Basic properties
Modulus: | \(3549\) | |
Conductor: | \(3549\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | 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.dp
\(\chi_{3549}(38,\cdot)\) \(\chi_{3549}(194,\cdot)\) \(\chi_{3549}(311,\cdot)\) \(\chi_{3549}(467,\cdot)\) \(\chi_{3549}(584,\cdot)\) \(\chi_{3549}(740,\cdot)\) \(\chi_{3549}(857,\cdot)\) \(\chi_{3549}(1130,\cdot)\) \(\chi_{3549}(1286,\cdot)\) \(\chi_{3549}(1403,\cdot)\) \(\chi_{3549}(1559,\cdot)\) \(\chi_{3549}(1676,\cdot)\) \(\chi_{3549}(1832,\cdot)\) \(\chi_{3549}(1949,\cdot)\) \(\chi_{3549}(2105,\cdot)\) \(\chi_{3549}(2222,\cdot)\) \(\chi_{3549}(2378,\cdot)\) \(\chi_{3549}(2495,\cdot)\) \(\chi_{3549}(2651,\cdot)\) \(\chi_{3549}(2768,\cdot)\) \(\chi_{3549}(2924,\cdot)\) \(\chi_{3549}(3197,\cdot)\) \(\chi_{3549}(3314,\cdot)\) \(\chi_{3549}(3470,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((1184,1522,3382)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{11}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(2\) | \(4\) | \(5\) | \(8\) | \(10\) | \(11\) | \(16\) | \(17\) | \(19\) | \(20\) |
\( \chi_{ 3549 }(38, a) \) | \(1\) | \(1\) | \(e\left(\frac{10}{39}\right)\) | \(e\left(\frac{20}{39}\right)\) | \(e\left(\frac{11}{78}\right)\) | \(e\left(\frac{10}{13}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{1}{39}\right)\) | \(e\left(\frac{17}{39}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{17}{26}\right)\) |