Basic properties
| Modulus: | \(2169\) | |
| Conductor: | \(723\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(240\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{723}(35,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2169.dt
\(\chi_{2169}(35,\cdot)\) \(\chi_{2169}(62,\cdot)\) \(\chi_{2169}(71,\cdot)\) \(\chi_{2169}(170,\cdot)\) \(\chi_{2169}(179,\cdot)\) \(\chi_{2169}(206,\cdot)\) \(\chi_{2169}(278,\cdot)\) \(\chi_{2169}(287,\cdot)\) \(\chi_{2169}(296,\cdot)\) \(\chi_{2169}(350,\cdot)\) \(\chi_{2169}(368,\cdot)\) \(\chi_{2169}(404,\cdot)\) \(\chi_{2169}(413,\cdot)\) \(\chi_{2169}(431,\cdot)\) \(\chi_{2169}(440,\cdot)\) \(\chi_{2169}(521,\cdot)\) \(\chi_{2169}(548,\cdot)\) \(\chi_{2169}(566,\cdot)\) \(\chi_{2169}(611,\cdot)\) \(\chi_{2169}(692,\cdot)\) \(\chi_{2169}(710,\cdot)\) \(\chi_{2169}(737,\cdot)\) \(\chi_{2169}(791,\cdot)\) \(\chi_{2169}(809,\cdot)\) \(\chi_{2169}(818,\cdot)\) \(\chi_{2169}(827,\cdot)\) \(\chi_{2169}(854,\cdot)\) \(\chi_{2169}(872,\cdot)\) \(\chi_{2169}(890,\cdot)\) \(\chi_{2169}(908,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{240})$ |
| Fixed field: | Number field defined by a degree 240 polynomial (not computed) |
Values on generators
\((965,730)\) → \((-1,e\left(\frac{139}{240}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2169 }(35, a) \) | \(1\) | \(1\) | \(e\left(\frac{13}{24}\right)\) | \(e\left(\frac{1}{12}\right)\) | \(e\left(\frac{17}{40}\right)\) | \(e\left(\frac{139}{240}\right)\) | \(e\left(\frac{5}{8}\right)\) | \(e\left(\frac{29}{30}\right)\) | \(e\left(\frac{47}{48}\right)\) | \(e\left(\frac{53}{240}\right)\) | \(e\left(\frac{29}{240}\right)\) | \(e\left(\frac{1}{6}\right)\) |