Basic properties
| Modulus: | \(8041\) | |
| Conductor: | \(8041\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(840\) | 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.fw
\(\chi_{8041}(19,\cdot)\) \(\chi_{8041}(134,\cdot)\) \(\chi_{8041}(162,\cdot)\) \(\chi_{8041}(206,\cdot)\) \(\chi_{8041}(270,\cdot)\) \(\chi_{8041}(304,\cdot)\) \(\chi_{8041}(321,\cdot)\) \(\chi_{8041}(349,\cdot)\) \(\chi_{8041}(491,\cdot)\) \(\chi_{8041}(501,\cdot)\) \(\chi_{8041}(502,\cdot)\) \(\chi_{8041}(519,\cdot)\) \(\chi_{8041}(535,\cdot)\) \(\chi_{8041}(536,\cdot)\) \(\chi_{8041}(546,\cdot)\) \(\chi_{8041}(678,\cdot)\) \(\chi_{8041}(706,\cdot)\) \(\chi_{8041}(722,\cdot)\) \(\chi_{8041}(750,\cdot)\) \(\chi_{8041}(865,\cdot)\) \(\chi_{8041}(886,\cdot)\) \(\chi_{8041}(893,\cdot)\) \(\chi_{8041}(937,\cdot)\) \(\chi_{8041}(1018,\cdot)\) \(\chi_{8041}(1052,\cdot)\) \(\chi_{8041}(1062,\cdot)\) \(\chi_{8041}(1080,\cdot)\) \(\chi_{8041}(1130,\cdot)\) \(\chi_{8041}(1216,\cdot)\) \(\chi_{8041}(1250,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{840})$ |
| Fixed field: | Number field defined by a degree 840 polynomial (not computed) |
Values on generators
\((6580,2366,562)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{5}{8}\right),e\left(\frac{5}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 8041 }(501, a) \) | \(1\) | \(1\) | \(e\left(\frac{121}{140}\right)\) | \(e\left(\frac{793}{840}\right)\) | \(e\left(\frac{51}{70}\right)\) | \(e\left(\frac{589}{840}\right)\) | \(e\left(\frac{97}{120}\right)\) | \(e\left(\frac{41}{120}\right)\) | \(e\left(\frac{83}{140}\right)\) | \(e\left(\frac{373}{420}\right)\) | \(e\left(\frac{95}{168}\right)\) | \(e\left(\frac{113}{168}\right)\) |