Basic properties
| Modulus: | \(87362\) | |
| Conductor: | \(43681\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(18810\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{43681}(63,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 87362.dp
\(\chi_{87362}(17,\cdot)\) \(\chi_{87362}(35,\cdot)\) \(\chi_{87362}(61,\cdot)\) \(\chi_{87362}(63,\cdot)\) \(\chi_{87362}(73,\cdot)\) \(\chi_{87362}(85,\cdot)\) \(\chi_{87362}(101,\cdot)\) \(\chi_{87362}(123,\cdot)\) \(\chi_{87362}(139,\cdot)\) \(\chi_{87362}(149,\cdot)\) \(\chi_{87362}(195,\cdot)\) \(\chi_{87362}(237,\cdot)\) \(\chi_{87362}(271,\cdot)\) \(\chi_{87362}(283,\cdot)\) \(\chi_{87362}(321,\cdot)\) \(\chi_{87362}(327,\cdot)\) \(\chi_{87362}(347,\cdot)\) \(\chi_{87362}(359,\cdot)\) \(\chi_{87362}(365,\cdot)\) \(\chi_{87362}(435,\cdot)\) \(\chi_{87362}(453,\cdot)\) \(\chi_{87362}(479,\cdot)\) \(\chi_{87362}(491,\cdot)\) \(\chi_{87362}(503,\cdot)\) \(\chi_{87362}(519,\cdot)\) \(\chi_{87362}(541,\cdot)\) \(\chi_{87362}(557,\cdot)\) \(\chi_{87362}(567,\cdot)\) \(\chi_{87362}(579,\cdot)\) \(\chi_{87362}(613,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{9405})$ |
| Fixed field: | Number field defined by a degree 18810 polynomial (not computed) |
Values on generators
\((21661,22023)\) → \((e\left(\frac{73}{110}\right),e\left(\frac{43}{171}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 87362 }(63, a) \) | \(-1\) | \(1\) | \(e\left(\frac{302}{855}\right)\) | \(e\left(\frac{4216}{9405}\right)\) | \(e\left(\frac{2287}{6270}\right)\) | \(e\left(\frac{604}{855}\right)\) | \(e\left(\frac{14263}{18810}\right)\) | \(e\left(\frac{7538}{9405}\right)\) | \(e\left(\frac{6557}{18810}\right)\) | \(e\left(\frac{2701}{3762}\right)\) | \(e\left(\frac{316}{1881}\right)\) | \(e\left(\frac{8432}{9405}\right)\) |