Basic properties
| Modulus: | \(8007\) | |
| Conductor: | \(2669\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(52\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2669}(310,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8007.dn
\(\chi_{8007}(310,\cdot)\) \(\chi_{8007}(667,\cdot)\) \(\chi_{8007}(727,\cdot)\) \(\chi_{8007}(1543,\cdot)\) \(\chi_{8007}(1645,\cdot)\) \(\chi_{8007}(1900,\cdot)\) \(\chi_{8007}(1951,\cdot)\) \(\chi_{8007}(2299,\cdot)\) \(\chi_{8007}(2401,\cdot)\) \(\chi_{8007}(2605,\cdot)\) \(\chi_{8007}(2665,\cdot)\) \(\chi_{8007}(3022,\cdot)\) \(\chi_{8007}(3625,\cdot)\) \(\chi_{8007}(4033,\cdot)\) \(\chi_{8007}(4654,\cdot)\) \(\chi_{8007}(4756,\cdot)\) \(\chi_{8007}(4960,\cdot)\) \(\chi_{8007}(5980,\cdot)\) \(\chi_{8007}(6379,\cdot)\) \(\chi_{8007}(6388,\cdot)\) \(\chi_{8007}(7195,\cdot)\) \(\chi_{8007}(7297,\cdot)\) \(\chi_{8007}(7552,\cdot)\) \(\chi_{8007}(7603,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{52})$ |
| Fixed field: | Number field defined by a degree 52 polynomial |
Values on generators
\((5339,1414,7855)\) → \((1,-i,e\left(\frac{4}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8007 }(310, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{3}{52}\right)\) | \(e\left(\frac{25}{52}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{45}{52}\right)\) | \(1\) | \(e\left(\frac{19}{52}\right)\) | \(e\left(\frac{7}{13}\right)\) |