Basic properties
Modulus: | \(229\) | |
Conductor: | \(229\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(114\) | 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 229.k
\(\chi_{229}(5,\cdot)\) \(\chi_{229}(12,\cdot)\) \(\chi_{229}(33,\cdot)\) \(\chi_{229}(36,\cdot)\) \(\chi_{229}(45,\cdot)\) \(\chi_{229}(46,\cdot)\) \(\chi_{229}(49,\cdot)\) \(\chi_{229}(56,\cdot)\) \(\chi_{229}(58,\cdot)\) \(\chi_{229}(62,\cdot)\) \(\chi_{229}(70,\cdot)\) \(\chi_{229}(71,\cdot)\) \(\chi_{229}(76,\cdot)\) \(\chi_{229}(78,\cdot)\) \(\chi_{229}(80,\cdot)\) \(\chi_{229}(85,\cdot)\) \(\chi_{229}(97,\cdot)\) \(\chi_{229}(99,\cdot)\) \(\chi_{229}(100,\cdot)\) \(\chi_{229}(103,\cdot)\) \(\chi_{229}(118,\cdot)\) \(\chi_{229}(138,\cdot)\) \(\chi_{229}(146,\cdot)\) \(\chi_{229}(147,\cdot)\) \(\chi_{229}(148,\cdot)\) \(\chi_{229}(154,\cdot)\) \(\chi_{229}(174,\cdot)\) \(\chi_{229}(178,\cdot)\) \(\chi_{229}(181,\cdot)\) \(\chi_{229}(192,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{57})$ |
Fixed field: | Number field defined by a degree 114 polynomial (not computed) |
Values on generators
\(6\) → \(e\left(\frac{53}{114}\right)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 229 }(192, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{38}\right)\) | \(e\left(\frac{40}{57}\right)\) | \(e\left(\frac{10}{19}\right)\) | \(e\left(\frac{32}{57}\right)\) | \(e\left(\frac{53}{114}\right)\) | \(e\left(\frac{85}{114}\right)\) | \(e\left(\frac{11}{38}\right)\) | \(e\left(\frac{23}{57}\right)\) | \(e\left(\frac{37}{114}\right)\) | \(e\left(\frac{6}{19}\right)\) |