Basic properties
| Modulus: | \(929\) | |
| Conductor: | \(929\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(29\) | 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 929.f
\(\chi_{929}(20,\cdot)\) \(\chi_{929}(72,\cdot)\) \(\chi_{929}(148,\cdot)\) \(\chi_{929}(173,\cdot)\) \(\chi_{929}(201,\cdot)\) \(\chi_{929}(212,\cdot)\) \(\chi_{929}(261,\cdot)\) \(\chi_{929}(304,\cdot)\) \(\chi_{929}(347,\cdot)\) \(\chi_{929}(352,\cdot)\) \(\chi_{929}(379,\cdot)\) \(\chi_{929}(400,\cdot)\) \(\chi_{929}(437,\cdot)\) \(\chi_{929}(445,\cdot)\) \(\chi_{929}(454,\cdot)\) \(\chi_{929}(506,\cdot)\) \(\chi_{929}(511,\cdot)\) \(\chi_{929}(521,\cdot)\) \(\chi_{929}(524,\cdot)\) \(\chi_{929}(537,\cdot)\) \(\chi_{929}(539,\cdot)\) \(\chi_{929}(561,\cdot)\) \(\chi_{929}(568,\cdot)\) \(\chi_{929}(575,\cdot)\) \(\chi_{929}(673,\cdot)\) \(\chi_{929}(719,\cdot)\) \(\chi_{929}(807,\cdot)\) \(\chi_{929}(830,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | Number field defined by a degree 29 polynomial |
Values on generators
\(3\) → \(e\left(\frac{8}{29}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 929 }(304, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{29}\right)\) | \(e\left(\frac{8}{29}\right)\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{19}{29}\right)\) | \(e\left(\frac{21}{29}\right)\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{10}{29}\right)\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{5}{29}\right)\) |