Basic properties
Modulus: | \(6762\) | |
Conductor: | \(1127\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(462\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{1127}(61,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6762.ch
\(\chi_{6762}(61,\cdot)\) \(\chi_{6762}(103,\cdot)\) \(\chi_{6762}(145,\cdot)\) \(\chi_{6762}(157,\cdot)\) \(\chi_{6762}(199,\cdot)\) \(\chi_{6762}(241,\cdot)\) \(\chi_{6762}(283,\cdot)\) \(\chi_{6762}(355,\cdot)\) \(\chi_{6762}(451,\cdot)\) \(\chi_{6762}(481,\cdot)\) \(\chi_{6762}(493,\cdot)\) \(\chi_{6762}(523,\cdot)\) \(\chi_{6762}(649,\cdot)\) \(\chi_{6762}(661,\cdot)\) \(\chi_{6762}(733,\cdot)\) \(\chi_{6762}(787,\cdot)\) \(\chi_{6762}(871,\cdot)\) \(\chi_{6762}(985,\cdot)\) \(\chi_{6762}(1027,\cdot)\) \(\chi_{6762}(1069,\cdot)\) \(\chi_{6762}(1111,\cdot)\) \(\chi_{6762}(1123,\cdot)\) \(\chi_{6762}(1165,\cdot)\) \(\chi_{6762}(1249,\cdot)\) \(\chi_{6762}(1279,\cdot)\) \(\chi_{6762}(1321,\cdot)\) \(\chi_{6762}(1417,\cdot)\) \(\chi_{6762}(1447,\cdot)\) \(\chi_{6762}(1459,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{231})$ |
Fixed field: | Number field defined by a degree 462 polynomial (not computed) |
Values on generators
\((2255,3727,3823)\) → \((1,e\left(\frac{11}{42}\right),e\left(\frac{17}{22}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 6762 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{85}{231}\right)\) | \(e\left(\frac{199}{462}\right)\) | \(e\left(\frac{71}{154}\right)\) | \(e\left(\frac{221}{231}\right)\) | \(e\left(\frac{25}{33}\right)\) | \(e\left(\frac{170}{231}\right)\) | \(e\left(\frac{48}{77}\right)\) | \(e\left(\frac{31}{66}\right)\) | \(e\left(\frac{281}{462}\right)\) | \(e\left(\frac{31}{154}\right)\) |