Basic properties
| Modulus: | \(6272\) | |
| Conductor: | \(3136\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(112\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3136}(2211,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6272.cy
\(\chi_{6272}(55,\cdot)\) \(\chi_{6272}(167,\cdot)\) \(\chi_{6272}(279,\cdot)\) \(\chi_{6272}(503,\cdot)\) \(\chi_{6272}(615,\cdot)\) \(\chi_{6272}(727,\cdot)\) \(\chi_{6272}(839,\cdot)\) \(\chi_{6272}(951,\cdot)\) \(\chi_{6272}(1063,\cdot)\) \(\chi_{6272}(1287,\cdot)\) \(\chi_{6272}(1399,\cdot)\) \(\chi_{6272}(1511,\cdot)\) \(\chi_{6272}(1623,\cdot)\) \(\chi_{6272}(1735,\cdot)\) \(\chi_{6272}(1847,\cdot)\) \(\chi_{6272}(2071,\cdot)\) \(\chi_{6272}(2183,\cdot)\) \(\chi_{6272}(2295,\cdot)\) \(\chi_{6272}(2407,\cdot)\) \(\chi_{6272}(2519,\cdot)\) \(\chi_{6272}(2631,\cdot)\) \(\chi_{6272}(2855,\cdot)\) \(\chi_{6272}(2967,\cdot)\) \(\chi_{6272}(3079,\cdot)\) \(\chi_{6272}(3191,\cdot)\) \(\chi_{6272}(3303,\cdot)\) \(\chi_{6272}(3415,\cdot)\) \(\chi_{6272}(3639,\cdot)\) \(\chi_{6272}(3751,\cdot)\) \(\chi_{6272}(3863,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{112})$ |
| Fixed field: | Number field defined by a degree 112 polynomial (not computed) |
Values on generators
\((4607,3333,4609)\) → \((-1,e\left(\frac{11}{16}\right),e\left(\frac{9}{14}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 6272 }(55, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{112}\right)\) | \(e\left(\frac{37}{112}\right)\) | \(e\left(\frac{23}{56}\right)\) | \(e\left(\frac{73}{112}\right)\) | \(e\left(\frac{59}{112}\right)\) | \(e\left(\frac{15}{28}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{13}{16}\right)\) | \(e\left(\frac{31}{56}\right)\) | \(e\left(\frac{37}{56}\right)\) |