Basic properties
| Modulus: | \(1073\) | |
| Conductor: | \(1073\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(84\) | 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.bv
\(\chi_{1073}(10,\cdot)\) \(\chi_{1073}(26,\cdot)\) \(\chi_{1073}(47,\cdot)\) \(\chi_{1073}(84,\cdot)\) \(\chi_{1073}(137,\cdot)\) \(\chi_{1073}(195,\cdot)\) \(\chi_{1073}(211,\cdot)\) \(\chi_{1073}(269,\cdot)\) \(\chi_{1073}(322,\cdot)\) \(\chi_{1073}(359,\cdot)\) \(\chi_{1073}(380,\cdot)\) \(\chi_{1073}(396,\cdot)\) \(\chi_{1073}(417,\cdot)\) \(\chi_{1073}(433,\cdot)\) \(\chi_{1073}(454,\cdot)\) \(\chi_{1073}(491,\cdot)\) \(\chi_{1073}(507,\cdot)\) \(\chi_{1073}(565,\cdot)\) \(\chi_{1073}(914,\cdot)\) \(\chi_{1073}(972,\cdot)\) \(\chi_{1073}(988,\cdot)\) \(\chi_{1073}(1025,\cdot)\) \(\chi_{1073}(1046,\cdot)\) \(\chi_{1073}(1062,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{84})$ |
| Fixed field: | Number field defined by a degree 84 polynomial |
Values on generators
\((408,668)\) → \((e\left(\frac{23}{28}\right),e\left(\frac{2}{3}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1073 }(10, a) \) | \(-1\) | \(1\) | \(e\left(\frac{41}{84}\right)\) | \(e\left(\frac{37}{84}\right)\) | \(e\left(\frac{41}{42}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{4}{21}\right)\) | \(e\left(\frac{13}{28}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{25}{28}\right)\) | \(e\left(\frac{15}{28}\right)\) |