Basic properties
Modulus: | \(177\) | |
Conductor: | \(59\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(58\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{59}(55,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 177.g
\(\chi_{177}(10,\cdot)\) \(\chi_{177}(13,\cdot)\) \(\chi_{177}(31,\cdot)\) \(\chi_{177}(34,\cdot)\) \(\chi_{177}(37,\cdot)\) \(\chi_{177}(40,\cdot)\) \(\chi_{177}(43,\cdot)\) \(\chi_{177}(52,\cdot)\) \(\chi_{177}(55,\cdot)\) \(\chi_{177}(61,\cdot)\) \(\chi_{177}(67,\cdot)\) \(\chi_{177}(70,\cdot)\) \(\chi_{177}(73,\cdot)\) \(\chi_{177}(82,\cdot)\) \(\chi_{177}(91,\cdot)\) \(\chi_{177}(97,\cdot)\) \(\chi_{177}(103,\cdot)\) \(\chi_{177}(106,\cdot)\) \(\chi_{177}(109,\cdot)\) \(\chi_{177}(115,\cdot)\) \(\chi_{177}(124,\cdot)\) \(\chi_{177}(136,\cdot)\) \(\chi_{177}(142,\cdot)\) \(\chi_{177}(148,\cdot)\) \(\chi_{177}(151,\cdot)\) \(\chi_{177}(157,\cdot)\) \(\chi_{177}(160,\cdot)\) \(\chi_{177}(172,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{29})$ |
Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((119,61)\) → \((1,e\left(\frac{31}{58}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 177 }(55, a) \) | \(-1\) | \(1\) | \(e\left(\frac{31}{58}\right)\) | \(e\left(\frac{2}{29}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{18}{29}\right)\) | \(e\left(\frac{35}{58}\right)\) | \(e\left(\frac{43}{58}\right)\) | \(e\left(\frac{21}{58}\right)\) | \(e\left(\frac{3}{58}\right)\) | \(e\left(\frac{9}{58}\right)\) | \(e\left(\frac{4}{29}\right)\) |