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
\(2\) → \(e\left(\frac{185}{378}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 379 }(71, a) \) | \(-1\) | \(1\) | \(e\left(\frac{185}{378}\right)\) | \(e\left(\frac{19}{378}\right)\) | \(e\left(\frac{185}{189}\right)\) | \(e\left(\frac{10}{21}\right)\) | \(e\left(\frac{34}{63}\right)\) | \(e\left(\frac{325}{378}\right)\) | \(e\left(\frac{59}{126}\right)\) | \(e\left(\frac{19}{189}\right)\) | \(e\left(\frac{365}{378}\right)\) | \(e\left(\frac{11}{54}\right)\) |