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.cy
\(\chi_{1309}(39,\cdot)\) \(\chi_{1309}(46,\cdot)\) \(\chi_{1309}(74,\cdot)\) \(\chi_{1309}(79,\cdot)\) \(\chi_{1309}(95,\cdot)\) \(\chi_{1309}(107,\cdot)\) \(\chi_{1309}(116,\cdot)\) \(\chi_{1309}(156,\cdot)\) \(\chi_{1309}(184,\cdot)\) \(\chi_{1309}(193,\cdot)\) \(\chi_{1309}(226,\cdot)\) \(\chi_{1309}(228,\cdot)\) \(\chi_{1309}(233,\cdot)\) \(\chi_{1309}(249,\cdot)\) \(\chi_{1309}(261,\cdot)\) \(\chi_{1309}(277,\cdot)\) \(\chi_{1309}(282,\cdot)\) \(\chi_{1309}(303,\cdot)\) \(\chi_{1309}(326,\cdot)\) \(\chi_{1309}(347,\cdot)\) \(\chi_{1309}(354,\cdot)\) \(\chi_{1309}(380,\cdot)\) \(\chi_{1309}(403,\cdot)\) \(\chi_{1309}(415,\cdot)\) \(\chi_{1309}(431,\cdot)\) \(\chi_{1309}(436,\cdot)\) \(\chi_{1309}(464,\cdot)\) \(\chi_{1309}(513,\cdot)\) \(\chi_{1309}(534,\cdot)\) \(\chi_{1309}(541,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{240})$ |
| Fixed field: | Number field defined by a degree 240 polynomial (not computed) |
Values on generators
\((1123,596,309)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{3}{10}\right),e\left(\frac{5}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(12\) | \(13\) |
| \( \chi_{ 1309 }(107, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{120}\right)\) | \(e\left(\frac{11}{240}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{103}{240}\right)\) | \(e\left(\frac{31}{80}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{11}{120}\right)\) | \(e\left(\frac{37}{48}\right)\) | \(e\left(\frac{35}{48}\right)\) | \(e\left(\frac{11}{20}\right)\) |