Basic properties
| Modulus: | \(8041\) | |
| Conductor: | \(8041\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(560\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| 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.fs
\(\chi_{8041}(41,\cdot)\) \(\chi_{8041}(90,\cdot)\) \(\chi_{8041}(107,\cdot)\) \(\chi_{8041}(150,\cdot)\) \(\chi_{8041}(193,\cdot)\) \(\chi_{8041}(226,\cdot)\) \(\chi_{8041}(250,\cdot)\) \(\chi_{8041}(299,\cdot)\) \(\chi_{8041}(360,\cdot)\) \(\chi_{8041}(398,\cdot)\) \(\chi_{8041}(403,\cdot)\) \(\chi_{8041}(600,\cdot)\) \(\chi_{8041}(618,\cdot)\) \(\chi_{8041}(623,\cdot)\) \(\chi_{8041}(656,\cdot)\) \(\chi_{8041}(666,\cdot)\) \(\chi_{8041}(772,\cdot)\) \(\chi_{8041}(809,\cdot)\) \(\chi_{8041}(821,\cdot)\) \(\chi_{8041}(838,\cdot)\) \(\chi_{8041}(864,\cdot)\) \(\chi_{8041}(981,\cdot)\) \(\chi_{8041}(1030,\cdot)\) \(\chi_{8041}(1091,\cdot)\) \(\chi_{8041}(1129,\cdot)\) \(\chi_{8041}(1196,\cdot)\) \(\chi_{8041}(1251,\cdot)\) \(\chi_{8041}(1282,\cdot)\) \(\chi_{8041}(1306,\cdot)\) \(\chi_{8041}(1337,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{560})$ |
| Fixed field: | Number field defined by a degree 560 polynomial (not computed) |
Values on generators
\((6580,2366,562)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{5}{16}\right),e\left(\frac{1}{7}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 8041 }(600, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{280}\right)\) | \(e\left(\frac{367}{560}\right)\) | \(e\left(\frac{37}{140}\right)\) | \(e\left(\frac{411}{560}\right)\) | \(e\left(\frac{63}{80}\right)\) | \(e\left(\frac{59}{80}\right)\) | \(e\left(\frac{111}{280}\right)\) | \(e\left(\frac{87}{280}\right)\) | \(e\left(\frac{97}{112}\right)\) | \(e\left(\frac{103}{112}\right)\) |