Basic properties
Modulus: | \(389\) | |
Conductor: | \(389\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(388\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 389.f
\(\chi_{389}(2,\cdot)\) \(\chi_{389}(3,\cdot)\) \(\chi_{389}(8,\cdot)\) \(\chi_{389}(10,\cdot)\) \(\chi_{389}(12,\cdot)\) \(\chi_{389}(14,\cdot)\) \(\chi_{389}(15,\cdot)\) \(\chi_{389}(18,\cdot)\) \(\chi_{389}(21,\cdot)\) \(\chi_{389}(22,\cdot)\) \(\chi_{389}(23,\cdot)\) \(\chi_{389}(26,\cdot)\) \(\chi_{389}(27,\cdot)\) \(\chi_{389}(29,\cdot)\) \(\chi_{389}(31,\cdot)\) \(\chi_{389}(32,\cdot)\) \(\chi_{389}(33,\cdot)\) \(\chi_{389}(34,\cdot)\) \(\chi_{389}(37,\cdot)\) \(\chi_{389}(38,\cdot)\) \(\chi_{389}(39,\cdot)\) \(\chi_{389}(40,\cdot)\) \(\chi_{389}(43,\cdot)\) \(\chi_{389}(47,\cdot)\) \(\chi_{389}(48,\cdot)\) \(\chi_{389}(50,\cdot)\) \(\chi_{389}(51,\cdot)\) \(\chi_{389}(53,\cdot)\) \(\chi_{389}(56,\cdot)\) \(\chi_{389}(57,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{388})$ |
Fixed field: | Number field defined by a degree 388 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{173}{388}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 389 }(22, a) \) | \(-1\) | \(1\) | \(e\left(\frac{173}{388}\right)\) | \(e\left(\frac{323}{388}\right)\) | \(e\left(\frac{173}{194}\right)\) | \(e\left(\frac{44}{97}\right)\) | \(e\left(\frac{27}{97}\right)\) | \(e\left(\frac{24}{97}\right)\) | \(e\left(\frac{131}{388}\right)\) | \(e\left(\frac{129}{194}\right)\) | \(e\left(\frac{349}{388}\right)\) | \(e\left(\frac{67}{97}\right)\) |