Basic properties
| Modulus: | \(1723\) | |
| Conductor: | \(1723\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(246\) | 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 1723.l
\(\chi_{1723}(22,\cdot)\) \(\chi_{1723}(57,\cdot)\) \(\chi_{1723}(68,\cdot)\) \(\chi_{1723}(72,\cdot)\) \(\chi_{1723}(79,\cdot)\) \(\chi_{1723}(139,\cdot)\) \(\chi_{1723}(143,\cdot)\) \(\chi_{1723}(161,\cdot)\) \(\chi_{1723}(185,\cdot)\) \(\chi_{1723}(197,\cdot)\) \(\chi_{1723}(226,\cdot)\) \(\chi_{1723}(227,\cdot)\) \(\chi_{1723}(235,\cdot)\) \(\chi_{1723}(273,\cdot)\) \(\chi_{1723}(283,\cdot)\) \(\chi_{1723}(300,\cdot)\) \(\chi_{1723}(341,\cdot)\) \(\chi_{1723}(362,\cdot)\) \(\chi_{1723}(363,\cdot)\) \(\chi_{1723}(401,\cdot)\) \(\chi_{1723}(419,\cdot)\) \(\chi_{1723}(442,\cdot)\) \(\chi_{1723}(464,\cdot)\) \(\chi_{1723}(468,\cdot)\) \(\chi_{1723}(469,\cdot)\) \(\chi_{1723}(545,\cdot)\) \(\chi_{1723}(583,\cdot)\) \(\chi_{1723}(586,\cdot)\) \(\chi_{1723}(595,\cdot)\) \(\chi_{1723}(614,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{123})$ |
| Fixed field: | Number field defined by a degree 246 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{53}{246}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1723 }(22, a) \) | \(-1\) | \(1\) | \(e\left(\frac{49}{82}\right)\) | \(e\left(\frac{53}{246}\right)\) | \(e\left(\frac{8}{41}\right)\) | \(e\left(\frac{19}{82}\right)\) | \(e\left(\frac{100}{123}\right)\) | \(e\left(\frac{29}{82}\right)\) | \(e\left(\frac{65}{82}\right)\) | \(e\left(\frac{53}{123}\right)\) | \(e\left(\frac{34}{41}\right)\) | \(e\left(\frac{1}{3}\right)\) |