Basic properties
| Modulus: | \(1058\) | |
| Conductor: | \(529\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(253\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{529}(105,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1058.g
\(\chi_{1058}(3,\cdot)\) \(\chi_{1058}(9,\cdot)\) \(\chi_{1058}(13,\cdot)\) \(\chi_{1058}(25,\cdot)\) \(\chi_{1058}(27,\cdot)\) \(\chi_{1058}(29,\cdot)\) \(\chi_{1058}(31,\cdot)\) \(\chi_{1058}(35,\cdot)\) \(\chi_{1058}(39,\cdot)\) \(\chi_{1058}(41,\cdot)\) \(\chi_{1058}(49,\cdot)\) \(\chi_{1058}(55,\cdot)\) \(\chi_{1058}(59,\cdot)\) \(\chi_{1058}(71,\cdot)\) \(\chi_{1058}(73,\cdot)\) \(\chi_{1058}(75,\cdot)\) \(\chi_{1058}(77,\cdot)\) \(\chi_{1058}(81,\cdot)\) \(\chi_{1058}(85,\cdot)\) \(\chi_{1058}(87,\cdot)\) \(\chi_{1058}(95,\cdot)\) \(\chi_{1058}(101,\cdot)\) \(\chi_{1058}(105,\cdot)\) \(\chi_{1058}(117,\cdot)\) \(\chi_{1058}(119,\cdot)\) \(\chi_{1058}(121,\cdot)\) \(\chi_{1058}(123,\cdot)\) \(\chi_{1058}(127,\cdot)\) \(\chi_{1058}(131,\cdot)\) \(\chi_{1058}(133,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{253})$ |
| Fixed field: | Number field defined by a degree 253 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{73}{253}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1058 }(105, a) \) | \(1\) | \(1\) | \(e\left(\frac{156}{253}\right)\) | \(e\left(\frac{73}{253}\right)\) | \(e\left(\frac{56}{253}\right)\) | \(e\left(\frac{59}{253}\right)\) | \(e\left(\frac{140}{253}\right)\) | \(e\left(\frac{208}{253}\right)\) | \(e\left(\frac{229}{253}\right)\) | \(e\left(\frac{93}{253}\right)\) | \(e\left(\frac{248}{253}\right)\) | \(e\left(\frac{212}{253}\right)\) |