sage: H = DirichletGroup_conrey(229)
sage: chi = H[106]
Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 229 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
| ||
| Order | = | 76 |
| Real | = | No |
| sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
| ||
| Primitive | = | Yes |
| sage: chi.is_odd()
pari: zncharisodd(g,chi)
| ||
| Parity | = | Odd |
| Orbit label | = | 229.j |
| Orbit index | = | 10 |
Galois orbit
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
\(\chi_{229}(2,\cdot)\) \(\chi_{229}(8,\cdot)\) \(\chi_{229}(13,\cdot)\) \(\chi_{229}(21,\cdot)\) \(\chi_{229}(22,\cdot)\) \(\chi_{229}(30,\cdot)\) \(\chi_{229}(32,\cdot)\) \(\chi_{229}(34,\cdot)\) \(\chi_{229}(52,\cdot)\) \(\chi_{229}(54,\cdot)\) \(\chi_{229}(84,\cdot)\) \(\chi_{229}(86,\cdot)\) \(\chi_{229}(88,\cdot)\) \(\chi_{229}(93,\cdot)\) \(\chi_{229}(101,\cdot)\) \(\chi_{229}(106,\cdot)\) \(\chi_{229}(109,\cdot)\) \(\chi_{229}(114,\cdot)\) \(\chi_{229}(115,\cdot)\) \(\chi_{229}(120,\cdot)\) \(\chi_{229}(123,\cdot)\) \(\chi_{229}(128,\cdot)\) \(\chi_{229}(136,\cdot)\) \(\chi_{229}(141,\cdot)\) \(\chi_{229}(143,\cdot)\) \(\chi_{229}(145,\cdot)\) \(\chi_{229}(175,\cdot)\) \(\chi_{229}(177,\cdot)\) \(\chi_{229}(195,\cdot)\) \(\chi_{229}(197,\cdot)\) ...
Values on generators
\(6\) → \(e\left(\frac{51}{76}\right)\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| \(-1\) | \(1\) | \(e\left(\frac{7}{76}\right)\) | \(e\left(\frac{11}{19}\right)\) | \(e\left(\frac{7}{38}\right)\) | \(e\left(\frac{29}{38}\right)\) | \(e\left(\frac{51}{76}\right)\) | \(e\left(\frac{61}{76}\right)\) | \(e\left(\frac{21}{76}\right)\) | \(e\left(\frac{3}{19}\right)\) | \(e\left(\frac{65}{76}\right)\) | \(e\left(\frac{27}{38}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{76})\) |