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
\(2\) → \(e\left(\frac{34}{57}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 361 }(121, a) \) | \(1\) | \(1\) | \(e\left(\frac{34}{57}\right)\) | \(e\left(\frac{52}{57}\right)\) | \(e\left(\frac{11}{57}\right)\) | \(e\left(\frac{22}{57}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{9}{19}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{47}{57}\right)\) | \(e\left(\frac{56}{57}\right)\) | \(e\left(\frac{16}{19}\right)\) |