Basic properties
| Modulus: | \(289\) | |
| Conductor: | \(289\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(136\) | 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 289.i
\(\chi_{289}(2,\cdot)\) \(\chi_{289}(8,\cdot)\) \(\chi_{289}(9,\cdot)\) \(\chi_{289}(15,\cdot)\) \(\chi_{289}(19,\cdot)\) \(\chi_{289}(25,\cdot)\) \(\chi_{289}(26,\cdot)\) \(\chi_{289}(32,\cdot)\) \(\chi_{289}(36,\cdot)\) \(\chi_{289}(42,\cdot)\) \(\chi_{289}(43,\cdot)\) \(\chi_{289}(49,\cdot)\) \(\chi_{289}(53,\cdot)\) \(\chi_{289}(59,\cdot)\) \(\chi_{289}(60,\cdot)\) \(\chi_{289}(66,\cdot)\) \(\chi_{289}(70,\cdot)\) \(\chi_{289}(76,\cdot)\) \(\chi_{289}(77,\cdot)\) \(\chi_{289}(83,\cdot)\) \(\chi_{289}(87,\cdot)\) \(\chi_{289}(93,\cdot)\) \(\chi_{289}(94,\cdot)\) \(\chi_{289}(100,\cdot)\) \(\chi_{289}(104,\cdot)\) \(\chi_{289}(111,\cdot)\) \(\chi_{289}(117,\cdot)\) \(\chi_{289}(121,\cdot)\) \(\chi_{289}(127,\cdot)\) \(\chi_{289}(128,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{136})$ |
| Fixed field: | Number field defined by a degree 136 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{23}{136}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 289 }(121, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{68}\right)\) | \(e\left(\frac{23}{136}\right)\) | \(e\left(\frac{9}{34}\right)\) | \(e\left(\frac{99}{136}\right)\) | \(e\left(\frac{41}{136}\right)\) | \(e\left(\frac{29}{136}\right)\) | \(e\left(\frac{27}{68}\right)\) | \(e\left(\frac{23}{68}\right)\) | \(e\left(\frac{117}{136}\right)\) | \(e\left(\frac{121}{136}\right)\) |