Basic properties
| Modulus: | \(2365\) | |
| Conductor: | \(2365\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(420\) | 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 2365.dq
\(\chi_{2365}(3,\cdot)\) \(\chi_{2365}(48,\cdot)\) \(\chi_{2365}(147,\cdot)\) \(\chi_{2365}(148,\cdot)\) \(\chi_{2365}(157,\cdot)\) \(\chi_{2365}(158,\cdot)\) \(\chi_{2365}(163,\cdot)\) \(\chi_{2365}(192,\cdot)\) \(\chi_{2365}(202,\cdot)\) \(\chi_{2365}(218,\cdot)\) \(\chi_{2365}(278,\cdot)\) \(\chi_{2365}(313,\cdot)\) \(\chi_{2365}(372,\cdot)\) \(\chi_{2365}(377,\cdot)\) \(\chi_{2365}(378,\cdot)\) \(\chi_{2365}(433,\cdot)\) \(\chi_{2365}(478,\cdot)\) \(\chi_{2365}(493,\cdot)\) \(\chi_{2365}(542,\cdot)\) \(\chi_{2365}(577,\cdot)\) \(\chi_{2365}(587,\cdot)\) \(\chi_{2365}(588,\cdot)\) \(\chi_{2365}(592,\cdot)\) \(\chi_{2365}(632,\cdot)\) \(\chi_{2365}(663,\cdot)\) \(\chi_{2365}(707,\cdot)\) \(\chi_{2365}(708,\cdot)\) \(\chi_{2365}(718,\cdot)\) \(\chi_{2365}(757,\cdot)\) \(\chi_{2365}(807,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{420})$ |
| Fixed field: | Number field defined by a degree 420 polynomial (not computed) |
Values on generators
\((947,431,1981)\) → \((-i,e\left(\frac{4}{5}\right),e\left(\frac{1}{42}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(6\) | \(7\) | \(8\) | \(9\) | \(12\) | \(13\) | \(14\) |
| \( \chi_{ 2365 }(3, a) \) | \(1\) | \(1\) | \(e\left(\frac{27}{140}\right)\) | \(e\left(\frac{283}{420}\right)\) | \(e\left(\frac{27}{70}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{81}{140}\right)\) | \(e\left(\frac{73}{210}\right)\) | \(e\left(\frac{5}{84}\right)\) | \(e\left(\frac{341}{420}\right)\) | \(e\left(\frac{79}{210}\right)\) |