Basic properties
| Modulus: | \(87362\) | |
| Conductor: | \(43681\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(9405\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{43681}(5,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 87362.do
\(\chi_{87362}(5,\cdot)\) \(\chi_{87362}(25,\cdot)\) \(\chi_{87362}(47,\cdot)\) \(\chi_{87362}(93,\cdot)\) \(\chi_{87362}(119,\cdot)\) \(\chi_{87362}(137,\cdot)\) \(\chi_{87362}(157,\cdot)\) \(\chi_{87362}(169,\cdot)\) \(\chi_{87362}(207,\cdot)\) \(\chi_{87362}(213,\cdot)\) \(\chi_{87362}(225,\cdot)\) \(\chi_{87362}(289,\cdot)\) \(\chi_{87362}(291,\cdot)\) \(\chi_{87362}(301,\cdot)\) \(\chi_{87362}(313,\cdot)\) \(\chi_{87362}(339,\cdot)\) \(\chi_{87362}(367,\cdot)\) \(\chi_{87362}(377,\cdot)\) \(\chi_{87362}(405,\cdot)\) \(\chi_{87362}(427,\cdot)\) \(\chi_{87362}(443,\cdot)\) \(\chi_{87362}(465,\cdot)\) \(\chi_{87362}(499,\cdot)\) \(\chi_{87362}(537,\cdot)\) \(\chi_{87362}(555,\cdot)\) \(\chi_{87362}(575,\cdot)\) \(\chi_{87362}(587,\cdot)\) \(\chi_{87362}(625,\cdot)\) \(\chi_{87362}(631,\cdot)\) \(\chi_{87362}(643,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{9405})$ |
| Fixed field: | Number field defined by a degree 9405 polynomial (not computed) |
Values on generators
\((21661,22023)\) → \((e\left(\frac{37}{55}\right),e\left(\frac{116}{171}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 87362 }(5, a) \) | \(1\) | \(1\) | \(e\left(\frac{421}{855}\right)\) | \(e\left(\frac{1523}{9405}\right)\) | \(e\left(\frac{1453}{3135}\right)\) | \(e\left(\frac{842}{855}\right)\) | \(e\left(\frac{1192}{9405}\right)\) | \(e\left(\frac{6154}{9405}\right)\) | \(e\left(\frac{2573}{9405}\right)\) | \(e\left(\frac{1798}{1881}\right)\) | \(e\left(\frac{248}{1881}\right)\) | \(e\left(\frac{3046}{9405}\right)\) |