Basic properties
| Modulus: | \(3249\) | |
| Conductor: | \(3249\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(171\) | 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 3249.cb
\(\chi_{3249}(25,\cdot)\) \(\chi_{3249}(61,\cdot)\) \(\chi_{3249}(112,\cdot)\) \(\chi_{3249}(130,\cdot)\) \(\chi_{3249}(142,\cdot)\) \(\chi_{3249}(157,\cdot)\) \(\chi_{3249}(196,\cdot)\) \(\chi_{3249}(232,\cdot)\) \(\chi_{3249}(283,\cdot)\) \(\chi_{3249}(301,\cdot)\) \(\chi_{3249}(313,\cdot)\) \(\chi_{3249}(328,\cdot)\) \(\chi_{3249}(367,\cdot)\) \(\chi_{3249}(403,\cdot)\) \(\chi_{3249}(454,\cdot)\) \(\chi_{3249}(472,\cdot)\) \(\chi_{3249}(484,\cdot)\) \(\chi_{3249}(499,\cdot)\) \(\chi_{3249}(538,\cdot)\) \(\chi_{3249}(574,\cdot)\) \(\chi_{3249}(625,\cdot)\) \(\chi_{3249}(643,\cdot)\) \(\chi_{3249}(655,\cdot)\) \(\chi_{3249}(670,\cdot)\) \(\chi_{3249}(709,\cdot)\) \(\chi_{3249}(745,\cdot)\) \(\chi_{3249}(796,\cdot)\) \(\chi_{3249}(814,\cdot)\) \(\chi_{3249}(826,\cdot)\) \(\chi_{3249}(841,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{171})$ |
| Fixed field: | Number field defined by a degree 171 polynomial (not computed) |
Values on generators
\((362,2890)\) → \((e\left(\frac{1}{3}\right),e\left(\frac{11}{171}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(7\) | \(8\) | \(10\) | \(11\) | \(13\) | \(14\) | \(16\) |
| \( \chi_{ 3249 }(2011, a) \) | \(1\) | \(1\) | \(e\left(\frac{68}{171}\right)\) | \(e\left(\frac{136}{171}\right)\) | \(e\left(\frac{101}{171}\right)\) | \(e\left(\frac{56}{57}\right)\) | \(e\left(\frac{11}{57}\right)\) | \(e\left(\frac{169}{171}\right)\) | \(e\left(\frac{17}{19}\right)\) | \(e\left(\frac{142}{171}\right)\) | \(e\left(\frac{65}{171}\right)\) | \(e\left(\frac{101}{171}\right)\) |