Basic properties
| Modulus: | \(1069\) | |
| Conductor: | \(1069\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1068\) | 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 1069.l
\(\chi_{1069}(6,\cdot)\) \(\chi_{1069}(7,\cdot)\) \(\chi_{1069}(10,\cdot)\) \(\chi_{1069}(11,\cdot)\) \(\chi_{1069}(18,\cdot)\) \(\chi_{1069}(23,\cdot)\) \(\chi_{1069}(24,\cdot)\) \(\chi_{1069}(26,\cdot)\) \(\chi_{1069}(28,\cdot)\) \(\chi_{1069}(30,\cdot)\) \(\chi_{1069}(33,\cdot)\) \(\chi_{1069}(38,\cdot)\) \(\chi_{1069}(40,\cdot)\) \(\chi_{1069}(41,\cdot)\) \(\chi_{1069}(43,\cdot)\) \(\chi_{1069}(44,\cdot)\) \(\chi_{1069}(47,\cdot)\) \(\chi_{1069}(50,\cdot)\) \(\chi_{1069}(55,\cdot)\) \(\chi_{1069}(61,\cdot)\) \(\chi_{1069}(63,\cdot)\) \(\chi_{1069}(72,\cdot)\) \(\chi_{1069}(83,\cdot)\) \(\chi_{1069}(91,\cdot)\) \(\chi_{1069}(92,\cdot)\) \(\chi_{1069}(93,\cdot)\) \(\chi_{1069}(96,\cdot)\) \(\chi_{1069}(98,\cdot)\) \(\chi_{1069}(101,\cdot)\) \(\chi_{1069}(103,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1068})$ |
| Fixed field: | Number field defined by a degree 1068 polynomial (not computed) |
Values on generators
\(6\) → \(e\left(\frac{535}{1068}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1069 }(1063, a) \) | \(-1\) | \(1\) | \(e\left(\frac{111}{356}\right)\) | \(e\left(\frac{101}{534}\right)\) | \(e\left(\frac{111}{178}\right)\) | \(e\left(\frac{64}{267}\right)\) | \(e\left(\frac{535}{1068}\right)\) | \(e\left(\frac{173}{1068}\right)\) | \(e\left(\frac{333}{356}\right)\) | \(e\left(\frac{101}{267}\right)\) | \(e\left(\frac{589}{1068}\right)\) | \(e\left(\frac{793}{1068}\right)\) |