Basic properties
| Modulus: | \(8001\) | |
| Conductor: | \(8001\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | 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 8001.mq
\(\chi_{8001}(41,\cdot)\) \(\chi_{8001}(335,\cdot)\) \(\chi_{8001}(587,\cdot)\) \(\chi_{8001}(650,\cdot)\) \(\chi_{8001}(671,\cdot)\) \(\chi_{8001}(860,\cdot)\) \(\chi_{8001}(902,\cdot)\) \(\chi_{8001}(923,\cdot)\) \(\chi_{8001}(1595,\cdot)\) \(\chi_{8001}(1721,\cdot)\) \(\chi_{8001}(2120,\cdot)\) \(\chi_{8001}(2561,\cdot)\) \(\chi_{8001}(2624,\cdot)\) \(\chi_{8001}(2729,\cdot)\) \(\chi_{8001}(2876,\cdot)\) \(\chi_{8001}(2918,\cdot)\) \(\chi_{8001}(2939,\cdot)\) \(\chi_{8001}(2981,\cdot)\) \(\chi_{8001}(3065,\cdot)\) \(\chi_{8001}(3296,\cdot)\) \(\chi_{8001}(3422,\cdot)\) \(\chi_{8001}(3821,\cdot)\) \(\chi_{8001}(3884,\cdot)\) \(\chi_{8001}(4052,\cdot)\) \(\chi_{8001}(4073,\cdot)\) \(\chi_{8001}(4136,\cdot)\) \(\chi_{8001}(4304,\cdot)\) \(\chi_{8001}(4514,\cdot)\) \(\chi_{8001}(5438,\cdot)\) \(\chi_{8001}(6131,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((3557,1144,7750)\) → \((e\left(\frac{5}{6}\right),-1,e\left(\frac{40}{63}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 8001 }(41, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{2}{21}\right)\) | \(e\left(\frac{19}{21}\right)\) | \(e\left(\frac{9}{14}\right)\) | \(e\left(\frac{19}{42}\right)\) | \(e\left(\frac{1}{126}\right)\) | \(e\left(\frac{107}{126}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{8}{63}\right)\) | \(e\left(\frac{5}{6}\right)\) |