Basic properties
Modulus: | \(1033\) | |
Conductor: | \(1033\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(129\) | 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 1033.k
\(\chi_{1033}(4,\cdot)\) \(\chi_{1033}(16,\cdot)\) \(\chi_{1033}(18,\cdot)\) \(\chi_{1033}(19,\cdot)\) \(\chi_{1033}(21,\cdot)\) \(\chi_{1033}(72,\cdot)\) \(\chi_{1033}(74,\cdot)\) \(\chi_{1033}(75,\cdot)\) \(\chi_{1033}(76,\cdot)\) \(\chi_{1033}(81,\cdot)\) \(\chi_{1033}(84,\cdot)\) \(\chi_{1033}(98,\cdot)\) \(\chi_{1033}(102,\cdot)\) \(\chi_{1033}(119,\cdot)\) \(\chi_{1033}(151,\cdot)\) \(\chi_{1033}(163,\cdot)\) \(\chi_{1033}(167,\cdot)\) \(\chi_{1033}(183,\cdot)\) \(\chi_{1033}(186,\cdot)\) \(\chi_{1033}(211,\cdot)\) \(\chi_{1033}(217,\cdot)\) \(\chi_{1033}(235,\cdot)\) \(\chi_{1033}(246,\cdot)\) \(\chi_{1033}(249,\cdot)\) \(\chi_{1033}(256,\cdot)\) \(\chi_{1033}(277,\cdot)\) \(\chi_{1033}(287,\cdot)\) \(\chi_{1033}(307,\cdot)\) \(\chi_{1033}(311,\cdot)\) \(\chi_{1033}(324,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{129})$ |
Fixed field: | Number field defined by a degree 129 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{49}{129}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1033 }(18, a) \) | \(1\) | \(1\) | \(e\left(\frac{34}{129}\right)\) | \(e\left(\frac{41}{129}\right)\) | \(e\left(\frac{68}{129}\right)\) | \(e\left(\frac{49}{129}\right)\) | \(e\left(\frac{25}{43}\right)\) | \(e\left(\frac{3}{43}\right)\) | \(e\left(\frac{34}{43}\right)\) | \(e\left(\frac{82}{129}\right)\) | \(e\left(\frac{83}{129}\right)\) | \(e\left(\frac{79}{129}\right)\) |