Basic properties
| Modulus: | \(4022\) | |
| Conductor: | \(2011\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(670\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2011}(55,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4022.n
\(\chi_{4022}(27,\cdot)\) \(\chi_{4022}(47,\cdot)\) \(\chi_{4022}(55,\cdot)\) \(\chi_{4022}(59,\cdot)\) \(\chi_{4022}(75,\cdot)\) \(\chi_{4022}(85,\cdot)\) \(\chi_{4022}(95,\cdot)\) \(\chi_{4022}(113,\cdot)\) \(\chi_{4022}(149,\cdot)\) \(\chi_{4022}(253,\cdot)\) \(\chi_{4022}(257,\cdot)\) \(\chi_{4022}(261,\cdot)\) \(\chi_{4022}(267,\cdot)\) \(\chi_{4022}(305,\cdot)\) \(\chi_{4022}(313,\cdot)\) \(\chi_{4022}(333,\cdot)\) \(\chi_{4022}(335,\cdot)\) \(\chi_{4022}(343,\cdot)\) \(\chi_{4022}(345,\cdot)\) \(\chi_{4022}(351,\cdot)\) \(\chi_{4022}(391,\cdot)\) \(\chi_{4022}(437,\cdot)\) \(\chi_{4022}(439,\cdot)\) \(\chi_{4022}(449,\cdot)\) \(\chi_{4022}(463,\cdot)\) \(\chi_{4022}(497,\cdot)\) \(\chi_{4022}(521,\cdot)\) \(\chi_{4022}(535,\cdot)\) \(\chi_{4022}(541,\cdot)\) \(\chi_{4022}(569,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{335})$ |
| Fixed field: | Number field defined by a degree 670 polynomial (not computed) |
Values on generators
\(3\) → \(e\left(\frac{17}{670}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 4022 }(55, a) \) | \(-1\) | \(1\) | \(e\left(\frac{17}{670}\right)\) | \(e\left(\frac{329}{335}\right)\) | \(e\left(\frac{569}{670}\right)\) | \(e\left(\frac{17}{335}\right)\) | \(e\left(\frac{209}{670}\right)\) | \(e\left(\frac{58}{335}\right)\) | \(e\left(\frac{1}{134}\right)\) | \(e\left(\frac{539}{670}\right)\) | \(e\left(\frac{341}{670}\right)\) | \(e\left(\frac{293}{335}\right)\) |