Basic properties
Modulus: | \(419\) | |
Conductor: | \(419\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(209\) | 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 419.g
\(\chi_{419}(3,\cdot)\) \(\chi_{419}(4,\cdot)\) \(\chi_{419}(5,\cdot)\) \(\chi_{419}(9,\cdot)\) \(\chi_{419}(12,\cdot)\) \(\chi_{419}(15,\cdot)\) \(\chi_{419}(16,\cdot)\) \(\chi_{419}(20,\cdot)\) \(\chi_{419}(21,\cdot)\) \(\chi_{419}(22,\cdot)\) \(\chi_{419}(23,\cdot)\) \(\chi_{419}(25,\cdot)\) \(\chi_{419}(27,\cdot)\) \(\chi_{419}(28,\cdot)\) \(\chi_{419}(29,\cdot)\) \(\chi_{419}(34,\cdot)\) \(\chi_{419}(35,\cdot)\) \(\chi_{419}(36,\cdot)\) \(\chi_{419}(37,\cdot)\) \(\chi_{419}(38,\cdot)\) \(\chi_{419}(39,\cdot)\) \(\chi_{419}(41,\cdot)\) \(\chi_{419}(43,\cdot)\) \(\chi_{419}(45,\cdot)\) \(\chi_{419}(48,\cdot)\) \(\chi_{419}(52,\cdot)\) \(\chi_{419}(62,\cdot)\) \(\chi_{419}(63,\cdot)\) \(\chi_{419}(64,\cdot)\) \(\chi_{419}(65,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{209})$ |
Fixed field: | Number field defined by a degree 209 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{51}{209}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 419 }(12, a) \) | \(1\) | \(1\) | \(e\left(\frac{51}{209}\right)\) | \(e\left(\frac{84}{209}\right)\) | \(e\left(\frac{102}{209}\right)\) | \(e\left(\frac{78}{209}\right)\) | \(e\left(\frac{135}{209}\right)\) | \(e\left(\frac{14}{19}\right)\) | \(e\left(\frac{153}{209}\right)\) | \(e\left(\frac{168}{209}\right)\) | \(e\left(\frac{129}{209}\right)\) | \(e\left(\frac{7}{209}\right)\) |