Basic properties
| Modulus: | \(2169\) | |
| Conductor: | \(2169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | 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 2169.dh
\(\chi_{2169}(67,\cdot)\) \(\chi_{2169}(133,\cdot)\) \(\chi_{2169}(223,\cdot)\) \(\chi_{2169}(229,\cdot)\) \(\chi_{2169}(259,\cdot)\) \(\chi_{2169}(349,\cdot)\) \(\chi_{2169}(502,\cdot)\) \(\chi_{2169}(562,\cdot)\) \(\chi_{2169}(643,\cdot)\) \(\chi_{2169}(646,\cdot)\) \(\chi_{2169}(772,\cdot)\) \(\chi_{2169}(889,\cdot)\) \(\chi_{2169}(961,\cdot)\) \(\chi_{2169}(976,\cdot)\) \(\chi_{2169}(1138,\cdot)\) \(\chi_{2169}(1255,\cdot)\) \(\chi_{2169}(1258,\cdot)\) \(\chi_{2169}(1264,\cdot)\) \(\chi_{2169}(1393,\cdot)\) \(\chi_{2169}(1417,\cdot)\) \(\chi_{2169}(1615,\cdot)\) \(\chi_{2169}(1642,\cdot)\) \(\chi_{2169}(1690,\cdot)\) \(\chi_{2169}(1732,\cdot)\) \(\chi_{2169}(1759,\cdot)\) \(\chi_{2169}(1762,\cdot)\) \(\chi_{2169}(1879,\cdot)\) \(\chi_{2169}(1957,\cdot)\) \(\chi_{2169}(2005,\cdot)\) \(\chi_{2169}(2110,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((965,730)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{83}{120}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2169 }(67, a) \) | \(1\) | \(1\) | \(-i\) | \(-1\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(i\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(1\) |