Basic properties
Modulus: | \(179\) | |
Conductor: | \(179\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(89\) | 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 179.c
\(\chi_{179}(3,\cdot)\) \(\chi_{179}(4,\cdot)\) \(\chi_{179}(5,\cdot)\) \(\chi_{179}(9,\cdot)\) \(\chi_{179}(12,\cdot)\) \(\chi_{179}(13,\cdot)\) \(\chi_{179}(14,\cdot)\) \(\chi_{179}(15,\cdot)\) \(\chi_{179}(16,\cdot)\) \(\chi_{179}(17,\cdot)\) \(\chi_{179}(19,\cdot)\) \(\chi_{179}(20,\cdot)\) \(\chi_{179}(22,\cdot)\) \(\chi_{179}(25,\cdot)\) \(\chi_{179}(27,\cdot)\) \(\chi_{179}(29,\cdot)\) \(\chi_{179}(31,\cdot)\) \(\chi_{179}(36,\cdot)\) \(\chi_{179}(39,\cdot)\) \(\chi_{179}(42,\cdot)\) \(\chi_{179}(43,\cdot)\) \(\chi_{179}(45,\cdot)\) \(\chi_{179}(46,\cdot)\) \(\chi_{179}(47,\cdot)\) \(\chi_{179}(48,\cdot)\) \(\chi_{179}(49,\cdot)\) \(\chi_{179}(51,\cdot)\) \(\chi_{179}(52,\cdot)\) \(\chi_{179}(56,\cdot)\) \(\chi_{179}(57,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{89})$ |
Fixed field: | Number field defined by a degree 89 polynomial |
Values on generators
\(2\) → \(e\left(\frac{29}{89}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 179 }(125, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{89}\right)\) | \(e\left(\frac{17}{89}\right)\) | \(e\left(\frac{58}{89}\right)\) | \(e\left(\frac{86}{89}\right)\) | \(e\left(\frac{46}{89}\right)\) | \(e\left(\frac{64}{89}\right)\) | \(e\left(\frac{87}{89}\right)\) | \(e\left(\frac{34}{89}\right)\) | \(e\left(\frac{26}{89}\right)\) | \(e\left(\frac{79}{89}\right)\) |