Basic properties
| Modulus: | \(8007\) | |
| Conductor: | \(157\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{157}(48,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8007.dt
\(\chi_{8007}(205,\cdot)\) \(\chi_{8007}(358,\cdot)\) \(\chi_{8007}(460,\cdot)\) \(\chi_{8007}(664,\cdot)\) \(\chi_{8007}(766,\cdot)\) \(\chi_{8007}(1378,\cdot)\) \(\chi_{8007}(1837,\cdot)\) \(\chi_{8007}(2092,\cdot)\) \(\chi_{8007}(2755,\cdot)\) \(\chi_{8007}(2857,\cdot)\) \(\chi_{8007}(3571,\cdot)\) \(\chi_{8007}(3928,\cdot)\) \(\chi_{8007}(4030,\cdot)\) \(\chi_{8007}(4387,\cdot)\) \(\chi_{8007}(4438,\cdot)\) \(\chi_{8007}(4693,\cdot)\) \(\chi_{8007}(5458,\cdot)\) \(\chi_{8007}(5662,\cdot)\) \(\chi_{8007}(5866,\cdot)\) \(\chi_{8007}(6784,\cdot)\) \(\chi_{8007}(7090,\cdot)\) \(\chi_{8007}(7141,\cdot)\) \(\chi_{8007}(7192,\cdot)\) \(\chi_{8007}(7447,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((5339,1414,7855)\) → \((1,1,e\left(\frac{11}{78}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 8007 }(205, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{19}{26}\right)\) | \(e\left(\frac{17}{26}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{37}{39}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{7}{13}\right)\) |