Basic properties
| Modulus: | \(4016\) | |
| Conductor: | \(4016\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(500\) | 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 4016.bu
\(\chi_{4016}(13,\cdot)\) \(\chi_{4016}(21,\cdot)\) \(\chi_{4016}(45,\cdot)\) \(\chi_{4016}(85,\cdot)\) \(\chi_{4016}(93,\cdot)\) \(\chi_{4016}(101,\cdot)\) \(\chi_{4016}(117,\cdot)\) \(\chi_{4016}(173,\cdot)\) \(\chi_{4016}(181,\cdot)\) \(\chi_{4016}(189,\cdot)\) \(\chi_{4016}(197,\cdot)\) \(\chi_{4016}(205,\cdot)\) \(\chi_{4016}(221,\cdot)\) \(\chi_{4016}(237,\cdot)\) \(\chi_{4016}(245,\cdot)\) \(\chi_{4016}(309,\cdot)\) \(\chi_{4016}(317,\cdot)\) \(\chi_{4016}(325,\cdot)\) \(\chi_{4016}(357,\cdot)\) \(\chi_{4016}(365,\cdot)\) \(\chi_{4016}(373,\cdot)\) \(\chi_{4016}(405,\cdot)\) \(\chi_{4016}(445,\cdot)\) \(\chi_{4016}(469,\cdot)\) \(\chi_{4016}(509,\cdot)\) \(\chi_{4016}(517,\cdot)\) \(\chi_{4016}(525,\cdot)\) \(\chi_{4016}(533,\cdot)\) \(\chi_{4016}(541,\cdot)\) \(\chi_{4016}(581,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{500})$ |
| Fixed field: | Number field defined by a degree 500 polynomial (not computed) |
Values on generators
\((2511,3013,257)\) → \((1,i,e\left(\frac{7}{125}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 4016 }(21, a) \) | \(1\) | \(1\) | \(e\left(\frac{323}{500}\right)\) | \(e\left(\frac{53}{100}\right)\) | \(e\left(\frac{97}{250}\right)\) | \(e\left(\frac{73}{250}\right)\) | \(e\left(\frac{33}{500}\right)\) | \(e\left(\frac{471}{500}\right)\) | \(e\left(\frac{22}{125}\right)\) | \(e\left(\frac{18}{125}\right)\) | \(e\left(\frac{439}{500}\right)\) | \(e\left(\frac{17}{500}\right)\) |