Basic properties
| Modulus: | \(8040\) | |
| Conductor: | \(1005\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1005}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8040.gu
\(\chi_{8040}(17,\cdot)\) \(\chi_{8040}(257,\cdot)\) \(\chi_{8040}(473,\cdot)\) \(\chi_{8040}(977,\cdot)\) \(\chi_{8040}(1193,\cdot)\) \(\chi_{8040}(1433,\cdot)\) \(\chi_{8040}(1577,\cdot)\) \(\chi_{8040}(1673,\cdot)\) \(\chi_{8040}(2033,\cdot)\) \(\chi_{8040}(2057,\cdot)\) \(\chi_{8040}(2177,\cdot)\) \(\chi_{8040}(2297,\cdot)\) \(\chi_{8040}(2753,\cdot)\) \(\chi_{8040}(2897,\cdot)\) \(\chi_{8040}(3137,\cdot)\) \(\chi_{8040}(3233,\cdot)\) \(\chi_{8040}(3473,\cdot)\) \(\chi_{8040}(4097,\cdot)\) \(\chi_{8040}(4193,\cdot)\) \(\chi_{8040}(4337,\cdot)\) \(\chi_{8040}(4457,\cdot)\) \(\chi_{8040}(4577,\cdot)\) \(\chi_{8040}(4793,\cdot)\) \(\chi_{8040}(4817,\cdot)\) \(\chi_{8040}(5273,\cdot)\) \(\chi_{8040}(5297,\cdot)\) \(\chi_{8040}(5393,\cdot)\) \(\chi_{8040}(5513,\cdot)\) \(\chi_{8040}(6017,\cdot)\) \(\chi_{8040}(6113,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((6031,4021,2681,3217,5161)\) → \((1,1,-1,i,e\left(\frac{32}{33}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 8040 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{73}{132}\right)\) | \(e\left(\frac{47}{66}\right)\) | \(e\left(\frac{23}{132}\right)\) | \(e\left(\frac{107}{132}\right)\) | \(e\left(\frac{13}{66}\right)\) | \(e\left(\frac{53}{132}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{19}{33}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{59}{66}\right)\) |