Basic properties
| Modulus: | \(13520\) | |
| Conductor: | \(13520\) | 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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 13520.hv
\(\chi_{13520}(859,\cdot)\) \(\chi_{13520}(1379,\cdot)\) \(\chi_{13520}(1899,\cdot)\) \(\chi_{13520}(2419,\cdot)\) \(\chi_{13520}(2939,\cdot)\) \(\chi_{13520}(3459,\cdot)\) \(\chi_{13520}(3979,\cdot)\) \(\chi_{13520}(4499,\cdot)\) \(\chi_{13520}(5019,\cdot)\) \(\chi_{13520}(5539,\cdot)\) \(\chi_{13520}(6059,\cdot)\) \(\chi_{13520}(6579,\cdot)\) \(\chi_{13520}(7619,\cdot)\) \(\chi_{13520}(8139,\cdot)\) \(\chi_{13520}(8659,\cdot)\) \(\chi_{13520}(9179,\cdot)\) \(\chi_{13520}(9699,\cdot)\) \(\chi_{13520}(10219,\cdot)\) \(\chi_{13520}(10739,\cdot)\) \(\chi_{13520}(11259,\cdot)\) \(\chi_{13520}(11779,\cdot)\) \(\chi_{13520}(12299,\cdot)\) \(\chi_{13520}(12819,\cdot)\) \(\chi_{13520}(13339,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((5071,3381,10817,12001)\) → \((-1,i,-1,e\left(\frac{2}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) | \(29\) |
| \( \chi_{ 13520 }(10219, a) \) | \(-1\) | \(1\) | \(e\left(\frac{43}{52}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{31}{52}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(i\) | \(e\left(\frac{41}{52}\right)\) | \(-1\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{47}{52}\right)\) |