Basic properties
| Modulus: | \(251\) | |
| Conductor: | \(251\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(250\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 251.h
\(\chi_{251}(6,\cdot)\) \(\chi_{251}(11,\cdot)\) \(\chi_{251}(14,\cdot)\) \(\chi_{251}(18,\cdot)\) \(\chi_{251}(19,\cdot)\) \(\chi_{251}(24,\cdot)\) \(\chi_{251}(26,\cdot)\) \(\chi_{251}(29,\cdot)\) \(\chi_{251}(30,\cdot)\) \(\chi_{251}(33,\cdot)\) \(\chi_{251}(34,\cdot)\) \(\chi_{251}(37,\cdot)\) \(\chi_{251}(42,\cdot)\) \(\chi_{251}(43,\cdot)\) \(\chi_{251}(44,\cdot)\) \(\chi_{251}(46,\cdot)\) \(\chi_{251}(53,\cdot)\) \(\chi_{251}(54,\cdot)\) \(\chi_{251}(55,\cdot)\) \(\chi_{251}(56,\cdot)\) \(\chi_{251}(57,\cdot)\) \(\chi_{251}(59,\cdot)\) \(\chi_{251}(61,\cdot)\) \(\chi_{251}(62,\cdot)\) \(\chi_{251}(70,\cdot)\) \(\chi_{251}(71,\cdot)\) \(\chi_{251}(72,\cdot)\) \(\chi_{251}(76,\cdot)\) \(\chi_{251}(77,\cdot)\) \(\chi_{251}(78,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{125})$ |
| Fixed field: | Number field defined by a degree 250 polynomial (not computed) |
Values on generators
\(6\) → \(e\left(\frac{81}{250}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 251 }(203, a) \) | \(-1\) | \(1\) | \(e\left(\frac{7}{50}\right)\) | \(e\left(\frac{23}{125}\right)\) | \(e\left(\frac{7}{25}\right)\) | \(e\left(\frac{3}{25}\right)\) | \(e\left(\frac{81}{250}\right)\) | \(e\left(\frac{44}{125}\right)\) | \(e\left(\frac{21}{50}\right)\) | \(e\left(\frac{46}{125}\right)\) | \(e\left(\frac{13}{50}\right)\) | \(e\left(\frac{91}{250}\right)\) |