Basic properties
| Modulus: | \(8007\) | |
| Conductor: | \(2669\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(104\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2669}(196,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8007.dz
\(\chi_{8007}(196,\cdot)\) \(\chi_{8007}(886,\cdot)\) \(\chi_{8007}(988,\cdot)\) \(\chi_{8007}(1192,\cdot)\) \(\chi_{8007}(1198,\cdot)\) \(\chi_{8007}(1828,\cdot)\) \(\chi_{8007}(1930,\cdot)\) \(\chi_{8007}(2014,\cdot)\) \(\chi_{8007}(2116,\cdot)\) \(\chi_{8007}(2134,\cdot)\) \(\chi_{8007}(2140,\cdot)\) \(\chi_{8007}(2212,\cdot)\) \(\chi_{8007}(2371,\cdot)\) \(\chi_{8007}(2422,\cdot)\) \(\chi_{8007}(2620,\cdot)\) \(\chi_{8007}(2956,\cdot)\) \(\chi_{8007}(3058,\cdot)\) \(\chi_{8007}(3136,\cdot)\) \(\chi_{8007}(3154,\cdot)\) \(\chi_{8007}(3313,\cdot)\) \(\chi_{8007}(3364,\cdot)\) \(\chi_{8007}(3493,\cdot)\) \(\chi_{8007}(3562,\cdot)\) \(\chi_{8007}(4078,\cdot)\) \(\chi_{8007}(4435,\cdot)\) \(\chi_{8007}(4966,\cdot)\) \(\chi_{8007}(5125,\cdot)\) \(\chi_{8007}(5227,\cdot)\) \(\chi_{8007}(5431,\cdot)\) \(\chi_{8007}(5782,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{104})$ |
| Fixed field: | Number field defined by a degree 104 polynomial (not computed) |
Values on generators
\((5339,1414,7855)\) → \((1,e\left(\frac{1}{8}\right),e\left(\frac{9}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8007 }(196, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{52}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{33}{104}\right)\) | \(e\left(\frac{15}{104}\right)\) | \(e\left(\frac{5}{52}\right)\) | \(e\left(\frac{71}{104}\right)\) | \(e\left(\frac{27}{104}\right)\) | \(-1\) | \(e\left(\frac{53}{104}\right)\) | \(e\left(\frac{6}{13}\right)\) |