Basic properties
| Modulus: | \(6042\) | |
| Conductor: | \(1007\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(117\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1007}(169,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6042.ce
\(\chi_{6042}(169,\cdot)\) \(\chi_{6042}(175,\cdot)\) \(\chi_{6042}(187,\cdot)\) \(\chi_{6042}(289,\cdot)\) \(\chi_{6042}(301,\cdot)\) \(\chi_{6042}(367,\cdot)\) \(\chi_{6042}(415,\cdot)\) \(\chi_{6042}(625,\cdot)\) \(\chi_{6042}(757,\cdot)\) \(\chi_{6042}(823,\cdot)\) \(\chi_{6042}(841,\cdot)\) \(\chi_{6042}(937,\cdot)\) \(\chi_{6042}(967,\cdot)\) \(\chi_{6042}(1051,\cdot)\) \(\chi_{6042}(1213,\cdot)\) \(\chi_{6042}(1393,\cdot)\) \(\chi_{6042}(1441,\cdot)\) \(\chi_{6042}(1639,\cdot)\) \(\chi_{6042}(1765,\cdot)\) \(\chi_{6042}(1795,\cdot)\) \(\chi_{6042}(1849,\cdot)\) \(\chi_{6042}(1879,\cdot)\) \(\chi_{6042}(1897,\cdot)\) \(\chi_{6042}(2077,\cdot)\) \(\chi_{6042}(2095,\cdot)\) \(\chi_{6042}(2113,\cdot)\) \(\chi_{6042}(2209,\cdot)\) \(\chi_{6042}(2239,\cdot)\) \(\chi_{6042}(2323,\cdot)\) \(\chi_{6042}(2533,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 117 polynomial (not computed) |
Values on generators
\((2015,4771,2281)\) → \((1,e\left(\frac{5}{9}\right),e\left(\frac{12}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(7\) | \(11\) | \(13\) | \(17\) | \(23\) | \(25\) | \(29\) | \(31\) | \(35\) |
| \( \chi_{ 6042 }(169, a) \) | \(1\) | \(1\) | \(e\left(\frac{32}{117}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{109}{117}\right)\) | \(e\left(\frac{92}{117}\right)\) | \(e\left(\frac{1}{9}\right)\) | \(e\left(\frac{64}{117}\right)\) | \(e\left(\frac{106}{117}\right)\) | \(e\left(\frac{31}{39}\right)\) | \(e\left(\frac{62}{117}\right)\) |