Properties

Label 4830.cw
Modulus $4830$
Conductor $2415$
Order $66$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(4830, base_ring=CyclotomicField(66))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([33,33,11,42]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(59,4830))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(4830\)
Conductor: \(2415\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(66\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 2415.de
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: \(\Q(\zeta_{33})\)
Fixed field: Number field defined by a degree 66 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(11\) \(13\) \(17\) \(19\) \(29\) \(31\) \(37\) \(41\) \(43\) \(47\)
\(\chi_{4830}(59,\cdot)\) \(1\) \(1\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{4830}(269,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{4830}(509,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{4830}(719,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{4830}(899,\cdot)\) \(1\) \(1\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{4830}(929,\cdot)\) \(1\) \(1\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{4830}(1139,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{13}{66}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{4830}(1319,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{4830}(1559,\cdot)\) \(1\) \(1\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{4830}(2189,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{4830}(2579,\cdot)\) \(1\) \(1\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{4830}(2789,\cdot)\) \(1\) \(1\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{4830}(2819,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{47}{66}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{4830}(2999,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{4830}(3029,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{66}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{4830}(3209,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{66}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{41}{66}\right)\) \(e\left(\frac{61}{66}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{4830}(3629,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{65}{66}\right)\) \(e\left(\frac{1}{66}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{5}{6}\right)\)
\(\chi_{4830}(3659,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{35}{66}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{25}{66}\right)\) \(e\left(\frac{5}{66}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{4830}(4079,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{66}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{49}{66}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{31}{66}\right)\) \(e\left(\frac{59}{66}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{1}{6}\right)\)
\(\chi_{4830}(4259,\cdot)\) \(1\) \(1\) \(e\left(\frac{53}{66}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{29}{66}\right)\) \(e\left(\frac{37}{66}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{17}{66}\right)\) \(e\left(\frac{43}{66}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{5}{6}\right)\)