Basic properties
| Modulus: | \(229\) | |
| Conductor: | \(229\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(228\) | 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 229.l
\(\chi_{229}(6,\cdot)\) \(\chi_{229}(7,\cdot)\) \(\chi_{229}(10,\cdot)\) \(\chi_{229}(23,\cdot)\) \(\chi_{229}(24,\cdot)\) \(\chi_{229}(28,\cdot)\) \(\chi_{229}(29,\cdot)\) \(\chi_{229}(31,\cdot)\) \(\chi_{229}(35,\cdot)\) \(\chi_{229}(38,\cdot)\) \(\chi_{229}(39,\cdot)\) \(\chi_{229}(40,\cdot)\) \(\chi_{229}(41,\cdot)\) \(\chi_{229}(47,\cdot)\) \(\chi_{229}(50,\cdot)\) \(\chi_{229}(59,\cdot)\) \(\chi_{229}(63,\cdot)\) \(\chi_{229}(65,\cdot)\) \(\chi_{229}(66,\cdot)\) \(\chi_{229}(67,\cdot)\) \(\chi_{229}(69,\cdot)\) \(\chi_{229}(72,\cdot)\) \(\chi_{229}(73,\cdot)\) \(\chi_{229}(74,\cdot)\) \(\chi_{229}(77,\cdot)\) \(\chi_{229}(79,\cdot)\) \(\chi_{229}(87,\cdot)\) \(\chi_{229}(90,\cdot)\) \(\chi_{229}(92,\cdot)\) \(\chi_{229}(96,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{228})$ |
| Fixed field: | Number field defined by a degree 228 polynomial (not computed) |
Values on generators
\(6\) → \(e\left(\frac{29}{228}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 229 }(31, a) \) | \(-1\) | \(1\) | \(e\left(\frac{51}{76}\right)\) | \(e\left(\frac{26}{57}\right)\) | \(e\left(\frac{13}{38}\right)\) | \(e\left(\frac{53}{114}\right)\) | \(e\left(\frac{29}{228}\right)\) | \(e\left(\frac{139}{228}\right)\) | \(e\left(\frac{1}{76}\right)\) | \(e\left(\frac{52}{57}\right)\) | \(e\left(\frac{31}{228}\right)\) | \(e\left(\frac{23}{38}\right)\) |