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 \(\chi_{2583}(157,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 5166.gd
\(\chi_{5166}(157,\cdot)\) \(\chi_{5166}(313,\cdot)\) \(\chi_{5166}(439,\cdot)\) \(\chi_{5166}(691,\cdot)\) \(\chi_{5166}(913,\cdot)\) \(\chi_{5166}(1165,\cdot)\) \(\chi_{5166}(1195,\cdot)\) \(\chi_{5166}(1447,\cdot)\) \(\chi_{5166}(1543,\cdot)\) \(\chi_{5166}(1573,\cdot)\) \(\chi_{5166}(1669,\cdot)\) \(\chi_{5166}(1921,\cdot)\) \(\chi_{5166}(1951,\cdot)\) \(\chi_{5166}(2203,\cdot)\) \(\chi_{5166}(2425,\cdot)\) \(\chi_{5166}(2677,\cdot)\) \(\chi_{5166}(2803,\cdot)\) \(\chi_{5166}(2959,\cdot)\) \(\chi_{5166}(3181,\cdot)\) \(\chi_{5166}(3211,\cdot)\) \(\chi_{5166}(3433,\cdot)\) \(\chi_{5166}(3463,\cdot)\) \(\chi_{5166}(3589,\cdot)\) \(\chi_{5166}(3841,\cdot)\) \(\chi_{5166}(4093,\cdot)\) \(\chi_{5166}(4189,\cdot)\) \(\chi_{5166}(4441,\cdot)\) \(\chi_{5166}(4693,\cdot)\) \(\chi_{5166}(4819,\cdot)\) \(\chi_{5166}(4849,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{120})$ |
| Fixed field: | Number field defined by a degree 120 polynomial (not computed) |
Values on generators
\((2297,2215,3655)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{1}{6}\right),e\left(\frac{19}{40}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(13\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) |
| \( \chi_{ 5166 }(157, a) \) | \(1\) | \(1\) | \(e\left(\frac{19}{20}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{107}{120}\right)\) | \(e\left(\frac{101}{120}\right)\) | \(e\left(\frac{13}{120}\right)\) | \(e\left(\frac{1}{10}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{79}{120}\right)\) | \(e\left(\frac{2}{15}\right)\) | \(e\left(\frac{8}{15}\right)\) |