Basic properties
| Modulus: | \(833\) | |
| Conductor: | \(833\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(112\) | 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 833.bi
\(\chi_{833}(6,\cdot)\) \(\chi_{833}(20,\cdot)\) \(\chi_{833}(27,\cdot)\) \(\chi_{833}(41,\cdot)\) \(\chi_{833}(62,\cdot)\) \(\chi_{833}(90,\cdot)\) \(\chi_{833}(125,\cdot)\) \(\chi_{833}(139,\cdot)\) \(\chi_{833}(160,\cdot)\) \(\chi_{833}(167,\cdot)\) \(\chi_{833}(181,\cdot)\) \(\chi_{833}(209,\cdot)\) \(\chi_{833}(216,\cdot)\) \(\chi_{833}(258,\cdot)\) \(\chi_{833}(265,\cdot)\) \(\chi_{833}(279,\cdot)\) \(\chi_{833}(286,\cdot)\) \(\chi_{833}(300,\cdot)\) \(\chi_{833}(328,\cdot)\) \(\chi_{833}(335,\cdot)\) \(\chi_{833}(363,\cdot)\) \(\chi_{833}(377,\cdot)\) \(\chi_{833}(384,\cdot)\) \(\chi_{833}(398,\cdot)\) \(\chi_{833}(405,\cdot)\) \(\chi_{833}(419,\cdot)\) \(\chi_{833}(447,\cdot)\) \(\chi_{833}(454,\cdot)\) \(\chi_{833}(482,\cdot)\) \(\chi_{833}(496,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{112})$ |
| Fixed field: | Number field defined by a degree 112 polynomial (not computed) |
Values on generators
\((52,785)\) → \((e\left(\frac{9}{14}\right),e\left(\frac{15}{16}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 833 }(6, a) \) | \(1\) | \(1\) | \(e\left(\frac{47}{56}\right)\) | \(e\left(\frac{65}{112}\right)\) | \(e\left(\frac{19}{28}\right)\) | \(e\left(\frac{37}{112}\right)\) | \(e\left(\frac{47}{112}\right)\) | \(e\left(\frac{29}{56}\right)\) | \(e\left(\frac{9}{56}\right)\) | \(e\left(\frac{19}{112}\right)\) | \(e\left(\frac{31}{112}\right)\) | \(e\left(\frac{29}{112}\right)\) |