Basic properties
| Modulus: | \(833\) | |
| Conductor: | \(833\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(168\) | 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.bl
\(\chi_{833}(2,\cdot)\) \(\chi_{833}(9,\cdot)\) \(\chi_{833}(25,\cdot)\) \(\chi_{833}(32,\cdot)\) \(\chi_{833}(53,\cdot)\) \(\chi_{833}(60,\cdot)\) \(\chi_{833}(93,\cdot)\) \(\chi_{833}(100,\cdot)\) \(\chi_{833}(121,\cdot)\) \(\chi_{833}(144,\cdot)\) \(\chi_{833}(151,\cdot)\) \(\chi_{833}(172,\cdot)\) \(\chi_{833}(179,\cdot)\) \(\chi_{833}(212,\cdot)\) \(\chi_{833}(219,\cdot)\) \(\chi_{833}(240,\cdot)\) \(\chi_{833}(247,\cdot)\) \(\chi_{833}(270,\cdot)\) \(\chi_{833}(291,\cdot)\) \(\chi_{833}(298,\cdot)\) \(\chi_{833}(331,\cdot)\) \(\chi_{833}(338,\cdot)\) \(\chi_{833}(359,\cdot)\) \(\chi_{833}(366,\cdot)\) \(\chi_{833}(382,\cdot)\) \(\chi_{833}(389,\cdot)\) \(\chi_{833}(417,\cdot)\) \(\chi_{833}(450,\cdot)\) \(\chi_{833}(457,\cdot)\) \(\chi_{833}(478,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{168})$ |
| Fixed field: | Number field defined by a degree 168 polynomial (not computed) |
Values on generators
\((52,785)\) → \((e\left(\frac{5}{21}\right),e\left(\frac{7}{8}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(8\) | \(9\) | \(10\) | \(11\) | \(12\) |
| \( \chi_{ 833 }(53, a) \) | \(1\) | \(1\) | \(e\left(\frac{37}{84}\right)\) | \(e\left(\frac{19}{168}\right)\) | \(e\left(\frac{37}{42}\right)\) | \(e\left(\frac{47}{168}\right)\) | \(e\left(\frac{31}{56}\right)\) | \(e\left(\frac{9}{28}\right)\) | \(e\left(\frac{19}{84}\right)\) | \(e\left(\frac{121}{168}\right)\) | \(e\left(\frac{109}{168}\right)\) | \(e\left(\frac{167}{168}\right)\) |