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: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8041.fz
\(\chi_{8041}(26,\cdot)\) \(\chi_{8041}(104,\cdot)\) \(\chi_{8041}(202,\cdot)\) \(\chi_{8041}(291,\cdot)\) \(\chi_{8041}(372,\cdot)\) \(\chi_{8041}(399,\cdot)\) \(\chi_{8041}(416,\cdot)\) \(\chi_{8041}(433,\cdot)\) \(\chi_{8041}(478,\cdot)\) \(\chi_{8041}(542,\cdot)\) \(\chi_{8041}(587,\cdot)\) \(\chi_{8041}(614,\cdot)\) \(\chi_{8041}(620,\cdot)\) \(\chi_{8041}(621,\cdot)\) \(\chi_{8041}(631,\cdot)\) \(\chi_{8041}(665,\cdot)\) \(\chi_{8041}(757,\cdot)\) \(\chi_{8041}(807,\cdot)\) \(\chi_{8041}(808,\cdot)\) \(\chi_{8041}(933,\cdot)\) \(\chi_{8041}(994,\cdot)\) \(\chi_{8041}(1103,\cdot)\) \(\chi_{8041}(1137,\cdot)\) \(\chi_{8041}(1147,\cdot)\) \(\chi_{8041}(1148,\cdot)\) \(\chi_{8041}(1164,\cdot)\) \(\chi_{8041}(1181,\cdot)\) \(\chi_{8041}(1318,\cdot)\) \(\chi_{8041}(1324,\cdot)\) \(\chi_{8041}(1345,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{840})$ |
| Fixed field: | Number field defined by a degree 840 polynomial (not computed) |
Values on generators
\((6580,2366,562)\) → \((e\left(\frac{1}{5}\right),e\left(\frac{1}{8}\right),e\left(\frac{17}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
| \( \chi_{ 8041 }(26, a) \) | \(-1\) | \(1\) | \(e\left(\frac{123}{140}\right)\) | \(e\left(\frac{109}{840}\right)\) | \(e\left(\frac{53}{70}\right)\) | \(e\left(\frac{457}{840}\right)\) | \(e\left(\frac{1}{120}\right)\) | \(e\left(\frac{113}{120}\right)\) | \(e\left(\frac{89}{140}\right)\) | \(e\left(\frac{109}{420}\right)\) | \(e\left(\frac{71}{168}\right)\) | \(e\left(\frac{149}{168}\right)\) |