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.ca
\(\chi_{8033}(28,\cdot)\) \(\chi_{8033}(57,\cdot)\) \(\chi_{8033}(144,\cdot)\) \(\chi_{8033}(202,\cdot)\) \(\chi_{8033}(492,\cdot)\) \(\chi_{8033}(840,\cdot)\) \(\chi_{8033}(898,\cdot)\) \(\chi_{8033}(985,\cdot)\) \(\chi_{8033}(1072,\cdot)\) \(\chi_{8033}(1101,\cdot)\) \(\chi_{8033}(1623,\cdot)\) \(\chi_{8033}(1710,\cdot)\) \(\chi_{8033}(1942,\cdot)\) \(\chi_{8033}(2029,\cdot)\) \(\chi_{8033}(2406,\cdot)\) \(\chi_{8033}(2464,\cdot)\) \(\chi_{8033}(2841,\cdot)\) \(\chi_{8033}(2870,\cdot)\) \(\chi_{8033}(3102,\cdot)\) \(\chi_{8033}(3218,\cdot)\) \(\chi_{8033}(3334,\cdot)\) \(\chi_{8033}(3624,\cdot)\) \(\chi_{8033}(3682,\cdot)\) \(\chi_{8033}(3856,\cdot)\) \(\chi_{8033}(4204,\cdot)\) \(\chi_{8033}(4291,\cdot)\) \(\chi_{8033}(4320,\cdot)\) \(\chi_{8033}(4349,\cdot)\) \(\chi_{8033}(4407,\cdot)\) \(\chi_{8033}(4523,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{69})$ |
Fixed field: | Number field defined by a degree 138 polynomial (not computed) |
Values on generators
\((5541,1944)\) → \((-1,e\left(\frac{64}{69}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8033 }(1072, a) \) | \(1\) | \(1\) | \(e\left(\frac{39}{46}\right)\) | \(e\left(\frac{121}{138}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{64}{69}\right)\) | \(e\left(\frac{50}{69}\right)\) | \(e\left(\frac{28}{69}\right)\) | \(e\left(\frac{25}{46}\right)\) | \(e\left(\frac{52}{69}\right)\) | \(e\left(\frac{107}{138}\right)\) | \(e\left(\frac{137}{138}\right)\) |