Basic properties
| Modulus: | \(379\) | |
| Conductor: | \(379\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(378\) | 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 379.p
\(\chi_{379}(2,\cdot)\) \(\chi_{379}(3,\cdot)\) \(\chi_{379}(7,\cdot)\) \(\chi_{379}(10,\cdot)\) \(\chi_{379}(12,\cdot)\) \(\chi_{379}(13,\cdot)\) \(\chi_{379}(15,\cdot)\) \(\chi_{379}(17,\cdot)\) \(\chi_{379}(18,\cdot)\) \(\chi_{379}(28,\cdot)\) \(\chi_{379}(31,\cdot)\) \(\chi_{379}(32,\cdot)\) \(\chi_{379}(35,\cdot)\) \(\chi_{379}(38,\cdot)\) \(\chi_{379}(42,\cdot)\) \(\chi_{379}(43,\cdot)\) \(\chi_{379}(46,\cdot)\) \(\chi_{379}(47,\cdot)\) \(\chi_{379}(50,\cdot)\) \(\chi_{379}(53,\cdot)\) \(\chi_{379}(55,\cdot)\) \(\chi_{379}(60,\cdot)\) \(\chi_{379}(65,\cdot)\) \(\chi_{379}(66,\cdot)\) \(\chi_{379}(71,\cdot)\) \(\chi_{379}(72,\cdot)\) \(\chi_{379}(74,\cdot)\) \(\chi_{379}(75,\cdot)\) \(\chi_{379}(78,\cdot)\) \(\chi_{379}(82,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{189})$ |
| Fixed field: | Number field defined by a degree 378 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{313}{378}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 379 }(13, a) \) | \(-1\) | \(1\) | \(e\left(\frac{313}{378}\right)\) | \(e\left(\frac{167}{378}\right)\) | \(e\left(\frac{124}{189}\right)\) | \(e\left(\frac{5}{21}\right)\) | \(e\left(\frac{17}{63}\right)\) | \(e\left(\frac{131}{378}\right)\) | \(e\left(\frac{61}{126}\right)\) | \(e\left(\frac{167}{189}\right)\) | \(e\left(\frac{25}{378}\right)\) | \(e\left(\frac{37}{54}\right)\) |