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.jm
\(\chi_{9072}(11,\cdot)\) \(\chi_{9072}(275,\cdot)\) \(\chi_{9072}(515,\cdot)\) \(\chi_{9072}(779,\cdot)\) \(\chi_{9072}(1019,\cdot)\) \(\chi_{9072}(1283,\cdot)\) \(\chi_{9072}(1523,\cdot)\) \(\chi_{9072}(1787,\cdot)\) \(\chi_{9072}(2027,\cdot)\) \(\chi_{9072}(2291,\cdot)\) \(\chi_{9072}(2531,\cdot)\) \(\chi_{9072}(2795,\cdot)\) \(\chi_{9072}(3035,\cdot)\) \(\chi_{9072}(3299,\cdot)\) \(\chi_{9072}(3539,\cdot)\) \(\chi_{9072}(3803,\cdot)\) \(\chi_{9072}(4043,\cdot)\) \(\chi_{9072}(4307,\cdot)\) \(\chi_{9072}(4547,\cdot)\) \(\chi_{9072}(4811,\cdot)\) \(\chi_{9072}(5051,\cdot)\) \(\chi_{9072}(5315,\cdot)\) \(\chi_{9072}(5555,\cdot)\) \(\chi_{9072}(5819,\cdot)\) \(\chi_{9072}(6059,\cdot)\) \(\chi_{9072}(6323,\cdot)\) \(\chi_{9072}(6563,\cdot)\) \(\chi_{9072}(6827,\cdot)\) \(\chi_{9072}(7067,\cdot)\) \(\chi_{9072}(7331,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1135,6805,3809,2593)\) → \((-1,i,e\left(\frac{13}{54}\right),e\left(\frac{2}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 9072 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{108}\right)\) | \(e\left(\frac{59}{108}\right)\) | \(e\left(\frac{73}{108}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{5}{36}\right)\) | \(e\left(\frac{53}{54}\right)\) | \(e\left(\frac{13}{54}\right)\) | \(e\left(\frac{71}{108}\right)\) | \(e\left(\frac{53}{54}\right)\) | \(e\left(\frac{25}{36}\right)\) |