Basic properties
Modulus: | \(8033\) | |
Conductor: | \(277\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(138\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{277}(121,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8033.cb
\(\chi_{8033}(407,\cdot)\) \(\chi_{8033}(871,\cdot)\) \(\chi_{8033}(1306,\cdot)\) \(\chi_{8033}(1973,\cdot)\) \(\chi_{8033}(2002,\cdot)\) \(\chi_{8033}(2031,\cdot)\) \(\chi_{8033}(2060,\cdot)\) \(\chi_{8033}(2263,\cdot)\) \(\chi_{8033}(2408,\cdot)\) \(\chi_{8033}(2582,\cdot)\) \(\chi_{8033}(2959,\cdot)\) \(\chi_{8033}(3133,\cdot)\) \(\chi_{8033}(3336,\cdot)\) \(\chi_{8033}(3394,\cdot)\) \(\chi_{8033}(3510,\cdot)\) \(\chi_{8033}(3626,\cdot)\) \(\chi_{8033}(3684,\cdot)\) \(\chi_{8033}(3713,\cdot)\) \(\chi_{8033}(3742,\cdot)\) \(\chi_{8033}(3829,\cdot)\) \(\chi_{8033}(4177,\cdot)\) \(\chi_{8033}(4351,\cdot)\) \(\chi_{8033}(4409,\cdot)\) \(\chi_{8033}(4699,\cdot)\) \(\chi_{8033}(4815,\cdot)\) \(\chi_{8033}(4931,\cdot)\) \(\chi_{8033}(5163,\cdot)\) \(\chi_{8033}(5192,\cdot)\) \(\chi_{8033}(5569,\cdot)\) \(\chi_{8033}(5627,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{69})$ |
Fixed field: | Number field defined by a degree 138 polynomial (not computed) |
Values on generators
\((5541,1944)\) → \((1,e\left(\frac{7}{138}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8033 }(2060, a) \) | \(1\) | \(1\) | \(e\left(\frac{21}{46}\right)\) | \(e\left(\frac{37}{69}\right)\) | \(e\left(\frac{21}{23}\right)\) | \(e\left(\frac{7}{138}\right)\) | \(e\left(\frac{137}{138}\right)\) | \(e\left(\frac{8}{69}\right)\) | \(e\left(\frac{17}{46}\right)\) | \(e\left(\frac{5}{69}\right)\) | \(e\left(\frac{35}{69}\right)\) | \(e\left(\frac{49}{138}\right)\) |