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.kb
\(\chi_{9072}(277,\cdot)\) \(\chi_{9072}(373,\cdot)\) \(\chi_{9072}(781,\cdot)\) \(\chi_{9072}(877,\cdot)\) \(\chi_{9072}(1285,\cdot)\) \(\chi_{9072}(1381,\cdot)\) \(\chi_{9072}(1789,\cdot)\) \(\chi_{9072}(1885,\cdot)\) \(\chi_{9072}(2293,\cdot)\) \(\chi_{9072}(2389,\cdot)\) \(\chi_{9072}(2797,\cdot)\) \(\chi_{9072}(2893,\cdot)\) \(\chi_{9072}(3301,\cdot)\) \(\chi_{9072}(3397,\cdot)\) \(\chi_{9072}(3805,\cdot)\) \(\chi_{9072}(3901,\cdot)\) \(\chi_{9072}(4309,\cdot)\) \(\chi_{9072}(4405,\cdot)\) \(\chi_{9072}(4813,\cdot)\) \(\chi_{9072}(4909,\cdot)\) \(\chi_{9072}(5317,\cdot)\) \(\chi_{9072}(5413,\cdot)\) \(\chi_{9072}(5821,\cdot)\) \(\chi_{9072}(5917,\cdot)\) \(\chi_{9072}(6325,\cdot)\) \(\chi_{9072}(6421,\cdot)\) \(\chi_{9072}(6829,\cdot)\) \(\chi_{9072}(6925,\cdot)\) \(\chi_{9072}(7333,\cdot)\) \(\chi_{9072}(7429,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1135,6805,3809,2593)\) → \((1,i,e\left(\frac{17}{27}\right),e\left(\frac{2}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 9072 }(277, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{108}\right)\) | \(e\left(\frac{11}{108}\right)\) | \(e\left(\frac{85}{108}\right)\) | \(e\left(\frac{4}{9}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{41}{54}\right)\) | \(e\left(\frac{7}{54}\right)\) | \(e\left(\frac{5}{108}\right)\) | \(e\left(\frac{7}{27}\right)\) | \(e\left(\frac{1}{36}\right)\) |