Basic properties
| Modulus: | \(4056\) | |
| Conductor: | \(4056\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | 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)
|
Galois orbit 4056.cp
\(\chi_{4056}(5,\cdot)\) \(\chi_{4056}(125,\cdot)\) \(\chi_{4056}(317,\cdot)\) \(\chi_{4056}(629,\cdot)\) \(\chi_{4056}(749,\cdot)\) \(\chi_{4056}(941,\cdot)\) \(\chi_{4056}(1061,\cdot)\) \(\chi_{4056}(1373,\cdot)\) \(\chi_{4056}(1565,\cdot)\) \(\chi_{4056}(1685,\cdot)\) \(\chi_{4056}(1877,\cdot)\) \(\chi_{4056}(1997,\cdot)\) \(\chi_{4056}(2189,\cdot)\) \(\chi_{4056}(2309,\cdot)\) \(\chi_{4056}(2501,\cdot)\) \(\chi_{4056}(2621,\cdot)\) \(\chi_{4056}(2813,\cdot)\) \(\chi_{4056}(2933,\cdot)\) \(\chi_{4056}(3125,\cdot)\) \(\chi_{4056}(3245,\cdot)\) \(\chi_{4056}(3437,\cdot)\) \(\chi_{4056}(3557,\cdot)\) \(\chi_{4056}(3749,\cdot)\) \(\chi_{4056}(3869,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((1015,2029,2705,3889)\) → \((1,-1,-1,e\left(\frac{7}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 4056 }(3749, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{52}\right)\) | \(e\left(\frac{21}{52}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(e\left(\frac{2}{13}\right)\) | \(i\) | \(1\) | \(e\left(\frac{11}{26}\right)\) | \(e\left(\frac{5}{13}\right)\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{8}{13}\right)\) |