Basic properties
| Modulus: | \(4016\) | |
| Conductor: | \(251\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(250\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{251}(33,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4016.bl
\(\chi_{4016}(33,\cdot)\) \(\chi_{4016}(97,\cdot)\) \(\chi_{4016}(129,\cdot)\) \(\chi_{4016}(145,\cdot)\) \(\chi_{4016}(177,\cdot)\) \(\chi_{4016}(193,\cdot)\) \(\chi_{4016}(257,\cdot)\) \(\chi_{4016}(305,\cdot)\) \(\chi_{4016}(321,\cdot)\) \(\chi_{4016}(385,\cdot)\) \(\chi_{4016}(401,\cdot)\) \(\chi_{4016}(417,\cdot)\) \(\chi_{4016}(481,\cdot)\) \(\chi_{4016}(513,\cdot)\) \(\chi_{4016}(545,\cdot)\) \(\chi_{4016}(561,\cdot)\) \(\chi_{4016}(609,\cdot)\) \(\chi_{4016}(641,\cdot)\) \(\chi_{4016}(705,\cdot)\) \(\chi_{4016}(849,\cdot)\) \(\chi_{4016}(929,\cdot)\) \(\chi_{4016}(977,\cdot)\) \(\chi_{4016}(1041,\cdot)\) \(\chi_{4016}(1057,\cdot)\) \(\chi_{4016}(1137,\cdot)\) \(\chi_{4016}(1169,\cdot)\) \(\chi_{4016}(1217,\cdot)\) \(\chi_{4016}(1233,\cdot)\) \(\chi_{4016}(1281,\cdot)\) \(\chi_{4016}(1297,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{125})$ |
| Fixed field: | Number field defined by a degree 250 polynomial (not computed) |
Values on generators
\((2511,3013,257)\) → \((1,1,e\left(\frac{227}{250}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 4016 }(33, a) \) | \(-1\) | \(1\) | \(e\left(\frac{66}{125}\right)\) | \(e\left(\frac{1}{25}\right)\) | \(e\left(\frac{23}{125}\right)\) | \(e\left(\frac{7}{125}\right)\) | \(e\left(\frac{147}{250}\right)\) | \(e\left(\frac{32}{125}\right)\) | \(e\left(\frac{71}{125}\right)\) | \(e\left(\frac{24}{125}\right)\) | \(e\left(\frac{1}{250}\right)\) | \(e\left(\frac{89}{125}\right)\) |