Basic properties
| Modulus: | \(4018\) | |
| Conductor: | \(2009\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(168\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2009}(3,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4018.cb
\(\chi_{4018}(3,\cdot)\) \(\chi_{4018}(243,\cdot)\) \(\chi_{4018}(355,\cdot)\) \(\chi_{4018}(383,\cdot)\) \(\chi_{4018}(437,\cdot)\) \(\chi_{4018}(465,\cdot)\) \(\chi_{4018}(495,\cdot)\) \(\chi_{4018}(577,\cdot)\) \(\chi_{4018}(817,\cdot)\) \(\chi_{4018}(899,\cdot)\) \(\chi_{4018}(929,\cdot)\) \(\chi_{4018}(957,\cdot)\) \(\chi_{4018}(1039,\cdot)\) \(\chi_{4018}(1069,\cdot)\) \(\chi_{4018}(1151,\cdot)\) \(\chi_{4018}(1473,\cdot)\) \(\chi_{4018}(1503,\cdot)\) \(\chi_{4018}(1531,\cdot)\) \(\chi_{4018}(1585,\cdot)\) \(\chi_{4018}(1613,\cdot)\) \(\chi_{4018}(1643,\cdot)\) \(\chi_{4018}(1725,\cdot)\) \(\chi_{4018}(1965,\cdot)\) \(\chi_{4018}(2047,\cdot)\) \(\chi_{4018}(2105,\cdot)\) \(\chi_{4018}(2159,\cdot)\) \(\chi_{4018}(2217,\cdot)\) \(\chi_{4018}(2299,\cdot)\) \(\chi_{4018}(2539,\cdot)\) \(\chi_{4018}(2621,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{168})$ |
| Fixed field: | Number field defined by a degree 168 polynomial (not computed) |
Values on generators
\((493,785)\) → \((e\left(\frac{1}{42}\right),e\left(\frac{3}{8}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(23\) | \(25\) |
| \( \chi_{ 4018 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{109}{168}\right)\) | \(e\left(\frac{79}{84}\right)\) | \(e\left(\frac{25}{84}\right)\) | \(e\left(\frac{13}{168}\right)\) | \(e\left(\frac{23}{56}\right)\) | \(e\left(\frac{33}{56}\right)\) | \(e\left(\frac{163}{168}\right)\) | \(e\left(\frac{5}{24}\right)\) | \(e\left(\frac{17}{42}\right)\) | \(e\left(\frac{37}{42}\right)\) |