Basic properties
Modulus: | \(8041\) | |
Conductor: | \(8041\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(140\) | 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.eo
\(\chi_{8041}(4,\cdot)\) \(\chi_{8041}(47,\cdot)\) \(\chi_{8041}(64,\cdot)\) \(\chi_{8041}(489,\cdot)\) \(\chi_{8041}(735,\cdot)\) \(\chi_{8041}(752,\cdot)\) \(\chi_{8041}(795,\cdot)\) \(\chi_{8041}(1466,\cdot)\) \(\chi_{8041}(1483,\cdot)\) \(\chi_{8041}(1798,\cdot)\) \(\chi_{8041}(1908,\cdot)\) \(\chi_{8041}(1951,\cdot)\) \(\chi_{8041}(2214,\cdot)\) \(\chi_{8041}(2682,\cdot)\) \(\chi_{8041}(3107,\cdot)\) \(\chi_{8041}(3217,\cdot)\) \(\chi_{8041}(3260,\cdot)\) \(\chi_{8041}(3370,\cdot)\) \(\chi_{8041}(3413,\cdot)\) \(\chi_{8041}(3481,\cdot)\) \(\chi_{8041}(3991,\cdot)\) \(\chi_{8041}(4101,\cdot)\) \(\chi_{8041}(4526,\cdot)\) \(\chi_{8041}(4569,\cdot)\) \(\chi_{8041}(4679,\cdot)\) \(\chi_{8041}(4722,\cdot)\) \(\chi_{8041}(4832,\cdot)\) \(\chi_{8041}(4900,\cdot)\) \(\chi_{8041}(4943,\cdot)\) \(\chi_{8041}(5164,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{140})$ |
Fixed field: | Number field defined by a degree 140 polynomial (not computed) |
Values on generators
\((6580,2366,562)\) → \((e\left(\frac{3}{5}\right),-i,e\left(\frac{4}{7}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(4101, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{70}\right)\) | \(e\left(\frac{17}{140}\right)\) | \(e\left(\frac{2}{35}\right)\) | \(e\left(\frac{61}{140}\right)\) | \(e\left(\frac{13}{20}\right)\) | \(e\left(\frac{9}{20}\right)\) | \(e\left(\frac{41}{70}\right)\) | \(e\left(\frac{17}{70}\right)\) | \(e\left(\frac{27}{28}\right)\) | \(e\left(\frac{5}{28}\right)\) |