Basic properties
| Modulus: | \(859\) | |
| Conductor: | \(859\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(429\) | 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 859.o
\(\chi_{859}(4,\cdot)\) \(\chi_{859}(5,\cdot)\) \(\chi_{859}(7,\cdot)\) \(\chi_{859}(9,\cdot)\) \(\chi_{859}(16,\cdot)\) \(\chi_{859}(17,\cdot)\) \(\chi_{859}(22,\cdot)\) \(\chi_{859}(24,\cdot)\) \(\chi_{859}(25,\cdot)\) \(\chi_{859}(30,\cdot)\) \(\chi_{859}(31,\cdot)\) \(\chi_{859}(41,\cdot)\) \(\chi_{859}(47,\cdot)\) \(\chi_{859}(49,\cdot)\) \(\chi_{859}(52,\cdot)\) \(\chi_{859}(53,\cdot)\) \(\chi_{859}(54,\cdot)\) \(\chi_{859}(57,\cdot)\) \(\chi_{859}(58,\cdot)\) \(\chi_{859}(63,\cdot)\) \(\chi_{859}(65,\cdot)\) \(\chi_{859}(68,\cdot)\) \(\chi_{859}(81,\cdot)\) \(\chi_{859}(85,\cdot)\) \(\chi_{859}(91,\cdot)\) \(\chi_{859}(96,\cdot)\) \(\chi_{859}(102,\cdot)\) \(\chi_{859}(111,\cdot)\) \(\chi_{859}(117,\cdot)\) \(\chi_{859}(127,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{429})$ |
| Fixed field: | Number field defined by a degree 429 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{400}{429}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 859 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{400}{429}\right)\) | \(e\left(\frac{410}{429}\right)\) | \(e\left(\frac{371}{429}\right)\) | \(e\left(\frac{227}{429}\right)\) | \(e\left(\frac{127}{143}\right)\) | \(e\left(\frac{61}{429}\right)\) | \(e\left(\frac{114}{143}\right)\) | \(e\left(\frac{391}{429}\right)\) | \(e\left(\frac{6}{13}\right)\) | \(e\left(\frac{120}{143}\right)\) |