Basic properties
| Modulus: | \(2583\) | |
| Conductor: | \(2583\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | 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 2583.fx
\(\chi_{2583}(67,\cdot)\) \(\chi_{2583}(130,\cdot)\) \(\chi_{2583}(142,\cdot)\) \(\chi_{2583}(193,\cdot)\) \(\chi_{2583}(268,\cdot)\) \(\chi_{2583}(382,\cdot)\) \(\chi_{2583}(445,\cdot)\) \(\chi_{2583}(457,\cdot)\) \(\chi_{2583}(520,\cdot)\) \(\chi_{2583}(634,\cdot)\) \(\chi_{2583}(709,\cdot)\) \(\chi_{2583}(760,\cdot)\) \(\chi_{2583}(772,\cdot)\) \(\chi_{2583}(835,\cdot)\) \(\chi_{2583}(949,\cdot)\) \(\chi_{2583}(1012,\cdot)\) \(\chi_{2583}(1201,\cdot)\) \(\chi_{2583}(1213,\cdot)\) \(\chi_{2583}(1264,\cdot)\) \(\chi_{2583}(1327,\cdot)\) \(\chi_{2583}(1465,\cdot)\) \(\chi_{2583}(1528,\cdot)\) \(\chi_{2583}(1705,\cdot)\) \(\chi_{2583}(1780,\cdot)\) \(\chi_{2583}(1957,\cdot)\) \(\chi_{2583}(2020,\cdot)\) \(\chi_{2583}(2158,\cdot)\) \(\chi_{2583}(2221,\cdot)\) \(\chi_{2583}(2272,\cdot)\) \(\chi_{2583}(2284,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((2297,2215,1072)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{2}{3}\right),e\left(\frac{17}{40}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 2583 }(67, a) \) | \(-1\) | \(1\) | \(e\left(\frac{43}{60}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{101}{120}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{19}{120}\right)\) |