Basic properties
| Modulus: | \(3549\) | |
| Conductor: | \(1183\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
| Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
| Real: | no | |
| Primitive: | no, induced from \(\chi_{1183}(40,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | odd | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 3549.do
\(\chi_{3549}(40,\cdot)\) \(\chi_{3549}(157,\cdot)\) \(\chi_{3549}(313,\cdot)\) \(\chi_{3549}(430,\cdot)\) \(\chi_{3549}(586,\cdot)\) \(\chi_{3549}(703,\cdot)\) \(\chi_{3549}(859,\cdot)\) \(\chi_{3549}(976,\cdot)\) \(\chi_{3549}(1132,\cdot)\) \(\chi_{3549}(1249,\cdot)\) \(\chi_{3549}(1405,\cdot)\) \(\chi_{3549}(1678,\cdot)\) \(\chi_{3549}(1795,\cdot)\) \(\chi_{3549}(1951,\cdot)\) \(\chi_{3549}(2068,\cdot)\) \(\chi_{3549}(2224,\cdot)\) \(\chi_{3549}(2341,\cdot)\) \(\chi_{3549}(2497,\cdot)\) \(\chi_{3549}(2614,\cdot)\) \(\chi_{3549}(2770,\cdot)\) \(\chi_{3549}(2887,\cdot)\) \(\chi_{3549}(3160,\cdot)\) \(\chi_{3549}(3316,\cdot)\) \(\chi_{3549}(3433,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1184,1522,3382)\) → \((1,e\left(\frac{5}{6}\right),e\left(\frac{1}{13}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
| \( \chi_{ 3549 }(40, a) \) | \(-1\) | \(1\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{67}{78}\right)\) | \(e\left(\frac{3}{13}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{9}{26}\right)\) |