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.jo
\(\chi_{9072}(293,\cdot)\) \(\chi_{9072}(461,\cdot)\) \(\chi_{9072}(797,\cdot)\) \(\chi_{9072}(965,\cdot)\) \(\chi_{9072}(1301,\cdot)\) \(\chi_{9072}(1469,\cdot)\) \(\chi_{9072}(1805,\cdot)\) \(\chi_{9072}(1973,\cdot)\) \(\chi_{9072}(2309,\cdot)\) \(\chi_{9072}(2477,\cdot)\) \(\chi_{9072}(2813,\cdot)\) \(\chi_{9072}(2981,\cdot)\) \(\chi_{9072}(3317,\cdot)\) \(\chi_{9072}(3485,\cdot)\) \(\chi_{9072}(3821,\cdot)\) \(\chi_{9072}(3989,\cdot)\) \(\chi_{9072}(4325,\cdot)\) \(\chi_{9072}(4493,\cdot)\) \(\chi_{9072}(4829,\cdot)\) \(\chi_{9072}(4997,\cdot)\) \(\chi_{9072}(5333,\cdot)\) \(\chi_{9072}(5501,\cdot)\) \(\chi_{9072}(5837,\cdot)\) \(\chi_{9072}(6005,\cdot)\) \(\chi_{9072}(6341,\cdot)\) \(\chi_{9072}(6509,\cdot)\) \(\chi_{9072}(6845,\cdot)\) \(\chi_{9072}(7013,\cdot)\) \(\chi_{9072}(7349,\cdot)\) \(\chi_{9072}(7517,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((1135,6805,3809,2593)\) → \((1,i,e\left(\frac{47}{54}\right),-1)\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 9072 }(293, a) \) | \(1\) | \(1\) | \(e\left(\frac{83}{108}\right)\) | \(e\left(\frac{61}{108}\right)\) | \(e\left(\frac{23}{108}\right)\) | \(e\left(\frac{2}{9}\right)\) | \(e\left(\frac{1}{36}\right)\) | \(e\left(\frac{2}{27}\right)\) | \(e\left(\frac{29}{54}\right)\) | \(e\left(\frac{103}{108}\right)\) | \(e\left(\frac{49}{54}\right)\) | \(e\left(\frac{29}{36}\right)\) |