Basic properties
| Modulus: | \(1073\) | |
| Conductor: | \(1073\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(126\) | 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 1073.ca
\(\chi_{1073}(25,\cdot)\) \(\chi_{1073}(65,\cdot)\) \(\chi_{1073}(78,\cdot)\) \(\chi_{1073}(132,\cdot)\) \(\chi_{1073}(136,\cdot)\) \(\chi_{1073}(139,\cdot)\) \(\chi_{1073}(141,\cdot)\) \(\chi_{1073}(152,\cdot)\) \(\chi_{1073}(169,\cdot)\) \(\chi_{1073}(210,\cdot)\) \(\chi_{1073}(226,\cdot)\) \(\chi_{1073}(252,\cdot)\) \(\chi_{1073}(284,\cdot)\) \(\chi_{1073}(326,\cdot)\) \(\chi_{1073}(373,\cdot)\) \(\chi_{1073}(400,\cdot)\) \(\chi_{1073}(484,\cdot)\) \(\chi_{1073}(509,\cdot)\) \(\chi_{1073}(546,\cdot)\) \(\chi_{1073}(558,\cdot)\) \(\chi_{1073}(576,\cdot)\) \(\chi_{1073}(596,\cdot)\) \(\chi_{1073}(632,\cdot)\) \(\chi_{1073}(633,\cdot)\) \(\chi_{1073}(654,\cdot)\) \(\chi_{1073}(687,\cdot)\) \(\chi_{1073}(691,\cdot)\) \(\chi_{1073}(761,\cdot)\) \(\chi_{1073}(770,\cdot)\) \(\chi_{1073}(807,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{63})$ |
| Fixed field: | Number field defined by a degree 126 polynomial (not computed) |
Values on generators
\((408,668)\) → \((e\left(\frac{4}{7}\right),e\left(\frac{5}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 1073 }(25, a) \) | \(1\) | \(1\) | \(e\left(\frac{107}{126}\right)\) | \(e\left(\frac{5}{63}\right)\) | \(e\left(\frac{44}{63}\right)\) | \(e\left(\frac{121}{126}\right)\) | \(e\left(\frac{13}{14}\right)\) | \(e\left(\frac{47}{63}\right)\) | \(e\left(\frac{23}{42}\right)\) | \(e\left(\frac{10}{63}\right)\) | \(e\left(\frac{17}{21}\right)\) | \(e\left(\frac{13}{21}\right)\) |