Basic properties
Modulus: | \(2583\) | |
Conductor: | \(2583\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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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.gc
\(\chi_{2583}(58,\cdot)\) \(\chi_{2583}(88,\cdot)\) \(\chi_{2583}(151,\cdot)\) \(\chi_{2583}(340,\cdot)\) \(\chi_{2583}(403,\cdot)\) \(\chi_{2583}(436,\cdot)\) \(\chi_{2583}(466,\cdot)\) \(\chi_{2583}(499,\cdot)\) \(\chi_{2583}(562,\cdot)\) \(\chi_{2583}(751,\cdot)\) \(\chi_{2583}(814,\cdot)\) \(\chi_{2583}(844,\cdot)\) \(\chi_{2583}(1003,\cdot)\) \(\chi_{2583}(1096,\cdot)\) \(\chi_{2583}(1129,\cdot)\) \(\chi_{2583}(1159,\cdot)\) \(\chi_{2583}(1318,\cdot)\) \(\chi_{2583}(1381,\cdot)\) \(\chi_{2583}(1411,\cdot)\) \(\chi_{2583}(1570,\cdot)\) \(\chi_{2583}(1633,\cdot)\) \(\chi_{2583}(1696,\cdot)\) \(\chi_{2583}(1789,\cdot)\) \(\chi_{2583}(1852,\cdot)\) \(\chi_{2583}(1915,\cdot)\) \(\chi_{2583}(2074,\cdot)\) \(\chi_{2583}(2104,\cdot)\) \(\chi_{2583}(2167,\cdot)\) \(\chi_{2583}(2326,\cdot)\) \(\chi_{2583}(2356,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{120})$ |
Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((2297,2215,1072)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{1}{3}\right),e\left(\frac{33}{40}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(13\) | \(16\) | \(17\) | \(19\) |
\( \chi_{ 2583 }(58, a) \) | \(-1\) | \(1\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{29}{60}\right)\) | \(e\left(\frac{7}{20}\right)\) | \(e\left(\frac{14}{15}\right)\) | \(e\left(\frac{17}{120}\right)\) | \(e\left(\frac{29}{120}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{11}{120}\right)\) |