Basic properties
Modulus: | \(139\) | |
Conductor: | \(139\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(138\) | 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 139.h
\(\chi_{139}(2,\cdot)\) \(\chi_{139}(3,\cdot)\) \(\chi_{139}(12,\cdot)\) \(\chi_{139}(15,\cdot)\) \(\chi_{139}(17,\cdot)\) \(\chi_{139}(18,\cdot)\) \(\chi_{139}(19,\cdot)\) \(\chi_{139}(21,\cdot)\) \(\chi_{139}(22,\cdot)\) \(\chi_{139}(26,\cdot)\) \(\chi_{139}(32,\cdot)\) \(\chi_{139}(40,\cdot)\) \(\chi_{139}(50,\cdot)\) \(\chi_{139}(53,\cdot)\) \(\chi_{139}(56,\cdot)\) \(\chi_{139}(58,\cdot)\) \(\chi_{139}(61,\cdot)\) \(\chi_{139}(68,\cdot)\) \(\chi_{139}(70,\cdot)\) \(\chi_{139}(72,\cdot)\) \(\chi_{139}(73,\cdot)\) \(\chi_{139}(85,\cdot)\) \(\chi_{139}(88,\cdot)\) \(\chi_{139}(90,\cdot)\) \(\chi_{139}(92,\cdot)\) \(\chi_{139}(93,\cdot)\) \(\chi_{139}(98,\cdot)\) \(\chi_{139}(101,\cdot)\) \(\chi_{139}(102,\cdot)\) \(\chi_{139}(104,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{69})$ |
Fixed field: | Number field defined by a degree 138 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{77}{138}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 139 }(22, a) \) | \(-1\) | \(1\) | \(e\left(\frac{77}{138}\right)\) | \(e\left(\frac{121}{138}\right)\) | \(e\left(\frac{8}{69}\right)\) | \(e\left(\frac{68}{69}\right)\) | \(e\left(\frac{10}{23}\right)\) | \(e\left(\frac{62}{69}\right)\) | \(e\left(\frac{31}{46}\right)\) | \(e\left(\frac{52}{69}\right)\) | \(e\left(\frac{25}{46}\right)\) | \(e\left(\frac{28}{69}\right)\) |