Basic properties
| Modulus: | \(8112\) | |
| Conductor: | \(8112\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | 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 8112.fx
\(\chi_{8112}(35,\cdot)\) \(\chi_{8112}(107,\cdot)\) \(\chi_{8112}(347,\cdot)\) \(\chi_{8112}(419,\cdot)\) \(\chi_{8112}(659,\cdot)\) \(\chi_{8112}(731,\cdot)\) \(\chi_{8112}(971,\cdot)\) \(\chi_{8112}(1043,\cdot)\) \(\chi_{8112}(1283,\cdot)\) \(\chi_{8112}(1355,\cdot)\) \(\chi_{8112}(1595,\cdot)\) \(\chi_{8112}(1907,\cdot)\) \(\chi_{8112}(1979,\cdot)\) \(\chi_{8112}(2291,\cdot)\) \(\chi_{8112}(2531,\cdot)\) \(\chi_{8112}(2603,\cdot)\) \(\chi_{8112}(2843,\cdot)\) \(\chi_{8112}(2915,\cdot)\) \(\chi_{8112}(3155,\cdot)\) \(\chi_{8112}(3227,\cdot)\) \(\chi_{8112}(3467,\cdot)\) \(\chi_{8112}(3539,\cdot)\) \(\chi_{8112}(3779,\cdot)\) \(\chi_{8112}(3851,\cdot)\) \(\chi_{8112}(4091,\cdot)\) \(\chi_{8112}(4163,\cdot)\) \(\chi_{8112}(4403,\cdot)\) \(\chi_{8112}(4475,\cdot)\) \(\chi_{8112}(4715,\cdot)\) \(\chi_{8112}(4787,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((5071,6085,2705,3889)\) → \((-1,-i,-1,e\left(\frac{29}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 8112 }(35, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{52}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{53}{156}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{23}{26}\right)\) | \(e\left(\frac{77}{156}\right)\) | \(e\left(\frac{3}{26}\right)\) | \(e\left(\frac{79}{156}\right)\) |