Basic properties
| Modulus: | \(6336\) | |
| Conductor: | \(6336\) | 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: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6336.fx
\(\chi_{6336}(29,\cdot)\) \(\chi_{6336}(101,\cdot)\) \(\chi_{6336}(149,\cdot)\) \(\chi_{6336}(173,\cdot)\) \(\chi_{6336}(293,\cdot)\) \(\chi_{6336}(365,\cdot)\) \(\chi_{6336}(437,\cdot)\) \(\chi_{6336}(677,\cdot)\) \(\chi_{6336}(821,\cdot)\) \(\chi_{6336}(893,\cdot)\) \(\chi_{6336}(941,\cdot)\) \(\chi_{6336}(965,\cdot)\) \(\chi_{6336}(1085,\cdot)\) \(\chi_{6336}(1157,\cdot)\) \(\chi_{6336}(1229,\cdot)\) \(\chi_{6336}(1469,\cdot)\) \(\chi_{6336}(1613,\cdot)\) \(\chi_{6336}(1685,\cdot)\) \(\chi_{6336}(1733,\cdot)\) \(\chi_{6336}(1757,\cdot)\) \(\chi_{6336}(1877,\cdot)\) \(\chi_{6336}(1949,\cdot)\) \(\chi_{6336}(2021,\cdot)\) \(\chi_{6336}(2261,\cdot)\) \(\chi_{6336}(2405,\cdot)\) \(\chi_{6336}(2477,\cdot)\) \(\chi_{6336}(2525,\cdot)\) \(\chi_{6336}(2549,\cdot)\) \(\chi_{6336}(2669,\cdot)\) \(\chi_{6336}(2741,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{240})$ |
| Fixed field: | Number field defined by a degree 240 polynomial (not computed) |
Values on generators
\((4159,4357,3521,1729)\) → \((1,e\left(\frac{9}{16}\right),e\left(\frac{1}{6}\right),e\left(\frac{1}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 6336 }(101, a) \) | \(1\) | \(1\) | \(e\left(\frac{191}{240}\right)\) | \(e\left(\frac{119}{120}\right)\) | \(e\left(\frac{209}{240}\right)\) | \(e\left(\frac{3}{20}\right)\) | \(e\left(\frac{19}{80}\right)\) | \(e\left(\frac{17}{24}\right)\) | \(e\left(\frac{71}{120}\right)\) | \(e\left(\frac{13}{240}\right)\) | \(e\left(\frac{13}{30}\right)\) | \(e\left(\frac{63}{80}\right)\) |