Basic properties
| Modulus: | \(2683\) | |
| Conductor: | \(2683\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(1341\) | 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 2683.k
\(\chi_{2683}(4,\cdot)\) \(\chi_{2683}(6,\cdot)\) \(\chi_{2683}(9,\cdot)\) \(\chi_{2683}(11,\cdot)\) \(\chi_{2683}(14,\cdot)\) \(\chi_{2683}(16,\cdot)\) \(\chi_{2683}(21,\cdot)\) \(\chi_{2683}(23,\cdot)\) \(\chi_{2683}(24,\cdot)\) \(\chi_{2683}(25,\cdot)\) \(\chi_{2683}(26,\cdot)\) \(\chi_{2683}(34,\cdot)\) \(\chi_{2683}(35,\cdot)\) \(\chi_{2683}(36,\cdot)\) \(\chi_{2683}(38,\cdot)\) \(\chi_{2683}(39,\cdot)\) \(\chi_{2683}(40,\cdot)\) \(\chi_{2683}(41,\cdot)\) \(\chi_{2683}(51,\cdot)\) \(\chi_{2683}(54,\cdot)\) \(\chi_{2683}(57,\cdot)\) \(\chi_{2683}(58,\cdot)\) \(\chi_{2683}(60,\cdot)\) \(\chi_{2683}(65,\cdot)\) \(\chi_{2683}(67,\cdot)\) \(\chi_{2683}(71,\cdot)\) \(\chi_{2683}(73,\cdot)\) \(\chi_{2683}(74,\cdot)\) \(\chi_{2683}(81,\cdot)\) \(\chi_{2683}(85,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{1341})$ |
| Fixed field: | Number field defined by a degree 1341 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{1286}{1341}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 2683 }(163, a) \) | \(1\) | \(1\) | \(e\left(\frac{1286}{1341}\right)\) | \(e\left(\frac{578}{1341}\right)\) | \(e\left(\frac{1231}{1341}\right)\) | \(e\left(\frac{1285}{1341}\right)\) | \(e\left(\frac{523}{1341}\right)\) | \(e\left(\frac{364}{447}\right)\) | \(e\left(\frac{392}{447}\right)\) | \(e\left(\frac{1156}{1341}\right)\) | \(e\left(\frac{410}{447}\right)\) | \(e\left(\frac{1022}{1341}\right)\) |