Basic properties
| Modulus: | \(2583\) | |
| Conductor: | \(369\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{369}(22,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2583.fo
\(\chi_{2583}(22,\cdot)\) \(\chi_{2583}(106,\cdot)\) \(\chi_{2583}(211,\cdot)\) \(\chi_{2583}(274,\cdot)\) \(\chi_{2583}(358,\cdot)\) \(\chi_{2583}(421,\cdot)\) \(\chi_{2583}(463,\cdot)\) \(\chi_{2583}(526,\cdot)\) \(\chi_{2583}(589,\cdot)\) \(\chi_{2583}(673,\cdot)\) \(\chi_{2583}(967,\cdot)\) \(\chi_{2583}(1051,\cdot)\) \(\chi_{2583}(1114,\cdot)\) \(\chi_{2583}(1177,\cdot)\) \(\chi_{2583}(1219,\cdot)\) \(\chi_{2583}(1282,\cdot)\) \(\chi_{2583}(1366,\cdot)\) \(\chi_{2583}(1429,\cdot)\) \(\chi_{2583}(1534,\cdot)\) \(\chi_{2583}(1618,\cdot)\) \(\chi_{2583}(1744,\cdot)\) \(\chi_{2583}(1912,\cdot)\) \(\chi_{2583}(1933,\cdot)\) \(\chi_{2583}(1975,\cdot)\) \(\chi_{2583}(1996,\cdot)\) \(\chi_{2583}(2038,\cdot)\) \(\chi_{2583}(2185,\cdot)\) \(\chi_{2583}(2227,\cdot)\) \(\chi_{2583}(2248,\cdot)\) \(\chi_{2583}(2290,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((2297,2215,1072)\) → \((e\left(\frac{1}{3}\right),1,e\left(\frac{29}{40}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
| \( \chi_{ 2583 }(22, a) \) | \(-1\) | \(1\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{11}{30}\right)\) | \(e\left(\frac{37}{60}\right)\) | \(e\left(\frac{11}{20}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{11}{15}\right)\) | \(e\left(\frac{37}{40}\right)\) | \(e\left(\frac{21}{40}\right)\) |