Basic properties
| Modulus: | \(547\) | |
| Conductor: | \(547\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(273\) | 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 547.o
\(\chi_{547}(4,\cdot)\) \(\chi_{547}(6,\cdot)\) \(\chi_{547}(15,\cdot)\) \(\chi_{547}(16,\cdot)\) \(\chi_{547}(19,\cdot)\) \(\chi_{547}(25,\cdot)\) \(\chi_{547}(34,\cdot)\) \(\chi_{547}(36,\cdot)\) \(\chi_{547}(49,\cdot)\) \(\chi_{547}(51,\cdot)\) \(\chi_{547}(53,\cdot)\) \(\chi_{547}(56,\cdot)\) \(\chi_{547}(60,\cdot)\) \(\chi_{547}(62,\cdot)\) \(\chi_{547}(66,\cdot)\) \(\chi_{547}(67,\cdot)\) \(\chi_{547}(69,\cdot)\) \(\chi_{547}(73,\cdot)\) \(\chi_{547}(74,\cdot)\) \(\chi_{547}(76,\cdot)\) \(\chi_{547}(78,\cdot)\) \(\chi_{547}(82,\cdot)\) \(\chi_{547}(86,\cdot)\) \(\chi_{547}(97,\cdot)\) \(\chi_{547}(99,\cdot)\) \(\chi_{547}(110,\cdot)\) \(\chi_{547}(111,\cdot)\) \(\chi_{547}(113,\cdot)\) \(\chi_{547}(115,\cdot)\) \(\chi_{547}(116,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{273})$ |
| Fixed field: | Number field defined by a degree 273 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{157}{273}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 547 }(36, a) \) | \(1\) | \(1\) | \(e\left(\frac{157}{273}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{41}{273}\right)\) | \(e\left(\frac{257}{273}\right)\) | \(e\left(\frac{79}{273}\right)\) | \(e\left(\frac{64}{273}\right)\) | \(e\left(\frac{66}{91}\right)\) | \(e\left(\frac{3}{7}\right)\) | \(e\left(\frac{47}{91}\right)\) | \(e\left(\frac{10}{39}\right)\) |