LMFDB - Dirichlet character orbit 3648.em

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3648, base_ring=CyclotomicField(144)) M = H._module chi = DirichletCharacter(H, M([72,9,72,8])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(59,3648)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$3648$
Conductor:	$3648$	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:	odd	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	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$23$	$25$	$29$	$31$	$35$
$\chi_{3648}(59,\cdot)$	$-1$	$1$	$e\left(\frac{65}{144}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{31}{144}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{19}{144}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{131}{144}\right)$
$\chi_{3648}(155,\cdot)$	$-1$	$1$	$e\left(\frac{89}{144}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{7}{144}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{139}{144}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{11}{144}\right)$
$\chi_{3648}(203,\cdot)$	$-1$	$1$	$e\left(\frac{37}{144}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{11}{144}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{95}{144}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{79}{144}\right)$
$\chi_{3648}(299,\cdot)$	$-1$	$1$	$e\left(\frac{77}{144}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{19}{144}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{7}{144}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{71}{144}\right)$
$\chi_{3648}(371,\cdot)$	$-1$	$1$	$e\left(\frac{79}{144}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{1}{48}\right)$	$e\left(\frac{113}{144}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{125}{144}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{13}{144}\right)$
$\chi_{3648}(395,\cdot)$	$-1$	$1$	$e\left(\frac{85}{144}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{107}{144}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{47}{144}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{127}{144}\right)$
$\chi_{3648}(515,\cdot)$	$-1$	$1$	$e\left(\frac{83}{144}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{13}{144}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{73}{144}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{41}{144}\right)$
$\chi_{3648}(611,\cdot)$	$-1$	$1$	$e\left(\frac{107}{144}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{133}{144}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{49}{144}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{65}{144}\right)$
$\chi_{3648}(659,\cdot)$	$-1$	$1$	$e\left(\frac{55}{144}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{137}{144}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{5}{144}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{133}{144}\right)$
$\chi_{3648}(755,\cdot)$	$-1$	$1$	$e\left(\frac{95}{144}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{1}{144}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{61}{144}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{125}{144}\right)$
$\chi_{3648}(827,\cdot)$	$-1$	$1$	$e\left(\frac{97}{144}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{31}{48}\right)$	$e\left(\frac{95}{144}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{35}{144}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{67}{144}\right)$
$\chi_{3648}(851,\cdot)$	$-1$	$1$	$e\left(\frac{103}{144}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{89}{144}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{101}{144}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{37}{144}\right)$
$\chi_{3648}(971,\cdot)$	$-1$	$1$	$e\left(\frac{101}{144}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{139}{144}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{127}{144}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{95}{144}\right)$
$\chi_{3648}(1067,\cdot)$	$-1$	$1$	$e\left(\frac{125}{144}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{35}{48}\right)$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{103}{144}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{119}{144}\right)$
$\chi_{3648}(1115,\cdot)$	$-1$	$1$	$e\left(\frac{73}{144}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{119}{144}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{59}{144}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{43}{144}\right)$
$\chi_{3648}(1211,\cdot)$	$-1$	$1$	$e\left(\frac{113}{144}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{127}{144}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{35}{144}\right)$
$\chi_{3648}(1283,\cdot)$	$-1$	$1$	$e\left(\frac{115}{144}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{13}{48}\right)$	$e\left(\frac{77}{144}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{89}{144}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{121}{144}\right)$
$\chi_{3648}(1307,\cdot)$	$-1$	$1$	$e\left(\frac{121}{144}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{7}{48}\right)$	$e\left(\frac{71}{144}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{11}{144}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{91}{144}\right)$
$\chi_{3648}(1427,\cdot)$	$-1$	$1$	$e\left(\frac{119}{144}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{41}{48}\right)$	$e\left(\frac{121}{144}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{37}{144}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{5}{144}\right)$
$\chi_{3648}(1523,\cdot)$	$-1$	$1$	$e\left(\frac{143}{144}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{17}{48}\right)$	$e\left(\frac{97}{144}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{13}{144}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{29}{144}\right)$
$\chi_{3648}(1571,\cdot)$	$-1$	$1$	$e\left(\frac{91}{144}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{101}{144}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{113}{144}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{97}{144}\right)$
$\chi_{3648}(1667,\cdot)$	$-1$	$1$	$e\left(\frac{131}{144}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{29}{48}\right)$	$e\left(\frac{109}{144}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{25}{144}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{89}{144}\right)$
$\chi_{3648}(1739,\cdot)$	$-1$	$1$	$e\left(\frac{133}{144}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{43}{48}\right)$	$e\left(\frac{59}{144}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{143}{144}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{31}{144}\right)$
$\chi_{3648}(1763,\cdot)$	$-1$	$1$	$e\left(\frac{139}{144}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{37}{48}\right)$	$e\left(\frac{53}{144}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{65}{144}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{1}{144}\right)$
$\chi_{3648}(1883,\cdot)$	$-1$	$1$	$e\left(\frac{137}{144}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{23}{48}\right)$	$e\left(\frac{103}{144}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{91}{144}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{59}{144}\right)$
$\chi_{3648}(1979,\cdot)$	$-1$	$1$	$e\left(\frac{17}{144}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{47}{48}\right)$	$e\left(\frac{79}{144}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{67}{144}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{83}{144}\right)$
$\chi_{3648}(2027,\cdot)$	$-1$	$1$	$e\left(\frac{109}{144}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{83}{144}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{23}{144}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{7}{144}\right)$
$\chi_{3648}(2123,\cdot)$	$-1$	$1$	$e\left(\frac{5}{144}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{11}{48}\right)$	$e\left(\frac{91}{144}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{79}{144}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{143}{144}\right)$
$\chi_{3648}(2195,\cdot)$	$-1$	$1$	$e\left(\frac{7}{144}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{25}{48}\right)$	$e\left(\frac{41}{144}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{53}{144}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{85}{144}\right)$
$\chi_{3648}(2219,\cdot)$	$-1$	$1$	$e\left(\frac{13}{144}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{19}{48}\right)$	$e\left(\frac{35}{144}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{119}{144}\right)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{55}{144}\right)$
$\chi_{3648}(2339,\cdot)$	$-1$	$1$	$e\left(\frac{11}{144}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{5}{48}\right)$	$e\left(\frac{85}{144}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{1}{144}\right)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{113}{144}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{3648}(59,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{65}{144}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{31}{144}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{19}{144}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{131}{144}\right)\)
\(\chi_{3648}(155,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{89}{144}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{7}{144}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{139}{144}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{11}{144}\right)\)
\(\chi_{3648}(203,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{37}{144}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{11}{144}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{95}{144}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{79}{144}\right)\)
\(\chi_{3648}(299,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{77}{144}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{19}{144}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{7}{144}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{71}{144}\right)\)
\(\chi_{3648}(371,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{79}{144}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{1}{48}\right)\)	\(e\left(\frac{113}{144}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{125}{144}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{13}{144}\right)\)
\(\chi_{3648}(395,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{85}{144}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{107}{144}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{47}{144}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{127}{144}\right)\)
\(\chi_{3648}(515,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{83}{144}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{13}{144}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{73}{144}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{41}{144}\right)\)
\(\chi_{3648}(611,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{107}{144}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{133}{144}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{49}{144}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{65}{144}\right)\)
\(\chi_{3648}(659,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{55}{144}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{137}{144}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{5}{144}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{133}{144}\right)\)
\(\chi_{3648}(755,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{95}{144}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{1}{144}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{61}{144}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{125}{144}\right)\)
\(\chi_{3648}(827,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{97}{144}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{31}{48}\right)\)	\(e\left(\frac{95}{144}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{35}{144}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{67}{144}\right)\)
\(\chi_{3648}(851,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{103}{144}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{89}{144}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{101}{144}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{37}{144}\right)\)
\(\chi_{3648}(971,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{101}{144}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{139}{144}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{127}{144}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{95}{144}\right)\)
\(\chi_{3648}(1067,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{125}{144}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{35}{48}\right)\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{103}{144}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{119}{144}\right)\)
\(\chi_{3648}(1115,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{73}{144}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{119}{144}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{59}{144}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{43}{144}\right)\)
\(\chi_{3648}(1211,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{113}{144}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{127}{144}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{35}{144}\right)\)
\(\chi_{3648}(1283,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{115}{144}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{13}{48}\right)\)	\(e\left(\frac{77}{144}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{89}{144}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{121}{144}\right)\)
\(\chi_{3648}(1307,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{121}{144}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{7}{48}\right)\)	\(e\left(\frac{71}{144}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{11}{144}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{91}{144}\right)\)
\(\chi_{3648}(1427,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{119}{144}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{41}{48}\right)\)	\(e\left(\frac{121}{144}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{37}{144}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{5}{144}\right)\)
\(\chi_{3648}(1523,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{143}{144}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{17}{48}\right)\)	\(e\left(\frac{97}{144}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{13}{144}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{29}{144}\right)\)
\(\chi_{3648}(1571,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{91}{144}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{101}{144}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{113}{144}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{97}{144}\right)\)
\(\chi_{3648}(1667,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{131}{144}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{29}{48}\right)\)	\(e\left(\frac{109}{144}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{25}{144}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{89}{144}\right)\)
\(\chi_{3648}(1739,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{133}{144}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{43}{48}\right)\)	\(e\left(\frac{59}{144}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{143}{144}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{31}{144}\right)\)
\(\chi_{3648}(1763,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{139}{144}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{37}{48}\right)\)	\(e\left(\frac{53}{144}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{65}{144}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{1}{144}\right)\)
\(\chi_{3648}(1883,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{137}{144}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{23}{48}\right)\)	\(e\left(\frac{103}{144}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{91}{144}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{59}{144}\right)\)
\(\chi_{3648}(1979,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{17}{144}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{47}{48}\right)\)	\(e\left(\frac{79}{144}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{67}{144}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{83}{144}\right)\)
\(\chi_{3648}(2027,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{109}{144}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{83}{144}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{23}{144}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{7}{144}\right)\)
\(\chi_{3648}(2123,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{5}{144}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{11}{48}\right)\)	\(e\left(\frac{91}{144}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{79}{144}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{143}{144}\right)\)
\(\chi_{3648}(2195,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{7}{144}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{25}{48}\right)\)	\(e\left(\frac{41}{144}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{53}{144}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{85}{144}\right)\)
\(\chi_{3648}(2219,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{13}{144}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{19}{48}\right)\)	\(e\left(\frac{35}{144}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{119}{144}\right)\)	\(e\left(\frac{1}{6}\right)\)	\(e\left(\frac{55}{144}\right)\)
\(\chi_{3648}(2339,\cdot)\)	\(-1\)	\(1\)	\(e\left(\frac{11}{144}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{5}{48}\right)\)	\(e\left(\frac{85}{144}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{1}{144}\right)\)	\(e\left(\frac{5}{6}\right)\)	\(e\left(\frac{113}{144}\right)\)

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more

Basic properties

Related number fields

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	3648.em
Modulus	$3648$
Conductor	$3648$
Order	$144$
Real	no
Primitive	yes
Minimal	yes
Parity	odd

Modulus:	\(3648\)
Conductor:	\(3648\)	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:	odd	sage:chi.is_odd() pari:zncharisodd(g,chi)