Basic properties
| Modulus: | \(5239\) | |
| Conductor: | \(5239\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(195\) | 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.dt
\(\chi_{5239}(14,\cdot)\) \(\chi_{5239}(40,\cdot)\) \(\chi_{5239}(131,\cdot)\) \(\chi_{5239}(144,\cdot)\) \(\chi_{5239}(183,\cdot)\) \(\chi_{5239}(196,\cdot)\) \(\chi_{5239}(235,\cdot)\) \(\chi_{5239}(391,\cdot)\) \(\chi_{5239}(417,\cdot)\) \(\chi_{5239}(443,\cdot)\) \(\chi_{5239}(534,\cdot)\) \(\chi_{5239}(547,\cdot)\) \(\chi_{5239}(586,\cdot)\) \(\chi_{5239}(599,\cdot)\) \(\chi_{5239}(638,\cdot)\) \(\chi_{5239}(794,\cdot)\) \(\chi_{5239}(820,\cdot)\) \(\chi_{5239}(937,\cdot)\) \(\chi_{5239}(950,\cdot)\) \(\chi_{5239}(989,\cdot)\) \(\chi_{5239}(1002,\cdot)\) \(\chi_{5239}(1041,\cdot)\) \(\chi_{5239}(1197,\cdot)\) \(\chi_{5239}(1223,\cdot)\) \(\chi_{5239}(1249,\cdot)\) \(\chi_{5239}(1340,\cdot)\) \(\chi_{5239}(1392,\cdot)\) \(\chi_{5239}(1405,\cdot)\) \(\chi_{5239}(1444,\cdot)\) \(\chi_{5239}(1600,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{195})$ |
| Fixed field: | Number field defined by a degree 195 polynomial (not computed) |
Values on generators
\((1861,1522)\) → \((e\left(\frac{7}{13}\right),e\left(\frac{4}{15}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 5239 }(950, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{65}\right)\) | \(e\left(\frac{7}{195}\right)\) | \(e\left(\frac{57}{65}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{16}{195}\right)\) | \(e\left(\frac{53}{65}\right)\) | \(e\left(\frac{14}{195}\right)\) | \(e\left(\frac{23}{195}\right)\) | \(e\left(\frac{116}{195}\right)\) |