Basic properties
| Modulus: | \(87362\) | |
| Conductor: | \(43681\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(3135\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{43681}(49,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 87362.dh
\(\chi_{87362}(49,\cdot)\) \(\chi_{87362}(125,\cdot)\) \(\chi_{87362}(159,\cdot)\) \(\chi_{87362}(163,\cdot)\) \(\chi_{87362}(201,\cdot)\) \(\chi_{87362}(235,\cdot)\) \(\chi_{87362}(273,\cdot)\) \(\chi_{87362}(311,\cdot)\) \(\chi_{87362}(467,\cdot)\) \(\chi_{87362}(543,\cdot)\) \(\chi_{87362}(577,\cdot)\) \(\chi_{87362}(581,\cdot)\) \(\chi_{87362}(619,\cdot)\) \(\chi_{87362}(691,\cdot)\) \(\chi_{87362}(885,\cdot)\) \(\chi_{87362}(961,\cdot)\) \(\chi_{87362}(999,\cdot)\) \(\chi_{87362}(1037,\cdot)\) \(\chi_{87362}(1071,\cdot)\) \(\chi_{87362}(1109,\cdot)\) \(\chi_{87362}(1147,\cdot)\) \(\chi_{87362}(1303,\cdot)\) \(\chi_{87362}(1379,\cdot)\) \(\chi_{87362}(1413,\cdot)\) \(\chi_{87362}(1417,\cdot)\) \(\chi_{87362}(1489,\cdot)\) \(\chi_{87362}(1527,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{3135})$ |
| Fixed field: | Number field defined by a degree 3135 polynomial (not computed) |
Values on generators
\((21661,22023)\) → \((e\left(\frac{7}{55}\right),e\left(\frac{50}{57}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 87362 }(49, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{285}\right)\) | \(e\left(\frac{2906}{3135}\right)\) | \(e\left(\frac{491}{1045}\right)\) | \(e\left(\frac{74}{285}\right)\) | \(e\left(\frac{1414}{3135}\right)\) | \(e\left(\frac{178}{3135}\right)\) | \(e\left(\frac{1511}{3135}\right)\) | \(e\left(\frac{376}{627}\right)\) | \(e\left(\frac{614}{627}\right)\) | \(e\left(\frac{2677}{3135}\right)\) |