Basic properties
| Modulus: | \(6336\) | |
| Conductor: | \(3168\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3168}(421,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6336.fu
\(\chi_{6336}(25,\cdot)\) \(\chi_{6336}(169,\cdot)\) \(\chi_{6336}(313,\cdot)\) \(\chi_{6336}(553,\cdot)\) \(\chi_{6336}(697,\cdot)\) \(\chi_{6336}(841,\cdot)\) \(\chi_{6336}(889,\cdot)\) \(\chi_{6336}(1417,\cdot)\) \(\chi_{6336}(1609,\cdot)\) \(\chi_{6336}(1753,\cdot)\) \(\chi_{6336}(1897,\cdot)\) \(\chi_{6336}(2137,\cdot)\) \(\chi_{6336}(2281,\cdot)\) \(\chi_{6336}(2425,\cdot)\) \(\chi_{6336}(2473,\cdot)\) \(\chi_{6336}(3001,\cdot)\) \(\chi_{6336}(3193,\cdot)\) \(\chi_{6336}(3337,\cdot)\) \(\chi_{6336}(3481,\cdot)\) \(\chi_{6336}(3721,\cdot)\) \(\chi_{6336}(3865,\cdot)\) \(\chi_{6336}(4009,\cdot)\) \(\chi_{6336}(4057,\cdot)\) \(\chi_{6336}(4585,\cdot)\) \(\chi_{6336}(4777,\cdot)\) \(\chi_{6336}(4921,\cdot)\) \(\chi_{6336}(5065,\cdot)\) \(\chi_{6336}(5305,\cdot)\) \(\chi_{6336}(5449,\cdot)\) \(\chi_{6336}(5593,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((4159,4357,3521,1729)\) → \((1,e\left(\frac{1}{8}\right),e\left(\frac{2}{3}\right),e\left(\frac{4}{5}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 6336 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{31}{60}\right)\) | \(e\left(\frac{1}{120}\right)\) | \(e\left(\frac{7}{10}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{7}{40}\right)\) |