sage: from sage.modular.dirichlet import DirichletCharacter
sage: H = DirichletGroup(5520, base_ring=CyclotomicField(22))
sage: M = H._module
sage: chi = DirichletCharacter(H, M([11,0,11,0,4]))
pari: [g,chi] = znchar(Mod(671,5520))
Basic properties
| Modulus: | \(5520\) | |
| Conductor: | \(276\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(22\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{276}(119,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5520.dv
\(\chi_{5520}(671,\cdot)\) \(\chi_{5520}(1871,\cdot)\) \(\chi_{5520}(2111,\cdot)\) \(\chi_{5520}(2831,\cdot)\) \(\chi_{5520}(3071,\cdot)\) \(\chi_{5520}(3551,\cdot)\) \(\chi_{5520}(4031,\cdot)\) \(\chi_{5520}(4271,\cdot)\) \(\chi_{5520}(4511,\cdot)\) \(\chi_{5520}(4751,\cdot)\)
sage: chi.galois_orbit()
pari: order = charorder(g,chi)
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
Related number fields
| Field of values: | \(\Q(\zeta_{11})\) |
| Fixed field: | 22.22.1275118148086621135238339811277472268288.1 |
Values on generators
\((4831,1381,1841,4417,1201)\) → \((-1,1,-1,1,e\left(\frac{2}{11}\right))\)
Values
| \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \(1\) | \(1\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{6}{11}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{17}{22}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{9}{11}\right)\) | \(e\left(\frac{15}{22}\right)\) | \(e\left(\frac{9}{22}\right)\) |