Basic properties
| Modulus: | \(8044\) | |
| Conductor: | \(2011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(201\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2011}(117,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8044.u
\(\chi_{8044}(117,\cdot)\) \(\chi_{8044}(189,\cdot)\) \(\chi_{8044}(193,\cdot)\) \(\chi_{8044}(209,\cdot)\) \(\chi_{8044}(225,\cdot)\) \(\chi_{8044}(237,\cdot)\) \(\chi_{8044}(297,\cdot)\) \(\chi_{8044}(577,\cdot)\) \(\chi_{8044}(717,\cdot)\) \(\chi_{8044}(845,\cdot)\) \(\chi_{8044}(893,\cdot)\) \(\chi_{8044}(901,\cdot)\) \(\chi_{8044}(909,\cdot)\) \(\chi_{8044}(1005,\cdot)\) \(\chi_{8044}(1093,\cdot)\) \(\chi_{8044}(1121,\cdot)\) \(\chi_{8044}(1369,\cdot)\) \(\chi_{8044}(1389,\cdot)\) \(\chi_{8044}(1417,\cdot)\) \(\chi_{8044}(1453,\cdot)\) \(\chi_{8044}(1537,\cdot)\) \(\chi_{8044}(1745,\cdot)\) \(\chi_{8044}(1777,\cdot)\) \(\chi_{8044}(1781,\cdot)\) \(\chi_{8044}(2009,\cdot)\) \(\chi_{8044}(2041,\cdot)\) \(\chi_{8044}(2145,\cdot)\) \(\chi_{8044}(2205,\cdot)\) \(\chi_{8044}(2297,\cdot)\) \(\chi_{8044}(2305,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{201})$ |
| Fixed field: | Number field defined by a degree 201 polynomial (not computed) |
Values on generators
\((4023,4025)\) → \((1,e\left(\frac{194}{201}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 8044 }(117, a) \) | \(1\) | \(1\) | \(e\left(\frac{194}{201}\right)\) | \(e\left(\frac{68}{201}\right)\) | \(e\left(\frac{14}{201}\right)\) | \(e\left(\frac{187}{201}\right)\) | \(e\left(\frac{178}{201}\right)\) | \(e\left(\frac{34}{67}\right)\) | \(e\left(\frac{61}{201}\right)\) | \(e\left(\frac{184}{201}\right)\) | \(e\left(\frac{100}{201}\right)\) | \(e\left(\frac{7}{201}\right)\) |