Basic properties
Modulus: | \(8036\) | |
Conductor: | \(287\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{287}(94,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | no | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8036.du
\(\chi_{8036}(117,\cdot)\) \(\chi_{8036}(129,\cdot)\) \(\chi_{8036}(313,\cdot)\) \(\chi_{8036}(509,\cdot)\) \(\chi_{8036}(521,\cdot)\) \(\chi_{8036}(913,\cdot)\) \(\chi_{8036}(1293,\cdot)\) \(\chi_{8036}(1305,\cdot)\) \(\chi_{8036}(1489,\cdot)\) \(\chi_{8036}(1893,\cdot)\) \(\chi_{8036}(2285,\cdot)\) \(\chi_{8036}(2677,\cdot)\) \(\chi_{8036}(3069,\cdot)\) \(\chi_{8036}(3265,\cdot)\) \(\chi_{8036}(3461,\cdot)\) \(\chi_{8036}(3841,\cdot)\) \(\chi_{8036}(4037,\cdot)\) \(\chi_{8036}(4245,\cdot)\) \(\chi_{8036}(4441,\cdot)\) \(\chi_{8036}(4821,\cdot)\) \(\chi_{8036}(5017,\cdot)\) \(\chi_{8036}(5213,\cdot)\) \(\chi_{8036}(5605,\cdot)\) \(\chi_{8036}(5997,\cdot)\) \(\chi_{8036}(6389,\cdot)\) \(\chi_{8036}(6793,\cdot)\) \(\chi_{8036}(6977,\cdot)\) \(\chi_{8036}(6989,\cdot)\) \(\chi_{8036}(7369,\cdot)\) \(\chi_{8036}(7761,\cdot)\) ...
Related number fields
Field of values: | $\Q(\zeta_{120})$ |
Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((4019,493,785)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{27}{40}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
\( \chi_{ 8036 }(2677, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{24}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{7}{12}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{39}{40}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{109}{120}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{11}{30}\right)\) |