Basic properties
Modulus: | \(8041\) | |
Conductor: | \(8041\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(280\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8041.fj
\(\chi_{8041}(2,\cdot)\) \(\chi_{8041}(8,\cdot)\) \(\chi_{8041}(94,\cdot)\) \(\chi_{8041}(151,\cdot)\) \(\chi_{8041}(161,\cdot)\) \(\chi_{8041}(376,\cdot)\) \(\chi_{8041}(457,\cdot)\) \(\chi_{8041}(512,\cdot)\) \(\chi_{8041}(733,\cdot)\) \(\chi_{8041}(739,\cdot)\) \(\chi_{8041}(882,\cdot)\) \(\chi_{8041}(899,\cdot)\) \(\chi_{8041}(954,\cdot)\) \(\chi_{8041}(1097,\cdot)\) \(\chi_{8041}(1107,\cdot)\) \(\chi_{8041}(1249,\cdot)\) \(\chi_{8041}(1317,\cdot)\) \(\chi_{8041}(1403,\cdot)\) \(\chi_{8041}(1470,\cdot)\) \(\chi_{8041}(1613,\cdot)\) \(\chi_{8041}(1623,\cdot)\) \(\chi_{8041}(1630,\cdot)\) \(\chi_{8041}(1685,\cdot)\) \(\chi_{8041}(1828,\cdot)\) \(\chi_{8041}(1845,\cdot)\) \(\chi_{8041}(2048,\cdot)\) \(\chi_{8041}(2195,\cdot)\) \(\chi_{8041}(2263,\cdot)\) \(\chi_{8041}(2361,\cdot)\) \(\chi_{8041}(2416,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{280})$ |
Fixed field: | Number field defined by a degree 280 polynomial (not computed) |
Values on generators
\((6580,2366,562)\) → \((e\left(\frac{7}{10}\right),e\left(\frac{5}{8}\right),e\left(\frac{3}{14}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(161, a) \) | \(1\) | \(1\) | \(e\left(\frac{33}{140}\right)\) | \(e\left(\frac{123}{280}\right)\) | \(e\left(\frac{33}{70}\right)\) | \(e\left(\frac{79}{280}\right)\) | \(e\left(\frac{27}{40}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{99}{140}\right)\) | \(e\left(\frac{123}{140}\right)\) | \(e\left(\frac{29}{56}\right)\) | \(e\left(\frac{51}{56}\right)\) |