Basic properties
| Modulus: | \(229\) | |
| Conductor: | \(229\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(76\) | 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.j
\(\chi_{229}(2,\cdot)\) \(\chi_{229}(8,\cdot)\) \(\chi_{229}(13,\cdot)\) \(\chi_{229}(21,\cdot)\) \(\chi_{229}(22,\cdot)\) \(\chi_{229}(30,\cdot)\) \(\chi_{229}(32,\cdot)\) \(\chi_{229}(34,\cdot)\) \(\chi_{229}(52,\cdot)\) \(\chi_{229}(54,\cdot)\) \(\chi_{229}(84,\cdot)\) \(\chi_{229}(86,\cdot)\) \(\chi_{229}(88,\cdot)\) \(\chi_{229}(93,\cdot)\) \(\chi_{229}(101,\cdot)\) \(\chi_{229}(106,\cdot)\) \(\chi_{229}(109,\cdot)\) \(\chi_{229}(114,\cdot)\) \(\chi_{229}(115,\cdot)\) \(\chi_{229}(120,\cdot)\) \(\chi_{229}(123,\cdot)\) \(\chi_{229}(128,\cdot)\) \(\chi_{229}(136,\cdot)\) \(\chi_{229}(141,\cdot)\) \(\chi_{229}(143,\cdot)\) \(\chi_{229}(145,\cdot)\) \(\chi_{229}(175,\cdot)\) \(\chi_{229}(177,\cdot)\) \(\chi_{229}(195,\cdot)\) \(\chi_{229}(197,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{76})$ |
| Fixed field: | Number field defined by a degree 76 polynomial |
Values on generators
\(6\) → \(e\left(\frac{65}{76}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 229 }(195, a) \) | \(-1\) | \(1\) | \(e\left(\frac{73}{76}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{35}{38}\right)\) | \(e\left(\frac{31}{38}\right)\) | \(e\left(\frac{65}{76}\right)\) | \(e\left(\frac{39}{76}\right)\) | \(e\left(\frac{67}{76}\right)\) | \(e\left(\frac{15}{19}\right)\) | \(e\left(\frac{59}{76}\right)\) | \(e\left(\frac{21}{38}\right)\) |