Basic properties
| Modulus: | \(8040\) | |
| Conductor: | \(1340\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1340}(103,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8040.ha
\(\chi_{8040}(103,\cdot)\) \(\chi_{8040}(127,\cdot)\) \(\chi_{8040}(583,\cdot)\) \(\chi_{8040}(607,\cdot)\) \(\chi_{8040}(703,\cdot)\) \(\chi_{8040}(823,\cdot)\) \(\chi_{8040}(1327,\cdot)\) \(\chi_{8040}(1423,\cdot)\) \(\chi_{8040}(1567,\cdot)\) \(\chi_{8040}(1663,\cdot)\) \(\chi_{8040}(1807,\cdot)\) \(\chi_{8040}(2167,\cdot)\) \(\chi_{8040}(2623,\cdot)\) \(\chi_{8040}(2863,\cdot)\) \(\chi_{8040}(2887,\cdot)\) \(\chi_{8040}(2983,\cdot)\) \(\chi_{8040}(3103,\cdot)\) \(\chi_{8040}(3343,\cdot)\) \(\chi_{8040}(3367,\cdot)\) \(\chi_{8040}(3607,\cdot)\) \(\chi_{8040}(3823,\cdot)\) \(\chi_{8040}(4327,\cdot)\) \(\chi_{8040}(4543,\cdot)\) \(\chi_{8040}(4783,\cdot)\) \(\chi_{8040}(4927,\cdot)\) \(\chi_{8040}(5023,\cdot)\) \(\chi_{8040}(5383,\cdot)\) \(\chi_{8040}(5407,\cdot)\) \(\chi_{8040}(5527,\cdot)\) \(\chi_{8040}(5647,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((6031,4021,2681,3217,5161)\) → \((-1,1,1,-i,e\left(\frac{7}{33}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 8040 }(103, a) \) | \(1\) | \(1\) | \(e\left(\frac{17}{132}\right)\) | \(e\left(\frac{1}{66}\right)\) | \(e\left(\frac{37}{132}\right)\) | \(e\left(\frac{43}{132}\right)\) | \(e\left(\frac{4}{33}\right)\) | \(e\left(\frac{91}{132}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{31}{66}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{8}{33}\right)\) |