Basic properties
| Modulus: | \(6480\) | |
| Conductor: | \(1296\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(108\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1296}(61,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6480.fu
\(\chi_{6480}(61,\cdot)\) \(\chi_{6480}(301,\cdot)\) \(\chi_{6480}(421,\cdot)\) \(\chi_{6480}(661,\cdot)\) \(\chi_{6480}(781,\cdot)\) \(\chi_{6480}(1021,\cdot)\) \(\chi_{6480}(1141,\cdot)\) \(\chi_{6480}(1381,\cdot)\) \(\chi_{6480}(1501,\cdot)\) \(\chi_{6480}(1741,\cdot)\) \(\chi_{6480}(1861,\cdot)\) \(\chi_{6480}(2101,\cdot)\) \(\chi_{6480}(2221,\cdot)\) \(\chi_{6480}(2461,\cdot)\) \(\chi_{6480}(2581,\cdot)\) \(\chi_{6480}(2821,\cdot)\) \(\chi_{6480}(2941,\cdot)\) \(\chi_{6480}(3181,\cdot)\) \(\chi_{6480}(3301,\cdot)\) \(\chi_{6480}(3541,\cdot)\) \(\chi_{6480}(3661,\cdot)\) \(\chi_{6480}(3901,\cdot)\) \(\chi_{6480}(4021,\cdot)\) \(\chi_{6480}(4261,\cdot)\) \(\chi_{6480}(4381,\cdot)\) \(\chi_{6480}(4621,\cdot)\) \(\chi_{6480}(4741,\cdot)\) \(\chi_{6480}(4981,\cdot)\) \(\chi_{6480}(5101,\cdot)\) \(\chi_{6480}(5341,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((2431,1621,6401,1297)\) → \((1,-i,e\left(\frac{26}{27}\right),1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 6480 }(61, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{54}\right)\) | \(e\left(\frac{29}{108}\right)\) | \(e\left(\frac{103}{108}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{5}{54}\right)\) | \(e\left(\frac{95}{108}\right)\) | \(e\left(\frac{7}{27}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{29}{54}\right)\) |