Basic properties
| Modulus: | \(4005\) | |
| Conductor: | \(801\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(264\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{801}(41,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4005.eb
\(\chi_{4005}(41,\cdot)\) \(\chi_{4005}(56,\cdot)\) \(\chi_{4005}(86,\cdot)\) \(\chi_{4005}(191,\cdot)\) \(\chi_{4005}(221,\cdot)\) \(\chi_{4005}(236,\cdot)\) \(\chi_{4005}(281,\cdot)\) \(\chi_{4005}(326,\cdot)\) \(\chi_{4005}(371,\cdot)\) \(\chi_{4005}(416,\cdot)\) \(\chi_{4005}(491,\cdot)\) \(\chi_{4005}(506,\cdot)\) \(\chi_{4005}(596,\cdot)\) \(\chi_{4005}(626,\cdot)\) \(\chi_{4005}(671,\cdot)\) \(\chi_{4005}(686,\cdot)\) \(\chi_{4005}(731,\cdot)\) \(\chi_{4005}(866,\cdot)\) \(\chi_{4005}(896,\cdot)\) \(\chi_{4005}(941,\cdot)\) \(\chi_{4005}(956,\cdot)\) \(\chi_{4005}(986,\cdot)\) \(\chi_{4005}(1091,\cdot)\) \(\chi_{4005}(1181,\cdot)\) \(\chi_{4005}(1211,\cdot)\) \(\chi_{4005}(1316,\cdot)\) \(\chi_{4005}(1361,\cdot)\) \(\chi_{4005}(1391,\cdot)\) \(\chi_{4005}(1451,\cdot)\) \(\chi_{4005}(1526,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{264})$ |
| Fixed field: | Number field defined by a degree 264 polynomial (not computed) |
Values on generators
\((3116,802,181)\) → \((e\left(\frac{5}{6}\right),1,e\left(\frac{21}{88}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 4005 }(41, a) \) | \(1\) | \(1\) | \(e\left(\frac{43}{66}\right)\) | \(e\left(\frac{10}{33}\right)\) | \(e\left(\frac{175}{264}\right)\) | \(e\left(\frac{21}{22}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{41}{264}\right)\) | \(e\left(\frac{83}{264}\right)\) | \(e\left(\frac{20}{33}\right)\) | \(e\left(\frac{41}{44}\right)\) | \(e\left(\frac{31}{88}\right)\) |