sage: H = DirichletGroup_conrey(4033)
sage: chi = H[2579]
Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 4033 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
| ||
| Order | = | 108 |
| 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 | = | 4033.ir |
| Orbit index | = | 226 |
Galois orbit
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
\(\chi_{4033}(10,\cdot)\) \(\chi_{4033}(174,\cdot)\) \(\chi_{4033}(232,\cdot)\) \(\chi_{4033}(248,\cdot)\) \(\chi_{4033}(269,\cdot)\) \(\chi_{4033}(285,\cdot)\) \(\chi_{4033}(380,\cdot)\) \(\chi_{4033}(602,\cdot)\) \(\chi_{4033}(750,\cdot)\) \(\chi_{4033}(787,\cdot)\) \(\chi_{4033}(914,\cdot)\) \(\chi_{4033}(951,\cdot)\) \(\chi_{4033}(1025,\cdot)\) \(\chi_{4033}(1210,\cdot)\) \(\chi_{4033}(1268,\cdot)\) \(\chi_{4033}(1358,\cdot)\) \(\chi_{4033}(1617,\cdot)\) \(\chi_{4033}(1675,\cdot)\) \(\chi_{4033}(2024,\cdot)\) \(\chi_{4033}(2156,\cdot)\) \(\chi_{4033}(2193,\cdot)\) \(\chi_{4033}(2341,\cdot)\) \(\chi_{4033}(2468,\cdot)\) \(\chi_{4033}(2563,\cdot)\) \(\chi_{4033}(2579,\cdot)\) \(\chi_{4033}(2653,\cdot)\) \(\chi_{4033}(2674,\cdot)\) \(\chi_{4033}(2711,\cdot)\) \(\chi_{4033}(2764,\cdot)\) \(\chi_{4033}(2933,\cdot)\) ...
Values on generators
\((1963,2295)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{59}{108}\right))\)
Values
| -1 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| \(-1\) | \(1\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{2}{27}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{5}{27}\right)\) | \(e\left(\frac{59}{108}\right)\) | \(e\left(\frac{14}{27}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{4}{27}\right)\) | \(e\left(\frac{71}{108}\right)\) | \(e\left(\frac{37}{108}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{108})\) |