Basic properties
| Modulus: | \(8007\) | |
| Conductor: | \(8007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(104\) | 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 8007.dx
\(\chi_{8007}(59,\cdot)\) \(\chi_{8007}(155,\cdot)\) \(\chi_{8007}(236,\cdot)\) \(\chi_{8007}(620,\cdot)\) \(\chi_{8007}(944,\cdot)\) \(\chi_{8007}(950,\cdot)\) \(\chi_{8007}(1301,\cdot)\) \(\chi_{8007}(1334,\cdot)\) \(\chi_{8007}(1454,\cdot)\) \(\chi_{8007}(1505,\cdot)\) \(\chi_{8007}(1511,\cdot)\) \(\chi_{8007}(1913,\cdot)\) \(\chi_{8007}(2378,\cdot)\) \(\chi_{8007}(2480,\cdot)\) \(\chi_{8007}(2990,\cdot)\) \(\chi_{8007}(3062,\cdot)\) \(\chi_{8007}(3086,\cdot)\) \(\chi_{8007}(3194,\cdot)\) \(\chi_{8007}(3290,\cdot)\) \(\chi_{8007}(3776,\cdot)\) \(\chi_{8007}(3800,\cdot)\) \(\chi_{8007}(3902,\cdot)\) \(\chi_{8007}(4241,\cdot)\) \(\chi_{8007}(4337,\cdot)\) \(\chi_{8007}(4367,\cdot)\) \(\chi_{8007}(4598,\cdot)\) \(\chi_{8007}(4751,\cdot)\) \(\chi_{8007}(4769,\cdot)\) \(\chi_{8007}(4775,\cdot)\) \(\chi_{8007}(4802,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{104})$ |
| Fixed field: | Number field defined by a degree 104 polynomial (not computed) |
Values on generators
\((5339,1414,7855)\) → \((-1,e\left(\frac{5}{8}\right),e\left(\frac{15}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8007 }(59, a) \) | \(1\) | \(1\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{95}{104}\right)\) | \(e\left(\frac{29}{104}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{87}{104}\right)\) | \(e\left(\frac{99}{104}\right)\) | \(1\) | \(e\left(\frac{21}{104}\right)\) | \(e\left(\frac{9}{13}\right)\) |