Basic properties
| Modulus: | \(4018\) | |
| 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 \(\chi_{287}(19,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4018.by
\(\chi_{4018}(19,\cdot)\) \(\chi_{4018}(117,\cdot)\) \(\chi_{4018}(129,\cdot)\) \(\chi_{4018}(227,\cdot)\) \(\chi_{4018}(313,\cdot)\) \(\chi_{4018}(423,\cdot)\) \(\chi_{4018}(509,\cdot)\) \(\chi_{4018}(521,\cdot)\) \(\chi_{4018}(803,\cdot)\) \(\chi_{4018}(913,\cdot)\) \(\chi_{4018}(999,\cdot)\) \(\chi_{4018}(1195,\cdot)\) \(\chi_{4018}(1293,\cdot)\) \(\chi_{4018}(1305,\cdot)\) \(\chi_{4018}(1489,\cdot)\) \(\chi_{4018}(1587,\cdot)\) \(\chi_{4018}(1893,\cdot)\) \(\chi_{4018}(1979,\cdot)\) \(\chi_{4018}(2285,\cdot)\) \(\chi_{4018}(2371,\cdot)\) \(\chi_{4018}(2677,\cdot)\) \(\chi_{4018}(2775,\cdot)\) \(\chi_{4018}(2959,\cdot)\) \(\chi_{4018}(2971,\cdot)\) \(\chi_{4018}(3069,\cdot)\) \(\chi_{4018}(3265,\cdot)\) \(\chi_{4018}(3351,\cdot)\) \(\chi_{4018}(3461,\cdot)\) \(\chi_{4018}(3743,\cdot)\) \(\chi_{4018}(3755,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((493,785)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{9}{40}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 4018 }(19, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{7}{60}\right)\) | \(e\left(\frac{5}{12}\right)\) | \(e\left(\frac{1}{120}\right)\) | \(e\left(\frac{19}{40}\right)\) | \(e\left(\frac{13}{40}\right)\) | \(e\left(\frac{31}{120}\right)\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{23}{30}\right)\) | \(e\left(\frac{7}{30}\right)\) |