Basic properties
| Modulus: | \(2500\) | |
| Conductor: | \(2500\) | 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 2500.v
\(\chi_{2500}(19,\cdot)\) \(\chi_{2500}(39,\cdot)\) \(\chi_{2500}(59,\cdot)\) \(\chi_{2500}(79,\cdot)\) \(\chi_{2500}(119,\cdot)\) \(\chi_{2500}(139,\cdot)\) \(\chi_{2500}(159,\cdot)\) \(\chi_{2500}(179,\cdot)\) \(\chi_{2500}(219,\cdot)\) \(\chi_{2500}(239,\cdot)\) \(\chi_{2500}(259,\cdot)\) \(\chi_{2500}(279,\cdot)\) \(\chi_{2500}(319,\cdot)\) \(\chi_{2500}(339,\cdot)\) \(\chi_{2500}(359,\cdot)\) \(\chi_{2500}(379,\cdot)\) \(\chi_{2500}(419,\cdot)\) \(\chi_{2500}(439,\cdot)\) \(\chi_{2500}(459,\cdot)\) \(\chi_{2500}(479,\cdot)\) \(\chi_{2500}(519,\cdot)\) \(\chi_{2500}(539,\cdot)\) \(\chi_{2500}(559,\cdot)\) \(\chi_{2500}(579,\cdot)\) \(\chi_{2500}(619,\cdot)\) \(\chi_{2500}(639,\cdot)\) \(\chi_{2500}(659,\cdot)\) \(\chi_{2500}(679,\cdot)\) \(\chi_{2500}(719,\cdot)\) \(\chi_{2500}(739,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{125})$ |
| Fixed field: | Number field defined by a degree 250 polynomial (not computed) |
Values on generators
\((1251,1877)\) → \((-1,e\left(\frac{67}{250}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 2500 }(59, a) \) | \(-1\) | \(1\) | \(e\left(\frac{22}{125}\right)\) | \(e\left(\frac{12}{25}\right)\) | \(e\left(\frac{44}{125}\right)\) | \(e\left(\frac{17}{250}\right)\) | \(e\left(\frac{63}{250}\right)\) | \(e\left(\frac{91}{250}\right)\) | \(e\left(\frac{131}{250}\right)\) | \(e\left(\frac{82}{125}\right)\) | \(e\left(\frac{1}{125}\right)\) | \(e\left(\frac{66}{125}\right)\) |