Basic properties
| Modulus: | \(1321\) | |
| Conductor: | \(1321\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1320\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1321.bf
\(\chi_{1321}(13,\cdot)\) \(\chi_{1321}(19,\cdot)\) \(\chi_{1321}(21,\cdot)\) \(\chi_{1321}(23,\cdot)\) \(\chi_{1321}(28,\cdot)\) \(\chi_{1321}(35,\cdot)\) \(\chi_{1321}(38,\cdot)\) \(\chi_{1321}(47,\cdot)\) \(\chi_{1321}(51,\cdot)\) \(\chi_{1321}(56,\cdot)\) \(\chi_{1321}(57,\cdot)\) \(\chi_{1321}(63,\cdot)\) \(\chi_{1321}(65,\cdot)\) \(\chi_{1321}(70,\cdot)\) \(\chi_{1321}(83,\cdot)\) \(\chi_{1321}(84,\cdot)\) \(\chi_{1321}(85,\cdot)\) \(\chi_{1321}(89,\cdot)\) \(\chi_{1321}(97,\cdot)\) \(\chi_{1321}(103,\cdot)\) \(\chi_{1321}(104,\cdot)\) \(\chi_{1321}(105,\cdot)\) \(\chi_{1321}(113,\cdot)\) \(\chi_{1321}(115,\cdot)\) \(\chi_{1321}(117,\cdot)\) \(\chi_{1321}(118,\cdot)\) \(\chi_{1321}(122,\cdot)\) \(\chi_{1321}(139,\cdot)\) \(\chi_{1321}(141,\cdot)\) \(\chi_{1321}(146,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1320})$ |
| Fixed field: | Number field defined by a degree 1320 polynomial (not computed) |
Values on generators
\(13\) → \(e\left(\frac{661}{1320}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1321 }(1308, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{6}{55}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{551}{660}\right)\) | \(e\left(\frac{193}{660}\right)\) | \(e\left(\frac{245}{264}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{12}{55}\right)\) | \(e\left(\frac{1}{55}\right)\) | \(e\left(\frac{1}{165}\right)\) |