Basic properties
Modulus: | \(8033\) | |
Conductor: | \(8033\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(138\) | 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 8033.bz
\(\chi_{8033}(86,\cdot)\) \(\chi_{8033}(289,\cdot)\) \(\chi_{8033}(347,\cdot)\) \(\chi_{8033}(463,\cdot)\) \(\chi_{8033}(579,\cdot)\) \(\chi_{8033}(637,\cdot)\) \(\chi_{8033}(666,\cdot)\) \(\chi_{8033}(695,\cdot)\) \(\chi_{8033}(782,\cdot)\) \(\chi_{8033}(1130,\cdot)\) \(\chi_{8033}(1304,\cdot)\) \(\chi_{8033}(1362,\cdot)\) \(\chi_{8033}(1652,\cdot)\) \(\chi_{8033}(1768,\cdot)\) \(\chi_{8033}(1884,\cdot)\) \(\chi_{8033}(2116,\cdot)\) \(\chi_{8033}(2145,\cdot)\) \(\chi_{8033}(2522,\cdot)\) \(\chi_{8033}(2580,\cdot)\) \(\chi_{8033}(2957,\cdot)\) \(\chi_{8033}(3044,\cdot)\) \(\chi_{8033}(3276,\cdot)\) \(\chi_{8033}(3363,\cdot)\) \(\chi_{8033}(3885,\cdot)\) \(\chi_{8033}(3914,\cdot)\) \(\chi_{8033}(4001,\cdot)\) \(\chi_{8033}(4088,\cdot)\) \(\chi_{8033}(4146,\cdot)\) \(\chi_{8033}(4494,\cdot)\) \(\chi_{8033}(4784,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{69})$ |
Fixed field: | Number field defined by a degree 138 polynomial (not computed) |
Values on generators
\((5541,1944)\) → \((-1,e\left(\frac{133}{138}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8033 }(637, a) \) | \(1\) | \(1\) | \(e\left(\frac{4}{23}\right)\) | \(e\left(\frac{95}{138}\right)\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{133}{138}\right)\) | \(e\left(\frac{119}{138}\right)\) | \(e\left(\frac{14}{69}\right)\) | \(e\left(\frac{12}{23}\right)\) | \(e\left(\frac{26}{69}\right)\) | \(e\left(\frac{19}{138}\right)\) | \(e\left(\frac{17}{69}\right)\) |