Basic properties
| Modulus: | \(289\) | |
| Conductor: | \(289\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(272\) | 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 289.j
\(\chi_{289}(3,\cdot)\) \(\chi_{289}(5,\cdot)\) \(\chi_{289}(6,\cdot)\) \(\chi_{289}(7,\cdot)\) \(\chi_{289}(10,\cdot)\) \(\chi_{289}(11,\cdot)\) \(\chi_{289}(12,\cdot)\) \(\chi_{289}(14,\cdot)\) \(\chi_{289}(20,\cdot)\) \(\chi_{289}(22,\cdot)\) \(\chi_{289}(23,\cdot)\) \(\chi_{289}(24,\cdot)\) \(\chi_{289}(27,\cdot)\) \(\chi_{289}(28,\cdot)\) \(\chi_{289}(29,\cdot)\) \(\chi_{289}(31,\cdot)\) \(\chi_{289}(37,\cdot)\) \(\chi_{289}(39,\cdot)\) \(\chi_{289}(41,\cdot)\) \(\chi_{289}(44,\cdot)\) \(\chi_{289}(45,\cdot)\) \(\chi_{289}(46,\cdot)\) \(\chi_{289}(48,\cdot)\) \(\chi_{289}(54,\cdot)\) \(\chi_{289}(56,\cdot)\) \(\chi_{289}(57,\cdot)\) \(\chi_{289}(58,\cdot)\) \(\chi_{289}(61,\cdot)\) \(\chi_{289}(62,\cdot)\) \(\chi_{289}(63,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{272})$ |
| Fixed field: | Number field defined by a degree 272 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{191}{272}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 289 }(6, a) \) | \(-1\) | \(1\) | \(e\left(\frac{57}{136}\right)\) | \(e\left(\frac{191}{272}\right)\) | \(e\left(\frac{57}{68}\right)\) | \(e\left(\frac{219}{272}\right)\) | \(e\left(\frac{33}{272}\right)\) | \(e\left(\frac{229}{272}\right)\) | \(e\left(\frac{35}{136}\right)\) | \(e\left(\frac{55}{136}\right)\) | \(e\left(\frac{61}{272}\right)\) | \(e\left(\frac{41}{272}\right)\) |