Basic properties
Modulus: | \(967\) | |
Conductor: | \(967\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(966\) | 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.p
\(\chi_{967}(5,\cdot)\) \(\chi_{967}(6,\cdot)\) \(\chi_{967}(7,\cdot)\) \(\chi_{967}(12,\cdot)\) \(\chi_{967}(13,\cdot)\) \(\chi_{967}(19,\cdot)\) \(\chi_{967}(28,\cdot)\) \(\chi_{967}(37,\cdot)\) \(\chi_{967}(38,\cdot)\) \(\chi_{967}(40,\cdot)\) \(\chi_{967}(43,\cdot)\) \(\chi_{967}(45,\cdot)\) \(\chi_{967}(46,\cdot)\) \(\chi_{967}(47,\cdot)\) \(\chi_{967}(48,\cdot)\) \(\chi_{967}(56,\cdot)\) \(\chi_{967}(58,\cdot)\) \(\chi_{967}(63,\cdot)\) \(\chi_{967}(66,\cdot)\) \(\chi_{967}(75,\cdot)\) \(\chi_{967}(77,\cdot)\) \(\chi_{967}(79,\cdot)\) \(\chi_{967}(82,\cdot)\) \(\chi_{967}(85,\cdot)\) \(\chi_{967}(86,\cdot)\) \(\chi_{967}(89,\cdot)\) \(\chi_{967}(102,\cdot)\) \(\chi_{967}(104,\cdot)\) \(\chi_{967}(105,\cdot)\) \(\chi_{967}(107,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{483})$ |
Fixed field: | Number field defined by a degree 966 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{223}{966}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 967 }(56, a) \) | \(-1\) | \(1\) | \(e\left(\frac{163}{483}\right)\) | \(e\left(\frac{229}{322}\right)\) | \(e\left(\frac{326}{483}\right)\) | \(e\left(\frac{223}{966}\right)\) | \(e\left(\frac{47}{966}\right)\) | \(e\left(\frac{451}{966}\right)\) | \(e\left(\frac{2}{161}\right)\) | \(e\left(\frac{68}{161}\right)\) | \(e\left(\frac{183}{322}\right)\) | \(e\left(\frac{160}{161}\right)\) |