Basic properties
| Modulus: | \(3549\) | |
| Conductor: | \(3549\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | 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 3549.ef
\(\chi_{3549}(44,\cdot)\) \(\chi_{3549}(86,\cdot)\) \(\chi_{3549}(200,\cdot)\) \(\chi_{3549}(242,\cdot)\) \(\chi_{3549}(317,\cdot)\) \(\chi_{3549}(359,\cdot)\) \(\chi_{3549}(473,\cdot)\) \(\chi_{3549}(515,\cdot)\) \(\chi_{3549}(590,\cdot)\) \(\chi_{3549}(632,\cdot)\) \(\chi_{3549}(788,\cdot)\) \(\chi_{3549}(863,\cdot)\) \(\chi_{3549}(905,\cdot)\) \(\chi_{3549}(1019,\cdot)\) \(\chi_{3549}(1061,\cdot)\) \(\chi_{3549}(1136,\cdot)\) \(\chi_{3549}(1178,\cdot)\) \(\chi_{3549}(1292,\cdot)\) \(\chi_{3549}(1334,\cdot)\) \(\chi_{3549}(1409,\cdot)\) \(\chi_{3549}(1565,\cdot)\) \(\chi_{3549}(1607,\cdot)\) \(\chi_{3549}(1682,\cdot)\) \(\chi_{3549}(1724,\cdot)\) \(\chi_{3549}(1838,\cdot)\) \(\chi_{3549}(1880,\cdot)\) \(\chi_{3549}(1955,\cdot)\) \(\chi_{3549}(1997,\cdot)\) \(\chi_{3549}(2111,\cdot)\) \(\chi_{3549}(2153,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((1184,1522,3382)\) → \((-1,e\left(\frac{1}{3}\right),e\left(\frac{29}{52}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 3549 }(1178, a) \) | \(1\) | \(1\) | \(e\left(\frac{113}{156}\right)\) | \(e\left(\frac{35}{78}\right)\) | \(e\left(\frac{29}{156}\right)\) | \(e\left(\frac{9}{52}\right)\) | \(e\left(\frac{71}{78}\right)\) | \(e\left(\frac{43}{156}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{33}{52}\right)\) |