Basic properties
| Modulus: | \(967\) | |
| Conductor: | \(967\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(483\) | 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.o
\(\chi_{967}(2,\cdot)\) \(\chi_{967}(4,\cdot)\) \(\chi_{967}(16,\cdot)\) \(\chi_{967}(18,\cdot)\) \(\chi_{967}(21,\cdot)\) \(\chi_{967}(22,\cdot)\) \(\chi_{967}(25,\cdot)\) \(\chi_{967}(31,\cdot)\) \(\chi_{967}(32,\cdot)\) \(\chi_{967}(34,\cdot)\) \(\chi_{967}(35,\cdot)\) \(\chi_{967}(36,\cdot)\) \(\chi_{967}(44,\cdot)\) \(\chi_{967}(49,\cdot)\) \(\chi_{967}(50,\cdot)\) \(\chi_{967}(57,\cdot)\) \(\chi_{967}(59,\cdot)\) \(\chi_{967}(60,\cdot)\) \(\chi_{967}(65,\cdot)\) \(\chi_{967}(70,\cdot)\) \(\chi_{967}(83,\cdot)\) \(\chi_{967}(84,\cdot)\) \(\chi_{967}(91,\cdot)\) \(\chi_{967}(98,\cdot)\) \(\chi_{967}(101,\cdot)\) \(\chi_{967}(103,\cdot)\) \(\chi_{967}(106,\cdot)\) \(\chi_{967}(111,\cdot)\) \(\chi_{967}(114,\cdot)\) \(\chi_{967}(115,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{483})$ |
| Fixed field: | Number field defined by a degree 483 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{265}{483}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 967 }(16, a) \) | \(1\) | \(1\) | \(e\left(\frac{95}{483}\right)\) | \(e\left(\frac{5}{161}\right)\) | \(e\left(\frac{190}{483}\right)\) | \(e\left(\frac{265}{483}\right)\) | \(e\left(\frac{110}{483}\right)\) | \(e\left(\frac{367}{483}\right)\) | \(e\left(\frac{95}{161}\right)\) | \(e\left(\frac{10}{161}\right)\) | \(e\left(\frac{120}{161}\right)\) | \(e\left(\frac{33}{161}\right)\) |