Basic properties
| Modulus: | \(1006\) | |
| Conductor: | \(503\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(251\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{503}(498,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1006.c
\(\chi_{1006}(3,\cdot)\) \(\chi_{1006}(7,\cdot)\) \(\chi_{1006}(9,\cdot)\) \(\chi_{1006}(11,\cdot)\) \(\chi_{1006}(13,\cdot)\) \(\chi_{1006}(21,\cdot)\) \(\chi_{1006}(23,\cdot)\) \(\chi_{1006}(25,\cdot)\) \(\chi_{1006}(27,\cdot)\) \(\chi_{1006}(33,\cdot)\) \(\chi_{1006}(39,\cdot)\) \(\chi_{1006}(43,\cdot)\) \(\chi_{1006}(47,\cdot)\) \(\chi_{1006}(49,\cdot)\) \(\chi_{1006}(59,\cdot)\) \(\chi_{1006}(61,\cdot)\) \(\chi_{1006}(63,\cdot)\) \(\chi_{1006}(67,\cdot)\) \(\chi_{1006}(69,\cdot)\) \(\chi_{1006}(73,\cdot)\) \(\chi_{1006}(75,\cdot)\) \(\chi_{1006}(77,\cdot)\) \(\chi_{1006}(79,\cdot)\) \(\chi_{1006}(81,\cdot)\) \(\chi_{1006}(83,\cdot)\) \(\chi_{1006}(85,\cdot)\) \(\chi_{1006}(91,\cdot)\) \(\chi_{1006}(95,\cdot)\) \(\chi_{1006}(97,\cdot)\) \(\chi_{1006}(99,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{251})$ |
| Fixed field: | Number field defined by a degree 251 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{126}{251}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1006 }(1001, a) \) | \(1\) | \(1\) | \(e\left(\frac{78}{251}\right)\) | \(e\left(\frac{126}{251}\right)\) | \(e\left(\frac{43}{251}\right)\) | \(e\left(\frac{156}{251}\right)\) | \(e\left(\frac{21}{251}\right)\) | \(e\left(\frac{62}{251}\right)\) | \(e\left(\frac{204}{251}\right)\) | \(e\left(\frac{240}{251}\right)\) | \(e\left(\frac{244}{251}\right)\) | \(e\left(\frac{121}{251}\right)\) |