Basic properties
| Modulus: | \(8040\) | |
| Conductor: | \(335\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{335}(2,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8040.gx
\(\chi_{8040}(337,\cdot)\) \(\chi_{8040}(433,\cdot)\) \(\chi_{8040}(577,\cdot)\) \(\chi_{8040}(817,\cdot)\) \(\chi_{8040}(1033,\cdot)\) \(\chi_{8040}(1537,\cdot)\) \(\chi_{8040}(1753,\cdot)\) \(\chi_{8040}(1993,\cdot)\) \(\chi_{8040}(2017,\cdot)\) \(\chi_{8040}(2257,\cdot)\) \(\chi_{8040}(2377,\cdot)\) \(\chi_{8040}(2473,\cdot)\) \(\chi_{8040}(2497,\cdot)\) \(\chi_{8040}(2737,\cdot)\) \(\chi_{8040}(3193,\cdot)\) \(\chi_{8040}(3553,\cdot)\) \(\chi_{8040}(3697,\cdot)\) \(\chi_{8040}(3793,\cdot)\) \(\chi_{8040}(3937,\cdot)\) \(\chi_{8040}(4033,\cdot)\) \(\chi_{8040}(4537,\cdot)\) \(\chi_{8040}(4657,\cdot)\) \(\chi_{8040}(4753,\cdot)\) \(\chi_{8040}(4777,\cdot)\) \(\chi_{8040}(5233,\cdot)\) \(\chi_{8040}(5257,\cdot)\) \(\chi_{8040}(5473,\cdot)\) \(\chi_{8040}(5593,\cdot)\) \(\chi_{8040}(5713,\cdot)\) \(\chi_{8040}(5857,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((6031,4021,2681,3217,5161)\) → \((1,1,1,i,e\left(\frac{1}{66}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 8040 }(337, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{132}\right)\) | \(e\left(\frac{59}{66}\right)\) | \(e\left(\frac{5}{132}\right)\) | \(e\left(\frac{29}{132}\right)\) | \(e\left(\frac{43}{66}\right)\) | \(e\left(\frac{23}{132}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{53}{66}\right)\) |