Basic properties
Modulus: | \(361\) | |
Conductor: | \(361\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(57\) | 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 361.i
\(\chi_{361}(7,\cdot)\) \(\chi_{361}(11,\cdot)\) \(\chi_{361}(26,\cdot)\) \(\chi_{361}(30,\cdot)\) \(\chi_{361}(45,\cdot)\) \(\chi_{361}(49,\cdot)\) \(\chi_{361}(64,\cdot)\) \(\chi_{361}(83,\cdot)\) \(\chi_{361}(87,\cdot)\) \(\chi_{361}(102,\cdot)\) \(\chi_{361}(106,\cdot)\) \(\chi_{361}(121,\cdot)\) \(\chi_{361}(125,\cdot)\) \(\chi_{361}(140,\cdot)\) \(\chi_{361}(144,\cdot)\) \(\chi_{361}(159,\cdot)\) \(\chi_{361}(163,\cdot)\) \(\chi_{361}(178,\cdot)\) \(\chi_{361}(182,\cdot)\) \(\chi_{361}(197,\cdot)\) \(\chi_{361}(201,\cdot)\) \(\chi_{361}(216,\cdot)\) \(\chi_{361}(220,\cdot)\) \(\chi_{361}(235,\cdot)\) \(\chi_{361}(239,\cdot)\) \(\chi_{361}(254,\cdot)\) \(\chi_{361}(258,\cdot)\) \(\chi_{361}(273,\cdot)\) \(\chi_{361}(277,\cdot)\) \(\chi_{361}(296,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 57 polynomial |
Values on generators
\(2\) → \(e\left(\frac{35}{57}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 361 }(163, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{57}\right)\) | \(e\left(\frac{20}{57}\right)\) | \(e\left(\frac{13}{57}\right)\) | \(e\left(\frac{26}{57}\right)\) | \(e\left(\frac{55}{57}\right)\) | \(e\left(\frac{2}{19}\right)\) | \(e\left(\frac{16}{19}\right)\) | \(e\left(\frac{40}{57}\right)\) | \(e\left(\frac{4}{57}\right)\) | \(e\left(\frac{12}{19}\right)\) |