Basic properties
| Modulus: | \(529\) | |
| Conductor: | \(529\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(253\) | 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 529.g
\(\chi_{529}(2,\cdot)\) \(\chi_{529}(3,\cdot)\) \(\chi_{529}(4,\cdot)\) \(\chi_{529}(6,\cdot)\) \(\chi_{529}(8,\cdot)\) \(\chi_{529}(9,\cdot)\) \(\chi_{529}(12,\cdot)\) \(\chi_{529}(13,\cdot)\) \(\chi_{529}(16,\cdot)\) \(\chi_{529}(18,\cdot)\) \(\chi_{529}(25,\cdot)\) \(\chi_{529}(26,\cdot)\) \(\chi_{529}(27,\cdot)\) \(\chi_{529}(29,\cdot)\) \(\chi_{529}(31,\cdot)\) \(\chi_{529}(32,\cdot)\) \(\chi_{529}(35,\cdot)\) \(\chi_{529}(36,\cdot)\) \(\chi_{529}(39,\cdot)\) \(\chi_{529}(41,\cdot)\) \(\chi_{529}(48,\cdot)\) \(\chi_{529}(49,\cdot)\) \(\chi_{529}(50,\cdot)\) \(\chi_{529}(52,\cdot)\) \(\chi_{529}(54,\cdot)\) \(\chi_{529}(55,\cdot)\) \(\chi_{529}(58,\cdot)\) \(\chi_{529}(59,\cdot)\) \(\chi_{529}(62,\cdot)\) \(\chi_{529}(64,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{253})$ |
| Fixed field: | Number field defined by a degree 253 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{155}{253}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 529 }(48, a) \) | \(1\) | \(1\) | \(e\left(\frac{134}{253}\right)\) | \(e\left(\frac{203}{253}\right)\) | \(e\left(\frac{15}{253}\right)\) | \(e\left(\frac{155}{253}\right)\) | \(e\left(\frac{84}{253}\right)\) | \(e\left(\frac{8}{253}\right)\) | \(e\left(\frac{149}{253}\right)\) | \(e\left(\frac{153}{253}\right)\) | \(e\left(\frac{36}{253}\right)\) | \(e\left(\frac{20}{253}\right)\) |