Basic properties
| Modulus: | \(87362\) | |
| Conductor: | \(3971\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(855\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3971}(9,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 87362.cs
\(\chi_{87362}(9,\cdot)\) \(\chi_{87362}(81,\cdot)\) \(\chi_{87362}(251,\cdot)\) \(\chi_{87362}(511,\cdot)\) \(\chi_{87362}(807,\cdot)\) \(\chi_{87362}(1049,\cdot)\) \(\chi_{87362}(1213,\cdot)\) \(\chi_{87362}(1461,\cdot)\) \(\chi_{87362}(1479,\cdot)\) \(\chi_{87362}(1697,\cdot)\) \(\chi_{87362}(1963,\cdot)\) \(\chi_{87362}(2259,\cdot)\) \(\chi_{87362}(2429,\cdot)\) \(\chi_{87362}(2665,\cdot)\) \(\chi_{87362}(2913,\cdot)\) \(\chi_{87362}(2931,\cdot)\) \(\chi_{87362}(3227,\cdot)\) \(\chi_{87362}(3391,\cdot)\) \(\chi_{87362}(3633,\cdot)\) \(\chi_{87362}(3657,\cdot)\) \(\chi_{87362}(3711,\cdot)\) \(\chi_{87362}(3881,\cdot)\) \(\chi_{87362}(3899,\cdot)\) \(\chi_{87362}(4607,\cdot)\) \(\chi_{87362}(4679,\cdot)\) \(\chi_{87362}(4843,\cdot)\) \(\chi_{87362}(4849,\cdot)\) \(\chi_{87362}(5109,\cdot)\) \(\chi_{87362}(5405,\cdot)\) \(\chi_{87362}(5647,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{855})$ |
| Fixed field: | Number field defined by a degree 855 polynomial (not computed) |
Values on generators
\((21661,22023)\) → \((e\left(\frac{3}{5}\right),e\left(\frac{139}{171}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 87362 }(9, a) \) | \(1\) | \(1\) | \(e\left(\frac{674}{855}\right)\) | \(e\left(\frac{842}{855}\right)\) | \(e\left(\frac{37}{285}\right)\) | \(e\left(\frac{493}{855}\right)\) | \(e\left(\frac{28}{855}\right)\) | \(e\left(\frac{661}{855}\right)\) | \(e\left(\frac{92}{855}\right)\) | \(e\left(\frac{157}{171}\right)\) | \(e\left(\frac{116}{171}\right)\) | \(e\left(\frac{829}{855}\right)\) |