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.cl
\(\chi_{1053}(5,\cdot)\) \(\chi_{1053}(47,\cdot)\) \(\chi_{1053}(83,\cdot)\) \(\chi_{1053}(86,\cdot)\) \(\chi_{1053}(122,\cdot)\) \(\chi_{1053}(164,\cdot)\) \(\chi_{1053}(200,\cdot)\) \(\chi_{1053}(203,\cdot)\) \(\chi_{1053}(239,\cdot)\) \(\chi_{1053}(281,\cdot)\) \(\chi_{1053}(317,\cdot)\) \(\chi_{1053}(320,\cdot)\) \(\chi_{1053}(356,\cdot)\) \(\chi_{1053}(398,\cdot)\) \(\chi_{1053}(434,\cdot)\) \(\chi_{1053}(437,\cdot)\) \(\chi_{1053}(473,\cdot)\) \(\chi_{1053}(515,\cdot)\) \(\chi_{1053}(551,\cdot)\) \(\chi_{1053}(554,\cdot)\) \(\chi_{1053}(590,\cdot)\) \(\chi_{1053}(632,\cdot)\) \(\chi_{1053}(668,\cdot)\) \(\chi_{1053}(671,\cdot)\) \(\chi_{1053}(707,\cdot)\) \(\chi_{1053}(749,\cdot)\) \(\chi_{1053}(785,\cdot)\) \(\chi_{1053}(788,\cdot)\) \(\chi_{1053}(824,\cdot)\) \(\chi_{1053}(866,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((326,730)\) → \((e\left(\frac{53}{54}\right),-i)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 1053 }(122, a) \) | \(1\) | \(1\) | \(e\left(\frac{79}{108}\right)\) | \(e\left(\frac{25}{54}\right)\) | \(e\left(\frac{35}{108}\right)\) | \(e\left(\frac{103}{108}\right)\) | \(e\left(\frac{7}{36}\right)\) | \(e\left(\frac{1}{18}\right)\) | \(e\left(\frac{1}{108}\right)\) | \(e\left(\frac{37}{54}\right)\) | \(e\left(\frac{25}{27}\right)\) | \(e\left(\frac{8}{9}\right)\) |