Basic properties
| Modulus: | \(87362\) | |
| Conductor: | \(43681\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(627\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{43681}(45,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 87362.cr
\(\chi_{87362}(45,\cdot)\) \(\chi_{87362}(353,\cdot)\) \(\chi_{87362}(463,\cdot)\) \(\chi_{87362}(771,\cdot)\) \(\chi_{87362}(881,\cdot)\) \(\chi_{87362}(1189,\cdot)\) \(\chi_{87362}(1299,\cdot)\) \(\chi_{87362}(1607,\cdot)\) \(\chi_{87362}(1717,\cdot)\) \(\chi_{87362}(2025,\cdot)\) \(\chi_{87362}(2135,\cdot)\) \(\chi_{87362}(2443,\cdot)\) \(\chi_{87362}(2553,\cdot)\) \(\chi_{87362}(2861,\cdot)\) \(\chi_{87362}(2971,\cdot)\) \(\chi_{87362}(3279,\cdot)\) \(\chi_{87362}(3697,\cdot)\) \(\chi_{87362}(3807,\cdot)\) \(\chi_{87362}(4225,\cdot)\) \(\chi_{87362}(4533,\cdot)\) \(\chi_{87362}(4643,\cdot)\) \(\chi_{87362}(4951,\cdot)\) \(\chi_{87362}(5061,\cdot)\) \(\chi_{87362}(5369,\cdot)\) \(\chi_{87362}(5479,\cdot)\) \(\chi_{87362}(5787,\cdot)\) \(\chi_{87362}(5897,\cdot)\) \(\chi_{87362}(6315,\cdot)\) \(\chi_{87362}(6623,\cdot)\) \(\chi_{87362}(6733,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{627})$ |
| Fixed field: | Number field defined by a degree 627 polynomial (not computed) |
Values on generators
\((21661,22023)\) → \((e\left(\frac{3}{11}\right),e\left(\frac{28}{57}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 87362 }(45, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{57}\right)\) | \(e\left(\frac{92}{627}\right)\) | \(e\left(\frac{124}{209}\right)\) | \(e\left(\frac{32}{57}\right)\) | \(e\left(\frac{100}{627}\right)\) | \(e\left(\frac{268}{627}\right)\) | \(e\left(\frac{239}{627}\right)\) | \(e\left(\frac{548}{627}\right)\) | \(e\left(\frac{508}{627}\right)\) | \(e\left(\frac{184}{627}\right)\) |