Basic properties
| Modulus: | \(361\) | |
| Conductor: | \(361\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(171\) | 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.k
\(\chi_{361}(4,\cdot)\) \(\chi_{361}(5,\cdot)\) \(\chi_{361}(6,\cdot)\) \(\chi_{361}(9,\cdot)\) \(\chi_{361}(16,\cdot)\) \(\chi_{361}(17,\cdot)\) \(\chi_{361}(23,\cdot)\) \(\chi_{361}(24,\cdot)\) \(\chi_{361}(25,\cdot)\) \(\chi_{361}(35,\cdot)\) \(\chi_{361}(36,\cdot)\) \(\chi_{361}(42,\cdot)\) \(\chi_{361}(43,\cdot)\) \(\chi_{361}(44,\cdot)\) \(\chi_{361}(47,\cdot)\) \(\chi_{361}(55,\cdot)\) \(\chi_{361}(61,\cdot)\) \(\chi_{361}(63,\cdot)\) \(\chi_{361}(66,\cdot)\) \(\chi_{361}(73,\cdot)\) \(\chi_{361}(74,\cdot)\) \(\chi_{361}(80,\cdot)\) \(\chi_{361}(81,\cdot)\) \(\chi_{361}(82,\cdot)\) \(\chi_{361}(85,\cdot)\) \(\chi_{361}(92,\cdot)\) \(\chi_{361}(93,\cdot)\) \(\chi_{361}(100,\cdot)\) \(\chi_{361}(101,\cdot)\) \(\chi_{361}(104,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 171 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{118}{171}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 361 }(80, a) \) | \(1\) | \(1\) | \(e\left(\frac{118}{171}\right)\) | \(e\left(\frac{157}{171}\right)\) | \(e\left(\frac{65}{171}\right)\) | \(e\left(\frac{16}{171}\right)\) | \(e\left(\frac{104}{171}\right)\) | \(e\left(\frac{29}{57}\right)\) | \(e\left(\frac{4}{57}\right)\) | \(e\left(\frac{143}{171}\right)\) | \(e\left(\frac{134}{171}\right)\) | \(e\left(\frac{22}{57}\right)\) |