Basic properties
| Modulus: | \(4005\) | |
| Conductor: | \(4005\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(264\) | 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 4005.eh
\(\chi_{4005}(14,\cdot)\) \(\chi_{4005}(29,\cdot)\) \(\chi_{4005}(59,\cdot)\) \(\chi_{4005}(74,\cdot)\) \(\chi_{4005}(104,\cdot)\) \(\chi_{4005}(119,\cdot)\) \(\chi_{4005}(149,\cdot)\) \(\chi_{4005}(164,\cdot)\) \(\chi_{4005}(209,\cdot)\) \(\chi_{4005}(239,\cdot)\) \(\chi_{4005}(254,\cdot)\) \(\chi_{4005}(329,\cdot)\) \(\chi_{4005}(389,\cdot)\) \(\chi_{4005}(419,\cdot)\) \(\chi_{4005}(464,\cdot)\) \(\chi_{4005}(569,\cdot)\) \(\chi_{4005}(599,\cdot)\) \(\chi_{4005}(689,\cdot)\) \(\chi_{4005}(794,\cdot)\) \(\chi_{4005}(824,\cdot)\) \(\chi_{4005}(839,\cdot)\) \(\chi_{4005}(884,\cdot)\) \(\chi_{4005}(914,\cdot)\) \(\chi_{4005}(1049,\cdot)\) \(\chi_{4005}(1094,\cdot)\) \(\chi_{4005}(1109,\cdot)\) \(\chi_{4005}(1154,\cdot)\) \(\chi_{4005}(1184,\cdot)\) \(\chi_{4005}(1274,\cdot)\) \(\chi_{4005}(1289,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{264})$ |
| Fixed field: | Number field defined by a degree 264 polynomial (not computed) |
Values on generators
\((3116,802,181)\) → \((e\left(\frac{5}{6}\right),-1,e\left(\frac{9}{88}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(7\) | \(8\) | \(11\) | \(13\) | \(14\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 4005 }(14, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{33}\right)\) | \(e\left(\frac{31}{33}\right)\) | \(e\left(\frac{31}{264}\right)\) | \(e\left(\frac{10}{11}\right)\) | \(e\left(\frac{14}{33}\right)\) | \(e\left(\frac{137}{264}\right)\) | \(e\left(\frac{23}{264}\right)\) | \(e\left(\frac{29}{33}\right)\) | \(e\left(\frac{27}{44}\right)\) | \(e\left(\frac{51}{88}\right)\) |