Basic properties
Modulus: | \(139\) | |
Conductor: | \(139\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(69\) | 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 139.g
\(\chi_{139}(4,\cdot)\) \(\chi_{139}(5,\cdot)\) \(\chi_{139}(7,\cdot)\) \(\chi_{139}(9,\cdot)\) \(\chi_{139}(11,\cdot)\) \(\chi_{139}(13,\cdot)\) \(\chi_{139}(16,\cdot)\) \(\chi_{139}(20,\cdot)\) \(\chi_{139}(24,\cdot)\) \(\chi_{139}(25,\cdot)\) \(\chi_{139}(28,\cdot)\) \(\chi_{139}(29,\cdot)\) \(\chi_{139}(30,\cdot)\) \(\chi_{139}(31,\cdot)\) \(\chi_{139}(35,\cdot)\) \(\chi_{139}(37,\cdot)\) \(\chi_{139}(38,\cdot)\) \(\chi_{139}(41,\cdot)\) \(\chi_{139}(46,\cdot)\) \(\chi_{139}(47,\cdot)\) \(\chi_{139}(49,\cdot)\) \(\chi_{139}(51,\cdot)\) \(\chi_{139}(54,\cdot)\) \(\chi_{139}(66,\cdot)\) \(\chi_{139}(67,\cdot)\) \(\chi_{139}(69,\cdot)\) \(\chi_{139}(71,\cdot)\) \(\chi_{139}(78,\cdot)\) \(\chi_{139}(81,\cdot)\) \(\chi_{139}(83,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{69})$ |
Fixed field: | Number field defined by a degree 69 polynomial |
Values on generators
\(2\) → \(e\left(\frac{34}{69}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 139 }(69, a) \) | \(1\) | \(1\) | \(e\left(\frac{34}{69}\right)\) | \(e\left(\frac{14}{69}\right)\) | \(e\left(\frac{68}{69}\right)\) | \(e\left(\frac{26}{69}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{44}{69}\right)\) | \(e\left(\frac{11}{23}\right)\) | \(e\left(\frac{28}{69}\right)\) | \(e\left(\frac{20}{23}\right)\) | \(e\left(\frac{31}{69}\right)\) |