Basic properties
| Modulus: | \(1259\) | |
| Conductor: | \(1259\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(629\) | 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 1259.g
\(\chi_{1259}(3,\cdot)\) \(\chi_{1259}(4,\cdot)\) \(\chi_{1259}(5,\cdot)\) \(\chi_{1259}(7,\cdot)\) \(\chi_{1259}(9,\cdot)\) \(\chi_{1259}(12,\cdot)\) \(\chi_{1259}(15,\cdot)\) \(\chi_{1259}(16,\cdot)\) \(\chi_{1259}(17,\cdot)\) \(\chi_{1259}(20,\cdot)\) \(\chi_{1259}(21,\cdot)\) \(\chi_{1259}(22,\cdot)\) \(\chi_{1259}(23,\cdot)\) \(\chi_{1259}(25,\cdot)\) \(\chi_{1259}(27,\cdot)\) \(\chi_{1259}(28,\cdot)\) \(\chi_{1259}(35,\cdot)\) \(\chi_{1259}(36,\cdot)\) \(\chi_{1259}(37,\cdot)\) \(\chi_{1259}(38,\cdot)\) \(\chi_{1259}(43,\cdot)\) \(\chi_{1259}(45,\cdot)\) \(\chi_{1259}(48,\cdot)\) \(\chi_{1259}(49,\cdot)\) \(\chi_{1259}(53,\cdot)\) \(\chi_{1259}(58,\cdot)\) \(\chi_{1259}(60,\cdot)\) \(\chi_{1259}(61,\cdot)\) \(\chi_{1259}(62,\cdot)\) \(\chi_{1259}(63,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{629})$ |
| Fixed field: | Number field defined by a degree 629 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{570}{629}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1259 }(1042, a) \) | \(1\) | \(1\) | \(e\left(\frac{570}{629}\right)\) | \(e\left(\frac{123}{629}\right)\) | \(e\left(\frac{511}{629}\right)\) | \(e\left(\frac{548}{629}\right)\) | \(e\left(\frac{64}{629}\right)\) | \(e\left(\frac{582}{629}\right)\) | \(e\left(\frac{452}{629}\right)\) | \(e\left(\frac{246}{629}\right)\) | \(e\left(\frac{489}{629}\right)\) | \(e\left(\frac{23}{629}\right)\) |