sage: H = DirichletGroup_conrey(373)
sage: chi = H[40]
Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 373 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
| ||
| Order | = | 93 |
| 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 | = | Even |
| Orbit label | = | 373.i |
| Orbit index | = | 9 |
Galois orbit
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
\(\chi_{373}(9,\cdot)\) \(\chi_{373}(16,\cdot)\) \(\chi_{373}(21,\cdot)\) \(\chi_{373}(28,\cdot)\) \(\chi_{373}(29,\cdot)\) \(\chi_{373}(38,\cdot)\) \(\chi_{373}(39,\cdot)\) \(\chi_{373}(40,\cdot)\) \(\chi_{373}(46,\cdot)\) \(\chi_{373}(51,\cdot)\) \(\chi_{373}(52,\cdot)\) \(\chi_{373}(66,\cdot)\) \(\chi_{373}(68,\cdot)\) \(\chi_{373}(70,\cdot)\) \(\chi_{373}(73,\cdot)\) \(\chi_{373}(81,\cdot)\) \(\chi_{373}(83,\cdot)\) \(\chi_{373}(93,\cdot)\) \(\chi_{373}(94,\cdot)\) \(\chi_{373}(95,\cdot)\) \(\chi_{373}(100,\cdot)\) \(\chi_{373}(101,\cdot)\) \(\chi_{373}(107,\cdot)\) \(\chi_{373}(108,\cdot)\) \(\chi_{373}(115,\cdot)\) \(\chi_{373}(124,\cdot)\) \(\chi_{373}(130,\cdot)\) \(\chi_{373}(148,\cdot)\) \(\chi_{373}(165,\cdot)\) \(\chi_{373}(170,\cdot)\) ...
Values on generators
\(2\) → \(e\left(\frac{43}{93}\right)\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| \(1\) | \(1\) | \(e\left(\frac{43}{93}\right)\) | \(e\left(\frac{4}{93}\right)\) | \(e\left(\frac{86}{93}\right)\) | \(e\left(\frac{13}{93}\right)\) | \(e\left(\frac{47}{93}\right)\) | \(e\left(\frac{17}{31}\right)\) | \(e\left(\frac{12}{31}\right)\) | \(e\left(\frac{8}{93}\right)\) | \(e\left(\frac{56}{93}\right)\) | \(e\left(\frac{26}{93}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{93})\) |