Basic properties
| Modulus: | \(5950\) | |
| Conductor: | \(2975\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2975}(984,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5950.ey
\(\chi_{5950}(9,\cdot)\) \(\chi_{5950}(179,\cdot)\) \(\chi_{5950}(219,\cdot)\) \(\chi_{5950}(359,\cdot)\) \(\chi_{5950}(389,\cdot)\) \(\chi_{5950}(529,\cdot)\) \(\chi_{5950}(569,\cdot)\) \(\chi_{5950}(739,\cdot)\) \(\chi_{5950}(1369,\cdot)\) \(\chi_{5950}(1409,\cdot)\) \(\chi_{5950}(1579,\cdot)\) \(\chi_{5950}(1719,\cdot)\) \(\chi_{5950}(1759,\cdot)\) \(\chi_{5950}(1929,\cdot)\) \(\chi_{5950}(2389,\cdot)\) \(\chi_{5950}(2559,\cdot)\) \(\chi_{5950}(2739,\cdot)\) \(\chi_{5950}(2769,\cdot)\) \(\chi_{5950}(2909,\cdot)\) \(\chi_{5950}(3119,\cdot)\) \(\chi_{5950}(3579,\cdot)\) \(\chi_{5950}(3789,\cdot)\) \(\chi_{5950}(3929,\cdot)\) \(\chi_{5950}(3959,\cdot)\) \(\chi_{5950}(4139,\cdot)\) \(\chi_{5950}(4309,\cdot)\) \(\chi_{5950}(4769,\cdot)\) \(\chi_{5950}(4939,\cdot)\) \(\chi_{5950}(4979,\cdot)\) \(\chi_{5950}(5119,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((477,2551,2451)\) → \((e\left(\frac{7}{10}\right),e\left(\frac{2}{3}\right),e\left(\frac{3}{8}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(33\) |
| \( \chi_{ 5950 }(3959, a) \) | \(1\) | \(1\) | \(e\left(\frac{113}{120}\right)\) | \(e\left(\frac{53}{60}\right)\) | \(e\left(\frac{59}{120}\right)\) | \(e\left(\frac{4}{5}\right)\) | \(e\left(\frac{11}{60}\right)\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{33}{40}\right)\) | \(e\left(\frac{11}{40}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{13}{30}\right)\) |