Basic properties
| Modulus: | \(9072\) | |
| Conductor: | \(9072\) | 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 9072.jt
\(\chi_{9072}(205,\cdot)\) \(\chi_{9072}(445,\cdot)\) \(\chi_{9072}(709,\cdot)\) \(\chi_{9072}(949,\cdot)\) \(\chi_{9072}(1213,\cdot)\) \(\chi_{9072}(1453,\cdot)\) \(\chi_{9072}(1717,\cdot)\) \(\chi_{9072}(1957,\cdot)\) \(\chi_{9072}(2221,\cdot)\) \(\chi_{9072}(2461,\cdot)\) \(\chi_{9072}(2725,\cdot)\) \(\chi_{9072}(2965,\cdot)\) \(\chi_{9072}(3229,\cdot)\) \(\chi_{9072}(3469,\cdot)\) \(\chi_{9072}(3733,\cdot)\) \(\chi_{9072}(3973,\cdot)\) \(\chi_{9072}(4237,\cdot)\) \(\chi_{9072}(4477,\cdot)\) \(\chi_{9072}(4741,\cdot)\) \(\chi_{9072}(4981,\cdot)\) \(\chi_{9072}(5245,\cdot)\) \(\chi_{9072}(5485,\cdot)\) \(\chi_{9072}(5749,\cdot)\) \(\chi_{9072}(5989,\cdot)\) \(\chi_{9072}(6253,\cdot)\) \(\chi_{9072}(6493,\cdot)\) \(\chi_{9072}(6757,\cdot)\) \(\chi_{9072}(6997,\cdot)\) \(\chi_{9072}(7261,\cdot)\) \(\chi_{9072}(7501,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1135,6805,3809,2593)\) → \((1,-i,e\left(\frac{11}{27}\right),e\left(\frac{1}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 9072 }(205, a) \) | \(1\) | \(1\) | \(e\left(\frac{85}{108}\right)\) | \(e\left(\frac{41}{108}\right)\) | \(e\left(\frac{55}{108}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{17}{36}\right)\) | \(e\left(\frac{35}{54}\right)\) | \(e\left(\frac{31}{54}\right)\) | \(e\left(\frac{35}{108}\right)\) | \(e\left(\frac{13}{27}\right)\) | \(e\left(\frac{19}{36}\right)\) |