Basic properties
Modulus: | \(179\) | |
Conductor: | \(179\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(178\) | 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 179.d
\(\chi_{179}(2,\cdot)\) \(\chi_{179}(6,\cdot)\) \(\chi_{179}(7,\cdot)\) \(\chi_{179}(8,\cdot)\) \(\chi_{179}(10,\cdot)\) \(\chi_{179}(11,\cdot)\) \(\chi_{179}(18,\cdot)\) \(\chi_{179}(21,\cdot)\) \(\chi_{179}(23,\cdot)\) \(\chi_{179}(24,\cdot)\) \(\chi_{179}(26,\cdot)\) \(\chi_{179}(28,\cdot)\) \(\chi_{179}(30,\cdot)\) \(\chi_{179}(32,\cdot)\) \(\chi_{179}(33,\cdot)\) \(\chi_{179}(34,\cdot)\) \(\chi_{179}(35,\cdot)\) \(\chi_{179}(37,\cdot)\) \(\chi_{179}(38,\cdot)\) \(\chi_{179}(40,\cdot)\) \(\chi_{179}(41,\cdot)\) \(\chi_{179}(44,\cdot)\) \(\chi_{179}(50,\cdot)\) \(\chi_{179}(53,\cdot)\) \(\chi_{179}(54,\cdot)\) \(\chi_{179}(55,\cdot)\) \(\chi_{179}(58,\cdot)\) \(\chi_{179}(62,\cdot)\) \(\chi_{179}(63,\cdot)\) \(\chi_{179}(69,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{89})$ |
Fixed field: | Number field defined by a degree 178 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{119}{178}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 179 }(58, a) \) | \(-1\) | \(1\) | \(e\left(\frac{119}{178}\right)\) | \(e\left(\frac{18}{89}\right)\) | \(e\left(\frac{30}{89}\right)\) | \(e\left(\frac{23}{89}\right)\) | \(e\left(\frac{155}{178}\right)\) | \(e\left(\frac{57}{178}\right)\) | \(e\left(\frac{1}{178}\right)\) | \(e\left(\frac{36}{89}\right)\) | \(e\left(\frac{165}{178}\right)\) | \(e\left(\frac{5}{178}\right)\) |