Basic properties
| Modulus: | \(8010\) | |
| Conductor: | \(4005\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(132\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4005}(3427,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8010.dw
\(\chi_{8010}(67,\cdot)\) \(\chi_{8010}(97,\cdot)\) \(\chi_{8010}(223,\cdot)\) \(\chi_{8010}(283,\cdot)\) \(\chi_{8010}(817,\cdot)\) \(\chi_{8010}(1057,\cdot)\) \(\chi_{8010}(1723,\cdot)\) \(\chi_{8010}(1933,\cdot)\) \(\chi_{8010}(2203,\cdot)\) \(\chi_{8010}(2227,\cdot)\) \(\chi_{8010}(2257,\cdot)\) \(\chi_{8010}(2353,\cdot)\) \(\chi_{8010}(2407,\cdot)\) \(\chi_{8010}(2767,\cdot)\) \(\chi_{8010}(2887,\cdot)\) \(\chi_{8010}(2893,\cdot)\) \(\chi_{8010}(3193,\cdot)\) \(\chi_{8010}(3427,\cdot)\) \(\chi_{8010}(3487,\cdot)\) \(\chi_{8010}(4363,\cdot)\) \(\chi_{8010}(4543,\cdot)\) \(\chi_{8010}(4603,\cdot)\) \(\chi_{8010}(4873,\cdot)\) \(\chi_{8010}(4903,\cdot)\) \(\chi_{8010}(4927,\cdot)\) \(\chi_{8010}(5137,\cdot)\) \(\chi_{8010}(5407,\cdot)\) \(\chi_{8010}(5557,\cdot)\) \(\chi_{8010}(5623,\cdot)\) \(\chi_{8010}(5863,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{132})$ |
| Fixed field: | Number field defined by a degree 132 polynomial (not computed) |
Values on generators
\((7121,4807,181)\) → \((e\left(\frac{2}{3}\right),i,e\left(\frac{9}{11}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 8010 }(3427, a) \) | \(-1\) | \(1\) | \(e\left(\frac{25}{132}\right)\) | \(e\left(\frac{13}{33}\right)\) | \(e\left(\frac{119}{132}\right)\) | \(e\left(\frac{7}{44}\right)\) | \(e\left(\frac{3}{22}\right)\) | \(e\left(\frac{95}{132}\right)\) | \(e\left(\frac{29}{66}\right)\) | \(e\left(\frac{23}{33}\right)\) | \(i\) | \(e\left(\frac{17}{33}\right)\) |