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.di
\(\chi_{2169}(61,\cdot)\) \(\chi_{2169}(79,\cdot)\) \(\chi_{2169}(193,\cdot)\) \(\chi_{2169}(214,\cdot)\) \(\chi_{2169}(268,\cdot)\) \(\chi_{2169}(403,\cdot)\) \(\chi_{2169}(421,\cdot)\) \(\chi_{2169}(529,\cdot)\) \(\chi_{2169}(598,\cdot)\) \(\chi_{2169}(607,\cdot)\) \(\chi_{2169}(682,\cdot)\) \(\chi_{2169}(718,\cdot)\) \(\chi_{2169}(916,\cdot)\) \(\chi_{2169}(1012,\cdot)\) \(\chi_{2169}(1210,\cdot)\) \(\chi_{2169}(1246,\cdot)\) \(\chi_{2169}(1321,\cdot)\) \(\chi_{2169}(1330,\cdot)\) \(\chi_{2169}(1399,\cdot)\) \(\chi_{2169}(1507,\cdot)\) \(\chi_{2169}(1525,\cdot)\) \(\chi_{2169}(1660,\cdot)\) \(\chi_{2169}(1714,\cdot)\) \(\chi_{2169}(1735,\cdot)\) \(\chi_{2169}(1849,\cdot)\) \(\chi_{2169}(1867,\cdot)\) \(\chi_{2169}(1933,\cdot)\) \(\chi_{2169}(1969,\cdot)\) \(\chi_{2169}(1975,\cdot)\) \(\chi_{2169}(2122,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((965,730)\) → \((e\left(\frac{2}{3}\right),e\left(\frac{7}{40}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2169 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{101}{120}\right)\) | \(-i\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{1}{24}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{91}{120}\right)\) | \(e\left(\frac{2}{3}\right)\) |