Basic properties
| Modulus: | \(379\) | |
| Conductor: | \(379\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(189\) | 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 379.o
\(\chi_{379}(4,\cdot)\) \(\chi_{379}(9,\cdot)\) \(\chi_{379}(16,\cdot)\) \(\chi_{379}(19,\cdot)\) \(\chi_{379}(20,\cdot)\) \(\chi_{379}(21,\cdot)\) \(\chi_{379}(22,\cdot)\) \(\chi_{379}(26,\cdot)\) \(\chi_{379}(34,\cdot)\) \(\chi_{379}(45,\cdot)\) \(\chi_{379}(49,\cdot)\) \(\chi_{379}(54,\cdot)\) \(\chi_{379}(56,\cdot)\) \(\chi_{379}(58,\cdot)\) \(\chi_{379}(62,\cdot)\) \(\chi_{379}(80,\cdot)\) \(\chi_{379}(81,\cdot)\) \(\chi_{379}(88,\cdot)\) \(\chi_{379}(92,\cdot)\) \(\chi_{379}(95,\cdot)\) \(\chi_{379}(96,\cdot)\) \(\chi_{379}(97,\cdot)\) \(\chi_{379}(100,\cdot)\) \(\chi_{379}(101,\cdot)\) \(\chi_{379}(103,\cdot)\) \(\chi_{379}(104,\cdot)\) \(\chi_{379}(105,\cdot)\) \(\chi_{379}(106,\cdot)\) \(\chi_{379}(110,\cdot)\) \(\chi_{379}(114,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{189})$ |
| Fixed field: | Number field defined by a degree 189 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{1}{189}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 379 }(4, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{189}\right)\) | \(e\left(\frac{137}{189}\right)\) | \(e\left(\frac{2}{189}\right)\) | \(e\left(\frac{16}{21}\right)\) | \(e\left(\frac{46}{63}\right)\) | \(e\left(\frac{155}{189}\right)\) | \(e\left(\frac{1}{63}\right)\) | \(e\left(\frac{85}{189}\right)\) | \(e\left(\frac{145}{189}\right)\) | \(e\left(\frac{4}{27}\right)\) |