Basic properties
| Modulus: | \(243\) | |
| Conductor: | \(243\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(162\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 243.j
\(\chi_{243}(2,\cdot)\) \(\chi_{243}(5,\cdot)\) \(\chi_{243}(11,\cdot)\) \(\chi_{243}(14,\cdot)\) \(\chi_{243}(20,\cdot)\) \(\chi_{243}(23,\cdot)\) \(\chi_{243}(29,\cdot)\) \(\chi_{243}(32,\cdot)\) \(\chi_{243}(38,\cdot)\) \(\chi_{243}(41,\cdot)\) \(\chi_{243}(47,\cdot)\) \(\chi_{243}(50,\cdot)\) \(\chi_{243}(56,\cdot)\) \(\chi_{243}(59,\cdot)\) \(\chi_{243}(65,\cdot)\) \(\chi_{243}(68,\cdot)\) \(\chi_{243}(74,\cdot)\) \(\chi_{243}(77,\cdot)\) \(\chi_{243}(83,\cdot)\) \(\chi_{243}(86,\cdot)\) \(\chi_{243}(92,\cdot)\) \(\chi_{243}(95,\cdot)\) \(\chi_{243}(101,\cdot)\) \(\chi_{243}(104,\cdot)\) \(\chi_{243}(110,\cdot)\) \(\chi_{243}(113,\cdot)\) \(\chi_{243}(119,\cdot)\) \(\chi_{243}(122,\cdot)\) \(\chi_{243}(128,\cdot)\) \(\chi_{243}(131,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{81})$ |
| Fixed field: | Number field defined by a degree 162 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{65}{162}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 243 }(23, a) \) | \(-1\) | \(1\) | \(e\left(\frac{65}{162}\right)\) | \(e\left(\frac{65}{81}\right)\) | \(e\left(\frac{37}{162}\right)\) | \(e\left(\frac{7}{81}\right)\) | \(e\left(\frac{11}{54}\right)\) | \(e\left(\frac{17}{27}\right)\) | \(e\left(\frac{89}{162}\right)\) | \(e\left(\frac{17}{81}\right)\) | \(e\left(\frac{79}{162}\right)\) | \(e\left(\frac{49}{81}\right)\) |