Basic properties
| Modulus: | \(8042\) | |
| Conductor: | \(4021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(670\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{4021}(17,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 8042.s
\(\chi_{8042}(17,\cdot)\) \(\chi_{8042}(73,\cdot)\) \(\chi_{8042}(103,\cdot)\) \(\chi_{8042}(127,\cdot)\) \(\chi_{8042}(151,\cdot)\) \(\chi_{8042}(179,\cdot)\) \(\chi_{8042}(181,\cdot)\) \(\chi_{8042}(183,\cdot)\) \(\chi_{8042}(193,\cdot)\) \(\chi_{8042}(233,\cdot)\) \(\chi_{8042}(239,\cdot)\) \(\chi_{8042}(267,\cdot)\) \(\chi_{8042}(305,\cdot)\) \(\chi_{8042}(313,\cdot)\) \(\chi_{8042}(351,\cdot)\) \(\chi_{8042}(393,\cdot)\) \(\chi_{8042}(437,\cdot)\) \(\chi_{8042}(445,\cdot)\) \(\chi_{8042}(449,\cdot)\) \(\chi_{8042}(459,\cdot)\) \(\chi_{8042}(467,\cdot)\) \(\chi_{8042}(477,\cdot)\) \(\chi_{8042}(479,\cdot)\) \(\chi_{8042}(483,\cdot)\) \(\chi_{8042}(523,\cdot)\) \(\chi_{8042}(531,\cdot)\) \(\chi_{8042}(585,\cdot)\) \(\chi_{8042}(607,\cdot)\) \(\chi_{8042}(613,\cdot)\) \(\chi_{8042}(655,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{335})$ |
| Fixed field: | Number field defined by a degree 670 polynomial (not computed) |
Values on generators
\(4023\) → \(e\left(\frac{37}{670}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 8042 }(17, a) \) | \(1\) | \(1\) | \(e\left(\frac{264}{335}\right)\) | \(e\left(\frac{314}{335}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{193}{335}\right)\) | \(e\left(\frac{139}{670}\right)\) | \(e\left(\frac{43}{67}\right)\) | \(e\left(\frac{243}{335}\right)\) | \(e\left(\frac{87}{335}\right)\) | \(e\left(\frac{577}{670}\right)\) | \(e\left(\frac{59}{670}\right)\) |