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.ga
\(\chi_{6480}(173,\cdot)\) \(\chi_{6480}(437,\cdot)\) \(\chi_{6480}(653,\cdot)\) \(\chi_{6480}(677,\cdot)\) \(\chi_{6480}(893,\cdot)\) \(\chi_{6480}(1157,\cdot)\) \(\chi_{6480}(1373,\cdot)\) \(\chi_{6480}(1397,\cdot)\) \(\chi_{6480}(1613,\cdot)\) \(\chi_{6480}(1877,\cdot)\) \(\chi_{6480}(2093,\cdot)\) \(\chi_{6480}(2117,\cdot)\) \(\chi_{6480}(2333,\cdot)\) \(\chi_{6480}(2597,\cdot)\) \(\chi_{6480}(2813,\cdot)\) \(\chi_{6480}(2837,\cdot)\) \(\chi_{6480}(3053,\cdot)\) \(\chi_{6480}(3317,\cdot)\) \(\chi_{6480}(3533,\cdot)\) \(\chi_{6480}(3557,\cdot)\) \(\chi_{6480}(3773,\cdot)\) \(\chi_{6480}(4037,\cdot)\) \(\chi_{6480}(4253,\cdot)\) \(\chi_{6480}(4277,\cdot)\) \(\chi_{6480}(4493,\cdot)\) \(\chi_{6480}(4757,\cdot)\) \(\chi_{6480}(4973,\cdot)\) \(\chi_{6480}(4997,\cdot)\) \(\chi_{6480}(5213,\cdot)\) \(\chi_{6480}(5477,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((2431,1621,6401,1297)\) → \((1,-i,e\left(\frac{13}{54}\right),-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 6480 }(173, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{108}\right)\) | \(e\left(\frac{95}{108}\right)\) | \(e\left(\frac{23}{54}\right)\) | \(e\left(\frac{25}{36}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{43}{108}\right)\) | \(e\left(\frac{71}{108}\right)\) | \(e\left(\frac{22}{27}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{7}{27}\right)\) |