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 \(\chi_{3549}(1244,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.dv
\(\chi_{7098}(185,\cdot)\) \(\chi_{7098}(425,\cdot)\) \(\chi_{7098}(731,\cdot)\) \(\chi_{7098}(971,\cdot)\) \(\chi_{7098}(1277,\cdot)\) \(\chi_{7098}(1517,\cdot)\) \(\chi_{7098}(1823,\cdot)\) \(\chi_{7098}(2063,\cdot)\) \(\chi_{7098}(2369,\cdot)\) \(\chi_{7098}(2609,\cdot)\) \(\chi_{7098}(2915,\cdot)\) \(\chi_{7098}(3155,\cdot)\) \(\chi_{7098}(3461,\cdot)\) \(\chi_{7098}(3701,\cdot)\) \(\chi_{7098}(4007,\cdot)\) \(\chi_{7098}(4553,\cdot)\) \(\chi_{7098}(4793,\cdot)\) \(\chi_{7098}(5099,\cdot)\) \(\chi_{7098}(5339,\cdot)\) \(\chi_{7098}(5645,\cdot)\) \(\chi_{7098}(5885,\cdot)\) \(\chi_{7098}(6191,\cdot)\) \(\chi_{7098}(6431,\cdot)\) \(\chi_{7098}(6977,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((4733,5071,6931)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{35}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
\( \chi_{ 7098 }(4793, a) \) | \(1\) | \(1\) | \(e\left(\frac{29}{39}\right)\) | \(e\left(\frac{7}{26}\right)\) | \(e\left(\frac{14}{39}\right)\) | \(-1\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{19}{39}\right)\) | \(e\left(\frac{31}{78}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{11}{39}\right)\) |