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.fh
\(\chi_{6480}(187,\cdot)\) \(\chi_{6480}(403,\cdot)\) \(\chi_{6480}(427,\cdot)\) \(\chi_{6480}(643,\cdot)\) \(\chi_{6480}(907,\cdot)\) \(\chi_{6480}(1123,\cdot)\) \(\chi_{6480}(1147,\cdot)\) \(\chi_{6480}(1363,\cdot)\) \(\chi_{6480}(1627,\cdot)\) \(\chi_{6480}(1843,\cdot)\) \(\chi_{6480}(1867,\cdot)\) \(\chi_{6480}(2083,\cdot)\) \(\chi_{6480}(2347,\cdot)\) \(\chi_{6480}(2563,\cdot)\) \(\chi_{6480}(2587,\cdot)\) \(\chi_{6480}(2803,\cdot)\) \(\chi_{6480}(3067,\cdot)\) \(\chi_{6480}(3283,\cdot)\) \(\chi_{6480}(3307,\cdot)\) \(\chi_{6480}(3523,\cdot)\) \(\chi_{6480}(3787,\cdot)\) \(\chi_{6480}(4003,\cdot)\) \(\chi_{6480}(4027,\cdot)\) \(\chi_{6480}(4243,\cdot)\) \(\chi_{6480}(4507,\cdot)\) \(\chi_{6480}(4723,\cdot)\) \(\chi_{6480}(4747,\cdot)\) \(\chi_{6480}(4963,\cdot)\) \(\chi_{6480}(5227,\cdot)\) \(\chi_{6480}(5443,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((2431,1621,6401,1297)\) → \((-1,i,e\left(\frac{8}{27}\right),i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 6480 }(1627, a) \) | \(1\) | \(1\) | \(e\left(\frac{107}{108}\right)\) | \(e\left(\frac{65}{108}\right)\) | \(e\left(\frac{47}{54}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{1}{108}\right)\) | \(e\left(\frac{23}{108}\right)\) | \(e\left(\frac{23}{54}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{11}{54}\right)\) |