Basic properties
| Modulus: | \(5239\) | |
| Conductor: | \(5239\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(390\) | 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.ec
\(\chi_{5239}(82,\cdot)\) \(\chi_{5239}(134,\cdot)\) \(\chi_{5239}(173,\cdot)\) \(\chi_{5239}(205,\cdot)\) \(\chi_{5239}(231,\cdot)\) \(\chi_{5239}(348,\cdot)\) \(\chi_{5239}(381,\cdot)\) \(\chi_{5239}(400,\cdot)\) \(\chi_{5239}(537,\cdot)\) \(\chi_{5239}(576,\cdot)\) \(\chi_{5239}(608,\cdot)\) \(\chi_{5239}(634,\cdot)\) \(\chi_{5239}(751,\cdot)\) \(\chi_{5239}(784,\cdot)\) \(\chi_{5239}(803,\cdot)\) \(\chi_{5239}(888,\cdot)\) \(\chi_{5239}(940,\cdot)\) \(\chi_{5239}(979,\cdot)\) \(\chi_{5239}(1011,\cdot)\) \(\chi_{5239}(1154,\cdot)\) \(\chi_{5239}(1187,\cdot)\) \(\chi_{5239}(1291,\cdot)\) \(\chi_{5239}(1343,\cdot)\) \(\chi_{5239}(1382,\cdot)\) \(\chi_{5239}(1414,\cdot)\) \(\chi_{5239}(1440,\cdot)\) \(\chi_{5239}(1557,\cdot)\) \(\chi_{5239}(1590,\cdot)\) \(\chi_{5239}(1609,\cdot)\) \(\chi_{5239}(1694,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{195})$ |
| Fixed field: | Number field defined by a degree 390 polynomial (not computed) |
Values on generators
\((1861,1522)\) → \((e\left(\frac{11}{78}\right),e\left(\frac{11}{15}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 5239 }(231, a) \) | \(1\) | \(1\) | \(e\left(\frac{289}{390}\right)\) | \(e\left(\frac{43}{195}\right)\) | \(e\left(\frac{94}{195}\right)\) | \(e\left(\frac{73}{78}\right)\) | \(e\left(\frac{25}{26}\right)\) | \(e\left(\frac{81}{130}\right)\) | \(e\left(\frac{29}{130}\right)\) | \(e\left(\frac{86}{195}\right)\) | \(e\left(\frac{44}{65}\right)\) | \(e\left(\frac{51}{130}\right)\) |