Basic properties
| Modulus: | \(3211\) | |
| Conductor: | \(3211\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(234\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3211.dd
\(\chi_{3211}(3,\cdot)\) \(\chi_{3211}(48,\cdot)\) \(\chi_{3211}(165,\cdot)\) \(\chi_{3211}(185,\cdot)\) \(\chi_{3211}(211,\cdot)\) \(\chi_{3211}(243,\cdot)\) \(\chi_{3211}(250,\cdot)\) \(\chi_{3211}(295,\cdot)\) \(\chi_{3211}(412,\cdot)\) \(\chi_{3211}(432,\cdot)\) \(\chi_{3211}(458,\cdot)\) \(\chi_{3211}(490,\cdot)\) \(\chi_{3211}(497,\cdot)\) \(\chi_{3211}(542,\cdot)\) \(\chi_{3211}(659,\cdot)\) \(\chi_{3211}(679,\cdot)\) \(\chi_{3211}(705,\cdot)\) \(\chi_{3211}(737,\cdot)\) \(\chi_{3211}(744,\cdot)\) \(\chi_{3211}(789,\cdot)\) \(\chi_{3211}(906,\cdot)\) \(\chi_{3211}(926,\cdot)\) \(\chi_{3211}(952,\cdot)\) \(\chi_{3211}(984,\cdot)\) \(\chi_{3211}(1153,\cdot)\) \(\chi_{3211}(1173,\cdot)\) \(\chi_{3211}(1199,\cdot)\) \(\chi_{3211}(1231,\cdot)\) \(\chi_{3211}(1238,\cdot)\) \(\chi_{3211}(1283,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{117})$ |
| Fixed field: | Number field defined by a degree 234 polynomial (not computed) |
Values on generators
\((1692,1522)\) → \((e\left(\frac{1}{39}\right),e\left(\frac{1}{18}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(3\) | \(4\) | \(5\) | \(6\) | \(7\) | \(8\) | \(9\) | \(10\) | \(11\) |
| \( \chi_{ 3211 }(1199, a) \) | \(-1\) | \(1\) | \(e\left(\frac{19}{234}\right)\) | \(e\left(\frac{211}{234}\right)\) | \(e\left(\frac{19}{117}\right)\) | \(e\left(\frac{14}{117}\right)\) | \(e\left(\frac{115}{117}\right)\) | \(e\left(\frac{1}{13}\right)\) | \(e\left(\frac{19}{78}\right)\) | \(e\left(\frac{94}{117}\right)\) | \(e\left(\frac{47}{234}\right)\) | \(e\left(\frac{4}{13}\right)\) |