Basic properties
| Modulus: | \(2169\) | |
| Conductor: | \(2169\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(240\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 2169.dv
\(\chi_{2169}(23,\cdot)\) \(\chi_{2169}(101,\cdot)\) \(\chi_{2169}(140,\cdot)\) \(\chi_{2169}(218,\cdot)\) \(\chi_{2169}(284,\cdot)\) \(\chi_{2169}(326,\cdot)\) \(\chi_{2169}(344,\cdot)\) \(\chi_{2169}(365,\cdot)\) \(\chi_{2169}(380,\cdot)\) \(\chi_{2169}(389,\cdot)\) \(\chi_{2169}(425,\cdot)\) \(\chi_{2169}(461,\cdot)\) \(\chi_{2169}(515,\cdot)\) \(\chi_{2169}(587,\cdot)\) \(\chi_{2169}(599,\cdot)\) \(\chi_{2169}(650,\cdot)\) \(\chi_{2169}(680,\cdot)\) \(\chi_{2169}(695,\cdot)\) \(\chi_{2169}(740,\cdot)\) \(\chi_{2169}(749,\cdot)\) \(\chi_{2169}(824,\cdot)\) \(\chi_{2169}(938,\cdot)\) \(\chi_{2169}(941,\cdot)\) \(\chi_{2169}(947,\cdot)\) \(\chi_{2169}(992,\cdot)\) \(\chi_{2169}(1037,\cdot)\) \(\chi_{2169}(1049,\cdot)\) \(\chi_{2169}(1067,\cdot)\) \(\chi_{2169}(1100,\cdot)\) \(\chi_{2169}(1103,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{240})$ |
| Fixed field: | Number field defined by a degree 240 polynomial (not computed) |
Values on generators
\((965,730)\) → \((e\left(\frac{5}{6}\right),e\left(\frac{19}{80}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 2169 }(23, a) \) | \(1\) | \(1\) | \(e\left(\frac{23}{24}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{113}{120}\right)\) | \(e\left(\frac{137}{240}\right)\) | \(e\left(\frac{7}{8}\right)\) | \(e\left(\frac{9}{10}\right)\) | \(e\left(\frac{37}{48}\right)\) | \(e\left(\frac{199}{240}\right)\) | \(e\left(\frac{127}{240}\right)\) | \(e\left(\frac{5}{6}\right)\) |