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
\(3\) → \(e\left(\frac{71}{136}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 289 }(138, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{68}\right)\) | \(e\left(\frac{71}{136}\right)\) | \(e\left(\frac{13}{34}\right)\) | \(e\left(\frac{75}{136}\right)\) | \(e\left(\frac{97}{136}\right)\) | \(e\left(\frac{125}{136}\right)\) | \(e\left(\frac{39}{68}\right)\) | \(e\left(\frac{3}{68}\right)\) | \(e\left(\frac{101}{136}\right)\) | \(e\left(\frac{1}{136}\right)\) |