LMFDB - Dirichlet character orbit 3648.ec

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(3648, base_ring=CyclotomicField(72)) M = H._module chi = DirichletCharacter(H, M([36,9,0,68])) chi.galois_orbit()

pari:[g,chi] = znchar(Mod(295,3648)) order = charorder(g,chi) [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]

Basic properties

Modulus:	$3648$
Conductor:	$608$	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	$72$	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 608.bt	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:	$\Q(\zeta_{72})$
Fixed field:	Number field defined by a degree 72 polynomial

Characters in Galois orbit

Character	$-1$	$1$	$5$	$7$	$11$	$13$	$17$	$23$	$25$	$29$	$31$	$35$
$\chi_{3648}(295,\cdot)$	$1$	$1$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{47}{72}\right)$
$\chi_{3648}(439,\cdot)$	$1$	$1$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{61}{72}\right)$
$\chi_{3648}(535,\cdot)$	$1$	$1$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{72}\right)$
$\chi_{3648}(583,\cdot)$	$1$	$1$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{35}{72}\right)$
$\chi_{3648}(679,\cdot)$	$1$	$1$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{31}{72}\right)$
$\chi_{3648}(775,\cdot)$	$1$	$1$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{31}{72}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{59}{72}\right)$
$\chi_{3648}(1207,\cdot)$	$1$	$1$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{29}{72}\right)$
$\chi_{3648}(1351,\cdot)$	$1$	$1$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{43}{72}\right)$
$\chi_{3648}(1447,\cdot)$	$1$	$1$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{55}{72}\right)$
$\chi_{3648}(1495,\cdot)$	$1$	$1$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{25}{72}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{17}{72}\right)$
$\chi_{3648}(1591,\cdot)$	$1$	$1$	$e\left(\frac{43}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{13}{72}\right)$
$\chi_{3648}(1687,\cdot)$	$1$	$1$	$e\left(\frac{47}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{41}{72}\right)$
$\chi_{3648}(2119,\cdot)$	$1$	$1$	$e\left(\frac{53}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{23}{24}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{11}{72}\right)$
$\chi_{3648}(2263,\cdot)$	$1$	$1$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{25}{72}\right)$
$\chi_{3648}(2359,\cdot)$	$1$	$1$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{1}{24}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{31}{36}\right)$	$e\left(\frac{29}{72}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{37}{72}\right)$
$\chi_{3648}(2407,\cdot)$	$1$	$1$	$e\left(\frac{41}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{19}{72}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{5}{36}\right)$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{71}{72}\right)$
$\chi_{3648}(2503,\cdot)$	$1$	$1$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{35}{72}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{67}{72}\right)$
$\chi_{3648}(2599,\cdot)$	$1$	$1$	$e\left(\frac{65}{72}\right)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{11}{24}\right)$	$e\left(\frac{67}{72}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{17}{36}\right)$	$e\left(\frac{29}{36}\right)$	$e\left(\frac{55}{72}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{23}{72}\right)$
$\chi_{3648}(3031,\cdot)$	$1$	$1$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{5}{24}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{17}{18}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{65}{72}\right)$
$\chi_{3648}(3175,\cdot)$	$1$	$1$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{19}{24}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{1}{18}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{1}{36}\right)$	$e\left(\frac{23}{72}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{7}{72}\right)$
$\chi_{3648}(3271,\cdot)$	$1$	$1$	$e\left(\frac{13}{72}\right)$	$e\left(\frac{1}{12}\right)$	$e\left(\frac{7}{24}\right)$	$e\left(\frac{71}{72}\right)$	$e\left(\frac{13}{18}\right)$	$e\left(\frac{25}{36}\right)$	$e\left(\frac{13}{36}\right)$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{19}{72}\right)$
$\chi_{3648}(3319,\cdot)$	$1$	$1$	$e\left(\frac{59}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{1}{72}\right)$	$e\left(\frac{5}{18}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{23}{36}\right)$	$e\left(\frac{61}{72}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{53}{72}\right)$
$\chi_{3648}(3415,\cdot)$	$1$	$1$	$e\left(\frac{7}{72}\right)$	$e\left(\frac{7}{12}\right)$	$e\left(\frac{13}{24}\right)$	$e\left(\frac{5}{72}\right)$	$e\left(\frac{7}{18}\right)$	$e\left(\frac{19}{36}\right)$	$e\left(\frac{7}{36}\right)$	$e\left(\frac{17}{72}\right)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{49}{72}\right)$
$\chi_{3648}(3511,\cdot)$	$1$	$1$	$e\left(\frac{11}{72}\right)$	$e\left(\frac{11}{12}\right)$	$e\left(\frac{17}{24}\right)$	$e\left(\frac{49}{72}\right)$	$e\left(\frac{11}{18}\right)$	$e\left(\frac{35}{36}\right)$	$e\left(\frac{11}{36}\right)$	$e\left(\frac{37}{72}\right)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{5}{72}\right)$

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	\(-1\)	\(1\)	\(5\)	\(7\)	\(11\)	\(13\)	\(17\)	\(23\)	\(25\)	\(29\)	\(31\)	\(35\)
\(\chi_{3648}(295,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{47}{72}\right)\)
\(\chi_{3648}(439,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{61}{72}\right)\)
\(\chi_{3648}(535,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{1}{72}\right)\)
\(\chi_{3648}(583,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{35}{72}\right)\)
\(\chi_{3648}(679,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{31}{72}\right)\)
\(\chi_{3648}(775,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{31}{72}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{59}{72}\right)\)
\(\chi_{3648}(1207,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{29}{72}\right)\)
\(\chi_{3648}(1351,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{43}{72}\right)\)
\(\chi_{3648}(1447,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{55}{72}\right)\)
\(\chi_{3648}(1495,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{25}{72}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{17}{72}\right)\)
\(\chi_{3648}(1591,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{43}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{13}{72}\right)\)
\(\chi_{3648}(1687,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{47}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{41}{72}\right)\)
\(\chi_{3648}(2119,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{53}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{23}{24}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{11}{72}\right)\)
\(\chi_{3648}(2263,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{25}{72}\right)\)
\(\chi_{3648}(2359,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{1}{24}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{31}{36}\right)\)	\(e\left(\frac{29}{72}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{37}{72}\right)\)
\(\chi_{3648}(2407,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{41}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{19}{72}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{5}{36}\right)\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{71}{72}\right)\)
\(\chi_{3648}(2503,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{35}{72}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{67}{72}\right)\)
\(\chi_{3648}(2599,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{65}{72}\right)\)	\(e\left(\frac{5}{12}\right)\)	\(e\left(\frac{11}{24}\right)\)	\(e\left(\frac{67}{72}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{17}{36}\right)\)	\(e\left(\frac{29}{36}\right)\)	\(e\left(\frac{55}{72}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{23}{72}\right)\)
\(\chi_{3648}(3031,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{5}{24}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{17}{18}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{65}{72}\right)\)
\(\chi_{3648}(3175,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{19}{24}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{1}{18}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{1}{36}\right)\)	\(e\left(\frac{23}{72}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{7}{72}\right)\)
\(\chi_{3648}(3271,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{13}{72}\right)\)	\(e\left(\frac{1}{12}\right)\)	\(e\left(\frac{7}{24}\right)\)	\(e\left(\frac{71}{72}\right)\)	\(e\left(\frac{13}{18}\right)\)	\(e\left(\frac{25}{36}\right)\)	\(e\left(\frac{13}{36}\right)\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{19}{72}\right)\)
\(\chi_{3648}(3319,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{59}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{1}{72}\right)\)	\(e\left(\frac{5}{18}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{23}{36}\right)\)	\(e\left(\frac{61}{72}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{53}{72}\right)\)
\(\chi_{3648}(3415,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{7}{72}\right)\)	\(e\left(\frac{7}{12}\right)\)	\(e\left(\frac{13}{24}\right)\)	\(e\left(\frac{5}{72}\right)\)	\(e\left(\frac{7}{18}\right)\)	\(e\left(\frac{19}{36}\right)\)	\(e\left(\frac{7}{36}\right)\)	\(e\left(\frac{17}{72}\right)\)	\(e\left(\frac{1}{3}\right)\)	\(e\left(\frac{49}{72}\right)\)
\(\chi_{3648}(3511,\cdot)\)	\(1\)	\(1\)	\(e\left(\frac{11}{72}\right)\)	\(e\left(\frac{11}{12}\right)\)	\(e\left(\frac{17}{24}\right)\)	\(e\left(\frac{49}{72}\right)\)	\(e\left(\frac{11}{18}\right)\)	\(e\left(\frac{35}{36}\right)\)	\(e\left(\frac{11}{36}\right)\)	\(e\left(\frac{37}{72}\right)\)	\(e\left(\frac{2}{3}\right)\)	\(e\left(\frac{5}{72}\right)\)

Introduction

L-functions

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Varieties

Fields

Representations

Groups

Database

Properties

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Basic properties

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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.ec
Modulus	$3648$
Conductor	$608$
Order	$72$
Real	no
Primitive	no
Minimal	no
Parity	even

Modulus:	\(3648\)
Conductor:	\(608\)	sage:chi.conductor() pari:znconreyconductor(g,chi)
Order:	\(72\)	sage:chi.multiplicative_order() pari:charorder(g,chi)
Real:	no
Primitive:	no, induced from 608.bt	sage:chi.is_primitive() pari:#znconreyconductor(g,chi)==1
Minimal:	no
Parity:	even	sage:chi.is_odd() pari:zncharisodd(g,chi)