Basic properties
| Modulus: | \(1309\) | |
| Conductor: | \(1309\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(240\) | 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 1309.db
\(\chi_{1309}(37,\cdot)\) \(\chi_{1309}(58,\cdot)\) \(\chi_{1309}(114,\cdot)\) \(\chi_{1309}(130,\cdot)\) \(\chi_{1309}(158,\cdot)\) \(\chi_{1309}(163,\cdot)\) \(\chi_{1309}(207,\cdot)\) \(\chi_{1309}(214,\cdot)\) \(\chi_{1309}(235,\cdot)\) \(\chi_{1309}(284,\cdot)\) \(\chi_{1309}(312,\cdot)\) \(\chi_{1309}(317,\cdot)\) \(\chi_{1309}(333,\cdot)\) \(\chi_{1309}(345,\cdot)\) \(\chi_{1309}(368,\cdot)\) \(\chi_{1309}(394,\cdot)\) \(\chi_{1309}(401,\cdot)\) \(\chi_{1309}(422,\cdot)\) \(\chi_{1309}(445,\cdot)\) \(\chi_{1309}(466,\cdot)\) \(\chi_{1309}(471,\cdot)\) \(\chi_{1309}(487,\cdot)\) \(\chi_{1309}(499,\cdot)\) \(\chi_{1309}(515,\cdot)\) \(\chi_{1309}(520,\cdot)\) \(\chi_{1309}(522,\cdot)\) \(\chi_{1309}(555,\cdot)\) \(\chi_{1309}(564,\cdot)\) \(\chi_{1309}(592,\cdot)\) \(\chi_{1309}(632,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{240})$ |
| Fixed field: | Number field defined by a degree 240 polynomial (not computed) |
Values on generators
\((1123,596,309)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{1}{5}\right),e\left(\frac{1}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 1309 }(37, a) \) | \(-1\) | \(1\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{239}{240}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{187}{240}\right)\) | \(e\left(\frac{59}{80}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{25}{48}\right)\) | \(e\left(\frac{23}{48}\right)\) | \(e\left(\frac{9}{20}\right)\) |