Properties

Label 5520.ei
Modulus $5520$
Conductor $1104$
Order $44$
Real no
Primitive no
Minimal yes
Parity even

Related objects

Learn more

Show commands for: Pari/GP / SageMath
sage: from sage.modular.dirichlet import DirichletCharacter
 
sage: H = DirichletGroup(5520, base_ring=CyclotomicField(44))
 
sage: M = H._module
 
sage: chi = DirichletCharacter(H, M([0,33,22,0,42]))
 
sage: chi.galois_orbit()
 
pari: [g,chi] = znchar(Mod(221,5520))
 
pari: order = charorder(g,chi)
 
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
 

Basic properties

Modulus: \(5520\)
Conductor: \(1104\)
sage: chi.conductor()
 
pari: znconreyconductor(g,chi)
 
Order: \(44\)
sage: chi.multiplicative_order()
 
pari: charorder(g,chi)
 
Real: no
Primitive: no, induced from 1104.bo
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 \(-1\) \(1\) \(7\) \(11\) \(13\) \(17\) \(19\) \(29\) \(31\) \(37\) \(41\) \(43\)
\(\chi_{5520}(221,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{23}{44}\right)\)
\(\chi_{5520}(341,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{29}{44}\right)\)
\(\chi_{5520}(701,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{35}{44}\right)\)
\(\chi_{5520}(941,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{31}{44}\right)\)
\(\chi_{5520}(1661,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{43}{44}\right)\)
\(\chi_{5520}(1781,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{41}{44}\right)\)
\(\chi_{5520}(1901,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{27}{44}\right)\)
\(\chi_{5520}(2021,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{17}{44}\right)\)
\(\chi_{5520}(2261,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{25}{44}\right)\)
\(\chi_{5520}(2501,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{43}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{41}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{37}{44}\right)\)
\(\chi_{5520}(2981,\cdot)\) \(1\) \(1\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{1}{44}\right)\)
\(\chi_{5520}(3101,\cdot)\) \(1\) \(1\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{35}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{7}{44}\right)\)
\(\chi_{5520}(3461,\cdot)\) \(1\) \(1\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{13}{44}\right)\)
\(\chi_{5520}(3701,\cdot)\) \(1\) \(1\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{9}{44}\right)\)
\(\chi_{5520}(4421,\cdot)\) \(1\) \(1\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{17}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{3}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{21}{44}\right)\)
\(\chi_{5520}(4541,\cdot)\) \(1\) \(1\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{5}{11}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{27}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{19}{44}\right)\)
\(\chi_{5520}(4661,\cdot)\) \(1\) \(1\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{25}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{7}{44}\right)\) \(e\left(\frac{7}{11}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{3}{11}\right)\) \(e\left(\frac{5}{44}\right)\)
\(\chi_{5520}(4781,\cdot)\) \(1\) \(1\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{1}{11}\right)\) \(e\left(\frac{29}{44}\right)\) \(e\left(\frac{37}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{23}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{39}{44}\right)\)
\(\chi_{5520}(5021,\cdot)\) \(1\) \(1\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{15}{44}\right)\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{9}{44}\right)\) \(e\left(\frac{13}{44}\right)\) \(e\left(\frac{2}{11}\right)\) \(e\left(\frac{39}{44}\right)\) \(e\left(\frac{4}{11}\right)\) \(e\left(\frac{3}{44}\right)\)
\(\chi_{5520}(5261,\cdot)\) \(1\) \(1\) \(e\left(\frac{6}{11}\right)\) \(e\left(\frac{5}{44}\right)\) \(e\left(\frac{31}{44}\right)\) \(e\left(\frac{8}{11}\right)\) \(e\left(\frac{1}{44}\right)\) \(e\left(\frac{21}{44}\right)\) \(e\left(\frac{10}{11}\right)\) \(e\left(\frac{19}{44}\right)\) \(e\left(\frac{9}{11}\right)\) \(e\left(\frac{15}{44}\right)\)