Basic properties
Modulus: | \(1259\) | |
Conductor: | \(1259\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(1258\) | 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 1259.h
\(\chi_{1259}(2,\cdot)\) \(\chi_{1259}(6,\cdot)\) \(\chi_{1259}(8,\cdot)\) \(\chi_{1259}(10,\cdot)\) \(\chi_{1259}(11,\cdot)\) \(\chi_{1259}(13,\cdot)\) \(\chi_{1259}(14,\cdot)\) \(\chi_{1259}(19,\cdot)\) \(\chi_{1259}(24,\cdot)\) \(\chi_{1259}(31,\cdot)\) \(\chi_{1259}(32,\cdot)\) \(\chi_{1259}(33,\cdot)\) \(\chi_{1259}(34,\cdot)\) \(\chi_{1259}(39,\cdot)\) \(\chi_{1259}(40,\cdot)\) \(\chi_{1259}(44,\cdot)\) \(\chi_{1259}(46,\cdot)\) \(\chi_{1259}(47,\cdot)\) \(\chi_{1259}(52,\cdot)\) \(\chi_{1259}(54,\cdot)\) \(\chi_{1259}(55,\cdot)\) \(\chi_{1259}(56,\cdot)\) \(\chi_{1259}(57,\cdot)\) \(\chi_{1259}(59,\cdot)\) \(\chi_{1259}(65,\cdot)\) \(\chi_{1259}(72,\cdot)\) \(\chi_{1259}(74,\cdot)\) \(\chi_{1259}(76,\cdot)\) \(\chi_{1259}(77,\cdot)\) \(\chi_{1259}(86,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{629})$ |
Fixed field: | Number field defined by a degree 1258 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{1}{1258}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 1259 }(2, a) \) | \(-1\) | \(1\) | \(e\left(\frac{1}{1258}\right)\) | \(e\left(\frac{548}{629}\right)\) | \(e\left(\frac{1}{629}\right)\) | \(e\left(\frac{38}{629}\right)\) | \(e\left(\frac{1097}{1258}\right)\) | \(e\left(\frac{123}{629}\right)\) | \(e\left(\frac{3}{1258}\right)\) | \(e\left(\frac{467}{629}\right)\) | \(e\left(\frac{77}{1258}\right)\) | \(e\left(\frac{1151}{1258}\right)\) |