sage: from sage.modular.dirichlet import DirichletCharacter
sage: H = DirichletGroup(5520, base_ring=CyclotomicField(44))
sage: M = H._module
sage: chi = DirichletCharacter(H, M([22,22,0,11,8]))
pari: [g,chi] = znchar(Mod(487,5520))
Basic properties
| Modulus: | \(5520\) | |
| Conductor: | \(920\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(44\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{920}(27,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5520.ev
\(\chi_{5520}(487,\cdot)\) \(\chi_{5520}(583,\cdot)\) \(\chi_{5520}(823,\cdot)\) \(\chi_{5520}(1543,\cdot)\) \(\chi_{5520}(1687,\cdot)\) \(\chi_{5520}(1783,\cdot)\) \(\chi_{5520}(1927,\cdot)\) \(\chi_{5520}(2263,\cdot)\) \(\chi_{5520}(2647,\cdot)\) \(\chi_{5520}(2743,\cdot)\) \(\chi_{5520}(2887,\cdot)\) \(\chi_{5520}(2983,\cdot)\) \(\chi_{5520}(3223,\cdot)\) \(\chi_{5520}(3367,\cdot)\) \(\chi_{5520}(3463,\cdot)\) \(\chi_{5520}(3847,\cdot)\) \(\chi_{5520}(4087,\cdot)\) \(\chi_{5520}(4327,\cdot)\) \(\chi_{5520}(4567,\cdot)\) \(\chi_{5520}(4903,\cdot)\)
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: | \(\Q(\zeta_{44})\) |
| Fixed field: | 44.44.25298996654427333182343480348559113656901710330851609956835131392000000000000000000000000000000000.1 |
Values on generators
\((4831,1381,1841,4417,1201)\) → \((-1,-1,1,i,e\left(\frac{2}{11}\right))\)
Values
| \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(29\) | \(31\) | \(37\) | \(41\) | \(43\) |
| \(1\) | \(1\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{7}{11}\right)\) | \(e\left(\frac{35}{44}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{5}{22}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{13}{22}\right)\) | \(e\left(\frac{25}{44}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{29}{44}\right)\) |