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 \(\chi_{43681}(11193,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 87362.dq
\(\chi_{87362}(13,\cdot)\) \(\chi_{87362}(29,\cdot)\) \(\chi_{87362}(41,\cdot)\) \(\chi_{87362}(51,\cdot)\) \(\chi_{87362}(79,\cdot)\) \(\chi_{87362}(105,\cdot)\) \(\chi_{87362}(117,\cdot)\) \(\chi_{87362}(129,\cdot)\) \(\chi_{87362}(167,\cdot)\) \(\chi_{87362}(173,\cdot)\) \(\chi_{87362}(193,\cdot)\) \(\chi_{87362}(205,\cdot)\) \(\chi_{87362}(211,\cdot)\) \(\chi_{87362}(249,\cdot)\) \(\chi_{87362}(261,\cdot)\) \(\chi_{87362}(281,\cdot)\) \(\chi_{87362}(325,\cdot)\) \(\chi_{87362}(337,\cdot)\) \(\chi_{87362}(371,\cdot)\) \(\chi_{87362}(393,\cdot)\) \(\chi_{87362}(409,\cdot)\) \(\chi_{87362}(413,\cdot)\) \(\chi_{87362}(431,\cdot)\) \(\chi_{87362}(447,\cdot)\) \(\chi_{87362}(459,\cdot)\) \(\chi_{87362}(469,\cdot)\) \(\chi_{87362}(497,\cdot)\) \(\chi_{87362}(523,\cdot)\) \(\chi_{87362}(535,\cdot)\) \(\chi_{87362}(545,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{9405})$ |
| Fixed field: | Number field defined by a degree 18810 polynomial (not computed) |
Values on generators
\((21661,22023)\) → \((e\left(\frac{109}{110}\right),e\left(\frac{1}{342}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) | \(25\) |
| \( \chi_{ 87362 }(11193, a) \) | \(1\) | \(1\) | \(e\left(\frac{1037}{1710}\right)\) | \(e\left(\frac{53}{9405}\right)\) | \(e\left(\frac{2351}{6270}\right)\) | \(e\left(\frac{182}{855}\right)\) | \(e\left(\frac{412}{9405}\right)\) | \(e\left(\frac{11513}{18810}\right)\) | \(e\left(\frac{4051}{18810}\right)\) | \(e\left(\frac{1846}{1881}\right)\) | \(e\left(\frac{1487}{1881}\right)\) | \(e\left(\frac{106}{9405}\right)\) |