Basic properties
| Modulus: | \(13132\) | |
| Conductor: | \(3283\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(462\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3283}(2889,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 13132.fi
\(\chi_{13132}(5,\cdot)\) \(\chi_{13132}(45,\cdot)\) \(\chi_{13132}(661,\cdot)\) \(\chi_{13132}(745,\cdot)\) \(\chi_{13132}(789,\cdot)\) \(\chi_{13132}(857,\cdot)\) \(\chi_{13132}(929,\cdot)\) \(\chi_{13132}(941,\cdot)\) \(\chi_{13132}(1013,\cdot)\) \(\chi_{13132}(1125,\cdot)\) \(\chi_{13132}(1181,\cdot)\) \(\chi_{13132}(1209,\cdot)\) \(\chi_{13132}(1249,\cdot)\) \(\chi_{13132}(1517,\cdot)\) \(\chi_{13132}(1613,\cdot)\) \(\chi_{13132}(1769,\cdot)\) \(\chi_{13132}(1921,\cdot)\) \(\chi_{13132}(2189,\cdot)\) \(\chi_{13132}(2397,\cdot)\) \(\chi_{13132}(2537,\cdot)\) \(\chi_{13132}(2621,\cdot)\) \(\chi_{13132}(2733,\cdot)\) \(\chi_{13132}(2789,\cdot)\) \(\chi_{13132}(2805,\cdot)\) \(\chi_{13132}(2817,\cdot)\) \(\chi_{13132}(2889,\cdot)\) \(\chi_{13132}(3001,\cdot)\) \(\chi_{13132}(3085,\cdot)\) \(\chi_{13132}(3125,\cdot)\) \(\chi_{13132}(3377,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{231})$ |
| Fixed field: | Number field defined by a degree 462 polynomial (not computed) |
Values on generators
\((6567,4021,7841)\) → \((1,e\left(\frac{5}{42}\right),e\left(\frac{1}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 13132 }(2889, a) \) | \(1\) | \(1\) | \(e\left(\frac{206}{231}\right)\) | \(e\left(\frac{31}{231}\right)\) | \(e\left(\frac{181}{231}\right)\) | \(e\left(\frac{205}{462}\right)\) | \(e\left(\frac{61}{77}\right)\) | \(e\left(\frac{2}{77}\right)\) | \(e\left(\frac{409}{462}\right)\) | \(e\left(\frac{41}{66}\right)\) | \(e\left(\frac{184}{231}\right)\) | \(e\left(\frac{62}{231}\right)\) |