Basic properties
| Modulus: | \(6336\) | |
| Conductor: | \(3168\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{3168}(1613,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | no | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6336.fv
\(\chi_{6336}(41,\cdot)\) \(\chi_{6336}(281,\cdot)\) \(\chi_{6336}(425,\cdot)\) \(\chi_{6336}(569,\cdot)\) \(\chi_{6336}(761,\cdot)\) \(\chi_{6336}(1289,\cdot)\) \(\chi_{6336}(1337,\cdot)\) \(\chi_{6336}(1481,\cdot)\) \(\chi_{6336}(1625,\cdot)\) \(\chi_{6336}(1865,\cdot)\) \(\chi_{6336}(2009,\cdot)\) \(\chi_{6336}(2153,\cdot)\) \(\chi_{6336}(2345,\cdot)\) \(\chi_{6336}(2873,\cdot)\) \(\chi_{6336}(2921,\cdot)\) \(\chi_{6336}(3065,\cdot)\) \(\chi_{6336}(3209,\cdot)\) \(\chi_{6336}(3449,\cdot)\) \(\chi_{6336}(3593,\cdot)\) \(\chi_{6336}(3737,\cdot)\) \(\chi_{6336}(3929,\cdot)\) \(\chi_{6336}(4457,\cdot)\) \(\chi_{6336}(4505,\cdot)\) \(\chi_{6336}(4649,\cdot)\) \(\chi_{6336}(4793,\cdot)\) \(\chi_{6336}(5033,\cdot)\) \(\chi_{6336}(5177,\cdot)\) \(\chi_{6336}(5321,\cdot)\) \(\chi_{6336}(5513,\cdot)\) \(\chi_{6336}(6041,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((4159,4357,3521,1729)\) → \((1,e\left(\frac{7}{8}\right),e\left(\frac{1}{6}\right),e\left(\frac{7}{10}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 6336 }(425, a) \) | \(1\) | \(1\) | \(e\left(\frac{61}{120}\right)\) | \(e\left(\frac{19}{60}\right)\) | \(e\left(\frac{19}{120}\right)\) | \(e\left(\frac{3}{10}\right)\) | \(e\left(\frac{9}{40}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{1}{60}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{8}{15}\right)\) | \(e\left(\frac{33}{40}\right)\) |