Basic properties
| Modulus: | \(6040\) | |
| Conductor: | \(1208\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(150\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1208}(51,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6040.ew
\(\chi_{6040}(51,\cdot)\) \(\chi_{6040}(291,\cdot)\) \(\chi_{6040}(411,\cdot)\) \(\chi_{6040}(611,\cdot)\) \(\chi_{6040}(811,\cdot)\) \(\chi_{6040}(851,\cdot)\) \(\chi_{6040}(1171,\cdot)\) \(\chi_{6040}(1371,\cdot)\) \(\chi_{6040}(1411,\cdot)\) \(\chi_{6040}(1571,\cdot)\) \(\chi_{6040}(1651,\cdot)\) \(\chi_{6040}(1691,\cdot)\) \(\chi_{6040}(2011,\cdot)\) \(\chi_{6040}(2371,\cdot)\) \(\chi_{6040}(2411,\cdot)\) \(\chi_{6040}(2451,\cdot)\) \(\chi_{6040}(2531,\cdot)\) \(\chi_{6040}(2731,\cdot)\) \(\chi_{6040}(2811,\cdot)\) \(\chi_{6040}(2851,\cdot)\) \(\chi_{6040}(2971,\cdot)\) \(\chi_{6040}(3091,\cdot)\) \(\chi_{6040}(3131,\cdot)\) \(\chi_{6040}(3291,\cdot)\) \(\chi_{6040}(3411,\cdot)\) \(\chi_{6040}(3451,\cdot)\) \(\chi_{6040}(4091,\cdot)\) \(\chi_{6040}(4131,\cdot)\) \(\chi_{6040}(4211,\cdot)\) \(\chi_{6040}(4291,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{75})$ |
| Fixed field: | Number field defined by a degree 150 polynomial (not computed) |
Values on generators
\((1511,3021,2417,761)\) → \((-1,-1,1,e\left(\frac{139}{150}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(3\) | \(7\) | \(9\) | \(11\) | \(13\) | \(17\) | \(19\) | \(21\) | \(23\) | \(27\) |
| \( \chi_{ 6040 }(51, a) \) | \(1\) | \(1\) | \(e\left(\frac{3}{50}\right)\) | \(e\left(\frac{44}{75}\right)\) | \(e\left(\frac{3}{25}\right)\) | \(e\left(\frac{8}{75}\right)\) | \(e\left(\frac{37}{75}\right)\) | \(e\left(\frac{56}{75}\right)\) | \(e\left(\frac{2}{5}\right)\) | \(e\left(\frac{97}{150}\right)\) | \(e\left(\frac{1}{15}\right)\) | \(e\left(\frac{9}{50}\right)\) |