Basic properties
Modulus: | \(8041\) | |
Conductor: | \(187\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(80\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{187}(61,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8041.dz
\(\chi_{8041}(173,\cdot)\) \(\chi_{8041}(216,\cdot)\) \(\chi_{8041}(431,\cdot)\) \(\chi_{8041}(904,\cdot)\) \(\chi_{8041}(1119,\cdot)\) \(\chi_{8041}(1162,\cdot)\) \(\chi_{8041}(1592,\cdot)\) \(\chi_{8041}(1635,\cdot)\) \(\chi_{8041}(1678,\cdot)\) \(\chi_{8041}(1850,\cdot)\) \(\chi_{8041}(2323,\cdot)\) \(\chi_{8041}(2538,\cdot)\) \(\chi_{8041}(2581,\cdot)\) \(\chi_{8041}(2624,\cdot)\) \(\chi_{8041}(3054,\cdot)\) \(\chi_{8041}(3097,\cdot)\) \(\chi_{8041}(3269,\cdot)\) \(\chi_{8041}(4000,\cdot)\) \(\chi_{8041}(4043,\cdot)\) \(\chi_{8041}(4430,\cdot)\) \(\chi_{8041}(4516,\cdot)\) \(\chi_{8041}(4903,\cdot)\) \(\chi_{8041}(5161,\cdot)\) \(\chi_{8041}(5462,\cdot)\) \(\chi_{8041}(5634,\cdot)\) \(\chi_{8041}(5892,\cdot)\) \(\chi_{8041}(6365,\cdot)\) \(\chi_{8041}(6795,\cdot)\) \(\chi_{8041}(7354,\cdot)\) \(\chi_{8041}(7526,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{80})$ |
Fixed field: | Number field defined by a degree 80 polynomial |
Values on generators
\((6580,2366,562)\) → \((e\left(\frac{9}{10}\right),e\left(\frac{3}{16}\right),1)\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(12\) |
\( \chi_{ 8041 }(7354, a) \) | \(1\) | \(1\) | \(e\left(\frac{21}{40}\right)\) | \(e\left(\frac{31}{80}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{43}{80}\right)\) | \(e\left(\frac{73}{80}\right)\) | \(e\left(\frac{29}{80}\right)\) | \(e\left(\frac{23}{40}\right)\) | \(e\left(\frac{31}{40}\right)\) | \(e\left(\frac{1}{16}\right)\) | \(e\left(\frac{7}{16}\right)\) |