Basic properties
| Modulus: | \(729\) | |
| Conductor: | \(243\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(162\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{243}(101,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 729.j
\(\chi_{729}(8,\cdot)\) \(\chi_{729}(17,\cdot)\) \(\chi_{729}(35,\cdot)\) \(\chi_{729}(44,\cdot)\) \(\chi_{729}(62,\cdot)\) \(\chi_{729}(71,\cdot)\) \(\chi_{729}(89,\cdot)\) \(\chi_{729}(98,\cdot)\) \(\chi_{729}(116,\cdot)\) \(\chi_{729}(125,\cdot)\) \(\chi_{729}(143,\cdot)\) \(\chi_{729}(152,\cdot)\) \(\chi_{729}(170,\cdot)\) \(\chi_{729}(179,\cdot)\) \(\chi_{729}(197,\cdot)\) \(\chi_{729}(206,\cdot)\) \(\chi_{729}(224,\cdot)\) \(\chi_{729}(233,\cdot)\) \(\chi_{729}(251,\cdot)\) \(\chi_{729}(260,\cdot)\) \(\chi_{729}(278,\cdot)\) \(\chi_{729}(287,\cdot)\) \(\chi_{729}(305,\cdot)\) \(\chi_{729}(314,\cdot)\) \(\chi_{729}(332,\cdot)\) \(\chi_{729}(341,\cdot)\) \(\chi_{729}(359,\cdot)\) \(\chi_{729}(368,\cdot)\) \(\chi_{729}(386,\cdot)\) \(\chi_{729}(395,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{81})$ |
| Fixed field: | Number field defined by a degree 162 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{133}{162}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 729 }(224, a) \) | \(-1\) | \(1\) | \(e\left(\frac{133}{162}\right)\) | \(e\left(\frac{52}{81}\right)\) | \(e\left(\frac{143}{162}\right)\) | \(e\left(\frac{38}{81}\right)\) | \(e\left(\frac{25}{54}\right)\) | \(e\left(\frac{19}{27}\right)\) | \(e\left(\frac{55}{162}\right)\) | \(e\left(\frac{46}{81}\right)\) | \(e\left(\frac{47}{162}\right)\) | \(e\left(\frac{23}{81}\right)\) |