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 \(\chi_{3971}(3633,\cdot)\) | 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
\((21661,22023)\) → \((e\left(\frac{4}{5}\right),e\left(\frac{73}{171}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
\( \chi_{ 87362 }(3633, a) \) | \(1\) | \(1\) | \(e\left(\frac{632}{855}\right)\) | \(e\left(\frac{206}{855}\right)\) | \(e\left(\frac{181}{285}\right)\) | \(e\left(\frac{409}{855}\right)\) | \(e\left(\frac{214}{855}\right)\) | \(e\left(\frac{838}{855}\right)\) | \(e\left(\frac{581}{855}\right)\) | \(e\left(\frac{64}{171}\right)\) | \(e\left(\frac{56}{171}\right)\) | \(e\left(\frac{412}{855}\right)\) |