Basic properties
| Modulus: | \(177\) | |
| Conductor: | \(59\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(29\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{59}(7,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 177.e
\(\chi_{177}(4,\cdot)\) \(\chi_{177}(7,\cdot)\) \(\chi_{177}(16,\cdot)\) \(\chi_{177}(19,\cdot)\) \(\chi_{177}(22,\cdot)\) \(\chi_{177}(25,\cdot)\) \(\chi_{177}(28,\cdot)\) \(\chi_{177}(46,\cdot)\) \(\chi_{177}(49,\cdot)\) \(\chi_{177}(64,\cdot)\) \(\chi_{177}(76,\cdot)\) \(\chi_{177}(79,\cdot)\) \(\chi_{177}(85,\cdot)\) \(\chi_{177}(88,\cdot)\) \(\chi_{177}(94,\cdot)\) \(\chi_{177}(100,\cdot)\) \(\chi_{177}(112,\cdot)\) \(\chi_{177}(121,\cdot)\) \(\chi_{177}(127,\cdot)\) \(\chi_{177}(130,\cdot)\) \(\chi_{177}(133,\cdot)\) \(\chi_{177}(139,\cdot)\) \(\chi_{177}(145,\cdot)\) \(\chi_{177}(154,\cdot)\) \(\chi_{177}(163,\cdot)\) \(\chi_{177}(166,\cdot)\) \(\chi_{177}(169,\cdot)\) \(\chi_{177}(175,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{29})$ |
| Fixed field: | \(\Q(\zeta_{59})^+\) |
Values on generators
\((119,61)\) → \((1,e\left(\frac{9}{29}\right))\)
Values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 177 }(7, a) \) | \(1\) | \(1\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{18}{29}\right)\) | \(e\left(\frac{25}{29}\right)\) | \(e\left(\frac{17}{29}\right)\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{5}{29}\right)\) | \(e\left(\frac{22}{29}\right)\) | \(e\left(\frac{28}{29}\right)\) | \(e\left(\frac{26}{29}\right)\) | \(e\left(\frac{7}{29}\right)\) |