	13.0000	−	13.8564i	0.684211	−	0.729285i
$362$	−2.00000			−0.105118
$363$	−3.50000	+	6.06218i	−0.183702	+	0.318182i
$364$	2.50000	−	4.33013i	0.131036	−	0.226960i
$365$		0			0
$366$	−6.50000	+	11.2583i	−0.339760	+	0.588482i
$367$	−3.50000	−	6.06218i	−0.182699	−	0.316443i	0.760100	−	0.649806i	$-0.225150\pi$
$367$	−3.50000	−	6.06218i	−0.182699	−	0.316443i	−0.942799	+	0.333363i	$0.891817\pi$
$368$	4.00000			0.208514
$369$	−12.0000			−0.624695
$370$		0			0
$371$	−2.00000	−	3.46410i	−0.103835	−	0.179847i
$372$	−3.00000			−0.155543
$373$	10.0000			0.517780			0.258890	−	0.965907i	$-0.416643\pi$
$373$	10.0000			0.517780			0.258890	+	0.965907i	$0.416643\pi$
$374$	−4.00000	−	6.92820i	−0.206835	−	0.358249i
$375$		0			0
$376$	−9.00000	−	15.5885i	−0.464140	−	0.803913i
$377$	20.0000	−	34.6410i	1.03005	−	1.78410i
$378$	0.500000	−	0.866025i	0.0257172	−	0.0445435i
$379$	−5.00000			−0.256833			−0.128416	−	0.991720i	$-0.540989\pi$
$379$	−5.00000			−0.256833			−0.128416	+	0.991720i	$0.540989\pi$
$380$		0			0
$381$	8.00000			0.409852
$382$	−12.0000	+	20.7846i	−0.613973	+	1.06343i
$383$	−7.00000	+	12.1244i	−0.357683	+	0.619526i	−0.987573	−	0.157159i	$-0.949767\pi$
$383$	−7.00000	+	12.1244i	−0.357683	+	0.619526i	0.629890	+	0.776684i	$0.283100\pi$
$384$	−1.50000	−	2.59808i	−0.0765466	−	0.132583i
$385$		0			0
$386$	−9.50000	−	16.4545i	−0.483537	−	0.837511i
$387$	−1.00000			−0.0508329
$388$	−2.00000			−0.101535
$389$	12.0000	+	20.7846i	0.608424	+	1.05382i	0.991500	+	0.130105i	$0.0415314\pi$
$389$	12.0000	+	20.7846i	0.608424	+	1.05382i	−0.383076	+	0.923717i	$0.625135\pi$
$390$		0			0
$391$	16.0000			0.809155
$392$	18.0000			0.909137
$393$	−7.00000	−	12.1244i	−0.353103	−	0.611593i
$394$	13.0000	−	22.5167i	0.654931	−	1.13437i
$395$		0			0
$396$	−1.00000	+	1.73205i	−0.0502519	+	0.0870388i
$397$	−3.50000	+	6.06218i	−0.175660	+	0.304252i	−0.940389	−	0.340099i	$-0.889539\pi$
$397$	−3.50000	+	6.06218i	−0.175660	+	0.304252i	0.764730	+	0.644351i	$0.222873\pi$
$398$	21.0000			1.05263
$399$	−0.500000	+	4.33013i	−0.0250313	+	0.216777i
$400$	5.00000			0.250000
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	−0.781345	−	0.624099i	$-0.785466\pi$
$401$	3.00000	−	5.19615i	0.149813	−	0.259483i	0.931158	+	0.364615i	$0.118800\pi$
$402$	5.50000	−	9.52628i	0.274315	−	0.475128i
$403$	7.50000	+	12.9904i	0.373602	+	0.647097i
$404$	7.00000	−	12.1244i	0.348263	−	0.603209i
$405$		0			0
$406$	−8.00000			−0.397033
$407$	−6.00000			−0.297409
$408$	6.00000	+	10.3923i	0.297044	+	0.514496i
$409$	7.00000	+	12.1244i	0.346128	+	0.599511i	0.985558	−	0.169338i	$-0.0541630\pi$
$409$	7.00000	+	12.1244i	0.346128	+	0.599511i	−0.639430	+	0.768849i	$0.720830\pi$
$410$		0			0
$411$	−18.0000			−0.887875
$412$	6.50000	+	11.2583i	0.320232	+	0.554658i
$413$	−5.00000	+	8.66025i	−0.246034	+	0.426143i
$414$	2.00000	+	3.46410i	0.0982946	+	0.170251i
$415$		0			0
$416$	−12.5000	+	21.6506i	−0.612863	+	1.06151i
$417$	−5.00000			−0.244851
$418$	−1.00000	+	8.66025i	−0.0489116	+	0.423587i
$419$	−14.0000			−0.683945			−0.341972	−	0.939710i	$-0.611095\pi$
$419$	−14.0000			−0.683945			−0.341972	+	0.939710i	$0.611095\pi$
$420$		0			0
$421$	11.0000	−	19.0526i	0.536107	−	0.928565i	−0.463002	−	0.886357i	$-0.653228\pi$
$421$	11.0000	−	19.0526i	0.536107	−	0.928565i	0.999109	−	0.0422075i	$-0.0134391\pi$
$422$	7.50000	+	12.9904i	0.365094	+	0.632362i
$423$	3.00000	−	5.19615i	0.145865	−	0.252646i
$424$	6.00000	+	10.3923i	0.291386	+	0.504695i
$425$	20.0000			0.970143
$426$	−6.00000			−0.290701
$427$	6.50000	+	11.2583i	0.314557	+	0.544829i
$428$	−9.00000	−	15.5885i	−0.435031	−	0.753497i
$429$	10.0000			0.482805
$430$		0			0
$431$	5.00000	+	8.66025i	0.240842	+	0.417150i	0.960954	−	0.276707i	$-0.0892433\pi$
$431$	5.00000	+	8.66025i	0.240842	+	0.417150i	−0.720113	+	0.693857i	$0.755910\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	4.50000	+	7.79423i	0.216256	+	0.374567i	0.953660	−	0.300885i	$-0.0972820\pi$
$433$	4.50000	+	7.79423i	0.216256	+	0.374567i	−0.737404	+	0.675452i	$0.763949\pi$
$434$	1.50000	−	2.59808i	0.0720023	−	0.124712i
$435$		0			0
$436$	2.00000			0.0957826
$437$	−14.0000	−	10.3923i	−0.669711	−	0.497131i
$438$	11.0000			0.525600
$439$	−17.5000	+	30.3109i	−0.835229	+	1.44666i	0.0586141	+	0.998281i	$0.481332\pi$
$439$	−17.5000	+	30.3109i	−0.835229	+	1.44666i	−0.893843	+	0.448379i	$0.852001\pi$
$440$		0			0
$441$	3.00000	+	5.19615i	0.142857	+	0.247436i
$442$	10.0000	−	17.3205i	0.475651	−	0.823853i
$443$	16.0000	+	27.7128i	0.760183	+	1.31668i	0.942756	+	0.333483i	$0.108224\pi$
$443$	16.0000	+	27.7128i	0.760183	+	1.31668i	−0.182573	+	0.983192i	$0.558443\pi$
$444$	3.00000			0.142374
$445$		0			0
$446$	−4.50000	−	7.79423i	−0.213081	−	0.369067i
$447$	−3.00000	−	5.19615i	−0.141895	−	0.245770i
$448$	7.00000			0.330719
$449$	−12.0000			−0.566315			−0.283158	−	0.959073i	$-0.591382\pi$
$449$	−12.0000			−0.566315			−0.283158	+	0.959073i	$0.591382\pi$
$450$	2.50000	+	4.33013i	0.117851	+	0.204124i
$451$	−12.0000	+	20.7846i	−0.565058	+	0.978709i
$452$	1.00000	+	1.73205i	0.0470360	+	0.0814688i
$453$	6.00000	−	10.3923i	0.281905	−	0.488273i
$454$	12.0000	−	20.7846i	0.563188	−	0.975470i
$455$		0			0
$456$	1.50000	−	12.9904i	0.0702439	−	0.608330i
$457$	−11.0000			−0.514558			−0.257279	−	0.966337i	$-0.582826\pi$
$457$	−11.0000			−0.514558			−0.257279	+	0.966337i	$0.582826\pi$
$458$	−6.50000	+	11.2583i	−0.303725	+	0.526067i
$459$	−2.00000	+	3.46410i	−0.0933520	+	0.161690i
$460$		0			0
$461$	−15.0000	+	25.9808i	−0.698620	+	1.21004i	0.270326	+	0.962769i	$0.412869\pi$
$461$	−15.0000	+	25.9808i	−0.698620	+	1.21004i	−0.968945	+	0.247276i	$0.920465\pi$
$462$	−1.00000	−	1.73205i	−0.0465242	−	0.0805823i
$463$	23.0000			1.06890			0.534450	−	0.845200i	$-0.320519\pi$
$463$	23.0000			1.06890			0.534450	+	0.845200i	$0.320519\pi$
$464$	8.00000			0.371391
$465$		0			0
$466$	3.00000	+	5.19615i	0.138972	+	0.240707i
$467$	−8.00000			−0.370196			−0.185098	−	0.982720i	$-0.559260\pi$
$467$	−8.00000			−0.370196			−0.185098	+	0.982720i	$0.559260\pi$
$468$	−5.00000			−0.231125
$469$	−5.50000	−	9.52628i	−0.253966	−	0.439883i
$470$		0			0
$471$	1.50000	+	2.59808i	0.0691164	+	0.119713i
$472$	15.0000	−	25.9808i	0.690431	−	1.19586i
$473$	−1.00000	+	1.73205i	−0.0459800	+	0.0796398i
$474$	−1.00000			−0.0459315
$475$	−17.5000	−	12.9904i	−0.802955	−	0.596040i
$476$	4.00000			0.183340
$477$	−2.00000	+	3.46410i	−0.0915737	+	0.158610i
$478$	6.00000	−	10.3923i	0.274434	−	0.475333i
$479$	−7.00000	−	12.1244i	−0.319838	−	0.553976i	0.660616	−	0.750724i	$-0.270295\pi$
$479$	−7.00000	−	12.1244i	−0.319838	−	0.553976i	−0.980454	+	0.196748i	$0.936962\pi$
$480$		0			0
$481$	−7.50000	−	12.9904i	−0.341971	−	0.592310i
$482$	−7.00000			−0.318841
$483$	4.00000			0.182006
$484$	−3.50000	−	6.06218i	−0.159091	−	0.275554i
$485$		0			0
$486$	−1.00000			−0.0453609
$487$	−16.0000			−0.725029			−0.362515	−	0.931978i	$-0.618082\pi$
$487$	−16.0000			−0.725029			−0.362515	+	0.931978i	$0.618082\pi$
$488$	−19.5000	−	33.7750i	−0.882724	−	1.52892i
$489$	1.50000	−	2.59808i	0.0678323	−	0.117489i
$490$		0			0
$491$	−3.00000	+	5.19615i	−0.135388	+	0.234499i	−0.925746	−	0.378147i	$-0.876561\pi$
$491$	−3.00000	+	5.19615i	−0.135388	+	0.234499i	0.790358	+	0.612646i	$0.209895\pi$
$492$	6.00000	−	10.3923i	0.270501	−	0.468521i
$493$	32.0000			1.44121
$494$	−20.0000	+	8.66025i	−0.899843	+	0.389643i
$495$		0			0
$496$	−1.50000	+	2.59808i	−0.0673520	+	0.116657i
$497$	−3.00000	+	5.19615i	−0.134568	+	0.233079i
$498$		0			0
$499$	−14.5000	+	25.1147i	−0.649109	+	1.12429i	0.334227	+	0.942493i	$0.391525\pi$
$499$	−14.5000	+	25.1147i	−0.649109	+	1.12429i	−0.983336	+	0.181797i	$0.941809\pi$
$500$		0			0
$501$	2.00000			0.0893534
$502$	−2.00000			−0.0892644
$503$	−20.0000	−	34.6410i	−0.891756	−	1.54457i	−0.837769	−	0.546025i	$-0.816140\pi$
$503$	−20.0000	−	34.6410i	−0.891756	−	1.54457i	−0.0539870	−	0.998542i	$-0.517193\pi$
$504$	1.50000	+	2.59808i	0.0668153	+	0.115728i
$505$		0			0
$506$	8.00000			0.355643
$507$	6.00000	+	10.3923i	0.266469	+	0.461538i
$508$	−4.00000	+	6.92820i	−0.177471	+	0.307389i
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	0.924821	−	0.380402i	$-0.124214\pi$
$509$	3.00000	+	5.19615i	0.132973	+	0.230315i	−0.791849	+	0.610718i	$0.790881\pi$
$510$		0			0
$511$	5.50000	−	9.52628i	0.243306	−	0.421418i
$512$	−11.0000			−0.486136
$513$	4.00000	−	1.73205i	0.176604	−	0.0764719i
$514$	−20.0000			−0.882162
$515$		0			0
$516$	0.500000	−	0.866025i	0.0220113	−	0.0381246i
$517$	−6.00000	−	10.3923i	−0.263880	−	0.457053i
$518$	−1.50000	+	2.59808i	−0.0659062	+	0.114153i
$519$		0			0
$520$		0			0
$521$	18.0000			0.788594			0.394297	−	0.918983i	$-0.370988\pi$
$521$	18.0000			0.788594			0.394297	+	0.918983i	$0.370988\pi$
$522$	4.00000	+	6.92820i	0.175075	+	0.303239i
$523$	−14.5000	−	25.1147i	−0.634041	−	1.09819i	−0.986718	−	0.162446i	$-0.948062\pi$
$523$	−14.5000	−	25.1147i	−0.634041	−	1.09819i	0.352677	−	0.935745i	$-0.385272\pi$
$524$	14.0000			0.611593
$525$	5.00000			0.218218
$526$	−13.0000	−	22.5167i	−0.566827	−	0.981773i
$527$	−6.00000	+	10.3923i	−0.261364	+	0.452696i
$528$	1.00000	+	1.73205i	0.0435194	+	0.0753778i
$529$	3.50000	−	6.06218i	0.152174	−	0.263573i
$530$		0			0
$531$	10.0000			0.433963
$532$	−3.50000	−	2.59808i	−0.151744	−	0.112641i
$533$	−60.0000			−2.59889
$534$	−3.00000	+	5.19615i	−0.129823	+	0.224860i
$535$		0			0
$536$	16.5000	+	28.5788i	0.712691	+	1.23442i
$537$	6.00000	−	10.3923i	0.258919	−	0.448461i
$538$	−5.00000	−	8.66025i	−0.215565	−	0.373370i
$539$	12.0000			0.516877
$540$		0			0
$541$	19.5000	+	33.7750i	0.838370	+	1.45210i	0.891256	+	0.453500i	$0.149825\pi$
$541$	19.5000	+	33.7750i	0.838370	+	1.45210i	−0.0528859	+	0.998601i	$0.516842\pi$
$542$		0			0
$543$	2.00000			0.0858282
$544$	−20.0000			−0.857493
$545$		0			0
$546$	2.50000	−	4.33013i	0.106990	−	0.185312i
$547$	14.5000	+	25.1147i	0.619975	+	1.07383i	0.989490	+	0.144604i	$0.0461907\pi$
$547$	14.5000	+	25.1147i	0.619975	+	1.07383i	−0.369514	+	0.929225i	$0.620476\pi$
$548$	9.00000	−	15.5885i	0.384461	−	0.665906i
$549$	6.50000	−	11.2583i	0.277413	−	0.480494i
$550$	10.0000			0.426401
$551$	−28.0000	−	20.7846i	−1.19284	−	0.885454i
$552$	−12.0000			−0.510754
$553$	−0.500000	+	0.866025i	−0.0212622	+	0.0368271i
$554$	1.00000	−	1.73205i	0.0424859	−	0.0735878i
$555$		0			0
$556$	2.50000	−	4.33013i	0.106024	−	0.183638i
$557$	19.0000	+	32.9090i	0.805056	+	1.39440i	0.916253	+	0.400599i	$0.131198\pi$
$557$	19.0000	+	32.9090i	0.805056	+	1.39440i	−0.111198	+	0.993798i	$0.535469\pi$
$558$	−3.00000			−0.127000
$559$	−5.00000			−0.211477
$560$		0			0
$561$	4.00000	+	6.92820i	0.168880	+	0.292509i
$562$	−8.00000			−0.337460
$563$	18.0000			0.758610			0.379305	−	0.925272i	$-0.376163\pi$
$563$	18.0000			0.758610			0.379305	+	0.925272i	$0.376163\pi$
$564$	3.00000	+	5.19615i	0.126323	+	0.218797i
$565$		0			0
$566$	2.00000	+	3.46410i	0.0840663	+	0.145607i
$567$	−0.500000	+	0.866025i	−0.0209980	+	0.0363696i
$568$	9.00000	−	15.5885i	0.377632	−	0.654077i
$569$	24.0000			1.00613			0.503066	−	0.864248i	$-0.332205\pi$
$569$	24.0000			1.00613			0.503066	+	0.864248i	$0.332205\pi$
$570$		0			0
$571$	33.0000			1.38101			0.690504	−	0.723329i	$-0.257389\pi$
$571$	33.0000			1.38101			0.690504	+	0.723329i	$0.257389\pi$
$572$	−5.00000	+	8.66025i	−0.209061	+	0.362103i
$573$	12.0000	−	20.7846i	0.501307	−	0.868290i
$574$	6.00000	+	10.3923i	0.250435	+	0.433766i
$575$	−10.0000	+	17.3205i	−0.417029	+	0.722315i
$576$	−3.50000	−	6.06218i	−0.145833	−	0.252591i
$577$	18.0000			0.749350			0.374675	−	0.927156i	$-0.377754\pi$
$577$	18.0000			0.749350			0.374675	+	0.927156i	$0.377754\pi$
$578$	−1.00000			−0.0415945
$579$	9.50000	+	16.4545i	0.394807	+	0.683825i
$580$		0			0
$581$		0			0
$582$	−2.00000			−0.0829027
$583$	4.00000	+	6.92820i	0.165663	+	0.286937i
$584$	−16.5000	+	28.5788i	−0.682775	+	1.18260i
$585$		0			0
$586$	−7.00000	+	12.1244i	−0.289167	+	0.500853i
$587$	13.0000	−	22.5167i	0.536567	−	0.929362i	−0.462518	−	0.886610i	$-0.653054\pi$
$587$	13.0000	−	22.5167i	0.536567	−	0.929362i	0.999086	−	0.0427523i	$-0.0136126\pi$
$588$	−6.00000			−0.247436
$589$	12.0000	−	5.19615i	0.494451	−	0.214104i
$590$		0			0
$591$	−13.0000	+	22.5167i	−0.534749	+	0.926212i
$592$	1.50000	−	2.59808i	0.0616496	−	0.106780i
$593$	3.00000	+	5.19615i	0.123195	+	0.213380i	0.921026	−	0.389501i	$-0.127353\pi$
$593$	3.00000	+	5.19615i	0.123195	+	0.213380i	−0.797831	+	0.602881i	$0.794019\pi$
$594$	−1.00000	+	1.73205i	−0.0410305	+	0.0710669i
$595$		0			0
$596$	6.00000			0.245770
$597$	−21.0000			−0.859473
$598$	10.0000	+	17.3205i	0.408930	+	0.708288i
$599$	−9.00000	−	15.5885i	−0.367730	−	0.636927i	0.621480	−	0.783430i	$-0.286532\pi$
$599$	−9.00000	−	15.5885i	−0.367730	−	0.636927i	−0.989210	+	0.146503i	$0.953198\pi$
$600$	−15.0000			−0.612372
$601$	−21.0000			−0.856608			−0.428304	−	0.903635i	$-0.640889\pi$
$601$	−21.0000			−0.856608			−0.428304	+	0.903635i	$0.640889\pi$
$602$	0.500000	+	0.866025i	0.0203785	+	0.0352966i
$603$	−5.50000	+	9.52628i	−0.223977	+	0.387940i
$604$	6.00000	+	10.3923i	0.244137	+	0.422857i
$605$		0			0
$606$	7.00000	−	12.1244i	0.284356	−	0.492518i
$607$	−43.0000			−1.74532			−0.872658	−	0.488332i	$-0.837606\pi$
$607$	−43.0000			−1.74532			−0.872658	+	0.488332i	$0.837606\pi$
$608$	17.5000	+	12.9904i	0.709719	+	0.526830i
$609$	8.00000			0.324176
$610$		0			0
$611$	15.0000	−	25.9808i	0.606835	−	1.05107i
$612$	−2.00000	−	3.46410i	−0.0808452	−	0.140028i
$613$	15.0000	−	25.9808i	0.605844	−	1.04935i	−0.386073	−	0.922468i	$-0.626169\pi$
$613$	15.0000	−	25.9808i	0.605844	−	1.04935i	0.991917	−	0.126885i	$-0.0404979\pi$
$614$	6.00000	+	10.3923i	0.242140	+	0.419399i
$615$		0			0
$616$	6.00000			0.241747
$617$	−3.00000	−	5.19615i	−0.120775	−	0.209189i	0.799298	−	0.600935i	$-0.205205\pi$
$617$	−3.00000	−	5.19615i	−0.120775	−	0.209189i	−0.920074	+	0.391745i	$0.871871\pi$
$618$	6.50000	+	11.2583i	0.261468	+	0.452876i
$619$	25.0000			1.00483			0.502417	−	0.864625i	$-0.332444\pi$
$619$	25.0000			1.00483			0.502417	+	0.864625i	$0.332444\pi$
$620$		0			0
$621$	−2.00000	−	3.46410i	−0.0802572	−	0.139010i
$622$	−9.00000	+	15.5885i	−0.360867	+	0.625040i
$623$	3.00000	+	5.19615i	0.120192	+	0.208179i
$624$	−2.50000	+	4.33013i	−0.100080	+	0.173344i
$625$	−12.5000	+	21.6506i	−0.500000	+	0.866025i
$626$	22.0000			0.879297
$627$	1.00000	−	8.66025i	0.0399362	−	0.345857i
$628$	−3.00000			−0.119713
$629$	6.00000	−	10.3923i	0.239236	−	0.414368i
$630$		0			0
$631$	7.50000	+	12.9904i	0.298570	+	0.517139i	0.975809	−	0.218624i	$-0.0701569\pi$
$631$	7.50000	+	12.9904i	0.298570	+	0.517139i	−0.677239	+	0.735763i	$0.736824\pi$
$632$	1.50000	−	2.59808i	0.0596668	−	0.103346i
$633$	−7.50000	−	12.9904i	−0.298098	−	0.516321i
$634$	−4.00000			−0.158860
$635$		0			0
$636$	−2.00000	−	3.46410i	−0.0793052	−	0.137361i
$637$	15.0000	+	25.9808i	0.594322	+	1.02940i
$638$	16.0000			0.633446
$639$	6.00000			0.237356
$640$		0			0
$641$	15.0000	−	25.9808i	0.592464	−	1.02618i	−0.401435	−	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
$643$	9.50000	−	16.4545i	0.374643	−	0.648901i	−0.615630	−	0.788035i	$-0.711098\pi$
$643$	9.50000	−	16.4545i	0.374643	−	0.648901i	0.990274	+	0.139134i	$0.0444318\pi$
$644$	−2.00000	+	3.46410i	−0.0788110	+	0.136505i
$645$		0			0
$646$	−14.0000	−	10.3923i	−0.550823	−	0.408880i
$647$	−24.0000			−0.943537			−0.471769	−	0.881722i	$-0.656384\pi$
$647$	−24.0000			−0.943537			−0.471769	+	0.881722i	$0.656384\pi$
$648$	1.50000	−	2.59808i	0.0589256	−	0.102062i
$649$	10.0000	−	17.3205i	0.392534	−	0.679889i
$650$	12.5000	+	21.6506i	0.490290	+	0.849208i
$651$	−1.50000	+	2.59808i	−0.0587896	+	0.101827i
$652$	1.50000	+	2.59808i	0.0587445	+	0.101749i
$653$	−18.0000			−0.704394			−0.352197	−	0.935926i	$-0.614565\pi$
$653$	−18.0000			−0.704394			−0.352197	+	0.935926i	$0.614565\pi$
$654$	2.00000			0.0782062
$655$		0			0
$656$	−6.00000	−	10.3923i	−0.234261	−	0.405751i
$657$	−11.0000			−0.429151
$658$	−6.00000			−0.233904
$659$	−17.0000	−	29.4449i	−0.662226	−	1.14701i	−0.980029	−	0.198852i	$-0.936279\pi$
$659$	−17.0000	−	29.4449i	−0.662226	−	1.14701i	0.317803	−	0.948157i	$-0.397055\pi$
$660$		0			0
$661$	−21.0000	−	36.3731i	−0.816805	−	1.41475i	−0.908024	−	0.418917i	$-0.862410\pi$
$661$	−21.0000	−	36.3731i	−0.816805	−	1.41475i	0.0912190	−	0.995831i	$-0.470924\pi$
$662$	12.5000	−	21.6506i	0.485826	−	0.841476i
$663$	−10.0000	+	17.3205i	−0.388368	+	0.672673i
$664$		0			0
$665$		0			0
$666$	3.00000			0.116248
$667$	−16.0000	+	27.7128i	−0.619522	+	1.07304i
$668$	−1.00000	+	1.73205i	−0.0386912	+	0.0670151i
$669$	4.50000	+	7.79423i	0.173980	+	0.301342i
$670$		0			0
$671$	−13.0000	−	22.5167i	−0.501859	−	0.869246i
$672$	−5.00000			−0.192879
$673$	−33.0000			−1.27206			−0.636028	−	0.771666i	$-0.719424\pi$
$673$	−33.0000			−1.27206			−0.636028	+	0.771666i	$0.719424\pi$
$674$	−6.50000	−	11.2583i	−0.250371	−	0.433655i
$675$	−2.50000	−	4.33013i	−0.0962250	−	0.166667i
$676$	−12.0000			−0.461538
$677$	34.0000			1.30673			0.653363	−	0.757045i	$-0.273358\pi$
$677$	34.0000			1.30673			0.653363	+	0.757045i	$0.273358\pi$
$678$	1.00000	+	1.73205i	0.0384048	+	0.0665190i
$679$	−1.00000	+	1.73205i	−0.0383765	+	0.0664700i
$680$		0			0
$681$	−12.0000	+	20.7846i	−0.459841	+	0.796468i
$682$	−3.00000	+	5.19615i	−0.114876	+	0.198971i
$683$	12.0000			0.459167			0.229584	−	0.973289i	$-0.426264\pi$
$683$	12.0000			0.459167			0.229584	+	0.973289i	$0.426264\pi$
$684$	−0.500000	+	4.33013i	−0.0191180	+	0.165567i
$685$		0			0
$686$	6.50000	−	11.2583i	0.248171	−	0.429845i
$687$	6.50000	−	11.2583i	0.247990	−	0.429532i
$688$	−0.500000	−	0.866025i	−0.0190623	−	0.0330169i
$689$	−10.0000	+	17.3205i	−0.380970	+	0.659859i
$690$		0			0
$691$	20.0000			0.760836			0.380418	−	0.924815i	$-0.375780\pi$
$691$	20.0000			0.760836			0.380418	+	0.924815i	$0.375780\pi$
$692$		0			0
$693$	1.00000	+	1.73205i	0.0379869	+	0.0657952i
$694$	8.00000	+	13.8564i	0.303676	+	0.525982i
$695$		0			0
$696$	−24.0000			−0.909718
$697$	−24.0000	−	41.5692i	−0.909065	−	1.57455i
$698$	10.5000	−	18.1865i	0.397431	−	0.688370i
$699$	−3.00000	−	5.19615i	−0.113470	−	0.196537i
$700$	−2.50000	+	4.33013i	−0.0944911	+	0.163663i
$701$	−10.0000	+	17.3205i	−0.377695	+	0.654187i	−0.990726	−	0.135872i	$-0.956616\pi$
$701$	−10.0000	+	17.3205i	−0.377695	+	0.654187i	0.613032	+	0.790058i	$0.289950\pi$
$702$	−5.00000			−0.188713
$703$	−12.0000	+	5.19615i	−0.452589	+	0.195977i
$704$	−14.0000			−0.527645
$705$		0			0
$706$	−2.00000	+	3.46410i	−0.0752710	+	0.130373i
$707$	−7.00000	−	12.1244i	−0.263262	−	0.455983i
$708$	−5.00000	+	8.66025i	−0.187912	+	0.325472i
$709$	19.5000	+	33.7750i	0.732338	+	1.26845i	0.955882	+	0.293752i	$0.0949041\pi$
$709$	19.5000	+	33.7750i	0.732338	+	1.26845i	−0.223544	+	0.974694i	$0.571763\pi$
$710$		0			0
$711$	1.00000			0.0375029
$712$	−9.00000	−	15.5885i	−0.337289	−	0.584202i
$713$	−6.00000	−	10.3923i	−0.224702	−	0.389195i
$714$	4.00000			0.149696
$715$		0			0
$716$	6.00000	+	10.3923i	0.224231	+	0.388379i
$717$	−6.00000	+	10.3923i	−0.224074	+	0.388108i
$718$	10.0000	+	17.3205i	0.373197	+	0.646396i
$719$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$719$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$720$		0			0
$721$	13.0000			0.484145
$722$	5.50000	+	18.1865i	0.204689	+	0.676833i
$723$	7.00000			0.260333
$724$	−1.00000	+	1.73205i	−0.0371647	+	0.0643712i
$725$	−20.0000	+	34.6410i	−0.742781	+	1.28654i
$726$	−3.50000	−	6.06218i	−0.129897	−	0.224989i
$727$	23.5000	−	40.7032i	0.871567	−	1.50960i	0.0111912	−	0.999937i	$-0.496438\pi$
$727$	23.5000	−	40.7032i	0.871567	−	1.50960i	0.860376	−	0.509661i	$-0.170229\pi$
$728$	7.50000	+	12.9904i	0.277968	+	0.481456i
$729$	1.00000			0.0370370
$730$		0			0
$731$	−2.00000	−	3.46410i	−0.0739727	−	0.128124i
$732$	6.50000	+	11.2583i	0.240247	+	0.416120i
$733$	−50.0000			−1.84679			−0.923396	−	0.383849i	$-0.874598\pi$
$733$	−50.0000			−1.84679			−0.923396	+	0.383849i	$0.874598\pi$
$734$	7.00000			0.258375
$735$		0			0
$736$	10.0000	−	17.3205i	0.368605	−	0.638442i
$737$	11.0000	+	19.0526i	0.405190	+	0.701810i
$738$	6.00000	−	10.3923i	0.220863	−	0.382546i
$739$	−9.50000	+	16.4545i	−0.349463	+	0.605288i	−0.986154	−	0.165831i	$-0.946969\pi$
$739$	−9.50000	+	16.4545i	−0.349463	+	0.605288i	0.636691	+	0.771119i	$0.280303\pi$
$740$		0			0
$741$	20.0000	−	8.66025i	0.734718	−	0.318142i
$742$	4.00000			0.146845
$743$	25.0000	−	43.3013i	0.917161	−	1.58857i	0.113455	−	0.993543i	$-0.463808\pi$
$743$	25.0000	−	43.3013i	0.917161	−	1.58857i	0.803706	−	0.595026i	$-0.202858\pi$
$744$	4.50000	−	7.79423i	0.164978	−	0.285750i
$745$		0			0
$746$	−5.00000	+	8.66025i	−0.183063	+	0.317074i
$747$		0			0
$748$	−8.00000			−0.292509
$749$	−18.0000			−0.657706
$750$		0			0
$751$	−22.5000	−	38.9711i	−0.821037	−	1.42208i	−0.904911	−	0.425601i	$-0.860063\pi$
$751$	−22.5000	−	38.9711i	−0.821037	−	1.42208i	0.0838743	−	0.996476i	$-0.473271\pi$
$752$	6.00000			0.218797
$753$	2.00000			0.0728841
$754$	20.0000	+	34.6410i	0.728357	+	1.26155i
$755$		0			0
$756$	−0.500000	−	0.866025i	−0.0181848	−	0.0314970i
$757$	−6.50000	+	11.2583i	−0.236247	+	0.409191i	−0.959634	−	0.281251i	$-0.909251\pi$
$757$	−6.50000	+	11.2583i	−0.236247	+	0.409191i	0.723388	+	0.690442i	$0.242584\pi$
$758$	2.50000	−	4.33013i	0.0908041	−	0.157277i
$759$	−8.00000			−0.290382
$760$		0			0
$761$	6.00000			0.217500			0.108750	−	0.994069i	$-0.465315\pi$
$761$	6.00000			0.217500			0.108750	+	0.994069i	$0.465315\pi$
$762$	−4.00000	+	6.92820i	−0.144905	+	0.250982i
$763$	1.00000	−	1.73205i	0.0362024	−	0.0627044i
$764$	12.0000	+	20.7846i	0.434145	+	0.751961i
$765$		0			0
$766$	−7.00000	−	12.1244i	−0.252920	−	0.438071i
$767$	50.0000			1.80540
$768$	17.0000			0.613435
$769$	18.5000	+	32.0429i	0.667127	+	1.15550i	0.978704	+	0.205277i	$0.0658095\pi$
$769$	18.5000	+	32.0429i	0.667127	+	1.15550i	−0.311577	+	0.950221i	$0.600857\pi$
$770$		0			0
$771$	20.0000			0.720282
$772$	−19.0000			−0.683825
$773$	−7.00000	−	12.1244i	−0.251773	−	0.436083i	0.712241	−	0.701935i	$-0.247680\pi$
$773$	−7.00000	−	12.1244i	−0.251773	−	0.436083i	−0.964014	+	0.265852i	$0.914347\pi$
$774$	0.500000	−	0.866025i	0.0179721	−	0.0311286i
$775$	−7.50000	−	12.9904i	−0.269408	−	0.466628i
$776$	3.00000	−	5.19615i	0.107694	−	0.186531i
$777$	1.50000	−	2.59808i	0.0538122	−	0.0932055i
$778$	−24.0000			−0.860442
$779$	−6.00000	+	51.9615i	−0.214972	+	1.86171i
$780$		0			0
$781$	6.00000	−	10.3923i	0.214697	−	0.371866i
$782$	−8.00000	+	13.8564i	−0.286079	+	0.495504i
$783$	−4.00000	−	6.92820i	−0.142948	−	0.247594i
$784$	−3.00000	+	5.19615i	−0.107143	+	0.185577i
$785$		0			0
$786$	14.0000			0.499363
$787$	25.0000			0.891154			0.445577	−	0.895244i	$-0.352999\pi$
$787$	25.0000			0.891154			0.445577	+	0.895244i	$0.352999\pi$
$788$	−13.0000	−	22.5167i	−0.463106	−	0.802123i
$789$	13.0000	+	22.5167i	0.462812	+	0.801614i
$790$		0			0
$791$	2.00000			0.0711118
$792$	−3.00000	−	5.19615i	−0.106600	−	0.184637i
$793$	32.5000	−	56.2917i	1.15411	−	1.99898i
$794$	−3.50000	−	6.06218i	−0.124210	−	0.215139i
$795$		0			0
$796$	10.5000	−	18.1865i	0.372163	−	0.644605i
$797$	−14.0000			−0.495905			−0.247953	−	0.968772i	$-0.579758\pi$
$797$	−14.0000			−0.495905			−0.247953	+	0.968772i	$0.579758\pi$
$798$	−3.50000	−	2.59808i	−0.123899	−	0.0919709i
$799$	24.0000			0.849059
$800$	12.5000	−	21.6506i	0.441942	−	0.765466i
$801$	3.00000	−	5.19615i	0.106000	−	0.183597i
$802$	3.00000	+	5.19615i	0.105934	+	0.183483i
$803$	−11.0000	+	19.0526i	−0.388182	+	0.672350i
$804$	−5.50000	−	9.52628i	−0.193970	−	0.335966i
$805$		0			0
$806$	−15.0000			−0.528352
$807$	5.00000	+	8.66025i	0.176008	+	0.304855i
$808$	21.0000	+	36.3731i	0.738777	+	1.27960i
$809$	−16.0000			−0.562530			−0.281265	−	0.959630i	$-0.590754\pi$
$809$	−16.0000			−0.562530			−0.281265	+	0.959630i	$0.590754\pi$
$810$		0			0
$811$	22.0000	+	38.1051i	0.772524	+	1.33805i	0.936175	+	0.351533i	$0.114340\pi$
$811$	22.0000	+	38.1051i	0.772524	+	1.33805i	−0.163651	+	0.986518i	$0.552327\pi$
$812$	−4.00000	+	6.92820i	−0.140372	+	0.243132i
$813$		0			0
$814$	3.00000	−	5.19615i	0.105150	−	0.182125i
$815$		0			0
$816$	−4.00000			−0.140028
$817$	−0.500000	+	4.33013i	−0.0174928	+	0.151492i
$818$	−14.0000			−0.489499
$819$	−2.50000	+	4.33013i	−0.0873571	+	0.151307i
$820$		0			0
$821$	−12.0000	−	20.7846i	−0.418803	−	0.725388i	0.577016	−	0.816733i	$-0.304217\pi$
$821$	−12.0000	−	20.7846i	−0.418803	−	0.725388i	−0.995819	+	0.0913446i	$0.970884\pi$
$822$	9.00000	−	15.5885i	0.313911	−	0.543710i
$823$	−2.00000	−	3.46410i	−0.0697156	−	0.120751i	0.829060	−	0.559159i	$-0.188876\pi$
$823$	−2.00000	−	3.46410i	−0.0697156	−	0.120751i	−0.898776	+	0.438408i	$0.855543\pi$
$824$	−39.0000			−1.35863
$825$	−10.0000			−0.348155
$826$	−5.00000	−	8.66025i	−0.173972	−	0.301329i
$827$	18.0000	+	31.1769i	0.625921	+	1.08413i	0.988362	+	0.152121i	$0.0486102\pi$
$827$	18.0000	+	31.1769i	0.625921	+	1.08413i	−0.362441	+	0.932007i	$0.618056\pi$
$828$	4.00000			0.139010
$829$	25.0000			0.868286			0.434143	−	0.900844i	$-0.357051\pi$
$829$	25.0000			0.868286			0.434143	+	0.900844i	$0.357051\pi$
$830$		0			0
$831$	−1.00000	+	1.73205i	−0.0346896	+	0.0600842i
$832$	−17.5000	−	30.3109i	−0.606703	−	1.05084i
$833$	−12.0000	+	20.7846i	−0.415775	+	0.720144i
$834$	2.50000	−	4.33013i	0.0865679	−	0.149940i
$835$		0			0
$836$	7.00000	+	5.19615i	0.242100	+	0.179713i
$837$	3.00000			0.103695
$838$	7.00000	−	12.1244i	0.241811	−	0.418829i
$839$	6.00000	−	10.3923i	0.207143	−	0.358782i	−0.743670	−	0.668546i	$-0.766917\pi$
$839$	6.00000	−	10.3923i	0.207143	−	0.358782i	0.950813	+	0.309764i	$0.100250\pi$
$840$		0			0
$841$	−17.5000	+	30.3109i	−0.603448	+	1.04520i
$842$	11.0000	+	19.0526i	0.379085	+	0.656595i
$843$	8.00000			0.275535
$844$	15.0000			0.516321
$845$		0			0
$846$	3.00000	+	5.19615i	0.103142	+	0.178647i
$847$	−7.00000			−0.240523
$848$	−4.00000			−0.137361
$849$	−2.00000	−	3.46410i	−0.0686398	−	0.118888i
$850$	−10.0000	+	17.3205i	−0.342997	+	0.594089i
$851$	6.00000	+	10.3923i	0.205677	+	0.356244i
$852$	−3.00000	+	5.19615i	−0.102778	+	0.178017i
$853$	2.50000	−	4.33013i	0.0855984	−	0.148261i	−0.820048	−	0.572295i	$-0.806053\pi$
$853$	2.50000	−	4.33013i	0.0855984	−	0.148261i	0.905646	+	0.424034i	$0.139386\pi$
$854$	−13.0000			−0.444851
$855$		0			0
$856$	54.0000			1.84568
$857$	−5.00000	+	8.66025i	−0.170797	+	0.295829i	−0.938699	−	0.344739i	$-0.887967\pi$
$857$	−5.00000	+	8.66025i	−0.170797	+	0.295829i	0.767902	+	0.640567i	$0.221301\pi$
$858$	−5.00000	+	8.66025i	−0.170697	+	0.295656i
$859$	−7.50000	−	12.9904i	−0.255897	−	0.443226i	0.709242	−	0.704965i	$-0.249037\pi$
$859$	−7.50000	−	12.9904i	−0.255897	−	0.443226i	−0.965139	+	0.261739i	$0.915704\pi$
$860$		0			0
$861$	−6.00000	−	10.3923i	−0.204479	−	0.354169i
$862$	−10.0000			−0.340601
$863$	10.0000			0.340404			0.170202	−	0.985409i	$-0.445558\pi$
$863$	10.0000			0.340404			0.170202	+	0.985409i	$0.445558\pi$
$864$	2.50000	+	4.33013i	0.0850517	+	0.147314i
$865$		0			0
$866$	−9.00000			−0.305832
$867$	1.00000			0.0339618
$868$	−1.50000	−	2.59808i	−0.0509133	−	0.0881845i
$869$	1.00000	−	1.73205i	0.0339227	−	0.0587558i
$870$		0			0
$871$	−27.5000	+	47.6314i	−0.931802	+	1.61393i
$872$	−3.00000	+	5.19615i	−0.101593	+	0.175964i
$873$	2.00000			0.0676897
$874$	16.0000	−	6.92820i	0.541208	−	0.234350i
$875$		0			0
$876$	5.50000	−	9.52628i	0.185828	−	0.321863i
$877$	−7.50000	+	12.9904i	−0.253257	+	0.438654i	−0.964421	−	0.264373i	$-0.914835\pi$
$877$	−7.50000	+	12.9904i	−0.253257	+	0.438654i	0.711164	+	0.703027i	$0.248168\pi$
$878$	−17.5000	−	30.3109i	−0.590596	−	1.02294i
$879$	7.00000	−	12.1244i	0.236104	−	0.408944i
$880$		0			0
$881$	−28.0000			−0.943344			−0.471672	−	0.881774i	$-0.656349\pi$
$881$	−28.0000			−0.943344			−0.471672	+	0.881774i	$0.656349\pi$
$882$	−6.00000			−0.202031
$883$	0.500000	+	0.866025i	0.0168263	+	0.0291441i	0.874316	−	0.485357i	$-0.161310\pi$
$883$	0.500000	+	0.866025i	0.0168263	+	0.0291441i	−0.857490	+	0.514501i	$0.827977\pi$
$884$	−10.0000	−	17.3205i	−0.336336	−	0.582552i
$885$		0			0
$886$	−32.0000			−1.07506
$887$	3.00000	+	5.19615i	0.100730	+	0.174470i	0.911986	−	0.410222i	$-0.134549\pi$
$887$	3.00000	+	5.19615i	0.100730	+	0.174470i	−0.811256	+	0.584692i	$0.801215\pi$
$888$	−4.50000	+	7.79423i	−0.151010	+	0.261557i
$889$	4.00000	+	6.92820i	0.134156	+	0.232364i
$890$		0			0
$891$	1.00000	−	1.73205i	0.0335013	−	0.0580259i
$892$	−9.00000			−0.301342
$893$	−21.0000	−	15.5885i	−0.702738	−	0.521648i
$894$	6.00000			0.200670
$895$		0			0
$896$	1.50000	−	2.59808i	0.0501115	−	0.0867956i
$897$	−10.0000	−	17.3205i	−0.333890	−	0.578315i
$898$	6.00000	−	10.3923i	0.200223	−	0.346796i
$899$	−12.0000	−	20.7846i	−0.400222	−	0.693206i
$900$	5.00000			0.166667
$901$	−16.0000			−0.533037
$902$	−12.0000	−	20.7846i	−0.399556	−	0.692052i
$903$	−0.500000	−	0.866025i	−0.0166390	−	0.0288195i
$904$	−6.00000			−0.199557
$905$		0			0
$906$	6.00000	+	10.3923i	0.199337	+	0.345261i
$907$	22.0000	−	38.1051i	0.730498	−	1.26526i	−0.226173	−	0.974087i	$-0.572621\pi$
$907$	22.0000	−	38.1051i	0.730498	−	1.26526i	0.956671	−	0.291172i	$-0.0940453\pi$
$908$	−12.0000	−	20.7846i	−0.398234	−	0.689761i
$909$	−7.00000	+	12.1244i	−0.232175	+	0.402139i
$910$		0			0
$911$	−12.0000			−0.397578			−0.198789	−	0.980042i	$-0.563701\pi$
$911$	−12.0000			−0.397578			−0.198789	+	0.980042i	$0.563701\pi$
$912$	3.50000	+	2.59808i	0.115897	+	0.0860309i
$913$		0			0
$914$	5.50000	−	9.52628i	0.181924	−	0.315101i
$915$		0			0
$916$	6.50000	+	11.2583i	0.214766	+	0.371986i
$917$	7.00000	−	12.1244i	0.231160	−	0.400381i
$918$	−2.00000	−	3.46410i	−0.0660098	−	0.114332i
$919$	−25.0000			−0.824674			−0.412337	−	0.911031i	$-0.635287\pi$
$919$	−25.0000			−0.824674			−0.412337	+	0.911031i	$0.635287\pi$
$920$		0			0
$921$	−6.00000	−	10.3923i	−0.197707	−	0.342438i
$922$	−15.0000	−	25.9808i	−0.493999	−	0.855631i
$923$	30.0000			0.987462
$924$	−2.00000			−0.0657952
$925$	7.50000	+	12.9904i	0.246598	+	0.427121i
$926$	−11.5000	+	19.9186i	−0.377913	+	0.654565i
$927$	−6.50000	−	11.2583i	−0.213488	−	0.369772i
$928$	20.0000	−	34.6410i	0.656532	−	1.13715i
$929$	−14.0000	+	24.2487i	−0.459325	+	0.795574i	−0.998925	−	0.0463469i	$-0.985242\pi$
$929$	−14.0000	+	24.2487i	−0.459325	+	0.795574i	0.539600	+	0.841921i	$0.318575\pi$
$930$		0			0
$931$	24.0000	−	10.3923i	0.786568	−	0.340594i
$932$	6.00000			0.196537
$933$	9.00000	−	15.5885i	0.294647	−	0.510343i
$934$	4.00000	−	6.92820i	0.130884	−	0.226698i
$935$		0			0
$936$	7.50000	−	12.9904i	0.245145	−	0.424604i
$937$	4.50000	+	7.79423i	0.147009	+	0.254626i	0.930121	−	0.367254i	$-0.119702\pi$
$937$	4.50000	+	7.79423i	0.147009	+	0.254626i	−0.783112	+	0.621881i	$0.786369\pi$
$938$	11.0000			0.359163
$939$	−22.0000			−0.717943
$940$		0			0
$941$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$941$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$942$	−3.00000			−0.0977453
$943$	48.0000			1.56310
$944$	5.00000	+	8.66025i	0.162736	+	0.281867i
$945$		0			0
$946$	−1.00000	−	1.73205i	−0.0325128	−	0.0563138i
$947$	−25.0000	+	43.3013i	−0.812391	+	1.40710i	0.0987955	+	0.995108i	$0.468501\pi$
$947$	−25.0000	+	43.3013i	−0.812391	+	1.40710i	−0.911186	+	0.411994i	$0.864832\pi$
$948$	−0.500000	+	0.866025i	−0.0162392	+	0.0281272i
$949$	−55.0000			−1.78538
$950$	20.0000	−	8.66025i	0.648886	−	0.280976i
$951$	4.00000			0.129709
$952$	−6.00000	+	10.3923i	−0.194461	+	0.336817i
$953$	−17.0000	+	29.4449i	−0.550684	+	0.953813i	0.447541	+	0.894263i	$0.352300\pi$
$953$	−17.0000	+	29.4449i	−0.550684	+	0.953813i	−0.998225	+	0.0595495i	$0.981034\pi$
$954$	−2.00000	−	3.46410i	−0.0647524	−	0.112154i
$955$		0			0
$956$	−6.00000	−	10.3923i	−0.194054	−	0.336111i
$957$	−16.0000			−0.517207
$958$	14.0000			0.452319
$959$	−9.00000	−	15.5885i	−0.290625	−	0.503378i
$960$		0			0
$961$	−22.0000			−0.709677
$962$	15.0000			0.483619
$963$	9.00000	+	15.5885i	0.290021	+	0.502331i
$964$	−3.50000	+	6.06218i	−0.112727	+	0.195250i
$965$		0			0
$966$	−2.00000	+	3.46410i	−0.0643489	+	0.111456i
$967$	14.5000	−	25.1147i	0.466289	−	0.807635i	−0.532970	−	0.846134i	$-0.678924\pi$
$967$	14.5000	−	25.1147i	0.466289	−	0.807635i	0.999259	+	0.0384986i	$0.0122575\pi$
$968$	21.0000			0.674966
$969$	14.0000	+	10.3923i	0.449745	+	0.333849i
$970$		0			0
$971$	21.0000	−	36.3731i	0.673922	−	1.16727i	−0.302861	−	0.953035i	$-0.597942\pi$
$971$	21.0000	−	36.3731i	0.673922	−	1.16727i	0.976783	−	0.214232i	$-0.0687250\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	−2.50000	−	4.33013i	−0.0801463	−	0.138817i
$974$	8.00000	−	13.8564i	0.256337	−	0.443988i
$975$	−12.5000	−	21.6506i	−0.400320	−	0.693375i
$976$	13.0000			0.416120
$977$	54.0000			1.72761			0.863807	−	0.503824i	$-0.168074\pi$
$977$	54.0000			1.72761			0.863807	+	0.503824i	$0.168074\pi$
$978$	1.50000	+	2.59808i	0.0479647	+	0.0830773i
$979$	−6.00000	−	10.3923i	−0.191761	−	0.332140i
$980$		0			0
$981$	−2.00000			−0.0638551
$982$	−3.00000	−	5.19615i	−0.0957338	−	0.165816i
$983$	−5.00000	+	8.66025i	−0.159475	+	0.276219i	−0.934680	−	0.355491i	$-0.884314\pi$
$983$	−5.00000	+	8.66025i	−0.159475	+	0.276219i	0.775204	+	0.631711i	$0.217647\pi$
$984$	18.0000	+	31.1769i	0.573819	+	0.993884i
$985$		0			0
$986$	−16.0000	+	27.7128i	−0.509544	+	0.882556i
$987$	6.00000			0.190982
$988$	−2.50000	+	21.6506i	−0.0795356	+	0.688798i
$989$	4.00000			0.127193
$990$		0			0
$991$	−23.5000	+	40.7032i	−0.746502	+	1.29298i	0.202988	+	0.979181i	$0.434935\pi$
$991$	−23.5000	+	40.7032i	−0.746502	+	1.29298i	−0.949490	+	0.313798i	$0.898398\pi$
$992$	7.50000	+	12.9904i	0.238125	+	0.412445i
$993$	−12.5000	+	21.6506i	−0.396676	+	0.687062i
$994$	−3.00000	−	5.19615i	−0.0951542	−	0.164812i
$995$		0			0
$996$		0			0
$997$	−3.50000	−	6.06218i	−0.110846	−	0.191991i	0.805266	−	0.592914i	$-0.202023\pi$
$997$	−3.50000	−	6.06218i	−0.110846	−	0.191991i	−0.916112	+	0.400923i	$0.868689\pi$
$998$	−14.5000	−	25.1147i	−0.458989	−	0.794993i
$999$	−3.00000			−0.0949158

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	57.2.e.a.49.1	yes	2
3.2	odd	2		171.2.f.a.163.1		2
4.3	odd	2		912.2.q.a.49.1		2
12.11	even	2		2736.2.s.j.1873.1		2
19.7	even	3	inner	57.2.e.a.7.1	✓	2
19.8	odd	6		1083.2.a.b.1.1		1
19.11	even	3		1083.2.a.c.1.1		1
57.8	even	6		3249.2.a.f.1.1		1
57.11	odd	6		3249.2.a.c.1.1		1
57.26	odd	6		171.2.f.a.64.1		2
76.7	odd	6		912.2.q.a.577.1		2
228.83	even	6		2736.2.s.j.577.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
57.2.e.a.7.1	✓	2	19.7	even	3	inner
57.2.e.a.49.1	yes	2	1.1	even	1	trivial
171.2.f.a.64.1		2	57.26	odd	6
171.2.f.a.163.1		2	3.2	odd	2
912.2.q.a.49.1		2	4.3	odd	2
912.2.q.a.577.1		2	76.7	odd	6
1083.2.a.b.1.1		1	19.8	odd	6
1083.2.a.c.1.1		1	19.11	even	3
2736.2.s.j.577.1		2	228.83	even	6
2736.2.s.j.1873.1		2	12.11	even	2
3249.2.a.c.1.1		1	57.11	odd	6
3249.2.a.f.1.1		1	57.8	even	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 $\F_{q}$
Belyi maps

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

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more