Basic properties
| Modulus: | \(1053\) | |
| Conductor: | \(1053\) | 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 1053.cn
\(\chi_{1053}(2,\cdot)\) \(\chi_{1053}(11,\cdot)\) \(\chi_{1053}(32,\cdot)\) \(\chi_{1053}(59,\cdot)\) \(\chi_{1053}(119,\cdot)\) \(\chi_{1053}(128,\cdot)\) \(\chi_{1053}(149,\cdot)\) \(\chi_{1053}(176,\cdot)\) \(\chi_{1053}(236,\cdot)\) \(\chi_{1053}(245,\cdot)\) \(\chi_{1053}(266,\cdot)\) \(\chi_{1053}(293,\cdot)\) \(\chi_{1053}(353,\cdot)\) \(\chi_{1053}(362,\cdot)\) \(\chi_{1053}(383,\cdot)\) \(\chi_{1053}(410,\cdot)\) \(\chi_{1053}(470,\cdot)\) \(\chi_{1053}(479,\cdot)\) \(\chi_{1053}(500,\cdot)\) \(\chi_{1053}(527,\cdot)\) \(\chi_{1053}(587,\cdot)\) \(\chi_{1053}(596,\cdot)\) \(\chi_{1053}(617,\cdot)\) \(\chi_{1053}(644,\cdot)\) \(\chi_{1053}(704,\cdot)\) \(\chi_{1053}(713,\cdot)\) \(\chi_{1053}(734,\cdot)\) \(\chi_{1053}(761,\cdot)\) \(\chi_{1053}(821,\cdot)\) \(\chi_{1053}(830,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((326,730)\) → \((e\left(\frac{1}{54}\right),e\left(\frac{1}{12}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 1053 }(2, a) \) | \(1\) | \(1\) | \(e\left(\frac{11}{108}\right)\) | \(e\left(\frac{11}{54}\right)\) | \(e\left(\frac{19}{108}\right)\) | \(e\left(\frac{23}{108}\right)\) | \(e\left(\frac{11}{36}\right)\) | \(e\left(\frac{5}{18}\right)\) | \(e\left(\frac{89}{108}\right)\) | \(e\left(\frac{17}{54}\right)\) | \(e\left(\frac{11}{27}\right)\) | \(e\left(\frac{7}{9}\right)\) |