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 \(\chi_{43681}(61,\cdot)\) | 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
\((21661,22023)\) → \((e\left(\frac{109}{110}\right),e\left(\frac{46}{171}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
\( \chi_{ 87362 }(61, a) \) | \(-1\) | \(1\) | \(e\left(\frac{506}{855}\right)\) | \(e\left(\frac{6928}{9405}\right)\) | \(e\left(\frac{1801}{6270}\right)\) | \(e\left(\frac{157}{855}\right)\) | \(e\left(\frac{10999}{18810}\right)\) | \(e\left(\frac{3089}{9405}\right)\) | \(e\left(\frac{6581}{18810}\right)\) | \(e\left(\frac{3307}{3762}\right)\) | \(e\left(\frac{1201}{1881}\right)\) | \(e\left(\frac{4451}{9405}\right)\) |