Basic properties
| Modulus: | \(4235\) | |
| Conductor: | \(4235\) | 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 4235.cy
\(\chi_{4235}(87,\cdot)\) \(\chi_{4235}(208,\cdot)\) \(\chi_{4235}(318,\cdot)\) \(\chi_{4235}(472,\cdot)\) \(\chi_{4235}(593,\cdot)\) \(\chi_{4235}(703,\cdot)\) \(\chi_{4235}(747,\cdot)\) \(\chi_{4235}(857,\cdot)\) \(\chi_{4235}(978,\cdot)\) \(\chi_{4235}(1132,\cdot)\) \(\chi_{4235}(1242,\cdot)\) \(\chi_{4235}(1363,\cdot)\) \(\chi_{4235}(1473,\cdot)\) \(\chi_{4235}(1517,\cdot)\) \(\chi_{4235}(1627,\cdot)\) \(\chi_{4235}(1748,\cdot)\) \(\chi_{4235}(1858,\cdot)\) \(\chi_{4235}(1902,\cdot)\) \(\chi_{4235}(2012,\cdot)\) \(\chi_{4235}(2133,\cdot)\) \(\chi_{4235}(2243,\cdot)\) \(\chi_{4235}(2287,\cdot)\) \(\chi_{4235}(2397,\cdot)\) \(\chi_{4235}(2518,\cdot)\) \(\chi_{4235}(2628,\cdot)\) \(\chi_{4235}(2672,\cdot)\) \(\chi_{4235}(3013,\cdot)\) \(\chi_{4235}(3057,\cdot)\) \(\chi_{4235}(3167,\cdot)\) \(\chi_{4235}(3288,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((2542,1816,2906)\) → \((i,e\left(\frac{5}{6}\right),e\left(\frac{5}{22}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(8\) | \(9\) | \(12\) | \(13\) | \(16\) | \(17\) |
| \( \chi_{ 4235 }(1132, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{132}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{19}{66}\right)\) | \(e\left(\frac{8}{11}\right)\) | \(e\left(\frac{19}{44}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{115}{132}\right)\) | \(e\left(\frac{9}{44}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{29}{132}\right)\) |