LMFDB - Dirichlet character orbit 1728.ch

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1728, base_ring=CyclotomicField(144)) M = H._module chi = DirichletCharacter(H, M([72,45,104])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(11,1728)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$1728$
Conductor:	$1728$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$144$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{144})$
Fixed field:	Number field defined by a degree 144 polynomial (not computed)

First 31 of 48 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{1728}(11,\cdot)$	$1$	$1$	$e\left(\frac{133}{144}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{65}{144}\right)$	$e\left(\frac{67}{144}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{23}{144}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{1728}(59,\cdot)$	$1$	$1$	$e\left(\frac{65}{144}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{61}{144}\right)$	$e\left(\frac{23}{144}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{139}{144}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{1728}(83,\cdot)$	$1$	$1$	$e\left(\frac{103}{144}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{59}{144}\right)$	$e\left(\frac{1}{144}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{125}{144}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{1728}(131,\cdot)$	$1$	$1$	$e\left(\frac{35}{144}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{55}{144}\right)$	$e\left(\frac{101}{144}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{97}{144}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{1728}(155,\cdot)$	$1$	$1$	$e\left(\frac{73}{144}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{53}{144}\right)$	$e\left(\frac{79}{144}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{83}{144}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{1728}(203,\cdot)$	$1$	$1$	$e\left(\frac{5}{144}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{49}{144}\right)$	$e\left(\frac{35}{144}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{55}{144}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{1728}(227,\cdot)$	$1$	$1$	$e\left(\frac{43}{144}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{47}{144}\right)$	$e\left(\frac{13}{144}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{41}{144}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{1728}(275,\cdot)$	$1$	$1$	$e\left(\frac{119}{144}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{43}{144}\right)$	$e\left(\frac{113}{144}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{13}{144}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{1728}(299,\cdot)$	$1$	$1$	$e\left(\frac{13}{144}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{41}{144}\right)$	$e\left(\frac{91}{144}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{143}{144}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{1728}(347,\cdot)$	$1$	$1$	$e\left(\frac{89}{144}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{37}{144}\right)$	$e\left(\frac{47}{144}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{1728}(371,\cdot)$	$1$	$1$	$e\left(\frac{127}{144}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{35}{144}\right)$	$e\left(\frac{25}{144}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{101}{144}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{1728}(419,\cdot)$	$1$	$1$	$e\left(\frac{59}{144}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{31}{144}\right)$	$e\left(\frac{125}{144}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{73}{144}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{1728}(443,\cdot)$	$1$	$1$	$e\left(\frac{97}{144}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{29}{144}\right)$	$e\left(\frac{103}{144}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{59}{144}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{1728}(491,\cdot)$	$1$	$1$	$e\left(\frac{29}{144}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{25}{144}\right)$	$e\left(\frac{59}{144}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{31}{144}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{1728}(515,\cdot)$	$1$	$1$	$e\left(\frac{67}{144}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{23}{144}\right)$	$e\left(\frac{37}{144}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{17}{144}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{1728}(563,\cdot)$	$1$	$1$	$e\left(\frac{143}{144}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{19}{144}\right)$	$e\left(\frac{137}{144}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{133}{144}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{1728}(587,\cdot)$	$1$	$1$	$e\left(\frac{37}{144}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{17}{144}\right)$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{119}{144}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{1728}(635,\cdot)$	$1$	$1$	$e\left(\frac{113}{144}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{13}{144}\right)$	$e\left(\frac{71}{144}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{91}{144}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{1728}(659,\cdot)$	$1$	$1$	$e\left(\frac{7}{144}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{11}{144}\right)$	$e\left(\frac{49}{144}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{77}{144}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{1728}(707,\cdot)$	$1$	$1$	$e\left(\frac{83}{144}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{7}{144}\right)$	$e\left(\frac{5}{144}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{49}{144}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{1728}(731,\cdot)$	$1$	$1$	$e\left(\frac{121}{144}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{5}{144}\right)$	$e\left(\frac{127}{144}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{35}{144}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{1728}(779,\cdot)$	$1$	$1$	$e\left(\frac{53}{144}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{1}{144}\right)$	$e\left(\frac{83}{144}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{7}{144}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{1728}(803,\cdot)$	$1$	$1$	$e\left(\frac{91}{144}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{143}{144}\right)$	$e\left(\frac{61}{144}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{137}{144}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{1728}(851,\cdot)$	$1$	$1$	$e\left(\frac{23}{144}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{139}{144}\right)$	$e\left(\frac{17}{144}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{109}{144}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{1728}(875,\cdot)$	$1$	$1$	$e\left(\frac{61}{144}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{137}{144}\right)$	$e\left(\frac{139}{144}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{95}{144}\right)$	$e\left(\frac{4}{9}\right)$
$\chi_{1728}(923,\cdot)$	$1$	$1$	$e\left(\frac{137}{144}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{133}{144}\right)$	$e\left(\frac{95}{144}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{67}{144}\right)$	$e\left(\frac{5}{9}\right)$
$\chi_{1728}(947,\cdot)$	$1$	$1$	$e\left(\frac{31}{144}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{131}{144}\right)$	$e\left(\frac{73}{144}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{53}{144}\right)$	$e\left(\frac{1}{9}\right)$
$\chi_{1728}(995,\cdot)$	$1$	$1$	$e\left(\frac{107}{144}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{127}{144}\right)$	$e\left(\frac{29}{144}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{25}{144}\right)$	$e\left(\frac{2}{9}\right)$
$\chi_{1728}(1019,\cdot)$	$1$	$1$	$e\left(\frac{1}{144}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{125}{144}\right)$	$e\left(\frac{7}{144}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{11}{144}\right)$	$e\left(\frac{7}{9}\right)$
$\chi_{1728}(1067,\cdot)$	$1$	$1$	$e\left(\frac{77}{144}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{121}{144}\right)$	$e\left(\frac{107}{144}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{127}{144}\right)$	$e\left(\frac{8}{9}\right)$
$\chi_{1728}(1091,\cdot)$	$1$	$1$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{119}{144}\right)$	$e\left(\frac{85}{144}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{113}{144}\right)$	$e\left(\frac{4}{9}\right)$

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

Character	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{1728}(11,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{133}{144}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{65}{144}\right)\)	\(e\left(\frac{67}{144}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{23}{144}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{1728}(59,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{144}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{61}{144}\right)\)	\(e\left(\frac{23}{144}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{139}{144}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{1728}(83,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{144}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{59}{144}\right)\)	\(e\left(\frac{1}{144}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{125}{144}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{1728}(131,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{144}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{55}{144}\right)\)	\(e\left(\frac{101}{144}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{97}{144}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{1728}(155,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{144}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{53}{144}\right)\)	\(e\left(\frac{79}{144}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{83}{144}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{1728}(203,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{144}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{49}{144}\right)\)	\(e\left(\frac{35}{144}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{55}{144}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{1728}(227,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{144}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{47}{144}\right)\)	\(e\left(\frac{13}{144}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{41}{144}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{1728}(275,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{119}{144}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{43}{144}\right)\)	\(e\left(\frac{113}{144}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{13}{144}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{1728}(299,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{144}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{41}{144}\right)\)	\(e\left(\frac{91}{144}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{143}{144}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{1728}(347,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{144}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{37}{144}\right)\)	\(e\left(\frac{47}{144}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{1728}(371,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{144}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{35}{144}\right)\)	\(e\left(\frac{25}{144}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{101}{144}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{1728}(419,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{144}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{31}{144}\right)\)	\(e\left(\frac{125}{144}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{73}{144}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{1728}(443,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{144}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{29}{144}\right)\)	\(e\left(\frac{103}{144}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{59}{144}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{1728}(491,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{144}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{25}{144}\right)\)	\(e\left(\frac{59}{144}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{31}{144}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{1728}(515,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{144}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{23}{144}\right)\)	\(e\left(\frac{37}{144}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{17}{144}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{1728}(563,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{143}{144}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{19}{144}\right)\)	\(e\left(\frac{137}{144}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{133}{144}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{1728}(587,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{144}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{17}{144}\right)\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{119}{144}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{1728}(635,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{144}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{13}{144}\right)\)	\(e\left(\frac{71}{144}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{91}{144}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{1728}(659,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{144}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{11}{144}\right)\)	\(e\left(\frac{49}{144}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{77}{144}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{1728}(707,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{83}{144}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{7}{144}\right)\)	\(e\left(\frac{5}{144}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{49}{144}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{1728}(731,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{144}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{5}{144}\right)\)	\(e\left(\frac{127}{144}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{35}{144}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{1728}(779,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{144}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{1}{144}\right)\)	\(e\left(\frac{83}{144}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{7}{144}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{1728}(803,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{144}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{143}{144}\right)\)	\(e\left(\frac{61}{144}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{137}{144}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{1728}(851,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{144}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{139}{144}\right)\)	\(e\left(\frac{17}{144}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{109}{144}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{1728}(875,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{144}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{137}{144}\right)\)	\(e\left(\frac{139}{144}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{95}{144}\right)\)	\(e\left(\frac{4}{9}\right)\)
\(\chi_{1728}(923,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{144}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{133}{144}\right)\)	\(e\left(\frac{95}{144}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{67}{144}\right)\)	\(e\left(\frac{5}{9}\right)\)
\(\chi_{1728}(947,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{144}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{131}{144}\right)\)	\(e\left(\frac{73}{144}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{53}{144}\right)\)	\(e\left(\frac{1}{9}\right)\)
\(\chi_{1728}(995,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{107}{144}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{127}{144}\right)\)	\(e\left(\frac{29}{144}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{25}{144}\right)\)	\(e\left(\frac{2}{9}\right)\)
\(\chi_{1728}(1019,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{144}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{125}{144}\right)\)	\(e\left(\frac{7}{144}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{11}{144}\right)\)	\(e\left(\frac{7}{9}\right)\)
\(\chi_{1728}(1067,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{144}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{121}{144}\right)\)	\(e\left(\frac{107}{144}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{127}{144}\right)\)	\(e\left(\frac{8}{9}\right)\)
\(\chi_{1728}(1091,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{119}{144}\right)\)	\(e\left(\frac{85}{144}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{113}{144}\right)\)	\(e\left(\frac{4}{9}\right)\)

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First 31 of 48 characters in Galois orbit

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	1728.ch
Modulus	$1728$
Conductor	$1728$
Order	$144$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(1728\)
Conductor:	\(1728\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(144\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	yes	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	yes
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)