Basic properties
Modulus: | \(177\) | |
Conductor: | \(177\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(58\) | 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 177.h
\(\chi_{177}(5,\cdot)\) \(\chi_{177}(17,\cdot)\) \(\chi_{177}(20,\cdot)\) \(\chi_{177}(26,\cdot)\) \(\chi_{177}(29,\cdot)\) \(\chi_{177}(35,\cdot)\) \(\chi_{177}(41,\cdot)\) \(\chi_{177}(53,\cdot)\) \(\chi_{177}(62,\cdot)\) \(\chi_{177}(68,\cdot)\) \(\chi_{177}(71,\cdot)\) \(\chi_{177}(74,\cdot)\) \(\chi_{177}(80,\cdot)\) \(\chi_{177}(86,\cdot)\) \(\chi_{177}(95,\cdot)\) \(\chi_{177}(104,\cdot)\) \(\chi_{177}(107,\cdot)\) \(\chi_{177}(110,\cdot)\) \(\chi_{177}(116,\cdot)\) \(\chi_{177}(122,\cdot)\) \(\chi_{177}(125,\cdot)\) \(\chi_{177}(134,\cdot)\) \(\chi_{177}(137,\cdot)\) \(\chi_{177}(140,\cdot)\) \(\chi_{177}(143,\cdot)\) \(\chi_{177}(146,\cdot)\) \(\chi_{177}(164,\cdot)\) \(\chi_{177}(167,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{29})$ |
Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((119,61)\) → \((-1,e\left(\frac{3}{29}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 177 }(5, a) \) | \(-1\) | \(1\) | \(e\left(\frac{35}{58}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{7}{58}\right)\) | \(e\left(\frac{25}{29}\right)\) | \(e\left(\frac{47}{58}\right)\) | \(e\left(\frac{21}{29}\right)\) | \(e\left(\frac{5}{58}\right)\) | \(e\left(\frac{19}{29}\right)\) | \(e\left(\frac{27}{58}\right)\) | \(e\left(\frac{12}{29}\right)\) |