Basic properties
| Modulus: | \(967\) | |
| Conductor: | \(967\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(322\) | 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 967.n
\(\chi_{967}(3,\cdot)\) \(\chi_{967}(10,\cdot)\) \(\chi_{967}(23,\cdot)\) \(\chi_{967}(24,\cdot)\) \(\chi_{967}(26,\cdot)\) \(\chi_{967}(27,\cdot)\) \(\chi_{967}(29,\cdot)\) \(\chi_{967}(33,\cdot)\) \(\chi_{967}(67,\cdot)\) \(\chi_{967}(76,\cdot)\) \(\chi_{967}(80,\cdot)\) \(\chi_{967}(90,\cdot)\) \(\chi_{967}(109,\cdot)\) \(\chi_{967}(110,\cdot)\) \(\chi_{967}(112,\cdot)\) \(\chi_{967}(125,\cdot)\) \(\chi_{967}(126,\cdot)\) \(\chi_{967}(154,\cdot)\) \(\chi_{967}(158,\cdot)\) \(\chi_{967}(167,\cdot)\) \(\chi_{967}(170,\cdot)\) \(\chi_{967}(178,\cdot)\) \(\chi_{967}(184,\cdot)\) \(\chi_{967}(186,\cdot)\) \(\chi_{967}(191,\cdot)\) \(\chi_{967}(192,\cdot)\) \(\chi_{967}(207,\cdot)\) \(\chi_{967}(208,\cdot)\) \(\chi_{967}(213,\cdot)\) \(\chi_{967}(214,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{161})$ |
| Fixed field: | Number field defined by a degree 322 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{1}{322}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 967 }(125, a) \) | \(-1\) | \(1\) | \(e\left(\frac{26}{161}\right)\) | \(e\left(\frac{237}{322}\right)\) | \(e\left(\frac{52}{161}\right)\) | \(e\left(\frac{1}{322}\right)\) | \(e\left(\frac{289}{322}\right)\) | \(e\left(\frac{67}{322}\right)\) | \(e\left(\frac{78}{161}\right)\) | \(e\left(\frac{76}{161}\right)\) | \(e\left(\frac{53}{322}\right)\) | \(e\left(\frac{122}{161}\right)\) |