sage: H = DirichletGroup_conrey(4000)
sage: chi = H[2353]
Basic properties
| sage: chi.conductor()
pari: znconreyconductor(g,chi)
| ||
| Conductor | = | 1000 |
| sage: chi.multiplicative_order()
pari: charorder(g,chi)
| ||
| Order | = | 100 |
| Real | = | No |
| sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1 \\ if not primitive returns [cond,factorization]
| ||
| Primitive | = | No |
| sage: chi.is_odd()
pari: zncharisodd(g,chi)
| ||
| Parity | = | Odd |
| Orbit label | = | 4000.ct |
| Orbit index | = | 72 |
Galois orbit
pari: [ charpow(g,chi, k % order) | k <-[1..order-1], gcd(k,order)==1 ]
\(\chi_{4000}(17,\cdot)\) \(\chi_{4000}(113,\cdot)\) \(\chi_{4000}(177,\cdot)\) \(\chi_{4000}(273,\cdot)\) \(\chi_{4000}(337,\cdot)\) \(\chi_{4000}(433,\cdot)\) \(\chi_{4000}(497,\cdot)\) \(\chi_{4000}(753,\cdot)\) \(\chi_{4000}(817,\cdot)\) \(\chi_{4000}(913,\cdot)\) \(\chi_{4000}(977,\cdot)\) \(\chi_{4000}(1073,\cdot)\) \(\chi_{4000}(1137,\cdot)\) \(\chi_{4000}(1233,\cdot)\) \(\chi_{4000}(1297,\cdot)\) \(\chi_{4000}(1553,\cdot)\) \(\chi_{4000}(1617,\cdot)\) \(\chi_{4000}(1713,\cdot)\) \(\chi_{4000}(1777,\cdot)\) \(\chi_{4000}(1873,\cdot)\) \(\chi_{4000}(1937,\cdot)\) \(\chi_{4000}(2033,\cdot)\) \(\chi_{4000}(2097,\cdot)\) \(\chi_{4000}(2353,\cdot)\) \(\chi_{4000}(2417,\cdot)\) \(\chi_{4000}(2513,\cdot)\) \(\chi_{4000}(2577,\cdot)\) \(\chi_{4000}(2673,\cdot)\) \(\chi_{4000}(2737,\cdot)\) \(\chi_{4000}(2833,\cdot)\) ...
Inducing primitive character
Values on generators
\((2751,2501,1377)\) → \((1,-1,e\left(\frac{27}{100}\right))\)
Values
| -1 | 1 | 3 | 7 | 9 | 11 | 13 | 17 | 19 | 21 | 23 | 27 |
| \(-1\) | \(1\) | \(e\left(\frac{39}{100}\right)\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{39}{50}\right)\) | \(e\left(\frac{1}{50}\right)\) | \(e\left(\frac{3}{100}\right)\) | \(e\left(\frac{71}{100}\right)\) | \(e\left(\frac{9}{25}\right)\) | \(e\left(\frac{17}{50}\right)\) | \(e\left(\frac{37}{100}\right)\) | \(e\left(\frac{17}{100}\right)\) |
Related number fields
| Field of values | \(\Q(\zeta_{100})\) |