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.js
\(\chi_{9072}(187,\cdot)\) \(\chi_{9072}(283,\cdot)\) \(\chi_{9072}(691,\cdot)\) \(\chi_{9072}(787,\cdot)\) \(\chi_{9072}(1195,\cdot)\) \(\chi_{9072}(1291,\cdot)\) \(\chi_{9072}(1699,\cdot)\) \(\chi_{9072}(1795,\cdot)\) \(\chi_{9072}(2203,\cdot)\) \(\chi_{9072}(2299,\cdot)\) \(\chi_{9072}(2707,\cdot)\) \(\chi_{9072}(2803,\cdot)\) \(\chi_{9072}(3211,\cdot)\) \(\chi_{9072}(3307,\cdot)\) \(\chi_{9072}(3715,\cdot)\) \(\chi_{9072}(3811,\cdot)\) \(\chi_{9072}(4219,\cdot)\) \(\chi_{9072}(4315,\cdot)\) \(\chi_{9072}(4723,\cdot)\) \(\chi_{9072}(4819,\cdot)\) \(\chi_{9072}(5227,\cdot)\) \(\chi_{9072}(5323,\cdot)\) \(\chi_{9072}(5731,\cdot)\) \(\chi_{9072}(5827,\cdot)\) \(\chi_{9072}(6235,\cdot)\) \(\chi_{9072}(6331,\cdot)\) \(\chi_{9072}(6739,\cdot)\) \(\chi_{9072}(6835,\cdot)\) \(\chi_{9072}(7243,\cdot)\) \(\chi_{9072}(7339,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1135,6805,3809,2593)\) → \((-1,i,e\left(\frac{23}{27}\right),e\left(\frac{5}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 9072 }(187, a) \) | \(1\) | \(1\) | \(e\left(\frac{1}{108}\right)\) | \(e\left(\frac{17}{108}\right)\) | \(e\left(\frac{7}{108}\right)\) | \(e\left(\frac{17}{18}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{1}{27}\right)\) | \(e\left(\frac{1}{54}\right)\) | \(e\left(\frac{29}{108}\right)\) | \(e\left(\frac{10}{27}\right)\) | \(e\left(\frac{25}{36}\right)\) |