Basic properties
| Modulus: | \(5166\) | |
| Conductor: | \(2583\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(120\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{2583}(11,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5166.gb
\(\chi_{5166}(11,\cdot)\) \(\chi_{5166}(149,\cdot)\) \(\chi_{5166}(263,\cdot)\) \(\chi_{5166}(275,\cdot)\) \(\chi_{5166}(527,\cdot)\) \(\chi_{5166}(641,\cdot)\) \(\chi_{5166}(767,\cdot)\) \(\chi_{5166}(1019,\cdot)\) \(\chi_{5166}(1031,\cdot)\) \(\chi_{5166}(1283,\cdot)\) \(\chi_{5166}(1409,\cdot)\) \(\chi_{5166}(1523,\cdot)\) \(\chi_{5166}(1775,\cdot)\) \(\chi_{5166}(1787,\cdot)\) \(\chi_{5166}(1901,\cdot)\) \(\chi_{5166}(2039,\cdot)\) \(\chi_{5166}(2279,\cdot)\) \(\chi_{5166}(2531,\cdot)\) \(\chi_{5166}(2795,\cdot)\) \(\chi_{5166}(3047,\cdot)\) \(\chi_{5166}(3287,\cdot)\) \(\chi_{5166}(3299,\cdot)\) \(\chi_{5166}(3425,\cdot)\) \(\chi_{5166}(3539,\cdot)\) \(\chi_{5166}(3677,\cdot)\) \(\chi_{5166}(3791,\cdot)\) \(\chi_{5166}(3917,\cdot)\) \(\chi_{5166}(3929,\cdot)\) \(\chi_{5166}(4169,\cdot)\) \(\chi_{5166}(4421,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((2297,2215,3655)\) → \((e\left(\frac{1}{6}\right),e\left(\frac{2}{3}\right),e\left(\frac{3}{40}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 5166 }(11, a) \) | \(1\) | \(1\) | \(e\left(\frac{49}{60}\right)\) | \(e\left(\frac{7}{120}\right)\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{77}{120}\right)\) | \(e\left(\frac{1}{120}\right)\) | \(e\left(\frac{13}{15}\right)\) | \(e\left(\frac{19}{30}\right)\) | \(e\left(\frac{83}{120}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{11}{15}\right)\) |