LMFDB - Dirichlet character orbit 5184.cy

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(5184, base_ring=CyclotomicField(432)) M = H._module chi = DirichletCharacter(H, M([0,405,64])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(13,5184)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$5184$
Conductor:	$5184$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$432$	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:	$\Q(\zeta_{432})$
Fixed field:	Number field defined by a degree 432 polynomial (not computed)

First 31 of 144 characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$19$	$23$	$25$	$29$	$31$
$\chi_{5184}(13,\cdot)$	$1$	$1$	$e\left(\frac{149}{432}\right)$	$e\left(\frac{161}{216}\right)$	$e\left(\frac{265}{432}\right)$	$e\left(\frac{107}{432}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{97}{144}\right)$	$e\left(\frac{163}{216}\right)$	$e\left(\frac{149}{216}\right)$	$e\left(\frac{343}{432}\right)$	$e\left(\frac{25}{54}\right)$
$\chi_{5184}(61,\cdot)$	$1$	$1$	$e\left(\frac{145}{432}\right)$	$e\left(\frac{61}{216}\right)$	$e\left(\frac{197}{432}\right)$	$e\left(\frac{223}{432}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{77}{144}\right)$	$e\left(\frac{47}{216}\right)$	$e\left(\frac{145}{216}\right)$	$e\left(\frac{299}{432}\right)$	$e\left(\frac{41}{54}\right)$
$\chi_{5184}(85,\cdot)$	$1$	$1$	$e\left(\frac{287}{432}\right)$	$e\left(\frac{155}{216}\right)$	$e\left(\frac{235}{432}\right)$	$e\left(\frac{209}{432}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{67}{144}\right)$	$e\left(\frac{169}{216}\right)$	$e\left(\frac{71}{216}\right)$	$e\left(\frac{133}{432}\right)$	$e\left(\frac{13}{54}\right)$
$\chi_{5184}(133,\cdot)$	$1$	$1$	$e\left(\frac{139}{432}\right)$	$e\left(\frac{127}{216}\right)$	$e\left(\frac{311}{432}\right)$	$e\left(\frac{181}{432}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{47}{144}\right)$	$e\left(\frac{197}{216}\right)$	$e\left(\frac{139}{216}\right)$	$e\left(\frac{233}{432}\right)$	$e\left(\frac{11}{54}\right)$
$\chi_{5184}(157,\cdot)$	$1$	$1$	$e\left(\frac{425}{432}\right)$	$e\left(\frac{149}{216}\right)$	$e\left(\frac{205}{432}\right)$	$e\left(\frac{311}{432}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{37}{144}\right)$	$e\left(\frac{175}{216}\right)$	$e\left(\frac{209}{216}\right)$	$e\left(\frac{355}{432}\right)$	$e\left(\frac{1}{54}\right)$
$\chi_{5184}(205,\cdot)$	$1$	$1$	$e\left(\frac{133}{432}\right)$	$e\left(\frac{193}{216}\right)$	$e\left(\frac{425}{432}\right)$	$e\left(\frac{139}{432}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{17}{144}\right)$	$e\left(\frac{131}{216}\right)$	$e\left(\frac{133}{216}\right)$	$e\left(\frac{167}{432}\right)$	$e\left(\frac{35}{54}\right)$
$\chi_{5184}(229,\cdot)$	$1$	$1$	$e\left(\frac{131}{432}\right)$	$e\left(\frac{143}{216}\right)$	$e\left(\frac{175}{432}\right)$	$e\left(\frac{413}{432}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{7}{144}\right)$	$e\left(\frac{181}{216}\right)$	$e\left(\frac{131}{216}\right)$	$e\left(\frac{145}{432}\right)$	$e\left(\frac{43}{54}\right)$
$\chi_{5184}(277,\cdot)$	$1$	$1$	$e\left(\frac{127}{432}\right)$	$e\left(\frac{43}{216}\right)$	$e\left(\frac{107}{432}\right)$	$e\left(\frac{97}{432}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{131}{144}\right)$	$e\left(\frac{65}{216}\right)$	$e\left(\frac{127}{216}\right)$	$e\left(\frac{101}{432}\right)$	$e\left(\frac{5}{54}\right)$
$\chi_{5184}(301,\cdot)$	$1$	$1$	$e\left(\frac{269}{432}\right)$	$e\left(\frac{137}{216}\right)$	$e\left(\frac{145}{432}\right)$	$e\left(\frac{83}{432}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{121}{144}\right)$	$e\left(\frac{187}{216}\right)$	$e\left(\frac{53}{216}\right)$	$e\left(\frac{367}{432}\right)$	$e\left(\frac{31}{54}\right)$
$\chi_{5184}(349,\cdot)$	$1$	$1$	$e\left(\frac{121}{432}\right)$	$e\left(\frac{109}{216}\right)$	$e\left(\frac{221}{432}\right)$	$e\left(\frac{55}{432}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{101}{144}\right)$	$e\left(\frac{215}{216}\right)$	$e\left(\frac{121}{216}\right)$	$e\left(\frac{35}{432}\right)$	$e\left(\frac{29}{54}\right)$
$\chi_{5184}(373,\cdot)$	$1$	$1$	$e\left(\frac{407}{432}\right)$	$e\left(\frac{131}{216}\right)$	$e\left(\frac{115}{432}\right)$	$e\left(\frac{185}{432}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{91}{144}\right)$	$e\left(\frac{193}{216}\right)$	$e\left(\frac{191}{216}\right)$	$e\left(\frac{157}{432}\right)$	$e\left(\frac{19}{54}\right)$
$\chi_{5184}(421,\cdot)$	$1$	$1$	$e\left(\frac{115}{432}\right)$	$e\left(\frac{175}{216}\right)$	$e\left(\frac{335}{432}\right)$	$e\left(\frac{13}{432}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{71}{144}\right)$	$e\left(\frac{149}{216}\right)$	$e\left(\frac{115}{216}\right)$	$e\left(\frac{401}{432}\right)$	$e\left(\frac{53}{54}\right)$
$\chi_{5184}(445,\cdot)$	$1$	$1$	$e\left(\frac{113}{432}\right)$	$e\left(\frac{125}{216}\right)$	$e\left(\frac{85}{432}\right)$	$e\left(\frac{287}{432}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{61}{144}\right)$	$e\left(\frac{199}{216}\right)$	$e\left(\frac{113}{216}\right)$	$e\left(\frac{379}{432}\right)$	$e\left(\frac{7}{54}\right)$
$\chi_{5184}(493,\cdot)$	$1$	$1$	$e\left(\frac{109}{432}\right)$	$e\left(\frac{25}{216}\right)$	$e\left(\frac{17}{432}\right)$	$e\left(\frac{403}{432}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{41}{144}\right)$	$e\left(\frac{83}{216}\right)$	$e\left(\frac{109}{216}\right)$	$e\left(\frac{335}{432}\right)$	$e\left(\frac{23}{54}\right)$
$\chi_{5184}(517,\cdot)$	$1$	$1$	$e\left(\frac{251}{432}\right)$	$e\left(\frac{119}{216}\right)$	$e\left(\frac{55}{432}\right)$	$e\left(\frac{389}{432}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{31}{144}\right)$	$e\left(\frac{205}{216}\right)$	$e\left(\frac{35}{216}\right)$	$e\left(\frac{169}{432}\right)$	$e\left(\frac{49}{54}\right)$
$\chi_{5184}(565,\cdot)$	$1$	$1$	$e\left(\frac{103}{432}\right)$	$e\left(\frac{91}{216}\right)$	$e\left(\frac{131}{432}\right)$	$e\left(\frac{361}{432}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{11}{144}\right)$	$e\left(\frac{17}{216}\right)$	$e\left(\frac{103}{216}\right)$	$e\left(\frac{269}{432}\right)$	$e\left(\frac{47}{54}\right)$
$\chi_{5184}(589,\cdot)$	$1$	$1$	$e\left(\frac{389}{432}\right)$	$e\left(\frac{113}{216}\right)$	$e\left(\frac{25}{432}\right)$	$e\left(\frac{59}{432}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{1}{144}\right)$	$e\left(\frac{211}{216}\right)$	$e\left(\frac{173}{216}\right)$	$e\left(\frac{391}{432}\right)$	$e\left(\frac{37}{54}\right)$
$\chi_{5184}(637,\cdot)$	$1$	$1$	$e\left(\frac{97}{432}\right)$	$e\left(\frac{157}{216}\right)$	$e\left(\frac{245}{432}\right)$	$e\left(\frac{319}{432}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{125}{144}\right)$	$e\left(\frac{167}{216}\right)$	$e\left(\frac{97}{216}\right)$	$e\left(\frac{203}{432}\right)$	$e\left(\frac{17}{54}\right)$
$\chi_{5184}(661,\cdot)$	$1$	$1$	$e\left(\frac{95}{432}\right)$	$e\left(\frac{107}{216}\right)$	$e\left(\frac{427}{432}\right)$	$e\left(\frac{161}{432}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{1}{216}\right)$	$e\left(\frac{95}{216}\right)$	$e\left(\frac{181}{432}\right)$	$e\left(\frac{25}{54}\right)$
$\chi_{5184}(709,\cdot)$	$1$	$1$	$e\left(\frac{91}{432}\right)$	$e\left(\frac{7}{216}\right)$	$e\left(\frac{359}{432}\right)$	$e\left(\frac{277}{432}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{95}{144}\right)$	$e\left(\frac{101}{216}\right)$	$e\left(\frac{91}{216}\right)$	$e\left(\frac{137}{432}\right)$	$e\left(\frac{41}{54}\right)$
$\chi_{5184}(733,\cdot)$	$1$	$1$	$e\left(\frac{233}{432}\right)$	$e\left(\frac{101}{216}\right)$	$e\left(\frac{397}{432}\right)$	$e\left(\frac{263}{432}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{85}{144}\right)$	$e\left(\frac{7}{216}\right)$	$e\left(\frac{17}{216}\right)$	$e\left(\frac{403}{432}\right)$	$e\left(\frac{13}{54}\right)$
$\chi_{5184}(781,\cdot)$	$1$	$1$	$e\left(\frac{85}{432}\right)$	$e\left(\frac{73}{216}\right)$	$e\left(\frac{41}{432}\right)$	$e\left(\frac{235}{432}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{65}{144}\right)$	$e\left(\frac{35}{216}\right)$	$e\left(\frac{85}{216}\right)$	$e\left(\frac{71}{432}\right)$	$e\left(\frac{11}{54}\right)$
$\chi_{5184}(805,\cdot)$	$1$	$1$	$e\left(\frac{371}{432}\right)$	$e\left(\frac{95}{216}\right)$	$e\left(\frac{367}{432}\right)$	$e\left(\frac{365}{432}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{55}{144}\right)$	$e\left(\frac{13}{216}\right)$	$e\left(\frac{155}{216}\right)$	$e\left(\frac{193}{432}\right)$	$e\left(\frac{1}{54}\right)$
$\chi_{5184}(853,\cdot)$	$1$	$1$	$e\left(\frac{79}{432}\right)$	$e\left(\frac{139}{216}\right)$	$e\left(\frac{155}{432}\right)$	$e\left(\frac{193}{432}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{35}{144}\right)$	$e\left(\frac{185}{216}\right)$	$e\left(\frac{79}{216}\right)$	$e\left(\frac{5}{432}\right)$	$e\left(\frac{35}{54}\right)$
$\chi_{5184}(877,\cdot)$	$1$	$1$	$e\left(\frac{77}{432}\right)$	$e\left(\frac{89}{216}\right)$	$e\left(\frac{337}{432}\right)$	$e\left(\frac{35}{432}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{25}{144}\right)$	$e\left(\frac{19}{216}\right)$	$e\left(\frac{77}{216}\right)$	$e\left(\frac{415}{432}\right)$	$e\left(\frac{43}{54}\right)$
$\chi_{5184}(925,\cdot)$	$1$	$1$	$e\left(\frac{73}{432}\right)$	$e\left(\frac{205}{216}\right)$	$e\left(\frac{269}{432}\right)$	$e\left(\frac{151}{432}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{5}{144}\right)$	$e\left(\frac{119}{216}\right)$	$e\left(\frac{73}{216}\right)$	$e\left(\frac{371}{432}\right)$	$e\left(\frac{5}{54}\right)$
$\chi_{5184}(949,\cdot)$	$1$	$1$	$e\left(\frac{215}{432}\right)$	$e\left(\frac{83}{216}\right)$	$e\left(\frac{307}{432}\right)$	$e\left(\frac{137}{432}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{139}{144}\right)$	$e\left(\frac{25}{216}\right)$	$e\left(\frac{215}{216}\right)$	$e\left(\frac{205}{432}\right)$	$e\left(\frac{31}{54}\right)$
$\chi_{5184}(997,\cdot)$	$1$	$1$	$e\left(\frac{67}{432}\right)$	$e\left(\frac{55}{216}\right)$	$e\left(\frac{383}{432}\right)$	$e\left(\frac{109}{432}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{119}{144}\right)$	$e\left(\frac{53}{216}\right)$	$e\left(\frac{67}{216}\right)$	$e\left(\frac{305}{432}\right)$	$e\left(\frac{29}{54}\right)$
$\chi_{5184}(1021,\cdot)$	$1$	$1$	$e\left(\frac{353}{432}\right)$	$e\left(\frac{77}{216}\right)$	$e\left(\frac{277}{432}\right)$	$e\left(\frac{239}{432}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{109}{144}\right)$	$e\left(\frac{31}{216}\right)$	$e\left(\frac{137}{216}\right)$	$e\left(\frac{427}{432}\right)$	$e\left(\frac{19}{54}\right)$
$\chi_{5184}(1069,\cdot)$	$1$	$1$	$e\left(\frac{61}{432}\right)$	$e\left(\frac{121}{216}\right)$	$e\left(\frac{65}{432}\right)$	$e\left(\frac{67}{432}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{89}{144}\right)$	$e\left(\frac{203}{216}\right)$	$e\left(\frac{61}{216}\right)$	$e\left(\frac{239}{432}\right)$	$e\left(\frac{53}{54}\right)$
$\chi_{5184}(1093,\cdot)$	$1$	$1$	$e\left(\frac{59}{432}\right)$	$e\left(\frac{71}{216}\right)$	$e\left(\frac{247}{432}\right)$	$e\left(\frac{341}{432}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{79}{144}\right)$	$e\left(\frac{37}{216}\right)$	$e\left(\frac{59}{216}\right)$	$e\left(\frac{217}{432}\right)$	$e\left(\frac{7}{54}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(19\)	\(23\)	\(25\)	\(29\)	\(31\)
\(\chi_{5184}(13,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{149}{432}\right)\)	\(e\left(\frac{161}{216}\right)\)	\(e\left(\frac{265}{432}\right)\)	\(e\left(\frac{107}{432}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{97}{144}\right)\)	\(e\left(\frac{163}{216}\right)\)	\(e\left(\frac{149}{216}\right)\)	\(e\left(\frac{343}{432}\right)\)	\(e\left(\frac{25}{54}\right)\)
\(\chi_{5184}(61,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{145}{432}\right)\)	\(e\left(\frac{61}{216}\right)\)	\(e\left(\frac{197}{432}\right)\)	\(e\left(\frac{223}{432}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{77}{144}\right)\)	\(e\left(\frac{47}{216}\right)\)	\(e\left(\frac{145}{216}\right)\)	\(e\left(\frac{299}{432}\right)\)	\(e\left(\frac{41}{54}\right)\)
\(\chi_{5184}(85,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{287}{432}\right)\)	\(e\left(\frac{155}{216}\right)\)	\(e\left(\frac{235}{432}\right)\)	\(e\left(\frac{209}{432}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{67}{144}\right)\)	\(e\left(\frac{169}{216}\right)\)	\(e\left(\frac{71}{216}\right)\)	\(e\left(\frac{133}{432}\right)\)	\(e\left(\frac{13}{54}\right)\)
\(\chi_{5184}(133,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{139}{432}\right)\)	\(e\left(\frac{127}{216}\right)\)	\(e\left(\frac{311}{432}\right)\)	\(e\left(\frac{181}{432}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{47}{144}\right)\)	\(e\left(\frac{197}{216}\right)\)	\(e\left(\frac{139}{216}\right)\)	\(e\left(\frac{233}{432}\right)\)	\(e\left(\frac{11}{54}\right)\)
\(\chi_{5184}(157,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{425}{432}\right)\)	\(e\left(\frac{149}{216}\right)\)	\(e\left(\frac{205}{432}\right)\)	\(e\left(\frac{311}{432}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{37}{144}\right)\)	\(e\left(\frac{175}{216}\right)\)	\(e\left(\frac{209}{216}\right)\)	\(e\left(\frac{355}{432}\right)\)	\(e\left(\frac{1}{54}\right)\)
\(\chi_{5184}(205,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{133}{432}\right)\)	\(e\left(\frac{193}{216}\right)\)	\(e\left(\frac{425}{432}\right)\)	\(e\left(\frac{139}{432}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{17}{144}\right)\)	\(e\left(\frac{131}{216}\right)\)	\(e\left(\frac{133}{216}\right)\)	\(e\left(\frac{167}{432}\right)\)	\(e\left(\frac{35}{54}\right)\)
\(\chi_{5184}(229,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{131}{432}\right)\)	\(e\left(\frac{143}{216}\right)\)	\(e\left(\frac{175}{432}\right)\)	\(e\left(\frac{413}{432}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{7}{144}\right)\)	\(e\left(\frac{181}{216}\right)\)	\(e\left(\frac{131}{216}\right)\)	\(e\left(\frac{145}{432}\right)\)	\(e\left(\frac{43}{54}\right)\)
\(\chi_{5184}(277,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{127}{432}\right)\)	\(e\left(\frac{43}{216}\right)\)	\(e\left(\frac{107}{432}\right)\)	\(e\left(\frac{97}{432}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{131}{144}\right)\)	\(e\left(\frac{65}{216}\right)\)	\(e\left(\frac{127}{216}\right)\)	\(e\left(\frac{101}{432}\right)\)	\(e\left(\frac{5}{54}\right)\)
\(\chi_{5184}(301,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{269}{432}\right)\)	\(e\left(\frac{137}{216}\right)\)	\(e\left(\frac{145}{432}\right)\)	\(e\left(\frac{83}{432}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{121}{144}\right)\)	\(e\left(\frac{187}{216}\right)\)	\(e\left(\frac{53}{216}\right)\)	\(e\left(\frac{367}{432}\right)\)	\(e\left(\frac{31}{54}\right)\)
\(\chi_{5184}(349,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{121}{432}\right)\)	\(e\left(\frac{109}{216}\right)\)	\(e\left(\frac{221}{432}\right)\)	\(e\left(\frac{55}{432}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{101}{144}\right)\)	\(e\left(\frac{215}{216}\right)\)	\(e\left(\frac{121}{216}\right)\)	\(e\left(\frac{35}{432}\right)\)	\(e\left(\frac{29}{54}\right)\)
\(\chi_{5184}(373,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{407}{432}\right)\)	\(e\left(\frac{131}{216}\right)\)	\(e\left(\frac{115}{432}\right)\)	\(e\left(\frac{185}{432}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{91}{144}\right)\)	\(e\left(\frac{193}{216}\right)\)	\(e\left(\frac{191}{216}\right)\)	\(e\left(\frac{157}{432}\right)\)	\(e\left(\frac{19}{54}\right)\)
\(\chi_{5184}(421,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{115}{432}\right)\)	\(e\left(\frac{175}{216}\right)\)	\(e\left(\frac{335}{432}\right)\)	\(e\left(\frac{13}{432}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{71}{144}\right)\)	\(e\left(\frac{149}{216}\right)\)	\(e\left(\frac{115}{216}\right)\)	\(e\left(\frac{401}{432}\right)\)	\(e\left(\frac{53}{54}\right)\)
\(\chi_{5184}(445,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{113}{432}\right)\)	\(e\left(\frac{125}{216}\right)\)	\(e\left(\frac{85}{432}\right)\)	\(e\left(\frac{287}{432}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{61}{144}\right)\)	\(e\left(\frac{199}{216}\right)\)	\(e\left(\frac{113}{216}\right)\)	\(e\left(\frac{379}{432}\right)\)	\(e\left(\frac{7}{54}\right)\)
\(\chi_{5184}(493,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{109}{432}\right)\)	\(e\left(\frac{25}{216}\right)\)	\(e\left(\frac{17}{432}\right)\)	\(e\left(\frac{403}{432}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{41}{144}\right)\)	\(e\left(\frac{83}{216}\right)\)	\(e\left(\frac{109}{216}\right)\)	\(e\left(\frac{335}{432}\right)\)	\(e\left(\frac{23}{54}\right)\)
\(\chi_{5184}(517,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{251}{432}\right)\)	\(e\left(\frac{119}{216}\right)\)	\(e\left(\frac{55}{432}\right)\)	\(e\left(\frac{389}{432}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{31}{144}\right)\)	\(e\left(\frac{205}{216}\right)\)	\(e\left(\frac{35}{216}\right)\)	\(e\left(\frac{169}{432}\right)\)	\(e\left(\frac{49}{54}\right)\)
\(\chi_{5184}(565,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{103}{432}\right)\)	\(e\left(\frac{91}{216}\right)\)	\(e\left(\frac{131}{432}\right)\)	\(e\left(\frac{361}{432}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{11}{144}\right)\)	\(e\left(\frac{17}{216}\right)\)	\(e\left(\frac{103}{216}\right)\)	\(e\left(\frac{269}{432}\right)\)	\(e\left(\frac{47}{54}\right)\)
\(\chi_{5184}(589,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{389}{432}\right)\)	\(e\left(\frac{113}{216}\right)\)	\(e\left(\frac{25}{432}\right)\)	\(e\left(\frac{59}{432}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{1}{144}\right)\)	\(e\left(\frac{211}{216}\right)\)	\(e\left(\frac{173}{216}\right)\)	\(e\left(\frac{391}{432}\right)\)	\(e\left(\frac{37}{54}\right)\)
\(\chi_{5184}(637,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{97}{432}\right)\)	\(e\left(\frac{157}{216}\right)\)	\(e\left(\frac{245}{432}\right)\)	\(e\left(\frac{319}{432}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{125}{144}\right)\)	\(e\left(\frac{167}{216}\right)\)	\(e\left(\frac{97}{216}\right)\)	\(e\left(\frac{203}{432}\right)\)	\(e\left(\frac{17}{54}\right)\)
\(\chi_{5184}(661,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{95}{432}\right)\)	\(e\left(\frac{107}{216}\right)\)	\(e\left(\frac{427}{432}\right)\)	\(e\left(\frac{161}{432}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{1}{216}\right)\)	\(e\left(\frac{95}{216}\right)\)	\(e\left(\frac{181}{432}\right)\)	\(e\left(\frac{25}{54}\right)\)
\(\chi_{5184}(709,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{91}{432}\right)\)	\(e\left(\frac{7}{216}\right)\)	\(e\left(\frac{359}{432}\right)\)	\(e\left(\frac{277}{432}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{95}{144}\right)\)	\(e\left(\frac{101}{216}\right)\)	\(e\left(\frac{91}{216}\right)\)	\(e\left(\frac{137}{432}\right)\)	\(e\left(\frac{41}{54}\right)\)
\(\chi_{5184}(733,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{233}{432}\right)\)	\(e\left(\frac{101}{216}\right)\)	\(e\left(\frac{397}{432}\right)\)	\(e\left(\frac{263}{432}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{85}{144}\right)\)	\(e\left(\frac{7}{216}\right)\)	\(e\left(\frac{17}{216}\right)\)	\(e\left(\frac{403}{432}\right)\)	\(e\left(\frac{13}{54}\right)\)
\(\chi_{5184}(781,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{85}{432}\right)\)	\(e\left(\frac{73}{216}\right)\)	\(e\left(\frac{41}{432}\right)\)	\(e\left(\frac{235}{432}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{65}{144}\right)\)	\(e\left(\frac{35}{216}\right)\)	\(e\left(\frac{85}{216}\right)\)	\(e\left(\frac{71}{432}\right)\)	\(e\left(\frac{11}{54}\right)\)
\(\chi_{5184}(805,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{371}{432}\right)\)	\(e\left(\frac{95}{216}\right)\)	\(e\left(\frac{367}{432}\right)\)	\(e\left(\frac{365}{432}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{55}{144}\right)\)	\(e\left(\frac{13}{216}\right)\)	\(e\left(\frac{155}{216}\right)\)	\(e\left(\frac{193}{432}\right)\)	\(e\left(\frac{1}{54}\right)\)
\(\chi_{5184}(853,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{79}{432}\right)\)	\(e\left(\frac{139}{216}\right)\)	\(e\left(\frac{155}{432}\right)\)	\(e\left(\frac{193}{432}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{35}{144}\right)\)	\(e\left(\frac{185}{216}\right)\)	\(e\left(\frac{79}{216}\right)\)	\(e\left(\frac{5}{432}\right)\)	\(e\left(\frac{35}{54}\right)\)
\(\chi_{5184}(877,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{77}{432}\right)\)	\(e\left(\frac{89}{216}\right)\)	\(e\left(\frac{337}{432}\right)\)	\(e\left(\frac{35}{432}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{25}{144}\right)\)	\(e\left(\frac{19}{216}\right)\)	\(e\left(\frac{77}{216}\right)\)	\(e\left(\frac{415}{432}\right)\)	\(e\left(\frac{43}{54}\right)\)
\(\chi_{5184}(925,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{73}{432}\right)\)	\(e\left(\frac{205}{216}\right)\)	\(e\left(\frac{269}{432}\right)\)	\(e\left(\frac{151}{432}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{5}{144}\right)\)	\(e\left(\frac{119}{216}\right)\)	\(e\left(\frac{73}{216}\right)\)	\(e\left(\frac{371}{432}\right)\)	\(e\left(\frac{5}{54}\right)\)
\(\chi_{5184}(949,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{215}{432}\right)\)	\(e\left(\frac{83}{216}\right)\)	\(e\left(\frac{307}{432}\right)\)	\(e\left(\frac{137}{432}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{139}{144}\right)\)	\(e\left(\frac{25}{216}\right)\)	\(e\left(\frac{215}{216}\right)\)	\(e\left(\frac{205}{432}\right)\)	\(e\left(\frac{31}{54}\right)\)
\(\chi_{5184}(997,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{432}\right)\)	\(e\left(\frac{55}{216}\right)\)	\(e\left(\frac{383}{432}\right)\)	\(e\left(\frac{109}{432}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{119}{144}\right)\)	\(e\left(\frac{53}{216}\right)\)	\(e\left(\frac{67}{216}\right)\)	\(e\left(\frac{305}{432}\right)\)	\(e\left(\frac{29}{54}\right)\)
\(\chi_{5184}(1021,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{353}{432}\right)\)	\(e\left(\frac{77}{216}\right)\)	\(e\left(\frac{277}{432}\right)\)	\(e\left(\frac{239}{432}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{109}{144}\right)\)	\(e\left(\frac{31}{216}\right)\)	\(e\left(\frac{137}{216}\right)\)	\(e\left(\frac{427}{432}\right)\)	\(e\left(\frac{19}{54}\right)\)
\(\chi_{5184}(1069,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{432}\right)\)	\(e\left(\frac{121}{216}\right)\)	\(e\left(\frac{65}{432}\right)\)	\(e\left(\frac{67}{432}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{89}{144}\right)\)	\(e\left(\frac{203}{216}\right)\)	\(e\left(\frac{61}{216}\right)\)	\(e\left(\frac{239}{432}\right)\)	\(e\left(\frac{53}{54}\right)\)
\(\chi_{5184}(1093,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{432}\right)\)	\(e\left(\frac{71}{216}\right)\)	\(e\left(\frac{247}{432}\right)\)	\(e\left(\frac{341}{432}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{79}{144}\right)\)	\(e\left(\frac{37}{216}\right)\)	\(e\left(\frac{59}{216}\right)\)	\(e\left(\frac{217}{432}\right)\)	\(e\left(\frac{7}{54}\right)\)

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First 31 of 144 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	5184.cy
Modulus	$5184$
Conductor	$5184$
Order	$432$
Real	no
Primitive	yes
Minimal	yes
Parity	even

Modulus:	\(5184\)
Conductor:	\(5184\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(432\)	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)