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.fs
\(\chi_{6480}(229,\cdot)\) \(\chi_{6480}(349,\cdot)\) \(\chi_{6480}(589,\cdot)\) \(\chi_{6480}(709,\cdot)\) \(\chi_{6480}(949,\cdot)\) \(\chi_{6480}(1069,\cdot)\) \(\chi_{6480}(1309,\cdot)\) \(\chi_{6480}(1429,\cdot)\) \(\chi_{6480}(1669,\cdot)\) \(\chi_{6480}(1789,\cdot)\) \(\chi_{6480}(2029,\cdot)\) \(\chi_{6480}(2149,\cdot)\) \(\chi_{6480}(2389,\cdot)\) \(\chi_{6480}(2509,\cdot)\) \(\chi_{6480}(2749,\cdot)\) \(\chi_{6480}(2869,\cdot)\) \(\chi_{6480}(3109,\cdot)\) \(\chi_{6480}(3229,\cdot)\) \(\chi_{6480}(3469,\cdot)\) \(\chi_{6480}(3589,\cdot)\) \(\chi_{6480}(3829,\cdot)\) \(\chi_{6480}(3949,\cdot)\) \(\chi_{6480}(4189,\cdot)\) \(\chi_{6480}(4309,\cdot)\) \(\chi_{6480}(4549,\cdot)\) \(\chi_{6480}(4669,\cdot)\) \(\chi_{6480}(4909,\cdot)\) \(\chi_{6480}(5029,\cdot)\) \(\chi_{6480}(5269,\cdot)\) \(\chi_{6480}(5389,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((2431,1621,6401,1297)\) → \((1,-i,e\left(\frac{1}{27}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 6480 }(2029, a) \) | \(1\) | \(1\) | \(e\left(\frac{16}{27}\right)\) | \(e\left(\frac{25}{108}\right)\) | \(e\left(\frac{5}{108}\right)\) | \(e\left(\frac{13}{18}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{11}{27}\right)\) | \(e\left(\frac{67}{108}\right)\) | \(e\left(\frac{20}{27}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{25}{54}\right)\) |