Basic properties
| Modulus: | \(8032\) | |
| Conductor: | \(4016\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(500\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4016}(1061,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8032.ce
\(\chi_{8032}(57,\cdot)\) \(\chi_{8032}(137,\cdot)\) \(\chi_{8032}(185,\cdot)\) \(\chi_{8032}(265,\cdot)\) \(\chi_{8032}(281,\cdot)\) \(\chi_{8032}(297,\cdot)\) \(\chi_{8032}(313,\cdot)\) \(\chi_{8032}(329,\cdot)\) \(\chi_{8032}(409,\cdot)\) \(\chi_{8032}(457,\cdot)\) \(\chi_{8032}(489,\cdot)\) \(\chi_{8032}(521,\cdot)\) \(\chi_{8032}(601,\cdot)\) \(\chi_{8032}(665,\cdot)\) \(\chi_{8032}(777,\cdot)\) \(\chi_{8032}(809,\cdot)\) \(\chi_{8032}(825,\cdot)\) \(\chi_{8032}(857,\cdot)\) \(\chi_{8032}(873,\cdot)\) \(\chi_{8032}(889,\cdot)\) \(\chi_{8032}(921,\cdot)\) \(\chi_{8032}(937,\cdot)\) \(\chi_{8032}(969,\cdot)\) \(\chi_{8032}(1001,\cdot)\) \(\chi_{8032}(1033,\cdot)\) \(\chi_{8032}(1065,\cdot)\) \(\chi_{8032}(1081,\cdot)\) \(\chi_{8032}(1113,\cdot)\) \(\chi_{8032}(1145,\cdot)\) \(\chi_{8032}(1273,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{500})$ |
| Fixed field: | Number field defined by a degree 500 polynomial (not computed) |
Values on generators
\((6527,3013,257)\) → \((1,i,e\left(\frac{179}{250}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 8032 }(57, a) \) | \(-1\) | \(1\) | \(e\left(\frac{103}{500}\right)\) | \(e\left(\frac{33}{100}\right)\) | \(e\left(\frac{17}{250}\right)\) | \(e\left(\frac{103}{250}\right)\) | \(e\left(\frac{163}{500}\right)\) | \(e\left(\frac{31}{500}\right)\) | \(e\left(\frac{67}{125}\right)\) | \(e\left(\frac{123}{125}\right)\) | \(e\left(\frac{229}{500}\right)\) | \(e\left(\frac{137}{500}\right)\) |