Basic properties
| Modulus: | \(967\) | |
| Conductor: | \(967\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(161\) | 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 967.m
\(\chi_{967}(8,\cdot)\) \(\chi_{967}(9,\cdot)\) \(\chi_{967}(11,\cdot)\) \(\chi_{967}(17,\cdot)\) \(\chi_{967}(30,\cdot)\) \(\chi_{967}(42,\cdot)\) \(\chi_{967}(62,\cdot)\) \(\chi_{967}(64,\cdot)\) \(\chi_{967}(71,\cdot)\) \(\chi_{967}(78,\cdot)\) \(\chi_{967}(81,\cdot)\) \(\chi_{967}(87,\cdot)\) \(\chi_{967}(88,\cdot)\) \(\chi_{967}(95,\cdot)\) \(\chi_{967}(99,\cdot)\) \(\chi_{967}(100,\cdot)\) \(\chi_{967}(118,\cdot)\) \(\chi_{967}(121,\cdot)\) \(\chi_{967}(122,\cdot)\) \(\chi_{967}(123,\cdot)\) \(\chi_{967}(131,\cdot)\) \(\chi_{967}(136,\cdot)\) \(\chi_{967}(140,\cdot)\) \(\chi_{967}(146,\cdot)\) \(\chi_{967}(153,\cdot)\) \(\chi_{967}(201,\cdot)\) \(\chi_{967}(206,\cdot)\) \(\chi_{967}(212,\cdot)\) \(\chi_{967}(215,\cdot)\) \(\chi_{967}(222,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{161})$ |
| Fixed field: | Number field defined by a degree 161 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{135}{161}\right)\)
Values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 967 }(121, a) \) | \(1\) | \(1\) | \(e\left(\frac{97}{161}\right)\) | \(e\left(\frac{117}{161}\right)\) | \(e\left(\frac{33}{161}\right)\) | \(e\left(\frac{135}{161}\right)\) | \(e\left(\frac{53}{161}\right)\) | \(e\left(\frac{29}{161}\right)\) | \(e\left(\frac{130}{161}\right)\) | \(e\left(\frac{73}{161}\right)\) | \(e\left(\frac{71}{161}\right)\) | \(e\left(\frac{96}{161}\right)\) |