Basic properties
Modulus: | \(8041\) | |
Conductor: | \(8041\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(210\) | 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.fa
\(\chi_{8041}(152,\cdot)\) \(\chi_{8041}(169,\cdot)\) \(\chi_{8041}(203,\cdot)\) \(\chi_{8041}(339,\cdot)\) \(\chi_{8041}(526,\cdot)\) \(\chi_{8041}(713,\cdot)\) \(\chi_{8041}(883,\cdot)\) \(\chi_{8041}(900,\cdot)\) \(\chi_{8041}(917,\cdot)\) \(\chi_{8041}(1070,\cdot)\) \(\chi_{8041}(1257,\cdot)\) \(\chi_{8041}(1444,\cdot)\) \(\chi_{8041}(1631,\cdot)\) \(\chi_{8041}(1648,\cdot)\) \(\chi_{8041}(1665,\cdot)\) \(\chi_{8041}(2073,\cdot)\) \(\chi_{8041}(2260,\cdot)\) \(\chi_{8041}(2379,\cdot)\) \(\chi_{8041}(2396,\cdot)\) \(\chi_{8041}(3127,\cdot)\) \(\chi_{8041}(3195,\cdot)\) \(\chi_{8041}(3535,\cdot)\) \(\chi_{8041}(3722,\cdot)\) \(\chi_{8041}(3756,\cdot)\) \(\chi_{8041}(4266,\cdot)\) \(\chi_{8041}(4317,\cdot)\) \(\chi_{8041}(4453,\cdot)\) \(\chi_{8041}(4657,\cdot)\) \(\chi_{8041}(4997,\cdot)\) \(\chi_{8041}(5184,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{105})$ |
Fixed field: | Number field defined by a degree 210 polynomial (not computed) |
Values on generators
\((6580,2366,562)\) → \((e\left(\frac{2}{5}\right),-1,e\left(\frac{16}{21}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(3195, a) \) | \(1\) | \(1\) | \(e\left(\frac{34}{35}\right)\) | \(e\left(\frac{97}{210}\right)\) | \(e\left(\frac{33}{35}\right)\) | \(e\left(\frac{31}{210}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{32}{35}\right)\) | \(e\left(\frac{97}{105}\right)\) | \(e\left(\frac{5}{42}\right)\) | \(e\left(\frac{17}{42}\right)\) |