Basic properties
| Modulus: | \(5239\) | |
| Conductor: | \(5239\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(260\) | 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 5239.du
\(\chi_{5239}(60,\cdot)\) \(\chi_{5239}(122,\cdot)\) \(\chi_{5239}(151,\cdot)\) \(\chi_{5239}(213,\cdot)\) \(\chi_{5239}(294,\cdot)\) \(\chi_{5239}(333,\cdot)\) \(\chi_{5239}(356,\cdot)\) \(\chi_{5239}(395,\cdot)\) \(\chi_{5239}(463,\cdot)\) \(\chi_{5239}(525,\cdot)\) \(\chi_{5239}(554,\cdot)\) \(\chi_{5239}(616,\cdot)\) \(\chi_{5239}(697,\cdot)\) \(\chi_{5239}(736,\cdot)\) \(\chi_{5239}(759,\cdot)\) \(\chi_{5239}(798,\cdot)\) \(\chi_{5239}(866,\cdot)\) \(\chi_{5239}(928,\cdot)\) \(\chi_{5239}(957,\cdot)\) \(\chi_{5239}(1019,\cdot)\) \(\chi_{5239}(1100,\cdot)\) \(\chi_{5239}(1139,\cdot)\) \(\chi_{5239}(1162,\cdot)\) \(\chi_{5239}(1201,\cdot)\) \(\chi_{5239}(1269,\cdot)\) \(\chi_{5239}(1331,\cdot)\) \(\chi_{5239}(1360,\cdot)\) \(\chi_{5239}(1503,\cdot)\) \(\chi_{5239}(1542,\cdot)\) \(\chi_{5239}(1565,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{260})$ |
| Fixed field: | Number field defined by a degree 260 polynomial (not computed) |
Values on generators
\((1861,1522)\) → \((e\left(\frac{31}{52}\right),e\left(\frac{9}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 5239 }(1201, a) \) | \(1\) | \(1\) | \(e\left(\frac{51}{260}\right)\) | \(e\left(\frac{107}{130}\right)\) | \(e\left(\frac{51}{130}\right)\) | \(e\left(\frac{19}{52}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{257}{260}\right)\) | \(e\left(\frac{153}{260}\right)\) | \(e\left(\frac{42}{65}\right)\) | \(e\left(\frac{73}{130}\right)\) | \(e\left(\frac{27}{260}\right)\) |