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 \(\chi_{3549}(1634,\cdot)\) | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
| Minimal: | yes | |
| Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 7098.do
\(\chi_{7098}(269,\cdot)\) \(\chi_{7098}(341,\cdot)\) \(\chi_{7098}(815,\cdot)\) \(\chi_{7098}(887,\cdot)\) \(\chi_{7098}(1361,\cdot)\) \(\chi_{7098}(1433,\cdot)\) \(\chi_{7098}(1907,\cdot)\) \(\chi_{7098}(1979,\cdot)\) \(\chi_{7098}(2453,\cdot)\) \(\chi_{7098}(2525,\cdot)\) \(\chi_{7098}(2999,\cdot)\) \(\chi_{7098}(3071,\cdot)\) \(\chi_{7098}(3545,\cdot)\) \(\chi_{7098}(3617,\cdot)\) \(\chi_{7098}(4091,\cdot)\) \(\chi_{7098}(4163,\cdot)\) \(\chi_{7098}(4637,\cdot)\) \(\chi_{7098}(5183,\cdot)\) \(\chi_{7098}(5255,\cdot)\) \(\chi_{7098}(5729,\cdot)\) \(\chi_{7098}(5801,\cdot)\) \(\chi_{7098}(6347,\cdot)\) \(\chi_{7098}(6821,\cdot)\) \(\chi_{7098}(6893,\cdot)\)
Related number fields
| Field of values: | $\Q(\zeta_{39})$ |
| Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((4733,5071,6931)\) → \((-1,e\left(\frac{1}{6}\right),e\left(\frac{8}{39}\right))\)
First values
| \(a\) | \(-1\) | \(1\) | \(5\) | \(11\) | \(17\) | \(19\) | \(23\) | \(25\) | \(29\) | \(31\) | \(37\) | \(41\) |
| \( \chi_{ 7098 }(5183, a) \) | \(1\) | \(1\) | \(e\left(\frac{7}{39}\right)\) | \(e\left(\frac{23}{78}\right)\) | \(e\left(\frac{8}{13}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(-1\) | \(e\left(\frac{14}{39}\right)\) | \(e\left(\frac{55}{78}\right)\) | \(e\left(\frac{37}{78}\right)\) | \(e\left(\frac{4}{13}\right)\) | \(e\left(\frac{17}{39}\right)\) |