Basic properties
| Modulus: | \(6480\) | |
| Conductor: | \(3240\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(108\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3240}(1757,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6480.fk
\(\chi_{6480}(137,\cdot)\) \(\chi_{6480}(473,\cdot)\) \(\chi_{6480}(617,\cdot)\) \(\chi_{6480}(713,\cdot)\) \(\chi_{6480}(857,\cdot)\) \(\chi_{6480}(1193,\cdot)\) \(\chi_{6480}(1337,\cdot)\) \(\chi_{6480}(1433,\cdot)\) \(\chi_{6480}(1577,\cdot)\) \(\chi_{6480}(1913,\cdot)\) \(\chi_{6480}(2057,\cdot)\) \(\chi_{6480}(2153,\cdot)\) \(\chi_{6480}(2297,\cdot)\) \(\chi_{6480}(2633,\cdot)\) \(\chi_{6480}(2777,\cdot)\) \(\chi_{6480}(2873,\cdot)\) \(\chi_{6480}(3017,\cdot)\) \(\chi_{6480}(3353,\cdot)\) \(\chi_{6480}(3497,\cdot)\) \(\chi_{6480}(3593,\cdot)\) \(\chi_{6480}(3737,\cdot)\) \(\chi_{6480}(4073,\cdot)\) \(\chi_{6480}(4217,\cdot)\) \(\chi_{6480}(4313,\cdot)\) \(\chi_{6480}(4457,\cdot)\) \(\chi_{6480}(4793,\cdot)\) \(\chi_{6480}(4937,\cdot)\) \(\chi_{6480}(5033,\cdot)\) \(\chi_{6480}(5177,\cdot)\) \(\chi_{6480}(5513,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((2431,1621,6401,1297)\) → \((1,-1,e\left(\frac{19}{54}\right),i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(7\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 6480 }(137, a) \) | \(1\) | \(1\) | \(e\left(\frac{95}{108}\right)\) | \(e\left(\frac{2}{27}\right)\) | \(e\left(\frac{7}{108}\right)\) | \(e\left(\frac{31}{36}\right)\) | \(e\left(\frac{8}{9}\right)\) | \(e\left(\frac{67}{108}\right)\) | \(e\left(\frac{1}{54}\right)\) | \(e\left(\frac{1}{27}\right)\) | \(e\left(\frac{19}{36}\right)\) | \(e\left(\frac{35}{54}\right)\) |