Basic properties
| Modulus: | \(4016\) | |
| Conductor: | \(2008\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(250\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2008}(1061,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4016.br
\(\chi_{4016}(57,\cdot)\) \(\chi_{4016}(137,\cdot)\) \(\chi_{4016}(185,\cdot)\) \(\chi_{4016}(265,\cdot)\) \(\chi_{4016}(281,\cdot)\) \(\chi_{4016}(297,\cdot)\) \(\chi_{4016}(313,\cdot)\) \(\chi_{4016}(329,\cdot)\) \(\chi_{4016}(409,\cdot)\) \(\chi_{4016}(457,\cdot)\) \(\chi_{4016}(489,\cdot)\) \(\chi_{4016}(521,\cdot)\) \(\chi_{4016}(601,\cdot)\) \(\chi_{4016}(665,\cdot)\) \(\chi_{4016}(777,\cdot)\) \(\chi_{4016}(809,\cdot)\) \(\chi_{4016}(825,\cdot)\) \(\chi_{4016}(857,\cdot)\) \(\chi_{4016}(873,\cdot)\) \(\chi_{4016}(889,\cdot)\) \(\chi_{4016}(921,\cdot)\) \(\chi_{4016}(937,\cdot)\) \(\chi_{4016}(969,\cdot)\) \(\chi_{4016}(1001,\cdot)\) \(\chi_{4016}(1033,\cdot)\) \(\chi_{4016}(1065,\cdot)\) \(\chi_{4016}(1081,\cdot)\) \(\chi_{4016}(1113,\cdot)\) \(\chi_{4016}(1145,\cdot)\) \(\chi_{4016}(1273,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{125})$ |
| Fixed field: | Number field defined by a degree 250 polynomial (not computed) |
Values on generators
\((2511,3013,257)\) → \((1,-1,e\left(\frac{179}{250}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 4016 }(57, a) \) | \(-1\) | \(1\) | \(e\left(\frac{239}{250}\right)\) | \(e\left(\frac{29}{50}\right)\) | \(e\left(\frac{71}{125}\right)\) | \(e\left(\frac{114}{125}\right)\) | \(e\left(\frac{72}{125}\right)\) | \(e\left(\frac{203}{250}\right)\) | \(e\left(\frac{67}{125}\right)\) | \(e\left(\frac{123}{125}\right)\) | \(e\left(\frac{26}{125}\right)\) | \(e\left(\frac{131}{250}\right)\) |