Properties

Label 1840.ck
Modulus $1840$
Conductor $1840$
Order $44$
Real no
Primitive yes
Minimal yes
Parity even

Related objects

Learn more

Show commands: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(1840, base_ring=CyclotomicField(44))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,33,22,36]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(29,1840))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(1840\)
Conductor: \(1840\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(44\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: yes
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: \(\Q(\zeta_{44})\)
Fixed field: Number field defined by a degree 44 polynomial

Characters in Galois orbit

Character \(-1\) \(1\) \(3\) \(7\) \(9\) \(11\) \(13\) \(17\) \(19\) \(21\) \(27\) \(29\)
\(\chi_{1840}(29,\cdot)\) \(1\) \(1\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{43}{44}\right)\)
\(\chi_{1840}(269,\cdot)\) \(1\) \(1\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{35}{44}\right)\)
\(\chi_{1840}(349,\cdot)\) \(1\) \(1\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{23}{44}\right)\)
\(\chi_{1840}(469,\cdot)\) \(1\) \(1\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{41}{44}\right)\)
\(\chi_{1840}(509,\cdot)\) \(1\) \(1\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{15}{44}\right)\)
\(\chi_{1840}(629,\cdot)\) \(1\) \(1\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{29}{44}\right)\)
\(\chi_{1840}(669,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{39}{44}\right)\)
\(\chi_{1840}(749,\cdot)\) \(1\) \(1\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{31}{44}\right)\)
\(\chi_{1840}(869,\cdot)\) \(1\) \(1\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{25}{44}\right)\)
\(\chi_{1840}(909,\cdot)\) \(1\) \(1\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{27}{44}\right)\)
\(\chi_{1840}(949,\cdot)\) \(1\) \(1\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{21}{44}\right)\)
\(\chi_{1840}(1189,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{13}{44}\right)\)
\(\chi_{1840}(1269,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{1}{44}\right)\)
\(\chi_{1840}(1389,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{1}{22}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{15}{22}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{19}{44}\right)\)
\(\chi_{1840}(1429,\cdot)\) \(1\) \(1\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{17}{22}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{37}{44}\right)\)
\(\chi_{1840}(1549,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{5}{22}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{7}{44}\right)\)
\(\chi_{1840}(1589,\cdot)\) \(1\) \(1\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{9}{22}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{3}{22}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{17}{44}\right)\)
\(\chi_{1840}(1669,\cdot)\) \(1\) \(1\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{9}{44}\right)\)
\(\chi_{1840}(1789,\cdot)\) \(1\) \(1\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{21}{22}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{7}{22}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{3}{44}\right)\)
\(\chi_{1840}(1829,\cdot)\) \(1\) \(1\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{13}{22}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{19}{22}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{5}{44}\right)\)