Basic properties
| Modulus: | \(3549\) | |
| Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(156\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1183}(1137,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3549.eo
\(\chi_{3549}(136,\cdot)\) \(\chi_{3549}(145,\cdot)\) \(\chi_{3549}(241,\cdot)\) \(\chi_{3549}(271,\cdot)\) \(\chi_{3549}(409,\cdot)\) \(\chi_{3549}(514,\cdot)\) \(\chi_{3549}(544,\cdot)\) \(\chi_{3549}(682,\cdot)\) \(\chi_{3549}(691,\cdot)\) \(\chi_{3549}(787,\cdot)\) \(\chi_{3549}(817,\cdot)\) \(\chi_{3549}(955,\cdot)\) \(\chi_{3549}(964,\cdot)\) \(\chi_{3549}(1060,\cdot)\) \(\chi_{3549}(1090,\cdot)\) \(\chi_{3549}(1228,\cdot)\) \(\chi_{3549}(1237,\cdot)\) \(\chi_{3549}(1363,\cdot)\) \(\chi_{3549}(1501,\cdot)\) \(\chi_{3549}(1510,\cdot)\) \(\chi_{3549}(1606,\cdot)\) \(\chi_{3549}(1636,\cdot)\) \(\chi_{3549}(1774,\cdot)\) \(\chi_{3549}(1783,\cdot)\) \(\chi_{3549}(1879,\cdot)\) \(\chi_{3549}(1909,\cdot)\) \(\chi_{3549}(2056,\cdot)\) \(\chi_{3549}(2152,\cdot)\) \(\chi_{3549}(2182,\cdot)\) \(\chi_{3549}(2320,\cdot)\) ...
Related number fields
| Field of values: | $\Q(\zeta_{156})$ |
| Fixed field: | Number field defined by a degree 156 polynomial (not computed) |
Values on generators
\((1184,1522,3382)\) → \((1,e\left(\frac{1}{6}\right),e\left(\frac{53}{156}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 3549 }(2320, a) \) | \(1\) | \(1\) | \(e\left(\frac{35}{52}\right)\) | \(e\left(\frac{9}{26}\right)\) | \(e\left(\frac{139}{156}\right)\) | \(e\left(\frac{1}{52}\right)\) | \(e\left(\frac{22}{39}\right)\) | \(e\left(\frac{103}{156}\right)\) | \(e\left(\frac{9}{13}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{11}{12}\right)\) | \(e\left(\frac{37}{156}\right)\) |