Basic properties
| Modulus: | \(1073\) | |
| Conductor: | \(1073\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(252\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1073.cc
\(\chi_{1073}(3,\cdot)\) \(\chi_{1073}(21,\cdot)\) \(\chi_{1073}(40,\cdot)\) \(\chi_{1073}(77,\cdot)\) \(\chi_{1073}(95,\cdot)\) \(\chi_{1073}(102,\cdot)\) \(\chi_{1073}(114,\cdot)\) \(\chi_{1073}(176,\cdot)\) \(\chi_{1073}(188,\cdot)\) \(\chi_{1073}(189,\cdot)\) \(\chi_{1073}(206,\cdot)\) \(\chi_{1073}(213,\cdot)\) \(\chi_{1073}(243,\cdot)\) \(\chi_{1073}(247,\cdot)\) \(\chi_{1073}(250,\cdot)\) \(\chi_{1073}(263,\cdot)\) \(\chi_{1073}(280,\cdot)\) \(\chi_{1073}(287,\cdot)\) \(\chi_{1073}(300,\cdot)\) \(\chi_{1073}(317,\cdot)\) \(\chi_{1073}(321,\cdot)\) \(\chi_{1073}(337,\cdot)\) \(\chi_{1073}(358,\cdot)\) \(\chi_{1073}(363,\cdot)\) \(\chi_{1073}(374,\cdot)\) \(\chi_{1073}(391,\cdot)\) \(\chi_{1073}(395,\cdot)\) \(\chi_{1073}(398,\cdot)\) \(\chi_{1073}(432,\cdot)\) \(\chi_{1073}(437,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{252})$ |
| Fixed field: | Number field defined by a degree 252 polynomial (not computed) |
Values on generators
\((408,668)\) → \((e\left(\frac{1}{28}\right),e\left(\frac{5}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1073 }(321, a) \) | \(-1\) | \(1\) | \(e\left(\frac{79}{252}\right)\) | \(e\left(\frac{101}{252}\right)\) | \(e\left(\frac{79}{126}\right)\) | \(e\left(\frac{11}{63}\right)\) | \(e\left(\frac{5}{7}\right)\) | \(e\left(\frac{20}{63}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{101}{126}\right)\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{19}{84}\right)\) |