LMFDB - Dirichlet character orbit 9984.hk

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9984, base_ring=CyclotomicField(192)) M = H._module chi = DirichletCharacter(H, M([0,63,96,112])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(245,9984)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$9984$
Conductor:	$9984$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$192$	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:	$\Q(\zeta_{192})$
Fixed field:	Number field defined by a degree 192 polynomial (not computed)

First 31 of 64 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$17$	$19$	$23$	$25$	$29$	$31$	$35$
$\chi_{9984}(245,\cdot)$	$1$	$1$	$e\left(\frac{5}{64}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{91}{192}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{89}{192}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{37}{192}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{149}{192}\right)$
$\chi_{9984}(293,\cdot)$	$1$	$1$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{23}{192}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{109}{192}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{41}{192}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{25}{192}\right)$
$\chi_{9984}(461,\cdot)$	$1$	$1$	$e\left(\frac{15}{64}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{17}{192}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{139}{192}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{47}{192}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{127}{192}\right)$
$\chi_{9984}(509,\cdot)$	$1$	$1$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{109}{192}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{191}{192}\right)$	$e\left(\frac{95}{96}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{19}{192}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{35}{192}\right)$
$\chi_{9984}(869,\cdot)$	$1$	$1$	$e\left(\frac{57}{64}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{103}{192}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{29}{192}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{25}{192}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{137}{192}\right)$
$\chi_{9984}(917,\cdot)$	$1$	$1$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{35}{192}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{49}{192}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{29}{192}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{13}{192}\right)$
$\chi_{9984}(1085,\cdot)$	$1$	$1$	$e\left(\frac{35}{64}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{125}{192}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{175}{192}\right)$	$e\left(\frac{79}{96}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{131}{192}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{19}{192}\right)$
$\chi_{9984}(1133,\cdot)$	$1$	$1$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{49}{96}\right)$	$e\left(\frac{25}{192}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{35}{192}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{103}{192}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{119}{192}\right)$
$\chi_{9984}(1493,\cdot)$	$1$	$1$	$e\left(\frac{45}{64}\right)$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{115}{192}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{161}{192}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{13}{192}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{125}{192}\right)$
$\chi_{9984}(1541,\cdot)$	$1$	$1$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{23}{96}\right)$	$e\left(\frac{47}{192}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{181}{192}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{17}{192}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{1}{192}\right)$
$\chi_{9984}(1709,\cdot)$	$1$	$1$	$e\left(\frac{55}{64}\right)$	$e\left(\frac{65}{96}\right)$	$e\left(\frac{41}{192}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{19}{192}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{23}{192}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{103}{192}\right)$
$\chi_{9984}(1757,\cdot)$	$1$	$1$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{133}{192}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{71}{192}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{187}{192}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{11}{192}\right)$
$\chi_{9984}(2117,\cdot)$	$1$	$1$	$e\left(\frac{33}{64}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{127}{192}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{101}{192}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{1}{192}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{113}{192}\right)$
$\chi_{9984}(2165,\cdot)$	$1$	$1$	$e\left(\frac{37}{64}\right)$	$e\left(\frac{35}{96}\right)$	$e\left(\frac{59}{192}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{121}{192}\right)$	$e\left(\frac{25}{96}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{5}{192}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{181}{192}\right)$
$\chi_{9984}(2333,\cdot)$	$1$	$1$	$e\left(\frac{11}{64}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{149}{192}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{55}{192}\right)$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{107}{192}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{187}{192}\right)$
$\chi_{9984}(2381,\cdot)$	$1$	$1$	$e\left(\frac{47}{64}\right)$	$e\left(\frac{73}{96}\right)$	$e\left(\frac{49}{192}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{107}{192}\right)$	$e\left(\frac{11}{96}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{79}{192}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{95}{192}\right)$
$\chi_{9984}(2741,\cdot)$	$1$	$1$	$e\left(\frac{21}{64}\right)$	$e\left(\frac{19}{96}\right)$	$e\left(\frac{139}{192}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{41}{192}\right)$	$e\left(\frac{41}{96}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{181}{192}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{101}{192}\right)$
$\chi_{9984}(2789,\cdot)$	$1$	$1$	$e\left(\frac{25}{64}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{71}{192}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{61}{192}\right)$	$e\left(\frac{61}{96}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{185}{192}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{169}{192}\right)$
$\chi_{9984}(2957,\cdot)$	$1$	$1$	$e\left(\frac{31}{64}\right)$	$e\left(\frac{89}{96}\right)$	$e\left(\frac{65}{192}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{91}{192}\right)$	$e\left(\frac{91}{96}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{191}{192}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{79}{192}\right)$
$\chi_{9984}(3005,\cdot)$	$1$	$1$	$e\left(\frac{3}{64}\right)$	$e\left(\frac{85}{96}\right)$	$e\left(\frac{157}{192}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{143}{192}\right)$	$e\left(\frac{47}{96}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{163}{192}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{179}{192}\right)$
$\chi_{9984}(3365,\cdot)$	$1$	$1$	$e\left(\frac{9}{64}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{151}{192}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{173}{192}\right)$	$e\left(\frac{77}{96}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{169}{192}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{89}{192}\right)$
$\chi_{9984}(3413,\cdot)$	$1$	$1$	$e\left(\frac{13}{64}\right)$	$e\left(\frac{59}{96}\right)$	$e\left(\frac{83}{192}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{1}{192}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{173}{192}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{157}{192}\right)$
$\chi_{9984}(3581,\cdot)$	$1$	$1$	$e\left(\frac{51}{64}\right)$	$e\left(\frac{5}{96}\right)$	$e\left(\frac{173}{192}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{127}{192}\right)$	$e\left(\frac{31}{96}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{83}{192}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{163}{192}\right)$
$\chi_{9984}(3629,\cdot)$	$1$	$1$	$e\left(\frac{23}{64}\right)$	$e\left(\frac{1}{96}\right)$	$e\left(\frac{73}{192}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{179}{192}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{55}{192}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{71}{192}\right)$
$\chi_{9984}(3989,\cdot)$	$1$	$1$	$e\left(\frac{61}{64}\right)$	$e\left(\frac{43}{96}\right)$	$e\left(\frac{163}{192}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{113}{192}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{157}{192}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{77}{192}\right)$
$\chi_{9984}(4037,\cdot)$	$1$	$1$	$e\left(\frac{1}{64}\right)$	$e\left(\frac{71}{96}\right)$	$e\left(\frac{95}{192}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{133}{192}\right)$	$e\left(\frac{37}{96}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{161}{192}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{145}{192}\right)$
$\chi_{9984}(4205,\cdot)$	$1$	$1$	$e\left(\frac{7}{64}\right)$	$e\left(\frac{17}{96}\right)$	$e\left(\frac{89}{192}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{163}{192}\right)$	$e\left(\frac{67}{96}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{167}{192}\right)$	$e\left(\frac{5}{8}\right)$	$e\left(\frac{55}{192}\right)$
$\chi_{9984}(4253,\cdot)$	$1$	$1$	$e\left(\frac{43}{64}\right)$	$e\left(\frac{13}{96}\right)$	$e\left(\frac{181}{192}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{23}{192}\right)$	$e\left(\frac{23}{96}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{139}{192}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{155}{192}\right)$
$\chi_{9984}(4613,\cdot)$	$1$	$1$	$e\left(\frac{49}{64}\right)$	$e\left(\frac{55}{96}\right)$	$e\left(\frac{175}{192}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{53}{192}\right)$	$e\left(\frac{53}{96}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{145}{192}\right)$	$e\left(\frac{3}{8}\right)$	$e\left(\frac{65}{192}\right)$
$\chi_{9984}(4661,\cdot)$	$1$	$1$	$e\left(\frac{53}{64}\right)$	$e\left(\frac{83}{96}\right)$	$e\left(\frac{107}{192}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{73}{192}\right)$	$e\left(\frac{73}{96}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{149}{192}\right)$	$e\left(\frac{7}{8}\right)$	$e\left(\frac{133}{192}\right)$
$\chi_{9984}(4829,\cdot)$	$1$	$1$	$e\left(\frac{27}{64}\right)$	$e\left(\frac{29}{96}\right)$	$e\left(\frac{5}{192}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{7}{192}\right)$	$e\left(\frac{7}{96}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{59}{192}\right)$	$e\left(\frac{1}{8}\right)$	$e\left(\frac{139}{192}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{9984}(245,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{64}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{91}{192}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{89}{192}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{37}{192}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{149}{192}\right)\)
\(\chi_{9984}(293,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{23}{192}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{109}{192}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{41}{192}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{25}{192}\right)\)
\(\chi_{9984}(461,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{15}{64}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{17}{192}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{139}{192}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{47}{192}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{127}{192}\right)\)
\(\chi_{9984}(509,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{109}{192}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{191}{192}\right)\)	\(e\left(\frac{95}{96}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{19}{192}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{35}{192}\right)\)
\(\chi_{9984}(869,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{57}{64}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{103}{192}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{29}{192}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{25}{192}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{137}{192}\right)\)
\(\chi_{9984}(917,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{35}{192}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{49}{192}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{29}{192}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{13}{192}\right)\)
\(\chi_{9984}(1085,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{64}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{125}{192}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{175}{192}\right)\)	\(e\left(\frac{79}{96}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{131}{192}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{19}{192}\right)\)
\(\chi_{9984}(1133,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{49}{96}\right)\)	\(e\left(\frac{25}{192}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{35}{192}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{103}{192}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{119}{192}\right)\)
\(\chi_{9984}(1493,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{45}{64}\right)\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{115}{192}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{161}{192}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{13}{192}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{125}{192}\right)\)
\(\chi_{9984}(1541,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{23}{96}\right)\)	\(e\left(\frac{47}{192}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{181}{192}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{17}{192}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{1}{192}\right)\)
\(\chi_{9984}(1709,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{64}\right)\)	\(e\left(\frac{65}{96}\right)\)	\(e\left(\frac{41}{192}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{19}{192}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{23}{192}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{103}{192}\right)\)
\(\chi_{9984}(1757,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{133}{192}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{71}{192}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{187}{192}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{11}{192}\right)\)
\(\chi_{9984}(2117,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{33}{64}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{127}{192}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{101}{192}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{1}{192}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{113}{192}\right)\)
\(\chi_{9984}(2165,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{64}\right)\)	\(e\left(\frac{35}{96}\right)\)	\(e\left(\frac{59}{192}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{121}{192}\right)\)	\(e\left(\frac{25}{96}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{5}{192}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{181}{192}\right)\)
\(\chi_{9984}(2333,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{64}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{149}{192}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{55}{192}\right)\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{107}{192}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{187}{192}\right)\)
\(\chi_{9984}(2381,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{64}\right)\)	\(e\left(\frac{73}{96}\right)\)	\(e\left(\frac{49}{192}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{107}{192}\right)\)	\(e\left(\frac{11}{96}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{79}{192}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{95}{192}\right)\)
\(\chi_{9984}(2741,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{21}{64}\right)\)	\(e\left(\frac{19}{96}\right)\)	\(e\left(\frac{139}{192}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{41}{192}\right)\)	\(e\left(\frac{41}{96}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{181}{192}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{101}{192}\right)\)
\(\chi_{9984}(2789,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{64}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{71}{192}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{61}{192}\right)\)	\(e\left(\frac{61}{96}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{185}{192}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{169}{192}\right)\)
\(\chi_{9984}(2957,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{64}\right)\)	\(e\left(\frac{89}{96}\right)\)	\(e\left(\frac{65}{192}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{91}{192}\right)\)	\(e\left(\frac{91}{96}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{191}{192}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{79}{192}\right)\)
\(\chi_{9984}(3005,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{3}{64}\right)\)	\(e\left(\frac{85}{96}\right)\)	\(e\left(\frac{157}{192}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{143}{192}\right)\)	\(e\left(\frac{47}{96}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{163}{192}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{179}{192}\right)\)
\(\chi_{9984}(3365,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{9}{64}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{151}{192}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{173}{192}\right)\)	\(e\left(\frac{77}{96}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{169}{192}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{89}{192}\right)\)
\(\chi_{9984}(3413,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{64}\right)\)	\(e\left(\frac{59}{96}\right)\)	\(e\left(\frac{83}{192}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{1}{192}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{173}{192}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{157}{192}\right)\)
\(\chi_{9984}(3581,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{51}{64}\right)\)	\(e\left(\frac{5}{96}\right)\)	\(e\left(\frac{173}{192}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{127}{192}\right)\)	\(e\left(\frac{31}{96}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{83}{192}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{163}{192}\right)\)
\(\chi_{9984}(3629,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{64}\right)\)	\(e\left(\frac{1}{96}\right)\)	\(e\left(\frac{73}{192}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{179}{192}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{55}{192}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{71}{192}\right)\)
\(\chi_{9984}(3989,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{64}\right)\)	\(e\left(\frac{43}{96}\right)\)	\(e\left(\frac{163}{192}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{113}{192}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{157}{192}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{77}{192}\right)\)
\(\chi_{9984}(4037,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{64}\right)\)	\(e\left(\frac{71}{96}\right)\)	\(e\left(\frac{95}{192}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{133}{192}\right)\)	\(e\left(\frac{37}{96}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{161}{192}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{145}{192}\right)\)
\(\chi_{9984}(4205,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{64}\right)\)	\(e\left(\frac{17}{96}\right)\)	\(e\left(\frac{89}{192}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{163}{192}\right)\)	\(e\left(\frac{67}{96}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{167}{192}\right)\)	\(e\left(\frac{5}{8}\right)\)	\(e\left(\frac{55}{192}\right)\)
\(\chi_{9984}(4253,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{64}\right)\)	\(e\left(\frac{13}{96}\right)\)	\(e\left(\frac{181}{192}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{23}{192}\right)\)	\(e\left(\frac{23}{96}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{139}{192}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{155}{192}\right)\)
\(\chi_{9984}(4613,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{64}\right)\)	\(e\left(\frac{55}{96}\right)\)	\(e\left(\frac{175}{192}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{53}{192}\right)\)	\(e\left(\frac{53}{96}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{145}{192}\right)\)	\(e\left(\frac{3}{8}\right)\)	\(e\left(\frac{65}{192}\right)\)
\(\chi_{9984}(4661,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{64}\right)\)	\(e\left(\frac{83}{96}\right)\)	\(e\left(\frac{107}{192}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{73}{192}\right)\)	\(e\left(\frac{73}{96}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{149}{192}\right)\)	\(e\left(\frac{7}{8}\right)\)	\(e\left(\frac{133}{192}\right)\)
\(\chi_{9984}(4829,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{27}{64}\right)\)	\(e\left(\frac{29}{96}\right)\)	\(e\left(\frac{5}{192}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{7}{192}\right)\)	\(e\left(\frac{7}{96}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{59}{192}\right)\)	\(e\left(\frac{1}{8}\right)\)	\(e\left(\frac{139}{192}\right)\)

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First 31 of 64 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	9984.hk
Modulus	$9984$
Conductor	$9984$
Order	$192$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(9984\)
Conductor:	\(9984\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(192\)	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)