Basic properties
| Modulus: | \(8007\) | |
| Conductor: | \(2669\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(312\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2669}(25,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8007.fd
\(\chi_{8007}(25,\cdot)\) \(\chi_{8007}(76,\cdot)\) \(\chi_{8007}(127,\cdot)\) \(\chi_{8007}(274,\cdot)\) \(\chi_{8007}(382,\cdot)\) \(\chi_{8007}(400,\cdot)\) \(\chi_{8007}(502,\cdot)\) \(\chi_{8007}(631,\cdot)\) \(\chi_{8007}(661,\cdot)\) \(\chi_{8007}(733,\cdot)\) \(\chi_{8007}(967,\cdot)\) \(\chi_{8007}(1018,\cdot)\) \(\chi_{8007}(1069,\cdot)\) \(\chi_{8007}(1090,\cdot)\) \(\chi_{8007}(1141,\cdot)\) \(\chi_{8007}(1147,\cdot)\) \(\chi_{8007}(1216,\cdot)\) \(\chi_{8007}(1300,\cdot)\) \(\chi_{8007}(1324,\cdot)\) \(\chi_{8007}(1396,\cdot)\) \(\chi_{8007}(1402,\cdot)\) \(\chi_{8007}(1573,\cdot)\) \(\chi_{8007}(1606,\cdot)\) \(\chi_{8007}(1675,\cdot)\) \(\chi_{8007}(1708,\cdot)\) \(\chi_{8007}(2032,\cdot)\) \(\chi_{8007}(2083,\cdot)\) \(\chi_{8007}(2089,\cdot)\) \(\chi_{8007}(2161,\cdot)\) \(\chi_{8007}(2242,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{312})$ |
| Fixed field: | Number field defined by a degree 312 polynomial (not computed) |
Values on generators
\((5339,1414,7855)\) → \((1,e\left(\frac{5}{8}\right),e\left(\frac{1}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8007 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{52}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{43}{312}\right)\) | \(e\left(\frac{79}{104}\right)\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{217}{312}\right)\) | \(e\left(\frac{229}{312}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{33}{104}\right)\) | \(e\left(\frac{3}{13}\right)\) |