Basic properties
Modulus: | \(8033\) | |
Conductor: | \(277\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(69\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{277}(241,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8033.bm
\(\chi_{8033}(88,\cdot)\) \(\chi_{8033}(465,\cdot)\) \(\chi_{8033}(639,\cdot)\) \(\chi_{8033}(784,\cdot)\) \(\chi_{8033}(987,\cdot)\) \(\chi_{8033}(1016,\cdot)\) \(\chi_{8033}(1045,\cdot)\) \(\chi_{8033}(1074,\cdot)\) \(\chi_{8033}(1741,\cdot)\) \(\chi_{8033}(2176,\cdot)\) \(\chi_{8033}(2640,\cdot)\) \(\chi_{8033}(3075,\cdot)\) \(\chi_{8033}(3104,\cdot)\) \(\chi_{8033}(3191,\cdot)\) \(\chi_{8033}(3249,\cdot)\) \(\chi_{8033}(3539,\cdot)\) \(\chi_{8033}(3887,\cdot)\) \(\chi_{8033}(3945,\cdot)\) \(\chi_{8033}(4032,\cdot)\) \(\chi_{8033}(4119,\cdot)\) \(\chi_{8033}(4148,\cdot)\) \(\chi_{8033}(4670,\cdot)\) \(\chi_{8033}(4757,\cdot)\) \(\chi_{8033}(4989,\cdot)\) \(\chi_{8033}(5076,\cdot)\) \(\chi_{8033}(5453,\cdot)\) \(\chi_{8033}(5511,\cdot)\) \(\chi_{8033}(5888,\cdot)\) \(\chi_{8033}(5917,\cdot)\) \(\chi_{8033}(6149,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{69})$ |
Fixed field: | Number field defined by a degree 69 polynomial |
Values on generators
\((5541,1944)\) → \((1,e\left(\frac{64}{69}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
\( \chi_{ 8033 }(4119, a) \) | \(1\) | \(1\) | \(e\left(\frac{8}{23}\right)\) | \(e\left(\frac{26}{69}\right)\) | \(e\left(\frac{16}{23}\right)\) | \(e\left(\frac{64}{69}\right)\) | \(e\left(\frac{50}{69}\right)\) | \(e\left(\frac{28}{69}\right)\) | \(e\left(\frac{1}{23}\right)\) | \(e\left(\frac{52}{69}\right)\) | \(e\left(\frac{19}{69}\right)\) | \(e\left(\frac{34}{69}\right)\) |