Basic properties
| Modulus: | \(1004\) | |
| Conductor: | \(251\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(125\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{251}(240,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1004.m
\(\chi_{1004}(9,\cdot)\) \(\chi_{1004}(13,\cdot)\) \(\chi_{1004}(17,\cdot)\) \(\chi_{1004}(21,\cdot)\) \(\chi_{1004}(41,\cdot)\) \(\chi_{1004}(45,\cdot)\) \(\chi_{1004}(49,\cdot)\) \(\chi_{1004}(65,\cdot)\) \(\chi_{1004}(73,\cdot)\) \(\chi_{1004}(81,\cdot)\) \(\chi_{1004}(85,\cdot)\) \(\chi_{1004}(89,\cdot)\) \(\chi_{1004}(93,\cdot)\) \(\chi_{1004}(101,\cdot)\) \(\chi_{1004}(105,\cdot)\) \(\chi_{1004}(117,\cdot)\) \(\chi_{1004}(121,\cdot)\) \(\chi_{1004}(153,\cdot)\) \(\chi_{1004}(161,\cdot)\) \(\chi_{1004}(169,\cdot)\) \(\chi_{1004}(173,\cdot)\) \(\chi_{1004}(181,\cdot)\) \(\chi_{1004}(189,\cdot)\) \(\chi_{1004}(197,\cdot)\) \(\chi_{1004}(205,\cdot)\) \(\chi_{1004}(209,\cdot)\) \(\chi_{1004}(217,\cdot)\) \(\chi_{1004}(221,\cdot)\) \(\chi_{1004}(225,\cdot)\) \(\chi_{1004}(233,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{125})$ |
| Fixed field: | Number field defined by a degree 125 polynomial (not computed) |
Values on generators
\((503,257)\) → \((1,e\left(\frac{43}{125}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1004 }(993, a) \) | \(1\) | \(1\) | \(e\left(\frac{63}{125}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{39}{125}\right)\) | \(e\left(\frac{1}{125}\right)\) | \(e\left(\frac{73}{125}\right)\) | \(e\left(\frac{76}{125}\right)\) | \(e\left(\frac{28}{125}\right)\) | \(e\left(\frac{57}{125}\right)\) | \(e\left(\frac{9}{125}\right)\) | \(e\left(\frac{102}{125}\right)\) |