Basic properties
| Modulus: | \(1004\) | |
| Conductor: | \(251\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(250\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{251}(29,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1004.n
\(\chi_{1004}(29,\cdot)\) \(\chi_{1004}(33,\cdot)\) \(\chi_{1004}(37,\cdot)\) \(\chi_{1004}(53,\cdot)\) \(\chi_{1004}(57,\cdot)\) \(\chi_{1004}(61,\cdot)\) \(\chi_{1004}(77,\cdot)\) \(\chi_{1004}(97,\cdot)\) \(\chi_{1004}(109,\cdot)\) \(\chi_{1004}(129,\cdot)\) \(\chi_{1004}(133,\cdot)\) \(\chi_{1004}(137,\cdot)\) \(\chi_{1004}(141,\cdot)\) \(\chi_{1004}(145,\cdot)\) \(\chi_{1004}(165,\cdot)\) \(\chi_{1004}(177,\cdot)\) \(\chi_{1004}(185,\cdot)\) \(\chi_{1004}(193,\cdot)\) \(\chi_{1004}(213,\cdot)\) \(\chi_{1004}(229,\cdot)\) \(\chi_{1004}(257,\cdot)\) \(\chi_{1004}(265,\cdot)\) \(\chi_{1004}(269,\cdot)\) \(\chi_{1004}(277,\cdot)\) \(\chi_{1004}(281,\cdot)\) \(\chi_{1004}(285,\cdot)\) \(\chi_{1004}(293,\cdot)\) \(\chi_{1004}(297,\cdot)\) \(\chi_{1004}(305,\cdot)\) \(\chi_{1004}(313,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{125})$ |
| Fixed field: | Number field defined by a degree 250 polynomial (not computed) |
Values on generators
\((503,257)\) → \((1,e\left(\frac{83}{250}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1004 }(29, a) \) | \(-1\) | \(1\) | \(e\left(\frac{39}{125}\right)\) | \(e\left(\frac{4}{25}\right)\) | \(e\left(\frac{42}{125}\right)\) | \(e\left(\frac{78}{125}\right)\) | \(e\left(\frac{13}{250}\right)\) | \(e\left(\frac{53}{125}\right)\) | \(e\left(\frac{59}{125}\right)\) | \(e\left(\frac{71}{125}\right)\) | \(e\left(\frac{29}{250}\right)\) | \(e\left(\frac{81}{125}\right)\) |