Basic properties
| Modulus: | \(4021\) | |
| Conductor: | \(4021\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(335\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 4021.q
\(\chi_{4021}(27,\cdot)\) \(\chi_{4021}(38,\cdot)\) \(\chi_{4021}(42,\cdot)\) \(\chi_{4021}(45,\cdot)\) \(\chi_{4021}(48,\cdot)\) \(\chi_{4021}(70,\cdot)\) \(\chi_{4021}(71,\cdot)\) \(\chi_{4021}(75,\cdot)\) \(\chi_{4021}(80,\cdot)\) \(\chi_{4021}(86,\cdot)\) \(\chi_{4021}(94,\cdot)\) \(\chi_{4021}(101,\cdot)\) \(\chi_{4021}(125,\cdot)\) \(\chi_{4021}(209,\cdot)\) \(\chi_{4021}(221,\cdot)\) \(\chi_{4021}(231,\cdot)\) \(\chi_{4021}(244,\cdot)\) \(\chi_{4021}(264,\cdot)\) \(\chi_{4021}(269,\cdot)\) \(\chi_{4021}(289,\cdot)\) \(\chi_{4021}(333,\cdot)\) \(\chi_{4021}(346,\cdot)\) \(\chi_{4021}(356,\cdot)\) \(\chi_{4021}(359,\cdot)\) \(\chi_{4021}(385,\cdot)\) \(\chi_{4021}(440,\cdot)\) \(\chi_{4021}(473,\cdot)\) \(\chi_{4021}(491,\cdot)\) \(\chi_{4021}(517,\cdot)\) \(\chi_{4021}(518,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{335})$ |
| Fixed field: | Number field defined by a degree 335 polynomial (not computed) |
Values on generators
\(2\) → \(e\left(\frac{177}{335}\right)\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 4021 }(231, a) \) | \(1\) | \(1\) | \(e\left(\frac{177}{335}\right)\) | \(e\left(\frac{208}{335}\right)\) | \(e\left(\frac{19}{335}\right)\) | \(e\left(\frac{288}{335}\right)\) | \(e\left(\frac{10}{67}\right)\) | \(e\left(\frac{3}{5}\right)\) | \(e\left(\frac{196}{335}\right)\) | \(e\left(\frac{81}{335}\right)\) | \(e\left(\frac{26}{67}\right)\) | \(e\left(\frac{4}{335}\right)\) |