Basic properties
| Modulus: | \(243\) | |
| Conductor: | \(243\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(81\) | 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 243.i
\(\chi_{243}(4,\cdot)\) \(\chi_{243}(7,\cdot)\) \(\chi_{243}(13,\cdot)\) \(\chi_{243}(16,\cdot)\) \(\chi_{243}(22,\cdot)\) \(\chi_{243}(25,\cdot)\) \(\chi_{243}(31,\cdot)\) \(\chi_{243}(34,\cdot)\) \(\chi_{243}(40,\cdot)\) \(\chi_{243}(43,\cdot)\) \(\chi_{243}(49,\cdot)\) \(\chi_{243}(52,\cdot)\) \(\chi_{243}(58,\cdot)\) \(\chi_{243}(61,\cdot)\) \(\chi_{243}(67,\cdot)\) \(\chi_{243}(70,\cdot)\) \(\chi_{243}(76,\cdot)\) \(\chi_{243}(79,\cdot)\) \(\chi_{243}(85,\cdot)\) \(\chi_{243}(88,\cdot)\) \(\chi_{243}(94,\cdot)\) \(\chi_{243}(97,\cdot)\) \(\chi_{243}(103,\cdot)\) \(\chi_{243}(106,\cdot)\) \(\chi_{243}(112,\cdot)\) \(\chi_{243}(115,\cdot)\) \(\chi_{243}(121,\cdot)\) \(\chi_{243}(124,\cdot)\) \(\chi_{243}(130,\cdot)\) \(\chi_{243}(133,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{81})$ |
| Fixed field: | Number field defined by a degree 81 polynomial |
Values on generators
\(2\) → \(e\left(\frac{77}{81}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 243 }(187, a) \) | \(1\) | \(1\) | \(e\left(\frac{77}{81}\right)\) | \(e\left(\frac{73}{81}\right)\) | \(e\left(\frac{70}{81}\right)\) | \(e\left(\frac{44}{81}\right)\) | \(e\left(\frac{23}{27}\right)\) | \(e\left(\frac{22}{27}\right)\) | \(e\left(\frac{2}{81}\right)\) | \(e\left(\frac{49}{81}\right)\) | \(e\left(\frac{40}{81}\right)\) | \(e\left(\frac{65}{81}\right)\) |