Basic properties
| Modulus: | \(43681\) | |
| Conductor: | \(43681\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(18810\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 43681.dp
\(\chi_{43681}(6,\cdot)\) \(\chi_{43681}(17,\cdot)\) \(\chi_{43681}(24,\cdot)\) \(\chi_{43681}(35,\cdot)\) \(\chi_{43681}(61,\cdot)\) \(\chi_{43681}(63,\cdot)\) \(\chi_{43681}(73,\cdot)\) \(\chi_{43681}(74,\cdot)\) \(\chi_{43681}(85,\cdot)\) \(\chi_{43681}(101,\cdot)\) \(\chi_{43681}(123,\cdot)\) \(\chi_{43681}(138,\cdot)\) \(\chi_{43681}(139,\cdot)\) \(\chi_{43681}(149,\cdot)\) \(\chi_{43681}(150,\cdot)\) \(\chi_{43681}(156,\cdot)\) \(\chi_{43681}(194,\cdot)\) \(\chi_{43681}(195,\cdot)\) \(\chi_{43681}(206,\cdot)\) \(\chi_{43681}(226,\cdot)\) \(\chi_{43681}(237,\cdot)\) \(\chi_{43681}(244,\cdot)\) \(\chi_{43681}(270,\cdot)\) \(\chi_{43681}(271,\cdot)\) \(\chi_{43681}(272,\cdot)\) \(\chi_{43681}(283,\cdot)\) \(\chi_{43681}(294,\cdot)\) \(\chi_{43681}(310,\cdot)\) \(\chi_{43681}(321,\cdot)\) \(\chi_{43681}(327,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{9405})$ |
| Fixed field: | Number field defined by a degree 18810 polynomial (not computed) |
Values on generators
\((21661,22023)\) → \((e\left(\frac{37}{110}\right),e\left(\frac{56}{171}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 43681 }(73, a) \) | \(-1\) | \(1\) | \(e\left(\frac{12487}{18810}\right)\) | \(e\left(\frac{103}{855}\right)\) | \(e\left(\frac{3082}{9405}\right)\) | \(e\left(\frac{8159}{9405}\right)\) | \(e\left(\frac{14753}{18810}\right)\) | \(e\left(\frac{2993}{6270}\right)\) | \(e\left(\frac{6217}{6270}\right)\) | \(e\left(\frac{206}{855}\right)\) | \(e\left(\frac{1999}{3762}\right)\) | \(e\left(\frac{281}{627}\right)\) |