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.cm
\(\chi_{1053}(20,\cdot)\) \(\chi_{1053}(41,\cdot)\) \(\chi_{1053}(50,\cdot)\) \(\chi_{1053}(110,\cdot)\) \(\chi_{1053}(137,\cdot)\) \(\chi_{1053}(158,\cdot)\) \(\chi_{1053}(167,\cdot)\) \(\chi_{1053}(227,\cdot)\) \(\chi_{1053}(254,\cdot)\) \(\chi_{1053}(275,\cdot)\) \(\chi_{1053}(284,\cdot)\) \(\chi_{1053}(344,\cdot)\) \(\chi_{1053}(371,\cdot)\) \(\chi_{1053}(392,\cdot)\) \(\chi_{1053}(401,\cdot)\) \(\chi_{1053}(461,\cdot)\) \(\chi_{1053}(488,\cdot)\) \(\chi_{1053}(509,\cdot)\) \(\chi_{1053}(518,\cdot)\) \(\chi_{1053}(578,\cdot)\) \(\chi_{1053}(605,\cdot)\) \(\chi_{1053}(626,\cdot)\) \(\chi_{1053}(635,\cdot)\) \(\chi_{1053}(695,\cdot)\) \(\chi_{1053}(722,\cdot)\) \(\chi_{1053}(743,\cdot)\) \(\chi_{1053}(752,\cdot)\) \(\chi_{1053}(812,\cdot)\) \(\chi_{1053}(839,\cdot)\) \(\chi_{1053}(860,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{108})$ |
| Fixed field: | Number field defined by a degree 108 polynomial (not computed) |
Values on generators
\((326,730)\) → \((e\left(\frac{19}{54}\right),e\left(\frac{11}{12}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(14\) | \(16\) | \(17\) |
| \( \chi_{ 1053 }(137, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{108}\right)\) | \(e\left(\frac{29}{54}\right)\) | \(e\left(\frac{37}{108}\right)\) | \(e\left(\frac{77}{108}\right)\) | \(e\left(\frac{29}{36}\right)\) | \(e\left(\frac{11}{18}\right)\) | \(e\left(\frac{107}{108}\right)\) | \(e\left(\frac{53}{54}\right)\) | \(e\left(\frac{2}{27}\right)\) | \(e\left(\frac{4}{9}\right)\) |