Basic properties
| Modulus: | \(6480\) | |
| Conductor: | \(6480\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(108\) | 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 6480.gd
\(\chi_{6480}(43,\cdot)\) \(\chi_{6480}(67,\cdot)\) \(\chi_{6480}(283,\cdot)\) \(\chi_{6480}(547,\cdot)\) \(\chi_{6480}(763,\cdot)\) \(\chi_{6480}(787,\cdot)\) \(\chi_{6480}(1003,\cdot)\) \(\chi_{6480}(1267,\cdot)\) \(\chi_{6480}(1483,\cdot)\) \(\chi_{6480}(1507,\cdot)\) \(\chi_{6480}(1723,\cdot)\) \(\chi_{6480}(1987,\cdot)\) \(\chi_{6480}(2203,\cdot)\) \(\chi_{6480}(2227,\cdot)\) \(\chi_{6480}(2443,\cdot)\) \(\chi_{6480}(2707,\cdot)\) \(\chi_{6480}(2923,\cdot)\) \(\chi_{6480}(2947,\cdot)\) \(\chi_{6480}(3163,\cdot)\) \(\chi_{6480}(3427,\cdot)\) \(\chi_{6480}(3643,\cdot)\) \(\chi_{6480}(3667,\cdot)\) \(\chi_{6480}(3883,\cdot)\) \(\chi_{6480}(4147,\cdot)\) \(\chi_{6480}(4363,\cdot)\) \(\chi_{6480}(4387,\cdot)\) \(\chi_{6480}(4603,\cdot)\) \(\chi_{6480}(4867,\cdot)\) \(\chi_{6480}(5083,\cdot)\) \(\chi_{6480}(5107,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((2431,1621,6401,1297)\) → \((-1,i,e\left(\frac{11}{27}\right),-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 6480 }(43, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{108}\right)\) | \(e\left(\frac{5}{108}\right)\) | \(e\left(\frac{7}{27}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{79}{108}\right)\) | \(e\left(\frac{35}{108}\right)\) | \(e\left(\frac{35}{54}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{5}{54}\right)\) |