Basic properties
| Modulus: | \(6023\) | |
| Conductor: | \(317\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(79\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{317}(121,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6023.s
\(\chi_{6023}(438,\cdot)\) \(\chi_{6023}(552,\cdot)\) \(\chi_{6023}(590,\cdot)\) \(\chi_{6023}(609,\cdot)\) \(\chi_{6023}(628,\cdot)\) \(\chi_{6023}(685,\cdot)\) \(\chi_{6023}(723,\cdot)\) \(\chi_{6023}(799,\cdot)\) \(\chi_{6023}(856,\cdot)\) \(\chi_{6023}(989,\cdot)\) \(\chi_{6023}(1008,\cdot)\) \(\chi_{6023}(1198,\cdot)\) \(\chi_{6023}(1331,\cdot)\) \(\chi_{6023}(1369,\cdot)\) \(\chi_{6023}(1502,\cdot)\) \(\chi_{6023}(1521,\cdot)\) \(\chi_{6023}(1559,\cdot)\) \(\chi_{6023}(1578,\cdot)\) \(\chi_{6023}(1616,\cdot)\) \(\chi_{6023}(1730,\cdot)\) \(\chi_{6023}(1806,\cdot)\) \(\chi_{6023}(1825,\cdot)\) \(\chi_{6023}(1844,\cdot)\) \(\chi_{6023}(1863,\cdot)\) \(\chi_{6023}(2015,\cdot)\) \(\chi_{6023}(2129,\cdot)\) \(\chi_{6023}(2243,\cdot)\) \(\chi_{6023}(2262,\cdot)\) \(\chi_{6023}(2300,\cdot)\) \(\chi_{6023}(2319,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{79})$ |
| Fixed field: | Number field defined by a degree 79 polynomial |
Values on generators
\((952,5074)\) → \((1,e\left(\frac{65}{79}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 6023 }(438, a) \) | \(1\) | \(1\) | \(e\left(\frac{65}{79}\right)\) | \(e\left(\frac{69}{79}\right)\) | \(e\left(\frac{51}{79}\right)\) | \(e\left(\frac{74}{79}\right)\) | \(e\left(\frac{55}{79}\right)\) | \(e\left(\frac{11}{79}\right)\) | \(e\left(\frac{37}{79}\right)\) | \(e\left(\frac{59}{79}\right)\) | \(e\left(\frac{60}{79}\right)\) | \(e\left(\frac{76}{79}\right)\) |