Basic properties
Modulus: | \(8041\) | |
Conductor: | \(8041\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(120\) | 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.em
\(\chi_{8041}(338,\cdot)\) \(\chi_{8041}(695,\cdot)\) \(\chi_{8041}(910,\cdot)\) \(\chi_{8041}(1069,\cdot)\) \(\chi_{8041}(1284,\cdot)\) \(\chi_{8041}(1426,\cdot)\) \(\chi_{8041}(1641,\cdot)\) \(\chi_{8041}(1800,\cdot)\) \(\chi_{8041}(2015,\cdot)\) \(\chi_{8041}(2372,\cdot)\) \(\chi_{8041}(2746,\cdot)\) \(\chi_{8041}(2888,\cdot)\) \(\chi_{8041}(3262,\cdot)\) \(\chi_{8041}(3748,\cdot)\) \(\chi_{8041}(3834,\cdot)\) \(\chi_{8041}(4122,\cdot)\) \(\chi_{8041}(4208,\cdot)\) \(\chi_{8041}(4479,\cdot)\) \(\chi_{8041}(4694,\cdot)\) \(\chi_{8041}(4853,\cdot)\) \(\chi_{8041}(5068,\cdot)\) \(\chi_{8041}(5210,\cdot)\) \(\chi_{8041}(5425,\cdot)\) \(\chi_{8041}(5584,\cdot)\) \(\chi_{8041}(5799,\cdot)\) \(\chi_{8041}(6156,\cdot)\) \(\chi_{8041}(6530,\cdot)\) \(\chi_{8041}(6672,\cdot)\) \(\chi_{8041}(7046,\cdot)\) \(\chi_{8041}(7618,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{120})$ |
Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((6580,2366,562)\) → \((e\left(\frac{7}{10}\right),e\left(\frac{1}{8}\right),e\left(\frac{5}{6}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(2372, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{67}{120}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{17}{20}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{11}{24}\right)\) |