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.jh
\(\chi_{9072}(173,\cdot)\) \(\chi_{9072}(437,\cdot)\) \(\chi_{9072}(677,\cdot)\) \(\chi_{9072}(941,\cdot)\) \(\chi_{9072}(1181,\cdot)\) \(\chi_{9072}(1445,\cdot)\) \(\chi_{9072}(1685,\cdot)\) \(\chi_{9072}(1949,\cdot)\) \(\chi_{9072}(2189,\cdot)\) \(\chi_{9072}(2453,\cdot)\) \(\chi_{9072}(2693,\cdot)\) \(\chi_{9072}(2957,\cdot)\) \(\chi_{9072}(3197,\cdot)\) \(\chi_{9072}(3461,\cdot)\) \(\chi_{9072}(3701,\cdot)\) \(\chi_{9072}(3965,\cdot)\) \(\chi_{9072}(4205,\cdot)\) \(\chi_{9072}(4469,\cdot)\) \(\chi_{9072}(4709,\cdot)\) \(\chi_{9072}(4973,\cdot)\) \(\chi_{9072}(5213,\cdot)\) \(\chi_{9072}(5477,\cdot)\) \(\chi_{9072}(5717,\cdot)\) \(\chi_{9072}(5981,\cdot)\) \(\chi_{9072}(6221,\cdot)\) \(\chi_{9072}(6485,\cdot)\) \(\chi_{9072}(6725,\cdot)\) \(\chi_{9072}(6989,\cdot)\) \(\chi_{9072}(7229,\cdot)\) \(\chi_{9072}(7493,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1135,6805,3809,2593)\) → \((1,-i,e\left(\frac{13}{54}\right),e\left(\frac{5}{6}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 9072 }(173, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{108}\right)\) | \(e\left(\frac{23}{108}\right)\) | \(e\left(\frac{73}{108}\right)\) | \(e\left(\frac{7}{9}\right)\) | \(e\left(\frac{35}{36}\right)\) | \(e\left(\frac{22}{27}\right)\) | \(e\left(\frac{49}{54}\right)\) | \(e\left(\frac{17}{108}\right)\) | \(e\left(\frac{35}{54}\right)\) | \(e\left(\frac{19}{36}\right)\) |