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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1309.da
\(\chi_{1309}(3,\cdot)\) \(\chi_{1309}(5,\cdot)\) \(\chi_{1309}(31,\cdot)\) \(\chi_{1309}(75,\cdot)\) \(\chi_{1309}(80,\cdot)\) \(\chi_{1309}(82,\cdot)\) \(\chi_{1309}(108,\cdot)\) \(\chi_{1309}(124,\cdot)\) \(\chi_{1309}(159,\cdot)\) \(\chi_{1309}(180,\cdot)\) \(\chi_{1309}(192,\cdot)\) \(\chi_{1309}(201,\cdot)\) \(\chi_{1309}(262,\cdot)\) \(\chi_{1309}(269,\cdot)\) \(\chi_{1309}(278,\cdot)\) \(\chi_{1309}(311,\cdot)\) \(\chi_{1309}(313,\cdot)\) \(\chi_{1309}(334,\cdot)\) \(\chi_{1309}(346,\cdot)\) \(\chi_{1309}(367,\cdot)\) \(\chi_{1309}(388,\cdot)\) \(\chi_{1309}(411,\cdot)\) \(\chi_{1309}(432,\cdot)\) \(\chi_{1309}(465,\cdot)\) \(\chi_{1309}(488,\cdot)\) \(\chi_{1309}(500,\cdot)\) \(\chi_{1309}(521,\cdot)\) \(\chi_{1309}(537,\cdot)\) \(\chi_{1309}(598,\cdot)\) \(\chi_{1309}(619,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{240})$ |
| Fixed field: | Number field defined by a degree 240 polynomial (not computed) |
Values on generators
\((1123,596,309)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{1}{5}\right),e\left(\frac{3}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 1309 }(180, a) \) | \(1\) | \(1\) | \(e\left(\frac{59}{120}\right)\) | \(e\left(\frac{149}{240}\right)\) | \(e\left(\frac{59}{60}\right)\) | \(e\left(\frac{217}{240}\right)\) | \(e\left(\frac{9}{80}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{29}{120}\right)\) | \(e\left(\frac{19}{48}\right)\) | \(e\left(\frac{29}{48}\right)\) | \(e\left(\frac{9}{20}\right)\) |