LMFDB - Dirichlet character orbit 9216.cn

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(9216, base_ring=CyclotomicField(384)) M = H._module chi = DirichletCharacter(H, M([192,213,320])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(23,9216)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$9216$
Conductor:	$4608$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$384$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4608.cj	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)

Related number fields

Field of values:	$\Q(\zeta_{384})$
Fixed field:	Number field defined by a degree 384 polynomial (not computed)

First 31 of 128 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{9216}(23,\cdot)$	$1$	$1$	$e\left(\frac{277}{384}\right)$	$e\left(\frac{169}{192}\right)$	$e\left(\frac{185}{384}\right)$	$e\left(\frac{91}{384}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{33}{128}\right)$	$e\left(\frac{83}{192}\right)$	$e\left(\frac{85}{192}\right)$	$e\left(\frac{23}{384}\right)$	$e\left(\frac{29}{48}\right)$
$\chi_{9216}(119,\cdot)$	$1$	$1$	$e\left(\frac{89}{384}\right)$	$e\left(\frac{125}{192}\right)$	$e\left(\frac{205}{384}\right)$	$e\left(\frac{215}{384}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{85}{128}\right)$	$e\left(\frac{175}{192}\right)$	$e\left(\frac{89}{192}\right)$	$e\left(\frac{67}{384}\right)$	$e\left(\frac{1}{48}\right)$
$\chi_{9216}(167,\cdot)$	$1$	$1$	$e\left(\frac{331}{384}\right)$	$e\left(\frac{55}{192}\right)$	$e\left(\frac{167}{384}\right)$	$e\left(\frac{325}{384}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{63}{128}\right)$	$e\left(\frac{77}{192}\right)$	$e\left(\frac{139}{192}\right)$	$e\left(\frac{137}{384}\right)$	$e\left(\frac{35}{48}\right)$
$\chi_{9216}(263,\cdot)$	$1$	$1$	$e\left(\frac{335}{384}\right)$	$e\left(\frac{11}{192}\right)$	$e\left(\frac{379}{384}\right)$	$e\left(\frac{257}{384}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{51}{128}\right)$	$e\left(\frac{169}{192}\right)$	$e\left(\frac{143}{192}\right)$	$e\left(\frac{373}{384}\right)$	$e\left(\frac{7}{48}\right)$
$\chi_{9216}(311,\cdot)$	$1$	$1$	$e\left(\frac{97}{384}\right)$	$e\left(\frac{37}{192}\right)$	$e\left(\frac{245}{384}\right)$	$e\left(\frac{79}{384}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{61}{128}\right)$	$e\left(\frac{167}{192}\right)$	$e\left(\frac{97}{192}\right)$	$e\left(\frac{155}{384}\right)$	$e\left(\frac{41}{48}\right)$
$\chi_{9216}(407,\cdot)$	$1$	$1$	$e\left(\frac{293}{384}\right)$	$e\left(\frac{185}{192}\right)$	$e\left(\frac{265}{384}\right)$	$e\left(\frac{203}{384}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{113}{128}\right)$	$e\left(\frac{67}{192}\right)$	$e\left(\frac{101}{192}\right)$	$e\left(\frac{199}{384}\right)$	$e\left(\frac{13}{48}\right)$
$\chi_{9216}(455,\cdot)$	$1$	$1$	$e\left(\frac{343}{384}\right)$	$e\left(\frac{115}{192}\right)$	$e\left(\frac{35}{384}\right)$	$e\left(\frac{121}{384}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{27}{128}\right)$	$e\left(\frac{161}{192}\right)$	$e\left(\frac{151}{192}\right)$	$e\left(\frac{77}{384}\right)$	$e\left(\frac{47}{48}\right)$
$\chi_{9216}(551,\cdot)$	$1$	$1$	$e\left(\frac{347}{384}\right)$	$e\left(\frac{71}{192}\right)$	$e\left(\frac{247}{384}\right)$	$e\left(\frac{53}{384}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{15}{128}\right)$	$e\left(\frac{61}{192}\right)$	$e\left(\frac{155}{192}\right)$	$e\left(\frac{313}{384}\right)$	$e\left(\frac{19}{48}\right)$
$\chi_{9216}(599,\cdot)$	$1$	$1$	$e\left(\frac{301}{384}\right)$	$e\left(\frac{97}{192}\right)$	$e\left(\frac{305}{384}\right)$	$e\left(\frac{67}{384}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{89}{128}\right)$	$e\left(\frac{59}{192}\right)$	$e\left(\frac{109}{192}\right)$	$e\left(\frac{287}{384}\right)$	$e\left(\frac{5}{48}\right)$
$\chi_{9216}(695,\cdot)$	$1$	$1$	$e\left(\frac{113}{384}\right)$	$e\left(\frac{53}{192}\right)$	$e\left(\frac{325}{384}\right)$	$e\left(\frac{191}{384}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{13}{128}\right)$	$e\left(\frac{151}{192}\right)$	$e\left(\frac{113}{192}\right)$	$e\left(\frac{331}{384}\right)$	$e\left(\frac{25}{48}\right)$
$\chi_{9216}(743,\cdot)$	$1$	$1$	$e\left(\frac{355}{384}\right)$	$e\left(\frac{175}{192}\right)$	$e\left(\frac{287}{384}\right)$	$e\left(\frac{301}{384}\right)$	$e\left(\frac{23}{32}\right)$	$e\left(\frac{119}{128}\right)$	$e\left(\frac{53}{192}\right)$	$e\left(\frac{163}{192}\right)$	$e\left(\frac{17}{384}\right)$	$e\left(\frac{11}{48}\right)$
$\chi_{9216}(839,\cdot)$	$1$	$1$	$e\left(\frac{359}{384}\right)$	$e\left(\frac{131}{192}\right)$	$e\left(\frac{115}{384}\right)$	$e\left(\frac{233}{384}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{107}{128}\right)$	$e\left(\frac{145}{192}\right)$	$e\left(\frac{167}{192}\right)$	$e\left(\frac{253}{384}\right)$	$e\left(\frac{31}{48}\right)$
$\chi_{9216}(887,\cdot)$	$1$	$1$	$e\left(\frac{121}{384}\right)$	$e\left(\frac{157}{192}\right)$	$e\left(\frac{365}{384}\right)$	$e\left(\frac{55}{384}\right)$	$e\left(\frac{21}{32}\right)$	$e\left(\frac{117}{128}\right)$	$e\left(\frac{143}{192}\right)$	$e\left(\frac{121}{192}\right)$	$e\left(\frac{35}{384}\right)$	$e\left(\frac{17}{48}\right)$
$\chi_{9216}(983,\cdot)$	$1$	$1$	$e\left(\frac{317}{384}\right)$	$e\left(\frac{113}{192}\right)$	$e\left(\frac{1}{384}\right)$	$e\left(\frac{179}{384}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{41}{128}\right)$	$e\left(\frac{43}{192}\right)$	$e\left(\frac{125}{192}\right)$	$e\left(\frac{79}{384}\right)$	$e\left(\frac{37}{48}\right)$
$\chi_{9216}(1031,\cdot)$	$1$	$1$	$e\left(\frac{367}{384}\right)$	$e\left(\frac{43}{192}\right)$	$e\left(\frac{155}{384}\right)$	$e\left(\frac{97}{384}\right)$	$e\left(\frac{19}{32}\right)$	$e\left(\frac{83}{128}\right)$	$e\left(\frac{137}{192}\right)$	$e\left(\frac{175}{192}\right)$	$e\left(\frac{341}{384}\right)$	$e\left(\frac{23}{48}\right)$
$\chi_{9216}(1127,\cdot)$	$1$	$1$	$e\left(\frac{371}{384}\right)$	$e\left(\frac{191}{192}\right)$	$e\left(\frac{367}{384}\right)$	$e\left(\frac{29}{384}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{71}{128}\right)$	$e\left(\frac{37}{192}\right)$	$e\left(\frac{179}{192}\right)$	$e\left(\frac{193}{384}\right)$	$e\left(\frac{43}{48}\right)$
$\chi_{9216}(1175,\cdot)$	$1$	$1$	$e\left(\frac{325}{384}\right)$	$e\left(\frac{25}{192}\right)$	$e\left(\frac{41}{384}\right)$	$e\left(\frac{43}{384}\right)$	$e\left(\frac{17}{32}\right)$	$e\left(\frac{17}{128}\right)$	$e\left(\frac{35}{192}\right)$	$e\left(\frac{133}{192}\right)$	$e\left(\frac{167}{384}\right)$	$e\left(\frac{29}{48}\right)$
$\chi_{9216}(1271,\cdot)$	$1$	$1$	$e\left(\frac{137}{384}\right)$	$e\left(\frac{173}{192}\right)$	$e\left(\frac{61}{384}\right)$	$e\left(\frac{167}{384}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{69}{128}\right)$	$e\left(\frac{127}{192}\right)$	$e\left(\frac{137}{192}\right)$	$e\left(\frac{211}{384}\right)$	$e\left(\frac{1}{48}\right)$
$\chi_{9216}(1319,\cdot)$	$1$	$1$	$e\left(\frac{379}{384}\right)$	$e\left(\frac{103}{192}\right)$	$e\left(\frac{23}{384}\right)$	$e\left(\frac{277}{384}\right)$	$e\left(\frac{15}{32}\right)$	$e\left(\frac{47}{128}\right)$	$e\left(\frac{29}{192}\right)$	$e\left(\frac{187}{192}\right)$	$e\left(\frac{281}{384}\right)$	$e\left(\frac{35}{48}\right)$
$\chi_{9216}(1415,\cdot)$	$1$	$1$	$e\left(\frac{383}{384}\right)$	$e\left(\frac{59}{192}\right)$	$e\left(\frac{235}{384}\right)$	$e\left(\frac{209}{384}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{35}{128}\right)$	$e\left(\frac{121}{192}\right)$	$e\left(\frac{191}{192}\right)$	$e\left(\frac{133}{384}\right)$	$e\left(\frac{7}{48}\right)$
$\chi_{9216}(1463,\cdot)$	$1$	$1$	$e\left(\frac{145}{384}\right)$	$e\left(\frac{85}{192}\right)$	$e\left(\frac{101}{384}\right)$	$e\left(\frac{31}{384}\right)$	$e\left(\frac{13}{32}\right)$	$e\left(\frac{45}{128}\right)$	$e\left(\frac{119}{192}\right)$	$e\left(\frac{145}{192}\right)$	$e\left(\frac{299}{384}\right)$	$e\left(\frac{41}{48}\right)$
$\chi_{9216}(1559,\cdot)$	$1$	$1$	$e\left(\frac{341}{384}\right)$	$e\left(\frac{41}{192}\right)$	$e\left(\frac{121}{384}\right)$	$e\left(\frac{155}{384}\right)$	$e\left(\frac{1}{32}\right)$	$e\left(\frac{97}{128}\right)$	$e\left(\frac{19}{192}\right)$	$e\left(\frac{149}{192}\right)$	$e\left(\frac{343}{384}\right)$	$e\left(\frac{13}{48}\right)$
$\chi_{9216}(1607,\cdot)$	$1$	$1$	$e\left(\frac{7}{384}\right)$	$e\left(\frac{163}{192}\right)$	$e\left(\frac{275}{384}\right)$	$e\left(\frac{73}{384}\right)$	$e\left(\frac{11}{32}\right)$	$e\left(\frac{11}{128}\right)$	$e\left(\frac{113}{192}\right)$	$e\left(\frac{7}{192}\right)$	$e\left(\frac{221}{384}\right)$	$e\left(\frac{47}{48}\right)$
$\chi_{9216}(1703,\cdot)$	$1$	$1$	$e\left(\frac{11}{384}\right)$	$e\left(\frac{119}{192}\right)$	$e\left(\frac{103}{384}\right)$	$e\left(\frac{5}{384}\right)$	$e\left(\frac{31}{32}\right)$	$e\left(\frac{127}{128}\right)$	$e\left(\frac{13}{192}\right)$	$e\left(\frac{11}{192}\right)$	$e\left(\frac{73}{384}\right)$	$e\left(\frac{19}{48}\right)$
$\chi_{9216}(1751,\cdot)$	$1$	$1$	$e\left(\frac{349}{384}\right)$	$e\left(\frac{145}{192}\right)$	$e\left(\frac{161}{384}\right)$	$e\left(\frac{19}{384}\right)$	$e\left(\frac{9}{32}\right)$	$e\left(\frac{73}{128}\right)$	$e\left(\frac{11}{192}\right)$	$e\left(\frac{157}{192}\right)$	$e\left(\frac{47}{384}\right)$	$e\left(\frac{5}{48}\right)$
$\chi_{9216}(1847,\cdot)$	$1$	$1$	$e\left(\frac{161}{384}\right)$	$e\left(\frac{101}{192}\right)$	$e\left(\frac{181}{384}\right)$	$e\left(\frac{143}{384}\right)$	$e\left(\frac{29}{32}\right)$	$e\left(\frac{125}{128}\right)$	$e\left(\frac{103}{192}\right)$	$e\left(\frac{161}{192}\right)$	$e\left(\frac{91}{384}\right)$	$e\left(\frac{25}{48}\right)$
$\chi_{9216}(1895,\cdot)$	$1$	$1$	$e\left(\frac{19}{384}\right)$	$e\left(\frac{31}{192}\right)$	$e\left(\frac{143}{384}\right)$	$e\left(\frac{253}{384}\right)$	$e\left(\frac{7}{32}\right)$	$e\left(\frac{103}{128}\right)$	$e\left(\frac{5}{192}\right)$	$e\left(\frac{19}{192}\right)$	$e\left(\frac{161}{384}\right)$	$e\left(\frac{11}{48}\right)$
$\chi_{9216}(1991,\cdot)$	$1$	$1$	$e\left(\frac{23}{384}\right)$	$e\left(\frac{179}{192}\right)$	$e\left(\frac{355}{384}\right)$	$e\left(\frac{185}{384}\right)$	$e\left(\frac{27}{32}\right)$	$e\left(\frac{91}{128}\right)$	$e\left(\frac{97}{192}\right)$	$e\left(\frac{23}{192}\right)$	$e\left(\frac{13}{384}\right)$	$e\left(\frac{31}{48}\right)$
$\chi_{9216}(2039,\cdot)$	$1$	$1$	$e\left(\frac{169}{384}\right)$	$e\left(\frac{13}{192}\right)$	$e\left(\frac{221}{384}\right)$	$e\left(\frac{7}{384}\right)$	$e\left(\frac{5}{32}\right)$	$e\left(\frac{101}{128}\right)$	$e\left(\frac{95}{192}\right)$	$e\left(\frac{169}{192}\right)$	$e\left(\frac{179}{384}\right)$	$e\left(\frac{17}{48}\right)$
$\chi_{9216}(2135,\cdot)$	$1$	$1$	$e\left(\frac{365}{384}\right)$	$e\left(\frac{161}{192}\right)$	$e\left(\frac{241}{384}\right)$	$e\left(\frac{131}{384}\right)$	$e\left(\frac{25}{32}\right)$	$e\left(\frac{25}{128}\right)$	$e\left(\frac{187}{192}\right)$	$e\left(\frac{173}{192}\right)$	$e\left(\frac{223}{384}\right)$	$e\left(\frac{37}{48}\right)$
$\chi_{9216}(2183,\cdot)$	$1$	$1$	$e\left(\frac{31}{384}\right)$	$e\left(\frac{91}{192}\right)$	$e\left(\frac{11}{384}\right)$	$e\left(\frac{49}{384}\right)$	$e\left(\frac{3}{32}\right)$	$e\left(\frac{67}{128}\right)$	$e\left(\frac{89}{192}\right)$	$e\left(\frac{31}{192}\right)$	$e\left(\frac{101}{384}\right)$	$e\left(\frac{23}{48}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{9216}(23,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{277}{384}\right)\)	\(e\left(\frac{169}{192}\right)\)	\(e\left(\frac{185}{384}\right)\)	\(e\left(\frac{91}{384}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{33}{128}\right)\)	\(e\left(\frac{83}{192}\right)\)	\(e\left(\frac{85}{192}\right)\)	\(e\left(\frac{23}{384}\right)\)	\(e\left(\frac{29}{48}\right)\)
\(\chi_{9216}(119,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{89}{384}\right)\)	\(e\left(\frac{125}{192}\right)\)	\(e\left(\frac{205}{384}\right)\)	\(e\left(\frac{215}{384}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{85}{128}\right)\)	\(e\left(\frac{175}{192}\right)\)	\(e\left(\frac{89}{192}\right)\)	\(e\left(\frac{67}{384}\right)\)	\(e\left(\frac{1}{48}\right)\)
\(\chi_{9216}(167,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{331}{384}\right)\)	\(e\left(\frac{55}{192}\right)\)	\(e\left(\frac{167}{384}\right)\)	\(e\left(\frac{325}{384}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{63}{128}\right)\)	\(e\left(\frac{77}{192}\right)\)	\(e\left(\frac{139}{192}\right)\)	\(e\left(\frac{137}{384}\right)\)	\(e\left(\frac{35}{48}\right)\)
\(\chi_{9216}(263,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{335}{384}\right)\)	\(e\left(\frac{11}{192}\right)\)	\(e\left(\frac{379}{384}\right)\)	\(e\left(\frac{257}{384}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{51}{128}\right)\)	\(e\left(\frac{169}{192}\right)\)	\(e\left(\frac{143}{192}\right)\)	\(e\left(\frac{373}{384}\right)\)	\(e\left(\frac{7}{48}\right)\)
\(\chi_{9216}(311,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{384}\right)\)	\(e\left(\frac{37}{192}\right)\)	\(e\left(\frac{245}{384}\right)\)	\(e\left(\frac{79}{384}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{61}{128}\right)\)	\(e\left(\frac{167}{192}\right)\)	\(e\left(\frac{97}{192}\right)\)	\(e\left(\frac{155}{384}\right)\)	\(e\left(\frac{41}{48}\right)\)
\(\chi_{9216}(407,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{293}{384}\right)\)	\(e\left(\frac{185}{192}\right)\)	\(e\left(\frac{265}{384}\right)\)	\(e\left(\frac{203}{384}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{113}{128}\right)\)	\(e\left(\frac{67}{192}\right)\)	\(e\left(\frac{101}{192}\right)\)	\(e\left(\frac{199}{384}\right)\)	\(e\left(\frac{13}{48}\right)\)
\(\chi_{9216}(455,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{343}{384}\right)\)	\(e\left(\frac{115}{192}\right)\)	\(e\left(\frac{35}{384}\right)\)	\(e\left(\frac{121}{384}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{27}{128}\right)\)	\(e\left(\frac{161}{192}\right)\)	\(e\left(\frac{151}{192}\right)\)	\(e\left(\frac{77}{384}\right)\)	\(e\left(\frac{47}{48}\right)\)
\(\chi_{9216}(551,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{347}{384}\right)\)	\(e\left(\frac{71}{192}\right)\)	\(e\left(\frac{247}{384}\right)\)	\(e\left(\frac{53}{384}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{15}{128}\right)\)	\(e\left(\frac{61}{192}\right)\)	\(e\left(\frac{155}{192}\right)\)	\(e\left(\frac{313}{384}\right)\)	\(e\left(\frac{19}{48}\right)\)
\(\chi_{9216}(599,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{301}{384}\right)\)	\(e\left(\frac{97}{192}\right)\)	\(e\left(\frac{305}{384}\right)\)	\(e\left(\frac{67}{384}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{89}{128}\right)\)	\(e\left(\frac{59}{192}\right)\)	\(e\left(\frac{109}{192}\right)\)	\(e\left(\frac{287}{384}\right)\)	\(e\left(\frac{5}{48}\right)\)
\(\chi_{9216}(695,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{384}\right)\)	\(e\left(\frac{53}{192}\right)\)	\(e\left(\frac{325}{384}\right)\)	\(e\left(\frac{191}{384}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{13}{128}\right)\)	\(e\left(\frac{151}{192}\right)\)	\(e\left(\frac{113}{192}\right)\)	\(e\left(\frac{331}{384}\right)\)	\(e\left(\frac{25}{48}\right)\)
\(\chi_{9216}(743,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{355}{384}\right)\)	\(e\left(\frac{175}{192}\right)\)	\(e\left(\frac{287}{384}\right)\)	\(e\left(\frac{301}{384}\right)\)	\(e\left(\frac{23}{32}\right)\)	\(e\left(\frac{119}{128}\right)\)	\(e\left(\frac{53}{192}\right)\)	\(e\left(\frac{163}{192}\right)\)	\(e\left(\frac{17}{384}\right)\)	\(e\left(\frac{11}{48}\right)\)
\(\chi_{9216}(839,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{359}{384}\right)\)	\(e\left(\frac{131}{192}\right)\)	\(e\left(\frac{115}{384}\right)\)	\(e\left(\frac{233}{384}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{107}{128}\right)\)	\(e\left(\frac{145}{192}\right)\)	\(e\left(\frac{167}{192}\right)\)	\(e\left(\frac{253}{384}\right)\)	\(e\left(\frac{31}{48}\right)\)
\(\chi_{9216}(887,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{384}\right)\)	\(e\left(\frac{157}{192}\right)\)	\(e\left(\frac{365}{384}\right)\)	\(e\left(\frac{55}{384}\right)\)	\(e\left(\frac{21}{32}\right)\)	\(e\left(\frac{117}{128}\right)\)	\(e\left(\frac{143}{192}\right)\)	\(e\left(\frac{121}{192}\right)\)	\(e\left(\frac{35}{384}\right)\)	\(e\left(\frac{17}{48}\right)\)
\(\chi_{9216}(983,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{317}{384}\right)\)	\(e\left(\frac{113}{192}\right)\)	\(e\left(\frac{1}{384}\right)\)	\(e\left(\frac{179}{384}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{41}{128}\right)\)	\(e\left(\frac{43}{192}\right)\)	\(e\left(\frac{125}{192}\right)\)	\(e\left(\frac{79}{384}\right)\)	\(e\left(\frac{37}{48}\right)\)
\(\chi_{9216}(1031,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{367}{384}\right)\)	\(e\left(\frac{43}{192}\right)\)	\(e\left(\frac{155}{384}\right)\)	\(e\left(\frac{97}{384}\right)\)	\(e\left(\frac{19}{32}\right)\)	\(e\left(\frac{83}{128}\right)\)	\(e\left(\frac{137}{192}\right)\)	\(e\left(\frac{175}{192}\right)\)	\(e\left(\frac{341}{384}\right)\)	\(e\left(\frac{23}{48}\right)\)
\(\chi_{9216}(1127,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{371}{384}\right)\)	\(e\left(\frac{191}{192}\right)\)	\(e\left(\frac{367}{384}\right)\)	\(e\left(\frac{29}{384}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{71}{128}\right)\)	\(e\left(\frac{37}{192}\right)\)	\(e\left(\frac{179}{192}\right)\)	\(e\left(\frac{193}{384}\right)\)	\(e\left(\frac{43}{48}\right)\)
\(\chi_{9216}(1175,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{325}{384}\right)\)	\(e\left(\frac{25}{192}\right)\)	\(e\left(\frac{41}{384}\right)\)	\(e\left(\frac{43}{384}\right)\)	\(e\left(\frac{17}{32}\right)\)	\(e\left(\frac{17}{128}\right)\)	\(e\left(\frac{35}{192}\right)\)	\(e\left(\frac{133}{192}\right)\)	\(e\left(\frac{167}{384}\right)\)	\(e\left(\frac{29}{48}\right)\)
\(\chi_{9216}(1271,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{137}{384}\right)\)	\(e\left(\frac{173}{192}\right)\)	\(e\left(\frac{61}{384}\right)\)	\(e\left(\frac{167}{384}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{69}{128}\right)\)	\(e\left(\frac{127}{192}\right)\)	\(e\left(\frac{137}{192}\right)\)	\(e\left(\frac{211}{384}\right)\)	\(e\left(\frac{1}{48}\right)\)
\(\chi_{9216}(1319,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{379}{384}\right)\)	\(e\left(\frac{103}{192}\right)\)	\(e\left(\frac{23}{384}\right)\)	\(e\left(\frac{277}{384}\right)\)	\(e\left(\frac{15}{32}\right)\)	\(e\left(\frac{47}{128}\right)\)	\(e\left(\frac{29}{192}\right)\)	\(e\left(\frac{187}{192}\right)\)	\(e\left(\frac{281}{384}\right)\)	\(e\left(\frac{35}{48}\right)\)
\(\chi_{9216}(1415,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{383}{384}\right)\)	\(e\left(\frac{59}{192}\right)\)	\(e\left(\frac{235}{384}\right)\)	\(e\left(\frac{209}{384}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{35}{128}\right)\)	\(e\left(\frac{121}{192}\right)\)	\(e\left(\frac{191}{192}\right)\)	\(e\left(\frac{133}{384}\right)\)	\(e\left(\frac{7}{48}\right)\)
\(\chi_{9216}(1463,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{145}{384}\right)\)	\(e\left(\frac{85}{192}\right)\)	\(e\left(\frac{101}{384}\right)\)	\(e\left(\frac{31}{384}\right)\)	\(e\left(\frac{13}{32}\right)\)	\(e\left(\frac{45}{128}\right)\)	\(e\left(\frac{119}{192}\right)\)	\(e\left(\frac{145}{192}\right)\)	\(e\left(\frac{299}{384}\right)\)	\(e\left(\frac{41}{48}\right)\)
\(\chi_{9216}(1559,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{341}{384}\right)\)	\(e\left(\frac{41}{192}\right)\)	\(e\left(\frac{121}{384}\right)\)	\(e\left(\frac{155}{384}\right)\)	\(e\left(\frac{1}{32}\right)\)	\(e\left(\frac{97}{128}\right)\)	\(e\left(\frac{19}{192}\right)\)	\(e\left(\frac{149}{192}\right)\)	\(e\left(\frac{343}{384}\right)\)	\(e\left(\frac{13}{48}\right)\)
\(\chi_{9216}(1607,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{384}\right)\)	\(e\left(\frac{163}{192}\right)\)	\(e\left(\frac{275}{384}\right)\)	\(e\left(\frac{73}{384}\right)\)	\(e\left(\frac{11}{32}\right)\)	\(e\left(\frac{11}{128}\right)\)	\(e\left(\frac{113}{192}\right)\)	\(e\left(\frac{7}{192}\right)\)	\(e\left(\frac{221}{384}\right)\)	\(e\left(\frac{47}{48}\right)\)
\(\chi_{9216}(1703,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{384}\right)\)	\(e\left(\frac{119}{192}\right)\)	\(e\left(\frac{103}{384}\right)\)	\(e\left(\frac{5}{384}\right)\)	\(e\left(\frac{31}{32}\right)\)	\(e\left(\frac{127}{128}\right)\)	\(e\left(\frac{13}{192}\right)\)	\(e\left(\frac{11}{192}\right)\)	\(e\left(\frac{73}{384}\right)\)	\(e\left(\frac{19}{48}\right)\)
\(\chi_{9216}(1751,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{349}{384}\right)\)	\(e\left(\frac{145}{192}\right)\)	\(e\left(\frac{161}{384}\right)\)	\(e\left(\frac{19}{384}\right)\)	\(e\left(\frac{9}{32}\right)\)	\(e\left(\frac{73}{128}\right)\)	\(e\left(\frac{11}{192}\right)\)	\(e\left(\frac{157}{192}\right)\)	\(e\left(\frac{47}{384}\right)\)	\(e\left(\frac{5}{48}\right)\)
\(\chi_{9216}(1847,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{161}{384}\right)\)	\(e\left(\frac{101}{192}\right)\)	\(e\left(\frac{181}{384}\right)\)	\(e\left(\frac{143}{384}\right)\)	\(e\left(\frac{29}{32}\right)\)	\(e\left(\frac{125}{128}\right)\)	\(e\left(\frac{103}{192}\right)\)	\(e\left(\frac{161}{192}\right)\)	\(e\left(\frac{91}{384}\right)\)	\(e\left(\frac{25}{48}\right)\)
\(\chi_{9216}(1895,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{384}\right)\)	\(e\left(\frac{31}{192}\right)\)	\(e\left(\frac{143}{384}\right)\)	\(e\left(\frac{253}{384}\right)\)	\(e\left(\frac{7}{32}\right)\)	\(e\left(\frac{103}{128}\right)\)	\(e\left(\frac{5}{192}\right)\)	\(e\left(\frac{19}{192}\right)\)	\(e\left(\frac{161}{384}\right)\)	\(e\left(\frac{11}{48}\right)\)
\(\chi_{9216}(1991,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{384}\right)\)	\(e\left(\frac{179}{192}\right)\)	\(e\left(\frac{355}{384}\right)\)	\(e\left(\frac{185}{384}\right)\)	\(e\left(\frac{27}{32}\right)\)	\(e\left(\frac{91}{128}\right)\)	\(e\left(\frac{97}{192}\right)\)	\(e\left(\frac{23}{192}\right)\)	\(e\left(\frac{13}{384}\right)\)	\(e\left(\frac{31}{48}\right)\)
\(\chi_{9216}(2039,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{169}{384}\right)\)	\(e\left(\frac{13}{192}\right)\)	\(e\left(\frac{221}{384}\right)\)	\(e\left(\frac{7}{384}\right)\)	\(e\left(\frac{5}{32}\right)\)	\(e\left(\frac{101}{128}\right)\)	\(e\left(\frac{95}{192}\right)\)	\(e\left(\frac{169}{192}\right)\)	\(e\left(\frac{179}{384}\right)\)	\(e\left(\frac{17}{48}\right)\)
\(\chi_{9216}(2135,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{365}{384}\right)\)	\(e\left(\frac{161}{192}\right)\)	\(e\left(\frac{241}{384}\right)\)	\(e\left(\frac{131}{384}\right)\)	\(e\left(\frac{25}{32}\right)\)	\(e\left(\frac{25}{128}\right)\)	\(e\left(\frac{187}{192}\right)\)	\(e\left(\frac{173}{192}\right)\)	\(e\left(\frac{223}{384}\right)\)	\(e\left(\frac{37}{48}\right)\)
\(\chi_{9216}(2183,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{384}\right)\)	\(e\left(\frac{91}{192}\right)\)	\(e\left(\frac{11}{384}\right)\)	\(e\left(\frac{49}{384}\right)\)	\(e\left(\frac{3}{32}\right)\)	\(e\left(\frac{67}{128}\right)\)	\(e\left(\frac{89}{192}\right)\)	\(e\left(\frac{31}{192}\right)\)	\(e\left(\frac{101}{384}\right)\)	\(e\left(\frac{23}{48}\right)\)

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First 31 of 128 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	9216.cn
Modulus	$9216$
Conductor	$4608$
Order	$384$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(9216\)
Conductor:	\(4608\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(384\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 4608.cj	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)