Basic properties
| Modulus: | \(729\) | |
| Conductor: | \(243\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(81\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{243}(187,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 729.i
\(\chi_{729}(10,\cdot)\) \(\chi_{729}(19,\cdot)\) \(\chi_{729}(37,\cdot)\) \(\chi_{729}(46,\cdot)\) \(\chi_{729}(64,\cdot)\) \(\chi_{729}(73,\cdot)\) \(\chi_{729}(91,\cdot)\) \(\chi_{729}(100,\cdot)\) \(\chi_{729}(118,\cdot)\) \(\chi_{729}(127,\cdot)\) \(\chi_{729}(145,\cdot)\) \(\chi_{729}(154,\cdot)\) \(\chi_{729}(172,\cdot)\) \(\chi_{729}(181,\cdot)\) \(\chi_{729}(199,\cdot)\) \(\chi_{729}(208,\cdot)\) \(\chi_{729}(226,\cdot)\) \(\chi_{729}(235,\cdot)\) \(\chi_{729}(253,\cdot)\) \(\chi_{729}(262,\cdot)\) \(\chi_{729}(280,\cdot)\) \(\chi_{729}(289,\cdot)\) \(\chi_{729}(307,\cdot)\) \(\chi_{729}(316,\cdot)\) \(\chi_{729}(334,\cdot)\) \(\chi_{729}(343,\cdot)\) \(\chi_{729}(361,\cdot)\) \(\chi_{729}(370,\cdot)\) \(\chi_{729}(388,\cdot)\) \(\chi_{729}(397,\cdot)\) ...
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
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 729 }(73, a) \) | \(1\) | \(1\) | \(e\left(\frac{77}{81}\right)\) | \(e\left(\frac{73}{81}\right)\) | \(e\left(\frac{70}{81}\right)\) | \(e\left(\frac{44}{81}\right)\) | \(e\left(\frac{23}{27}\right)\) | \(e\left(\frac{22}{27}\right)\) | \(e\left(\frac{2}{81}\right)\) | \(e\left(\frac{49}{81}\right)\) | \(e\left(\frac{40}{81}\right)\) | \(e\left(\frac{65}{81}\right)\) |