Basic properties
| Modulus: | \(8036\) | |
| Conductor: | \(1148\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1148}(67,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8036.dw
\(\chi_{8036}(67,\cdot)\) \(\chi_{8036}(263,\cdot)\) \(\chi_{8036}(275,\cdot)\) \(\chi_{8036}(667,\cdot)\) \(\chi_{8036}(1047,\cdot)\) \(\chi_{8036}(1059,\cdot)\) \(\chi_{8036}(1243,\cdot)\) \(\chi_{8036}(1647,\cdot)\) \(\chi_{8036}(2039,\cdot)\) \(\chi_{8036}(2431,\cdot)\) \(\chi_{8036}(2823,\cdot)\) \(\chi_{8036}(3019,\cdot)\) \(\chi_{8036}(3215,\cdot)\) \(\chi_{8036}(3595,\cdot)\) \(\chi_{8036}(3791,\cdot)\) \(\chi_{8036}(3999,\cdot)\) \(\chi_{8036}(4195,\cdot)\) \(\chi_{8036}(4575,\cdot)\) \(\chi_{8036}(4771,\cdot)\) \(\chi_{8036}(4967,\cdot)\) \(\chi_{8036}(5359,\cdot)\) \(\chi_{8036}(5751,\cdot)\) \(\chi_{8036}(6143,\cdot)\) \(\chi_{8036}(6547,\cdot)\) \(\chi_{8036}(6731,\cdot)\) \(\chi_{8036}(6743,\cdot)\) \(\chi_{8036}(7123,\cdot)\) \(\chi_{8036}(7515,\cdot)\) \(\chi_{8036}(7527,\cdot)\) \(\chi_{8036}(7723,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((4019,493,785)\) → \((-1,e\left(\frac{2}{3}\right),e\left(\frac{17}{40}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 8036 }(67, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{53}{120}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{11}{30}\right)\) |