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 \(\chi_{43681}(59,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 87362.dr
\(\chi_{87362}(15,\cdot)\) \(\chi_{87362}(53,\cdot)\) \(\chi_{87362}(59,\cdot)\) \(\chi_{87362}(71,\cdot)\) \(\chi_{87362}(91,\cdot)\) \(\chi_{87362}(97,\cdot)\) \(\chi_{87362}(135,\cdot)\) \(\chi_{87362}(147,\cdot)\) \(\chi_{87362}(181,\cdot)\) \(\chi_{87362}(185,\cdot)\) \(\chi_{87362}(203,\cdot)\) \(\chi_{87362}(223,\cdot)\) \(\chi_{87362}(257,\cdot)\) \(\chi_{87362}(279,\cdot)\) \(\chi_{87362}(295,\cdot)\) \(\chi_{87362}(317,\cdot)\) \(\chi_{87362}(345,\cdot)\) \(\chi_{87362}(355,\cdot)\) \(\chi_{87362}(357,\cdot)\) \(\chi_{87362}(383,\cdot)\) \(\chi_{87362}(401,\cdot)\) \(\chi_{87362}(421,\cdot)\) \(\chi_{87362}(433,\cdot)\) \(\chi_{87362}(471,\cdot)\) \(\chi_{87362}(489,\cdot)\) \(\chi_{87362}(509,\cdot)\) \(\chi_{87362}(515,\cdot)\) \(\chi_{87362}(553,\cdot)\) \(\chi_{87362}(599,\cdot)\) \(\chi_{87362}(603,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{9405})$ |
| Fixed field: | Number field defined by a degree 18810 polynomial (not computed) |
Values on generators
\((21661,22023)\) → \((e\left(\frac{16}{55}\right),e\left(\frac{181}{342}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 87362 }(59, a) \) | \(-1\) | \(1\) | \(e\left(\frac{281}{1710}\right)\) | \(e\left(\frac{2924}{9405}\right)\) | \(e\left(\frac{1324}{3135}\right)\) | \(e\left(\frac{281}{855}\right)\) | \(e\left(\frac{9437}{18810}\right)\) | \(e\left(\frac{8939}{18810}\right)\) | \(e\left(\frac{8114}{9405}\right)\) | \(e\left(\frac{2207}{3762}\right)\) | \(e\left(\frac{1190}{1881}\right)\) | \(e\left(\frac{5848}{9405}\right)\) |