Basic properties
| Modulus: | \(2093\) | |
| Conductor: | \(2093\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2093.ed
\(\chi_{2093}(5,\cdot)\) \(\chi_{2093}(122,\cdot)\) \(\chi_{2093}(304,\cdot)\) \(\chi_{2093}(320,\cdot)\) \(\chi_{2093}(411,\cdot)\) \(\chi_{2093}(502,\cdot)\) \(\chi_{2093}(619,\cdot)\) \(\chi_{2093}(642,\cdot)\) \(\chi_{2093}(684,\cdot)\) \(\chi_{2093}(710,\cdot)\) \(\chi_{2093}(733,\cdot)\) \(\chi_{2093}(801,\cdot)\) \(\chi_{2093}(824,\cdot)\) \(\chi_{2093}(866,\cdot)\) \(\chi_{2093}(941,\cdot)\) \(\chi_{2093}(957,\cdot)\) \(\chi_{2093}(983,\cdot)\) \(\chi_{2093}(1006,\cdot)\) \(\chi_{2093}(1032,\cdot)\) \(\chi_{2093}(1123,\cdot)\) \(\chi_{2093}(1165,\cdot)\) \(\chi_{2093}(1188,\cdot)\) \(\chi_{2093}(1230,\cdot)\) \(\chi_{2093}(1256,\cdot)\) \(\chi_{2093}(1279,\cdot)\) \(\chi_{2093}(1305,\cdot)\) \(\chi_{2093}(1321,\cdot)\) \(\chi_{2093}(1487,\cdot)\) \(\chi_{2093}(1529,\cdot)\) \(\chi_{2093}(1552,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((1795,1289,1730)\) → \((e\left(\frac{5}{6}\right),-i,e\left(\frac{1}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 2093 }(5, a) \) | \(-1\) | \(1\) | \(e\left(\frac{67}{132}\right)\) | \(e\left(\frac{37}{66}\right)\) | \(e\left(\frac{1}{66}\right)\) | \(e\left(\frac{127}{132}\right)\) | \(e\left(\frac{3}{44}\right)\) | \(e\left(\frac{23}{44}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{31}{66}\right)\) | \(e\left(\frac{131}{132}\right)\) | \(e\left(\frac{19}{33}\right)\) |