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 \(\chi_{2975}(1481,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5950.ff
\(\chi_{5950}(121,\cdot)\) \(\chi_{5950}(291,\cdot)\) \(\chi_{5950}(331,\cdot)\) \(\chi_{5950}(961,\cdot)\) \(\chi_{5950}(1131,\cdot)\) \(\chi_{5950}(1171,\cdot)\) \(\chi_{5950}(1311,\cdot)\) \(\chi_{5950}(1341,\cdot)\) \(\chi_{5950}(1481,\cdot)\) \(\chi_{5950}(1521,\cdot)\) \(\chi_{5950}(1691,\cdot)\) \(\chi_{5950}(2321,\cdot)\) \(\chi_{5950}(2361,\cdot)\) \(\chi_{5950}(2531,\cdot)\) \(\chi_{5950}(2671,\cdot)\) \(\chi_{5950}(2711,\cdot)\) \(\chi_{5950}(2881,\cdot)\) \(\chi_{5950}(3341,\cdot)\) \(\chi_{5950}(3511,\cdot)\) \(\chi_{5950}(3691,\cdot)\) \(\chi_{5950}(3721,\cdot)\) \(\chi_{5950}(3861,\cdot)\) \(\chi_{5950}(4071,\cdot)\) \(\chi_{5950}(4531,\cdot)\) \(\chi_{5950}(4741,\cdot)\) \(\chi_{5950}(4881,\cdot)\) \(\chi_{5950}(4911,\cdot)\) \(\chi_{5950}(5091,\cdot)\) \(\chi_{5950}(5261,\cdot)\) \(\chi_{5950}(5721,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((477,2551,2451)\) → \((e\left(\frac{2}{5}\right),e\left(\frac{2}{3}\right),e\left(\frac{7}{8}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(9\) | \(11\) | \(13\) | \(19\) | \(23\) | \(27\) | \(29\) | \(31\) | \(33\) |
| \( \chi_{ 5950 }(1481, a) \) | \(1\) | \(1\) | \(e\left(\frac{41}{120}\right)\) | \(e\left(\frac{41}{60}\right)\) | \(e\left(\frac{23}{120}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{47}{60}\right)\) | \(e\left(\frac{103}{120}\right)\) | \(e\left(\frac{1}{40}\right)\) | \(e\left(\frac{7}{40}\right)\) | \(e\left(\frac{89}{120}\right)\) | \(e\left(\frac{8}{15}\right)\) |