Basic properties
| Modulus: | \(1004\) | |
| Conductor: | \(1004\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1004.o
\(\chi_{1004}(11,\cdot)\) \(\chi_{1004}(19,\cdot)\) \(\chi_{1004}(43,\cdot)\) \(\chi_{1004}(55,\cdot)\) \(\chi_{1004}(59,\cdot)\) \(\chi_{1004}(71,\cdot)\) \(\chi_{1004}(87,\cdot)\) \(\chi_{1004}(95,\cdot)\) \(\chi_{1004}(99,\cdot)\) \(\chi_{1004}(107,\cdot)\) \(\chi_{1004}(111,\cdot)\) \(\chi_{1004}(127,\cdot)\) \(\chi_{1004}(139,\cdot)\) \(\chi_{1004}(143,\cdot)\) \(\chi_{1004}(159,\cdot)\) \(\chi_{1004}(163,\cdot)\) \(\chi_{1004}(167,\cdot)\) \(\chi_{1004}(183,\cdot)\) \(\chi_{1004}(191,\cdot)\) \(\chi_{1004}(199,\cdot)\) \(\chi_{1004}(203,\cdot)\) \(\chi_{1004}(215,\cdot)\) \(\chi_{1004}(223,\cdot)\) \(\chi_{1004}(239,\cdot)\) \(\chi_{1004}(275,\cdot)\) \(\chi_{1004}(295,\cdot)\) \(\chi_{1004}(307,\cdot)\) \(\chi_{1004}(323,\cdot)\) \(\chi_{1004}(327,\cdot)\) \(\chi_{1004}(347,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{125})$ |
| Fixed field: | Number field defined by a degree 250 polynomial (not computed) |
Values on generators
\((503,257)\) → \((-1,e\left(\frac{211}{250}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1004 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{250}\right)\) | \(e\left(\frac{18}{25}\right)\) | \(e\left(\frac{203}{250}\right)\) | \(e\left(\frac{1}{125}\right)\) | \(e\left(\frac{73}{125}\right)\) | \(e\left(\frac{76}{125}\right)\) | \(e\left(\frac{181}{250}\right)\) | \(e\left(\frac{57}{125}\right)\) | \(e\left(\frac{9}{125}\right)\) | \(e\left(\frac{102}{125}\right)\) |