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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 177.f
\(\chi_{177}(2,\cdot)\) \(\chi_{177}(8,\cdot)\) \(\chi_{177}(11,\cdot)\) \(\chi_{177}(14,\cdot)\) \(\chi_{177}(23,\cdot)\) \(\chi_{177}(32,\cdot)\) \(\chi_{177}(38,\cdot)\) \(\chi_{177}(44,\cdot)\) \(\chi_{177}(47,\cdot)\) \(\chi_{177}(50,\cdot)\) \(\chi_{177}(56,\cdot)\) \(\chi_{177}(65,\cdot)\) \(\chi_{177}(77,\cdot)\) \(\chi_{177}(83,\cdot)\) \(\chi_{177}(89,\cdot)\) \(\chi_{177}(92,\cdot)\) \(\chi_{177}(98,\cdot)\) \(\chi_{177}(101,\cdot)\) \(\chi_{177}(113,\cdot)\) \(\chi_{177}(128,\cdot)\) \(\chi_{177}(131,\cdot)\) \(\chi_{177}(149,\cdot)\) \(\chi_{177}(152,\cdot)\) \(\chi_{177}(155,\cdot)\) \(\chi_{177}(158,\cdot)\) \(\chi_{177}(161,\cdot)\) \(\chi_{177}(170,\cdot)\) \(\chi_{177}(173,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{29})$ |
Fixed field: | Number field defined by a degree 58 polynomial |
Values on generators
\((119,61)\) → \((-1,e\left(\frac{49}{58}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 177 }(149, a) \) | \(1\) | \(1\) | \(e\left(\frac{10}{29}\right)\) | \(e\left(\frac{20}{29}\right)\) | \(e\left(\frac{33}{58}\right)\) | \(e\left(\frac{6}{29}\right)\) | \(e\left(\frac{1}{29}\right)\) | \(e\left(\frac{53}{58}\right)\) | \(e\left(\frac{18}{29}\right)\) | \(e\left(\frac{1}{58}\right)\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{11}{29}\right)\) |