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 \(\chi_{59}(51,\cdot)\) | 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: | Number field defined by a degree 29 polynomial |
Values on generators
\((119,61)\) → \((1,e\left(\frac{16}{29}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
\( \chi_{ 177 }(169, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{29}\right)\) | \(e\left(\frac{3}{29}\right)\) | \(e\left(\frac{9}{29}\right)\) | \(e\left(\frac{27}{29}\right)\) | \(e\left(\frac{19}{29}\right)\) | \(e\left(\frac{25}{29}\right)\) | \(e\left(\frac{23}{29}\right)\) | \(e\left(\frac{24}{29}\right)\) | \(e\left(\frac{14}{29}\right)\) | \(e\left(\frac{6}{29}\right)\) |