Basic properties
| Modulus: | \(361\) | |
| Conductor: | \(361\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(342\) | 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 361.l
\(\chi_{361}(2,\cdot)\) \(\chi_{361}(3,\cdot)\) \(\chi_{361}(10,\cdot)\) \(\chi_{361}(13,\cdot)\) \(\chi_{361}(14,\cdot)\) \(\chi_{361}(15,\cdot)\) \(\chi_{361}(21,\cdot)\) \(\chi_{361}(22,\cdot)\) \(\chi_{361}(29,\cdot)\) \(\chi_{361}(32,\cdot)\) \(\chi_{361}(33,\cdot)\) \(\chi_{361}(34,\cdot)\) \(\chi_{361}(40,\cdot)\) \(\chi_{361}(41,\cdot)\) \(\chi_{361}(48,\cdot)\) \(\chi_{361}(51,\cdot)\) \(\chi_{361}(52,\cdot)\) \(\chi_{361}(53,\cdot)\) \(\chi_{361}(59,\cdot)\) \(\chi_{361}(60,\cdot)\) \(\chi_{361}(67,\cdot)\) \(\chi_{361}(70,\cdot)\) \(\chi_{361}(71,\cdot)\) \(\chi_{361}(72,\cdot)\) \(\chi_{361}(78,\cdot)\) \(\chi_{361}(79,\cdot)\) \(\chi_{361}(86,\cdot)\) \(\chi_{361}(89,\cdot)\) \(\chi_{361}(90,\cdot)\) \(\chi_{361}(91,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 342 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{281}{342}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 361 }(72, a) \) | \(-1\) | \(1\) | \(e\left(\frac{281}{342}\right)\) | \(e\left(\frac{71}{342}\right)\) | \(e\left(\frac{110}{171}\right)\) | \(e\left(\frac{106}{171}\right)\) | \(e\left(\frac{5}{171}\right)\) | \(e\left(\frac{14}{57}\right)\) | \(e\left(\frac{53}{114}\right)\) | \(e\left(\frac{71}{171}\right)\) | \(e\left(\frac{151}{342}\right)\) | \(e\left(\frac{46}{57}\right)\) |