Basic properties
| Modulus: | \(1984\) | |
| Conductor: | \(1984\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(240\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 1984.cz
\(\chi_{1984}(19,\cdot)\) \(\chi_{1984}(51,\cdot)\) \(\chi_{1984}(59,\cdot)\) \(\chi_{1984}(107,\cdot)\) \(\chi_{1984}(131,\cdot)\) \(\chi_{1984}(195,\cdot)\) \(\chi_{1984}(227,\cdot)\) \(\chi_{1984}(235,\cdot)\) \(\chi_{1984}(267,\cdot)\) \(\chi_{1984}(299,\cdot)\) \(\chi_{1984}(307,\cdot)\) \(\chi_{1984}(355,\cdot)\) \(\chi_{1984}(379,\cdot)\) \(\chi_{1984}(443,\cdot)\) \(\chi_{1984}(475,\cdot)\) \(\chi_{1984}(483,\cdot)\) \(\chi_{1984}(515,\cdot)\) \(\chi_{1984}(547,\cdot)\) \(\chi_{1984}(555,\cdot)\) \(\chi_{1984}(603,\cdot)\) \(\chi_{1984}(627,\cdot)\) \(\chi_{1984}(691,\cdot)\) \(\chi_{1984}(723,\cdot)\) \(\chi_{1984}(731,\cdot)\) \(\chi_{1984}(763,\cdot)\) \(\chi_{1984}(795,\cdot)\) \(\chi_{1984}(803,\cdot)\) \(\chi_{1984}(851,\cdot)\) \(\chi_{1984}(875,\cdot)\) \(\chi_{1984}(939,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{240})$ |
| Fixed field: | Number field defined by a degree 240 polynomial (not computed) |
Values on generators
\((63,1861,65)\) → \((-1,e\left(\frac{7}{16}\right),e\left(\frac{2}{15}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(19\) | \(21\) |
| \( \chi_{ 1984 }(19, a) \) | \(-1\) | \(1\) | \(e\left(\frac{227}{240}\right)\) | \(e\left(\frac{5}{48}\right)\) | \(e\left(\frac{73}{120}\right)\) | \(e\left(\frac{107}{120}\right)\) | \(e\left(\frac{181}{240}\right)\) | \(e\left(\frac{7}{240}\right)\) | \(e\left(\frac{1}{20}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{23}{240}\right)\) | \(e\left(\frac{133}{240}\right)\) |