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.bv
\(\chi_{4016}(11,\cdot)\) \(\chi_{4016}(19,\cdot)\) \(\chi_{4016}(43,\cdot)\) \(\chi_{4016}(59,\cdot)\) \(\chi_{4016}(99,\cdot)\) \(\chi_{4016}(107,\cdot)\) \(\chi_{4016}(139,\cdot)\) \(\chi_{4016}(163,\cdot)\) \(\chi_{4016}(203,\cdot)\) \(\chi_{4016}(275,\cdot)\) \(\chi_{4016}(307,\cdot)\) \(\chi_{4016}(323,\cdot)\) \(\chi_{4016}(347,\cdot)\) \(\chi_{4016}(355,\cdot)\) \(\chi_{4016}(371,\cdot)\) \(\chi_{4016}(387,\cdot)\) \(\chi_{4016}(419,\cdot)\) \(\chi_{4016}(427,\cdot)\) \(\chi_{4016}(435,\cdot)\) \(\chi_{4016}(467,\cdot)\) \(\chi_{4016}(475,\cdot)\) \(\chi_{4016}(499,\cdot)\) \(\chi_{4016}(531,\cdot)\) \(\chi_{4016}(539,\cdot)\) \(\chi_{4016}(555,\cdot)\) \(\chi_{4016}(563,\cdot)\) \(\chi_{4016}(579,\cdot)\) \(\chi_{4016}(611,\cdot)\) \(\chi_{4016}(635,\cdot)\) \(\chi_{4016}(643,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{500})$ |
| Fixed field: | Number field defined by a degree 500 polynomial (not computed) |
Values on generators
\((2511,3013,257)\) → \((-1,i,e\left(\frac{247}{250}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 4016 }(43, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{500}\right)\) | \(e\left(\frac{69}{100}\right)\) | \(e\left(\frac{3}{125}\right)\) | \(e\left(\frac{29}{250}\right)\) | \(e\left(\frac{109}{500}\right)\) | \(e\left(\frac{283}{500}\right)\) | \(e\left(\frac{187}{250}\right)\) | \(e\left(\frac{14}{125}\right)\) | \(e\left(\frac{147}{500}\right)\) | \(e\left(\frac{41}{500}\right)\) |