Properties

Label 3920.fn
Modulus $3920$
Conductor $980$
Order $84$
Real no
Primitive no
Minimal yes
Parity odd

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(3920, base_ring=CyclotomicField(84))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([42,0,21,10]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(47,3920))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(3920\)
Conductor: \(980\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(84\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 980.bt
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: $\Q(\zeta_{84})$
Fixed field: Number field defined by a degree 84 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(9\) \(11\) \(13\) \(17\) \(19\) \(23\) \(27\) \(29\) \(31\)
\(\chi_{3920}(47,\cdot)\) \(-1\) \(1\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{3920}(143,\cdot)\) \(-1\) \(1\) \(e\left(\frac{41}{84}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{17}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{67}{84}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{3920}(367,\cdot)\) \(-1\) \(1\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{23}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{3920}(383,\cdot)\) \(-1\) \(1\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{37}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{3920}(703,\cdot)\) \(-1\) \(1\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{53}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{3920}(927,\cdot)\) \(-1\) \(1\) \(e\left(\frac{83}{84}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{3920}(943,\cdot)\) \(-1\) \(1\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{3920}(1167,\cdot)\) \(-1\) \(1\) \(e\left(\frac{67}{84}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{79}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{84}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{3920}(1263,\cdot)\) \(-1\) \(1\) \(e\left(\frac{17}{84}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{5}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{79}{84}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{3920}(1487,\cdot)\) \(-1\) \(1\) \(e\left(\frac{71}{84}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{73}{84}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{3920}(1503,\cdot)\) \(-1\) \(1\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{13}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{71}{84}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{3920}(1727,\cdot)\) \(-1\) \(1\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{67}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{17}{84}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{3}{14}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{3920}(1823,\cdot)\) \(-1\) \(1\) \(e\left(\frac{5}{84}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{41}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{3920}(2047,\cdot)\) \(-1\) \(1\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{37}{84}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{3920}(2063,\cdot)\) \(-1\) \(1\) \(e\left(\frac{37}{84}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{83}{84}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{3920}(2287,\cdot)\) \(-1\) \(1\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{55}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{3920}(2607,\cdot)\) \(-1\) \(1\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{83}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{1}{14}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{3920}(2623,\cdot)\) \(-1\) \(1\) \(e\left(\frac{13}{84}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{73}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{3920}(2847,\cdot)\) \(-1\) \(1\) \(e\left(\frac{79}{84}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{41}{84}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{3920}(2943,\cdot)\) \(-1\) \(1\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{55}{84}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{3920}(3183,\cdot)\) \(-1\) \(1\) \(e\left(\frac{73}{84}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{23}{84}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{9}{14}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{3920}(3407,\cdot)\) \(-1\) \(1\) \(e\left(\frac{55}{84}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{53}{84}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{11}{14}\right)\) \(e\left(\frac{1}{3}\right)\)
\(\chi_{3920}(3503,\cdot)\) \(-1\) \(1\) \(e\left(\frac{53}{84}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{5}{14}\right)\) \(e\left(\frac{2}{3}\right)\)
\(\chi_{3920}(3727,\cdot)\) \(-1\) \(1\) \(e\left(\frac{23}{84}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{71}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{13}{84}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{13}{14}\right)\) \(e\left(\frac{2}{3}\right)\)