Basic properties
| Modulus: | \(8033\) | |
| Conductor: | \(8033\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(276\) | 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 8033.cg
\(\chi_{8033}(12,\cdot)\) \(\chi_{8033}(70,\cdot)\) \(\chi_{8033}(75,\cdot)\) \(\chi_{8033}(133,\cdot)\) \(\chi_{8033}(186,\cdot)\) \(\chi_{8033}(220,\cdot)\) \(\chi_{8033}(249,\cdot)\) \(\chi_{8033}(302,\cdot)\) \(\chi_{8033}(360,\cdot)\) \(\chi_{8033}(389,\cdot)\) \(\chi_{8033}(418,\cdot)\) \(\chi_{8033}(505,\cdot)\) \(\chi_{8033}(684,\cdot)\) \(\chi_{8033}(853,\cdot)\) \(\chi_{8033}(1027,\cdot)\) \(\chi_{8033}(1085,\cdot)\) \(\chi_{8033}(1148,\cdot)\) \(\chi_{8033}(1375,\cdot)\) \(\chi_{8033}(1491,\cdot)\) \(\chi_{8033}(1583,\cdot)\) \(\chi_{8033}(1607,\cdot)\) \(\chi_{8033}(1839,\cdot)\) \(\chi_{8033}(1868,\cdot)\) \(\chi_{8033}(2245,\cdot)\) \(\chi_{8033}(2250,\cdot)\) \(\chi_{8033}(2279,\cdot)\) \(\chi_{8033}(2303,\cdot)\) \(\chi_{8033}(2308,\cdot)\) \(\chi_{8033}(2337,\cdot)\) \(\chi_{8033}(2540,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{276})$ |
| Fixed field: | Number field defined by a degree 276 polynomial (not computed) |
Values on generators
\((5541,1944)\) → \((i,e\left(\frac{103}{138}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 8033 }(12, a) \) | \(-1\) | \(1\) | \(e\left(\frac{89}{92}\right)\) | \(e\left(\frac{157}{276}\right)\) | \(e\left(\frac{43}{46}\right)\) | \(e\left(\frac{17}{69}\right)\) | \(e\left(\frac{37}{69}\right)\) | \(e\left(\frac{29}{69}\right)\) | \(e\left(\frac{83}{92}\right)\) | \(e\left(\frac{19}{138}\right)\) | \(e\left(\frac{59}{276}\right)\) | \(e\left(\frac{131}{276}\right)\) |