Basic properties
Modulus: | \(7098\) | |
Conductor: | \(3549\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
|
Real: | no | |
Primitive: | no, induced from \(\chi_{3549}(1676,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.dj
\(\chi_{7098}(311,\cdot)\) \(\chi_{7098}(467,\cdot)\) \(\chi_{7098}(857,\cdot)\) \(\chi_{7098}(1403,\cdot)\) \(\chi_{7098}(1559,\cdot)\) \(\chi_{7098}(1949,\cdot)\) \(\chi_{7098}(2105,\cdot)\) \(\chi_{7098}(2495,\cdot)\) \(\chi_{7098}(2651,\cdot)\) \(\chi_{7098}(3197,\cdot)\) \(\chi_{7098}(3587,\cdot)\) \(\chi_{7098}(3743,\cdot)\) \(\chi_{7098}(4133,\cdot)\) \(\chi_{7098}(4289,\cdot)\) \(\chi_{7098}(4679,\cdot)\) \(\chi_{7098}(4835,\cdot)\) \(\chi_{7098}(5225,\cdot)\) \(\chi_{7098}(5381,\cdot)\) \(\chi_{7098}(5771,\cdot)\) \(\chi_{7098}(5927,\cdot)\) \(\chi_{7098}(6317,\cdot)\) \(\chi_{7098}(6473,\cdot)\) \(\chi_{7098}(6863,\cdot)\) \(\chi_{7098}(7019,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((4733,5071,6931)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{5}{26}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 7098 }(5225, a) \) | \(1\) | \(1\) | \(e\left(\frac{5}{78}\right)\) | \(e\left(\frac{38}{39}\right)\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{39}\right)\) | \(e\left(\frac{5}{26}\right)\) | \(e\left(\frac{8}{39}\right)\) | \(e\left(\frac{29}{78}\right)\) | \(e\left(\frac{9}{26}\right)\) |