Properties

Label 3920.fm
Modulus $3920$
Conductor $1960$
Order $84$
Real no
Primitive no
Minimal no
Parity even

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([0,42,63,74]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(73,3920))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(3920\)
Conductor: \(1960\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(84\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 1960.dm
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: $\Q(\zeta_{84})$
Fixed field: Number field defined by a degree 84 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(9\) \(11\) \(13\) \(17\) \(19\) \(23\) \(27\) \(29\) \(31\)
\(\chi_{3920}(73,\cdot)\) \(1\) \(1\) \(e\left(\frac{53}{84}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{3920}(297,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{84}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{71}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{55}{84}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{3920}(537,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{23}{84}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{3920}(633,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{84}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{17}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{3920}(857,\cdot)\) \(1\) \(1\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{23}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{3920}(873,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{37}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{5}{84}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{3920}(1193,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{53}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{73}{84}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{3920}(1417,\cdot)\) \(1\) \(1\) \(e\left(\frac{83}{84}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{67}{84}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{3920}(1433,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{25}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{17}{84}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{3920}(1657,\cdot)\) \(1\) \(1\) \(e\left(\frac{67}{84}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{79}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{11}{28}\right)\) \(e\left(\frac{6}{7}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{3920}(1753,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{84}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{5}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{37}{84}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{3920}(1977,\cdot)\) \(1\) \(1\) \(e\left(\frac{71}{84}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{3920}(1993,\cdot)\) \(1\) \(1\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{13}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{3920}(2217,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{1}{42}\right)\) \(e\left(\frac{41}{42}\right)\) \(e\left(\frac{25}{28}\right)\) \(e\left(\frac{67}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{5}{7}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{3920}(2313,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{84}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{41}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{3920}(2537,\cdot)\) \(1\) \(1\) \(e\left(\frac{59}{84}\right)\) \(e\left(\frac{17}{42}\right)\) \(e\left(\frac{25}{42}\right)\) \(e\left(\frac{5}{28}\right)\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{79}{84}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{3920}(2553,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{84}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{1}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{41}{84}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{3920}(2777,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{84}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{55}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{71}{84}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{3920}(3097,\cdot)\) \(1\) \(1\) \(e\left(\frac{47}{84}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{83}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{4}{7}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{3920}(3113,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{84}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{3}{28}\right)\) \(e\left(\frac{73}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{53}{84}\right)\) \(e\left(\frac{13}{28}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{3920}(3337,\cdot)\) \(1\) \(1\) \(e\left(\frac{79}{84}\right)\) \(e\left(\frac{37}{42}\right)\) \(e\left(\frac{5}{42}\right)\) \(e\left(\frac{1}{28}\right)\) \(e\left(\frac{43}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{83}{84}\right)\) \(e\left(\frac{23}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{3920}(3433,\cdot)\) \(1\) \(1\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{23}{42}\right)\) \(e\left(\frac{19}{42}\right)\) \(e\left(\frac{15}{28}\right)\) \(e\left(\frac{29}{84}\right)\) \(e\left(\frac{5}{6}\right)\) \(e\left(\frac{13}{84}\right)\) \(e\left(\frac{9}{28}\right)\) \(e\left(\frac{3}{7}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{3920}(3673,\cdot)\) \(1\) \(1\) \(e\left(\frac{73}{84}\right)\) \(e\left(\frac{31}{42}\right)\) \(e\left(\frac{11}{42}\right)\) \(e\left(\frac{19}{28}\right)\) \(e\left(\frac{61}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{65}{84}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{1}{7}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{3920}(3897,\cdot)\) \(1\) \(1\) \(e\left(\frac{55}{84}\right)\) \(e\left(\frac{13}{42}\right)\) \(e\left(\frac{29}{42}\right)\) \(e\left(\frac{17}{28}\right)\) \(e\left(\frac{31}{84}\right)\) \(e\left(\frac{1}{6}\right)\) \(e\left(\frac{11}{84}\right)\) \(e\left(\frac{27}{28}\right)\) \(e\left(\frac{2}{7}\right)\) \(e\left(\frac{5}{6}\right)\)