Basic properties
Modulus: | \(683\) | |
Conductor: | \(683\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(341\) | 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 683.g
\(\chi_{683}(10,\cdot)\) \(\chi_{683}(12,\cdot)\) \(\chi_{683}(14,\cdot)\) \(\chi_{683}(19,\cdot)\) \(\chi_{683}(22,\cdot)\) \(\chi_{683}(25,\cdot)\) \(\chi_{683}(26,\cdot)\) \(\chi_{683}(29,\cdot)\) \(\chi_{683}(30,\cdot)\) \(\chi_{683}(34,\cdot)\) \(\chi_{683}(35,\cdot)\) \(\chi_{683}(36,\cdot)\) \(\chi_{683}(40,\cdot)\) \(\chi_{683}(42,\cdot)\) \(\chi_{683}(48,\cdot)\) \(\chi_{683}(49,\cdot)\) \(\chi_{683}(53,\cdot)\) \(\chi_{683}(55,\cdot)\) \(\chi_{683}(56,\cdot)\) \(\chi_{683}(57,\cdot)\) \(\chi_{683}(59,\cdot)\) \(\chi_{683}(61,\cdot)\) \(\chi_{683}(62,\cdot)\) \(\chi_{683}(65,\cdot)\) \(\chi_{683}(66,\cdot)\) \(\chi_{683}(71,\cdot)\) \(\chi_{683}(74,\cdot)\) \(\chi_{683}(75,\cdot)\) \(\chi_{683}(77,\cdot)\) \(\chi_{683}(78,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{341})$ |
Fixed field: | Number field defined by a degree 341 polynomial (not computed) |
Values on generators
\(5\) → \(e\left(\frac{41}{341}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 683 }(12, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{11}\right)\) | \(e\left(\frac{21}{31}\right)\) | \(e\left(\frac{2}{11}\right)\) | \(e\left(\frac{41}{341}\right)\) | \(e\left(\frac{262}{341}\right)\) | \(e\left(\frac{294}{341}\right)\) | \(e\left(\frac{3}{11}\right)\) | \(e\left(\frac{11}{31}\right)\) | \(e\left(\frac{72}{341}\right)\) | \(e\left(\frac{339}{341}\right)\) |